Use of the Term

A ‘chronological bibliography’, in order to see the frequency, progression and trail of use of the term ‘parquet deformation’ in the literature. The term first appeared, not unnaturally, from William Huff, in an architecture journal in 1965. The listing is in two parts, deceived as ‘simplified’ and ‘detailed’. Simplified contains the journal without further comment, whist detailed retains the text as previously compiled from my bibliography, with on occasion updated for this specific new page. Note that I am strict here as to criteria; I accept no other term than ‘parquet deformation/s’, other than a slightly different rephrasing e.g. ’deformation of parquet patterns’. Parquet is the operative word here. Indeed, omitted are instances where although the author is clearly referring to parquet deformations, this is not described as such, e.g.

Kalay, Yehuda E (ed.). Computability of Design (Principles of Computer-Aided Design)

...Another example is in the creation of tilings of the plane, a design exercise originated by William Huff (Hofstadter 1983)

Bellos, Alex and Edmund Harriss. Snowflake Seashell Star.

deformation

Possibly (and arguably, with a proviso?), such implied instances should be included, but as the term is not used I have decided to omit.

1965 (1)

Huff, William S. ‘An Argument for Basic Design’. Journal of the Ulm School for Design, 1965. Pp. 12–13; 25–38. Issues 12/13 (combined)

1966 (0)

1967 (0)

1968 (1)

Drew, Jane. Author? David Lewis (editor). Architect's Year Book. Elek Books Limited, Volume 12, 1968

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Lewis, David (ed). Architects' Year Book: Urban Structure, Elek Books, 1968

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Also, see Jane Drew (same text, same book)

1969 (0)

1970 (0)

1971 (0)

1972 (1)

Wintermantel, Ed. ‘Designed To Be Different’. The Pittsburgh Press, Sunday, February 27, 1972, pp. 10–11.

1973 (0)

1974 (2)

Huff, William S. ‘Symmetry’. Oppositions. Issue 3, p. 23, 1974. Published for The Institute for Architecture and Urban Studies by The MIT Press

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Huff, William S. “Best Problems” from Basic Design - - 20 Feb. 1979. REVISED 20 Feb. 1979. THE PARQUET DEFORMATION (text and capitalization as given) N.B. Appears in Tim McGinty’s Best Beginning Design Projects (q.v)

1975 (0)

1976 (0)

1977 (0)

1978 (0)

1979 (0)

1980 (1)

Annual Report of the Director Issues 83-84, Carnegie Institute 1980, p. 51.

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1981 (0)

1982 (1)

Greenberg, Bob. Handbook of Practical Geometry. CDM Business Services, 1982, p. 177

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1983 (1)

Hofstadter, Douglas. 'Parquet deformations: patterns of tiles that shift gradually in one dimension'. ‘Metamagical Themas’, Scientific American, 1983, pp. 14–20

1984 (4)

Alpert, Richard. ‘Tracks of Motion in an Enclosed Space: Connections between Performance and Visual Imagery’. Leonardo, 1984, Vol. 17, No. 3 (1984), pp. 167–171.

Huff, William. ‘Geometrizzare and perceptualize’, in Rassegna, 1984.

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Joseph, M. and R. Shyamasundar. Foundations of Software Technology and Theoretical Computer Science: Fourth Conference, Bangalore, India December 13–15, 1984.

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Maldonado, Tomás and Giovanni Anceschi. Il contributo della scuola di Ulm, 1984, p. 39.

= The legacy of the School of Ulm

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Huff, William, ‘Geometrizzare and perceptualize’, in Rassegna, 1984. THE SAME?!

Science Digest, 1984, Vol. 92, p. 25?. P. 19

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1985 (6)

Anon. No Title. The Buffalo News 23 June 1985.

American Drawings and Watercolors in the Collection of the Museum of Art, Carnegie Institute. Publisher: Carnegie Museum Store; 1st edition, 1985, P. 276.

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Documentation Abstracts. American Chemical Society. Division of Chemical Literature. American Documentation Institute. Volume 20, Issues 7–12, 1985, p. 818

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————. ‘Parquet Deformations: A Subtle, Intricate Art Form’. July, 1983 pp. 190–199. In

Metamagical Themas: Questing for the Essence of Mind and Pattern. Basic Books; First printing 1985, New edition 1996

Krithivasan, Kamala and Anindya Das. ‘Terminal weighted grammars and picture description’. Computer Vision, Graphics, and Image Processing, Volume 30, Issue 1, April 1985, pp. 13-31.

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Rozenberg G. and ‎A. Salomaa. The Book of L. Springer-Verlag 1985 and 1986, p. 415

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1986 (3)

Durant, Stuart. Ornament: A Survey of Decoration Since 1830, 1986, p. 81

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Durant, Stuart. Ornament, from the Industrial Revolution to Today. Woodstock, N. Y. : Overlook Press 1986, p. 81

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Erland, Jonathon. ‘Front Projection: Tessellating the Screen’. SMPTE Journals, Volume: 95, Issue 3 March 1986) 1986, pp. 278–286

1987 (4)

Grünbaum, Branko and ‎G. C. Shephard. Tilings and Patterns. W. H. Freeman, 1987

Maldonado, Tomás. Il futuro della modernità. Feltrinelli, 1987, p. 52

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Mathematical Reviews. American Mathematical Society, Vol. 87, 1987

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SILTA - Volume 16, Studi italiani di linguistica teorica ed applicata (Italian studies of theoretical and appled linguistics) Liviana Publishing, 1987

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1988 (0)

1989 (2)

Akira, Ito*, ‎S. P. Patrick, P. Wang, and ‎K. G. Subramanian. Array Grammars, Patterns and Recognizers. World Scientific Publishing, 1989, p. 69.

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N. B. SAME BOOK AS ABOVE

Wang, Patrick Shen-Pei (editor). Array Grammars, Patterns and Recognizers. World Scientific Series in Computer Science. 1989. NOT SEEN, GOOGLE BOOKS REFERENCE

Miles, Thomas H. Critical Thinking and Writing for Science and Technology. Heinle & Heinle Publishers Inc., U.S. 1989, 1990 p. 232.

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1990 (2)

Crowell, Robert A. (editor). Intersight One. State University of New York at Buffalo 1990.

Nirma, N, and R. Rama. ‘Terminal Weighted L-Systems’. International Journal of Pattern Recognition and Artificial Intelligence. World Scientific, Vol. 4, No. 1, 1990, pp. 95-112

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1991 (4)

Jablokov, Alexander. ‘Living Will’. Isaac Asimov's Science Fiction Magazine, Davis Publications, Dozois, Gardner (ed). June 1991, Vol. 15, Issues 7–9, p. 64.

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Kappraff, Jay. Connections. The Geometric Bridge Between Art and Science. McGraw-Hill Inc. 1991

Kreutzer, Wolfgang and ‎Bruce McKenzie. Programming for Artificial Intelligence: Methods, Tools, and Applications. Addison-Wesley, 1991

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Talley, Charles (Editor). Surface Design Journal - Volumes 16-17. United States: Surface Design Association, pp. 8–10, 1991. Neither author nor article title is given.

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1992 (0)

1993 (0)

1994 (3)

Bigalke, Hans-Günther. Reguläre Parkettierungen. Mit Anwendungen in Kristallographie, Industrie, Baugewerbe, Design und Kunst. BI Science Publisher, 1994

Huff 1994 see

KPMG Peat Marwick Collection of American Craft: A Gift to the Renwick Gallery of the National Museum of American Art. Published by Smithsonian Institute. 1994. Foreword, Jon C. Madonna; introduction, Michael W. Monroe; essays, Jeremy Adamson

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1995 (1)

Hofstadter, D. R. Fluid Concepts and Creative Analogies. Computer Models of the Fundamental Mechanisms of Thought. Harvester Wheatsheaf 1995, and Allen Lane The Penguin Press 1997, 501 pp.

1996 (1)

Huff, William S. ‘The Landscape Handscroll and the Parquet Deformation’, In Katachi U Symmetry. Tohru Ogawa, ‎Koryo Miura, ‎and Takashi Masunari. Tokyo: Springer-Verlag 1996, pp. 307–314.

1997 (0)

1998 (1)

Brandstetter, Gabriele and Marta Ulvaeus. ‘Defigurative Choreography: From Marcel Duchamp to William Forsythe’. The Drama Review, Winter, 1998, Vol. 42, No. 4 (Winter, 1998), The MIT Press, pp. 37–55.

1999 (0)

2000 (1)

Kaplan, Craig S. and David H. Salesin. ‘Escherization’. SIGGRAPH '00: Proceedings of the 27th annual conference on Computer graphics and interactive techniques, July 2000 pp. 499–510

2001 (0)

2002 (2)

Kaplan, Craig S. Computer Graphics and Geometric Ornamental Design. A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2002

Kinsey, L. Christine and Teresa E. Moore. Symmetry, Shape and Space: An Introduction to Mathematics. Key College Publishing, 2002. Hardcover Wiley 2008, 494 pp.

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2003 (3)

Dawson, Robert J. MacG (probably). ‘Crooked Wallpaper’. Journal of Graphics Tools. Volumes 8–9, A. K. Peters, 2003, pp. 33–46

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————. "About Parquet Deformations" in Transforma, Book of Abstracts of the 2° Congreso Internacional y 4° Nacional de la Sociedad de Estudios Morfólogicos de la Argentina (SEMA), 9. Córdoba, Argentina, 2003 (page numbers not given)

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Inkpen, Kori and ‎Michiel Van de Panne. Graphics Interface 2003, A K Peters/CRC Press, 2005, pp. 179–181

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2004 (0)

2005 (3)

Comptes Rendus - Interface Graphique. National Research Council of Canada, 2005

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Inkpen, Kori and ‎Michiel Van de Panne. Graphics Interface 2003, A K Peters/CRC Press, 2005 pp. 179–181

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Kaplan, Craig S. ‘Islamic star patterns from polygons in contact’. Proceedings of Graphics Interface 2005, pp. 177–185

2006 (0)

2007 (1)

Horstadter, Douglas R. I Am a Strange Loop. Basic Books, 2007 Hardback, 2008 Paperback, 412 pp.

2008 (1)

Kaplan, Craig S. ‘Metamorphosis in Escher’s Art’. In Bridges 2008: Mathematical Connections in Art, Music and Science, pp. 39–46

2009 (2)

Bosch, Robert and Andrew Pike. Map-Colored Mosaics. Proceedings of the 2009 Bridges Banff Conference, held in Banff, Canada. Edited by Craig S. Kaplan and Reza Sarhangi, pp. 139–146

Kaplan, Craig S. Introductory Tiling Theory for Computer Graphics. Morgan and Claypool Publishers, 2009

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2010 (3)

Ellison, Elaine K. and John Sharp. ‘Tiled Torus Quilt with changing tiles’. Bridges 2010, pp. 67–74

Huff, William S. ‘Simulacra of Nonorientable Surfaces—Experienced through Timing’. In Spatial Lines, (Líneas espaciales) Patricia Muñoz, compiler. Buenos Aires: De la Forma, 2010, 128 pp.

PARTIALLY SEEN, TEXT ONLY, WITHOUT IMAGES

Kaplan, Craig S. ‘Curve Evolution Schemes for Parquet Deformations’. In Bridges 2010 Mathematical Connections in Art, Music and Science, by Reza Sarhargi (chief editors) Hart, George W. and Sarhangi (Author) Tessellations Publishing, pp. 95–102.

Schattschneider, Doris. ‘The Mathematical Side of M. C. Escher’. Notices of the American Mathematical Society. Volume 57, Number 6, June/July 2010, pp. 706–718

2011 (1)

Anceschi, Giovanni. New Basic Design a Venezia e Basic Design a Ulm, ISIA Urbino, Self Published on Issuu January 19, 2011, 72 pp.

2012 (5)

Hann, Michael. Structure and Form in Design: Critical Ideas for Creative Practice. Bloomsbury Academic, 2012

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Huff, William S. ‘Defining Basic Design as a Discipline’. In Symmetry: Art and Science, Vol. 2 (new series) Numbers 1–4, 2012, pp. 91–98

Laparidis, Stavros. ‘The Role of Allusion in Ligeti's Piano Music’. Dissertation, 2012, P. 22.

Pitici, Mircea. The Best Writing on Mathematics 2011. Princeton University Press, 2012

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Simmi, Simone (ed?). Eredità, 19 Nov 2012. 16 pp.

2013 (2)

Lawrence, Cindy. ‘Adding it all Up: Building the National Museum of Mathematics’. Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture, Edited by George Hart and Reza Sarhangi pp. 548-550

Olmsted, Zachary T., Tim D. Riehlman, Carmen Branca, Andrew G. Colliver, Adam M. Winnie, Janet L. Paluh. ‘Metamorphic Pattern Formation and Deformation: In Vivo and In Vitro Mechanisms’.

2014 (5)

Anon. ‘In Brief. Awards and Announcements’. B/a+p. News from the School of Architecture and Planning University at Buffalo, Spring 2014

Artist’s Page. Mutahir Arif. Crossing Disciplines – Scope: (Art & Design), 9, 2014

Bellos, Alex. ‘Crazy paving: the twisted world of parquet deformations’. The Guardian, 9 September 2014 (N.B. Online only)

Schaffer, Karl. ‘Dancing Deformations’. Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture, pp. 253–260

Schattschneider, Doris. M. C. Escher: Visions of Symmetry. W. H. Freeman, 2004

2015 (6)

‘BAD’ (Built by Associative Data). By ‘MUQ’?, ‘Computation Coding/Recoding Islamic Patterns’. Self Published on Issuu March 13, 2015, 102 pp.

Lamm, Dan. Material Systems, MIT Media Lab, 2015. Self Published on Issuu October 31, 2015, 169 pp.

Lee, Kevin. ‘Algorithms for Morphing Escher-Like Tessellations’. Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture pp. 483–48

Plender, Richard (ed.). Issues in International Migration Law. Brill - Nijhoff, first edition 2015

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Yao, Szu-An. Portfolio 2015. ‘Deformative Space Space Frame Structure by Adaptation of Parquet Patterns’. Self Published on Issuu, January 7, 2016, pp. 56

Ying, Fu. Portfolio. ‘Landscape Mosque’. Self Published on Issuu April 8, 2015, 37 pp.

2016 (0)

2017 (6)

Bonner, Jay, with contributions by Craig Kaplan. Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Construction. Springer, 2017

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Llonardi, Giulia. Portfolio. Self Published on Issuu May 19, 2017, 16 pp.

Uncertain author credit. DR. SEFIK MEMIS YRD. DOÇ.DR. MURAT SENTÜRK (Author) I. Çekmeköy sempozyumu: Sehir, tarih, toplum, gelecek. Tebligler kitabi: 22-23 Ekim 2016. Publisher: Çekmeköy Belediyesi, 2017

Şehir Çekmeköy, Tarih, Toplum ve Gelecek

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Schaffer, Karl. ‘Dichromatic Dances’. Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture, Edited by David Swart, Carlo H. Séquin, and Kristóf Fenyvesi, pp. 291–298

Sousa, J. P. ‘Calculated Geometries. Experiments in Architectural Education and Research’. In: Viana V., Murtinho V., Xavier J. (eds) Thinking, Drawing, Modelling. Geometrias 2017. Springer Proceedings in Mathematics & Statistics, Vol. 326. Springer, Cham. (2020)

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Tuğrul, Yazar. 'Revisiting Parquet Deformations from a computational perspective: A novel method for design and analysis'. In International Journal of Architectural Computing. Volume: 15 issue: 4, pp. 250–267, 2017.

2018 (1)

Kitchen, Paul. Portfolio. Student Architectural Portfolio. Self Published on Issuu March 5, 2018, 23 pp.

2019 (6)

Bosch, Robert. Opt Art: From Mathematical Optimization to Visual Design. Princeton University Press, 2019.

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Hann, Michael. The Grammar of Pattern. CRC Press, 2019, 229 pp.

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Hoeydonck, Werner Van. ‘William Huff’s Parquet Deformations: A Viennese Experiment’.

Conference: Symmetry: Art and Science, 2019 – 11th Congress and Exhibition of SIS Special Theme: Tradition and Innovation in Symmetry – Katachi 形 Kanazawa, Japan, November 25-30, 2019 (for unclear reasons, the article is apparently unpaginated. Four pages.

Kaplan, Craig S. ‘Animated Isohedral Tilings’. In Bridges 2019 Conference Proceedings, pp. 99-106.

Leone, Francesca. Portfolio Progettazione Grafica. Self Published on Issuu July 14, 2019, 68 pp.

In Italian.

Reddy, Hasitha. Architecture, Interiors and Urban Design Portfolio. Self Published on Issuu February 21, 2019. 58 pp.

2020 (3)

Fathauer, Robert. Tessellations: Mathematics, Art, and Recreation. A K Peters/CRC Press, 2020

Hoeydonck, Werner Van. ‘William Huff’s Parquet Deformations: Two Viennese Experiments’. Bridges 2020 Conference Proceedings, pp. 383–386.

Moradzadeh, Sam and Ahad Nejad Ebrahimi. ‘Islamic Geometric Patterns in Higher Dimensions’. Nexus Network Journal Vol. 22, 11 May 2020, pp. 777–798

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Table of References by Year, Frequency and Publication Type

So what can be drawn from this? As a general observation, how infrequent the references to parquet deformations there are! Of the 56 years after the inception of the term (by Huff), there are only 82 references. And further, some of these are bloated by including ‘semi-official’ publications in Issuu. Almost half, 22 of the years, do not have a single reference! Indeed, even as recently as 2016, there was not been a single reference. The most of any one year is just 6. From 1965 to 1983, save for one outlier of 1974, there was but at most one reference for any one year (and the outlier had just two). However, one can indeed see trends here. From 1984 onwards, and to the present day, there is a definite increase in frequency. This can be put down to a 1983 popular article by Douglas Hofstadter in Scientific American. It is the one piece that is frequently (and deservedly) quoted.

To better aid the publication type analysis, I have added a column listing the different fields. However, not all the entries are catalogued due to insufficient detail being available. Further, at times it was difficult as to how best describe a certain journal. At best, this is just a rough guide. Perhaps the most interesting is how little there is in mathematics books and journals, of which given its tessellation nature, may otherwise have been expected. Architecture features prominently throughout. Of interest, given Huff’s analogy with music, is any references in that field. However, there seems little interest, with just a handful of references.

BIBLIOGRAPHY IN FULL

1965 (1)

Huff, William S. ‘An Argument for Basic Design’. Journal of the Ulm School for Design, 1965. Pp. 12–13; 25–38. Issues 12/13 (combined)

In a general article on basic design, parquet deformations are essentially illustrated only, with brief caption text e.g. Parquet deformation Student: Fred Watts (1963). Oddly, there is no discussion in the main body of the text. This is not an outlier; such a presentation is throughout the article. Picture of Huff, p. 25. Parquet deformations by Fred Watts, Peter Hotz, and Richard Lane, p. 28, all untitled. Interestingly, Hotz uses a Cairo tiling here, of a transition from a square to basketweave, in a way (I believe) that I have not seen previously!

Interestingly, D'Arcy Thompson is mentioned extensively, re On Growth and Form. Speculating, was Huff influenced by the image on p. ? Fig. 133, first edition 1917? https://monoskop.org/images/8/80/Ulm_12-13.pdf

1966 (0)

1967 (0)

1968 (1)

Drew, Jane. Author? David Lewis (editor). Architect's Year Book. Elek Books Limited, Volume 12, 1968

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Snippet view on Google Books:

Top Parquet deformation A development on a square grid Centre Parquet deformation A development on the special rhombic grid

Also, see David Lewis below (same text, must be the same book)

Wikipedia

Dame Jane Drew, DBE, FRIBA (24 March 1911 – 27 July 1996) was an English modernist architect and town planner. She qualified at the Architectural Association School in London, and prior to World War II became one of the leading exponents of the Modern Movement in London.

Lewis, David (ed). Architects' Year Book: Urban Structure, Elek Books, 1968

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Snippet view on Google Books:

Top Parquet deformation A development on a square grid Centre Parquet deformation A development on the special rhombic grid

Also, see Jane Drew (same text, same book)

Amazon:

Useful survey of the latest in architectural theory and practice. Includes many articles including essays by Alison and Peter Smithson, Peter Cook, David Green and Michael Webb, Geoffrey Copcutt, Theo Crosby, John McHale, Anthony Vidler and Kenneth Frampton, and many more.

1969 (0)

1970 (0)

1971 (0)

1972 (1)

Wintermantel, Ed. ‘Designed To Be Different’. The Pittsburgh Press, Sunday, February 27, 1972, pp. 10–11.

Three mentions:

(1) [Caption] Roland Findlay is the artist: parquet deformation is the style. It must be viewed differently from most art because the shapes change progressively.

(2) Mostly produced by freshmen, the student designs are of five types: symmetry, parquet deformation, raster, conflicting depth cues and figure-ground figure without ground.

(3) Symmetry involves balanced proportions. Parquet deformation takes a basic shape and gradually changes it into another shape.

One of only two newspaper references on William Huff/parquet deformations I am aware of. Features Roland Findlay’s (two-dimensional) parquet deformation ‘All in the Family’, albeit oddly the designer and work are not titled or discussed in the main text.

Has an early photo of Huff, but not the first.

Also of significance as likely the first popular reference to parquet deformations in a non-specialised context.

1973 (0)

1974 (2)

Huff, William S. ‘Symmetry’. Oppositions. Issue 3, p. 23, 1974. Published for The Institute for Architecture and Urban Studies by The MIT Press

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Snippet view on Google Books:

Parquet deformation by Richard Lane. Basic Design course, 1963. Teacher: William S. Huff. departure from the Bauhaus tradition found clear expression in three sets of academic courses that were common to all four departments. First, in the …

Wikipedia

Oppositions was an architectural journal produced by the Institute for Architecture and Urban Studies from 1973 to 1984. Many of its articles contributed to advancing architectural theory and many of its contributors became distinguished practitioners in the field of architecture. Twenty-six issues were produced during its eleven years of existence.

There is some uncertainty as to what exactly this partial(?) document is. It is subtitled ‘The Parquet Deformation’. It appears to be a ‘study guide for students’, used in Huff’s classroom. Further, I only have two sheets (hand) numbered pp. 30–31 and 33. It is ordered in three sections as ‘The task’, ‘The principle’, and ‘The pedagogic goal’. Three parquet deformations, one of which, p. 31, made it into the Hofstadter Scientific American article.

Uncertainties aside, the document from Buffalo in 1979, discusses parquet deformation concepts. However, it is not a tutorial as such. Of interest is that it is stated a ruling pen was used to execute the designs.

Another like ‘guide’ (without reference to parquet deformations) is titled ‘The Mirror-Rotation Symmetry’, p. 34, with the same sections as given above. Are there more?

http://ncbds.la-ab.com/Best%20Projects%201.pdf (scroll to the end of the document)

1975 (0)

1976 (0)

1977 (0)

1978 (0)

1979 (0)

1980 (1)

Annual Report of the Director Issues 83-84, Carnegie Institute 1980, p. 51.

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Snippet view on Google Books:

...and Robert Skolnik Parquet Deformation …

I cannot find any more detail on this.

https://catalog.hathitrust.org/Record/005755782

1981 (0)

1982 (1)

Greenberg, Bob. Handbook of Practical Geometry. CDM Business Services, 1982, p. 177

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Snippet view on Google Books:

HOFSTADTER, D. R. Parquet deformations, Scientific American, July, 1983, p. 14 - 20 Demonstrates cross - deformation of field symmetry patterns.

Bio

Robert Greenberg was a Professor of Architecture at Ryerson University. Greenberg graduated Magna Cum Laude with a Bachelor of Architecture from Syracuse University. He taught at Ryerson for 28 years in Design Theory, Architectural History and Studio. He lectured widely throughout North America and the UK, particularly on the subject of Descriptive Geometry. He was Founder and Studio Master of the Ad Quadratum Studio of Geometry in Art and Architecture, which mounted exhibitions in Canada, the US, and the UK. He is the author of the Handbook of Practical Geometry (2nd ed., 1982) and retired to Emeritus status in 2000. He passed away May 28, 2007.

1983 (1)

Hofstadter, Douglas. 'Parquet deformations: patterns of tiles that shift gradually in one dimension'. ‘Metamagical Themas’, Scientific American, 1983, pp. 14–20

Eight mentions. First mention: One striking counterexample is the set of "parquet deformations" meta-composed by Wflliam S. Huff, professor of architectural design at the State University of New York at Buffalo.

The classic account. The importance of this article can hardly be overstated; the one article that overrides everything else. This is the first popular account of parquet deformations, with William Huff’s student-inspired works, of which Hofstadter does it full justice, with 12 stunning examples, with works by: Fred Watts (Fylfot Flipflop), Richard Lane (Crossover), Richard Mesnik (Dizzy Bee), Scott Grady (Consternation), Francis O’Donnell (Oddity out of Old Oriental Ornament), Leonard Chan (Y Knot), Arne Larson (Crazy Cogs), Glen Paris (Trifoliate), Joel Napach (Arabesque), unknown (Razor Blades), Jorge Guttierrez, (Curacha), Laird Pylkas (Beecombing Blossoms), and Vincent Marlowe (Clearing the Thicket).

And the titles are most amusing too! To pick a favourite is invidious. However, if pressed ‘Fylfot Flipflop’. Of note is that these are all linear. Absolutely delightful!

However, Hofstadter seems to have erred somewhat in his commentary; Branko Grünbaum and G. C. Shephard, in Tilings and Patterns, p. 170, takes him to task, concerning his comment on monohedral tiles, p. 14: ‘Despite the claims to the contrary most of the tilings shown in Hofstadter’s article include tiles which are not prototiles of any monohedral tilings’.

1984 (4)

Alpert, Richard. ‘Tracks of Motion in an Enclosed Space: Connections between Performance and Visual Imagery’. Leonardo, 1984, Vol. 17, No. 3 (1984), pp. 167–171.

First and only mention:

Inconsequential. P. 171, references, credits Hofstadter, and Alpert briefly alludes to them, p, 170.

Huff, William. ‘Geometrizzare and perceptualize’, in Rassegna, 1984.

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N.B. I believe this (obscure) piece is associated with Huff. it appears in other references on Google Books under different names, by editor; see Maldonado and ?

Joseph, M. and R. Shyamasundar. Foundations of Software Technology and Theoretical Computer Science: Fourth Conference, Bangalore, India December 13–15, 1984.

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Snippet view on Google Books:

Terminal weighted matrix grammars are used to describe parquet deformations. The hierarchy of families generated by putting various restrictions on the functions is studied. 1. INTRODUCTION It has been of interest to generate various …

Occasional discussions on parquet deformations. I am at a loss to explain ‘terminal weighted matrix grammars’. From what I have seen, it is abstruse.

Beecombing Blossoms, p. 198, Fylfot Flipflop p. 194, albeit at a most abstruse level.

Maldonado, Tomás and Giovanni Anceschi. Il contributo della scuola di Ulm, 1984, p. 39.

= The legacy of the School of Ulm

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Snippet view on Google Books:

Deformazione del parquet": Toccata, studente Robert Glenn, CIT 1965. "Parquet deformation” : Toccata, student Robert Glenn, CIT 1965. 14. “Deformazione del parquet" : Five to Four and Two Halves, studente Robert Nagel, CIT 1963 …

N.B. THIS IS THE SAME REFERENCE AS GREGOTTI!

Huff, William, ‘Geometrizzare and perceptualize’, in Rassegna, 1984. THE SAME?!

Science Digest, 1984, Vol. 92, p. 25?. P. 19

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‘How to read a fylfot flipflop’

A parquet deformation is not a warped apartment floor. It's an ingenious problem in design. The basic elements are called tiles: squares, hexagons ... look at it somewhat the way a composer might look at his compositions, says Huff. I tell students to let their eye tell then whether it's flowing or not. Then we look at the design analytically: What are the events? How long does it take to get from one to another? What are the rhymes?

An event is an eye-catching configuration...

return of the square but with the swastika reversed-the final event.

There are other interesting discovers to be made about vertical and horizontal lines. After 20 years, said Huff, I come to these new each time.

Illustrated with Fylfot Flipflop, shown vertically (curtailed, as above).

Caption to Fyflot Flipflop

HOW TO READ THIS FYLFOT FLIPFLOP, TURN IT COUNTERCLOCKWISE. A fyflot is a swastika. In this design, called a parquet deformation, the fylfot reverses at right.

Science Digest was a monthly American magazine published by the Hearst Corporation from 1937 through 1988. No known archive online.

https://www.google.co.uk/books/edition/Science_Digest/9kcUAQAAIAAJ?hl=en&gbpv=1&bsq=Science+Digest+fylfot&dq=Science+Digest+fylfot&printsec=frontcover

1985 (6)

Anon. No Title. The Buffalo News 23 June 1985.

On parquet deformation, Huff. One of only two newspaper references I am aware of. The whole article is not available to me, seen only by chance as a clipping next to a story on dancing that showed up when searching! Shows ‘Fylfot Flipflop’, with a discussion in a general sense.

American Drawings and Watercolors in the Collection of the Museum of Art, Carnegie Institute. Publisher: Carnegie Museum Store; 1st edition, 1985, P. 276.

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Parquet Deformation - Variant II, 1965 - 66 pen and ink on paper 39 516 X 28 in. ... Bibliography: Douglas R. Hofstadter, “Metamagical Themas, Parquet Deformations: Patterns of Tiles that Shift Gradually in One Dimension,” Scientific …

Documentation Abstracts. American Chemical Society. Division of Chemical Literature. American Documentation Institute. Volume 20, Issues 7–12, 1985, p. 818

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Motivated by the idea of describing parquet deformations using grammars… describing parquet deformations using grammars and also of describing an infinite number of terminals starting with only a finite set, this paper defines a terminal weighted grammar, where the terminal generated at any step of a derivation…

————. ‘Parquet Deformations: A Subtle, Intricate Art Form’. July, 1983 pp. 190–199. In

Metamagical Themas: Questing for the Essence of Mind and Pattern. Basic Books; First printing 1985, New edition 1996

19 mentions. First: One striking counterexample is the set of "parquet deformations" meta-composed by William Huff, a professor of architectural design at the State University of New York at Buffalo.

This essentially repeats Hofstadter's original July 1983 column in Scientific American (his last), with extra, minor text, but also, more importantly, a ‘post scriptum’, in which a new (not previously shown) parquet deformation of David Oleson’s ‘I at the Center’ is illustrated and discussed, and much praised.

Krithivasan, Kamala and Anindya Das. ‘Terminal weighted grammars and picture description’. Computer Vision, Graphics, and Image Processing, Volume 30, Issue 1, April 1985, pp. 13-31.

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Abstract

Motivated by the idea of describing parquet deformations using grammars and also of describing an infinite number of terminals starting with only a finite set, this paper defines a terminal weighted grammar, where the terminal generated at any step of a derivation is defined as a function of time. It is seen that terminal weighted regular grammars generate exactly the class of recursively enumerable sets. Terminal weighted matrix grammars are used to describe parquet deformations.

What exactly is a ‘terminal weighted grammars’ is unclear. From Ricardo Wandre Dias Pedro et al:

Grammars are widely used to describe string languages such as programming and natural languages and, more recently, biosequences. Moreover, since the 1980s grammars have been used in computer vision and related areas. Some factors accountable for this increasing use regard its relatively simple understanding and its ability to represent some semantic pattern models found in images, both spatially and temporally.

Rozenberg G. and ‎A. Salomaa. The Book of L. Springer-Verlag 1985 and 1986, p. 415

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Weights are attached to terminals in the sense that terminals are treated as functions of time and this interesting idea to describe parquet deformations [ 23 ] is extended to the model in [ 90 ] …

Likely, but not certainly, referring to a Huff-style deformation.

1986 (3)

Durant, Stuart. Ornament: A Survey of Decoration Since 1830, 1986, p. 81

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Parquet deformations', 1961 – 3. ULM 12 / 13. Zeitschrift der Hochschule für Gestaltung, March 1965. These exercises are reminiscent of Bauhaus methods, in which simple tessellated shapes are transformed sequentially, by deformation …

Durant, Stuart. Ornament, from the Industrial Revolution to Today. Woodstock, N. Y. : Overlook Press 1986, p. 81

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56 Left François MORELLET: Random design of isosceles deformation, into more complex forms. simple tessellated shapes are transformed sequentially, by... These exercises are reminiscent of Bauhaus ... Parquet deformations', 1961 –

Erland, Jonathon. ‘Front Projection: Tessellating the Screen’. SMPTE Journals, Volume: 95, Issue 3 March 1986) 1986, pp. 278–286

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Quotes Hofstadter’s article, p. 286, from superscript in the text, p. 280, but does not discuss parquet deformations as such. As an aside, discusses ‘apogee hexagons’.

D. R. Hofstadter, "Metamagical Themas: Parquet Deformations Patterns of Tiles that Shift Gradually in One Dimension", Scientific American, July 1983.

From SMPTE (Society of Motion Picture and Television Engineers)

SMPTE people form a global professional society of individuals and corporations collaborating for the advancement of all things technical in the motion picture, television and digital media industries. The Society fosters a diverse and engaged membership from both the technology and creative communities, delivering vast educational offerings, technical conferences and exhibitions, informational blog posts, and the renowned SMPTE Motion Imaging Journal…

Wikipedia:

The Society of Motion Picture and Television Engineers (SMPTE), founded in 1916 as the Society of Motion Picture Engineers or SMPE, is a global professional association of engineers, technologists, and executives working in the media and entertainment industry...

https://cdn.shopify.com/s/files/1/0143/5772/5241/files/SMPTE_FPTessellatingTheScreen.pdf?5851892044574547805

1987 (4)

Grünbaum, Branko and ‎G. C. Shephard. Tilings and Patterns. W. H. Freeman, 1987

P. 170: A concept akin to isotopy but distinct from it has been used by some artists. M. C. Escher utilized it in his famous woodcut “Metamorphosis III” and other works (see Escher [1971, [1982]). The tiling is represented on a long strip of paper and it changes gradually as one moves from one end to the other. For other examples of such tilings see Hofstadter [1983], Huff [1983]. It is quite challenging to design deformations of this kind in such a way that every tile can serve as a prototile of a monohedral tiling. Despite the claim to the contrary (see Hoftstadter [1983, p. 14]), most of the tilings shown in Hofstadter’s article include tiles which are not prototiles of any monohedral tilings.

A brief discussion of Hofstadter and Huff, p. 170. In matters of mathematical contention, I thus defer to Grünbaum and Shephard.

Maldonado, Tomás. Il futuro della modernità. Feltrinelli, 1987, p. 52

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Molto importanti sono anche gli studi di W. Huff nel campo delle “parquet deformations”. Vedasi al riguardo D. HOFSTADTER, Parquet deformations a subtle intricate art form, in Metamagical Themas: Questing for the Essence of Mind and…

Mathematical Reviews. American Mathematical Society, Vol. 87, 1987

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P. 433. The algorithms discussed in weights 'to matrix grammars for describing parquet deformations this paper have proved to be successful in delivering sequences of is extended to Ex - TMGs . ”pass directions of minimal length for several ..

SILTA - Volume 16, Studi italiani di linguistica teorica ed applicata (Italian studies of theoretical and appled linguistics) Liviana Publishing, 1987

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P. 281. Con “deformazione di parquet” Hofstadter indica un regolare tassellamento del piano, idealmente disegnato con segmenti e curve di spessore zero. Le trasformazioni che intervengono a modificare tale tassellamento devono rispondere a …

SILTA

Italian Studies of Theoretical and Applied Linguistics (SILTA) is an international magazine, published since 1972 under the direction of Luigi Heilmann and Enrico Arcaini, sole director from 1987 to 2015. The magazine acts as an international comparison point between the theoretical and methodological approaches to different analyzes in the linguistic field. The magazine publishes articles in Italian and foreign languages (French, English, German, Spanish) and also intends to outline an important cross-cultural exchange project.

1988 (0)

1989 (2)

Akira, Ito*, ‎S. P. Patrick, P. Wang, and ‎K. G. Subramanian. Array Grammars, Patterns and Recognizers. World Scientific Publishing, 1989, p. 69.

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SMG AND PARQUET DEFORMATION Yet another interesting application of the indexed SMG is in the description of parquet deformation. A parquet deformation is one in which a regular tessellation of the plane gets deformed progressively in ...Recognizers.

* Trove gives the editor as P. S. P. Wang below

N. B. SAME BOOK AS ABOVE

Wang, Patrick Shen-Pei (editor). Array Grammars, Patterns and Recognizers. World Scientific Series in Computer Science. 1989.

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Technical. Quotes Hofstadter’s article.

Google Snippets:

Subramanian, K. G. (article) ‘Siromoney Array Grammars’.

Pp. 69 347 : 6 SMG and Parquet Deformation Yet another interesting application of the indexed SMG is in the description of parquet deformation. A parquet deformation is one in which a regular tessellation of the plane gets deformed progressively in one dimension and at each stage is a unit cell that combines with itself so that it covers an infinite plane exactly. In Ref 6 some parquet deformations have been described using the concept of attacking a weight function to the terminals of an array. Here we illstre how indices in the vertical grammar help us to describe interesting parquet deformations in which the pattern shifts at varying speeds in the upper half and lower half of the picture. This is a feature that cannot be described by the earlier technique

P. 71. .. a parquet deformation known as Consternation...

P. 334. Finally the application of SMG with indices in describing parquet deformation is brought out

P. 350. Quotes Hofstadter's 1983 paper in references.

I must say I very much like the definition of a parquet deformation given here! I will suitably adopt and adapt it.

Miles, Thomas H. Critical Thinking and Writing for Science and Technology. Heinle & Heinle Publishers Inc., U.S. 1989, 1990 p. 232.

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...fair amount and understand only a little, but there is something in those articles in the Times and Science News and Scientific American — something compelling in the various terminologies (“dark matter," "flavor," "parquet deformation”, lepton. ..

Of an initial look, I couldn’t find any biographical or contact details on Miles.

1990 (2)

Crowell, Robert A. (editor). Intersight One. State University of New York at Buffalo 1990.

See (chapter) 10. William S. Huff. What is Basic Design?: 76–85 and in particular generic problems of synthetic design Students' work from the Basic Design Studios of William S. Huff 80–85.

With works by Jacqueline Damino (Right Right Left Right), Rodney Wadkins (In Two Movements), Darren Moritz (Enlarging on Four Points), Alexander Gelenscer (Hex-baton), Maurizio Sabini (Venetian Net), Robert Johnson (untitled).

A most impressive collection, second only to the Hofstadter article, and highly recommended.

Nirma, N, and R. Rama. ‘Terminal Weighted L-Systems’. International Journal of Pattern Recognition and Artificial Intelligence. World Scientific, Vol. 4, No. 1, 1990, pp. 95-112

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Abstract

Terminal weights are attached to L-systems by replacing each terminal generated by an OL-system by fa(i) in the ith step of a derivation...

…Now we give an example to illustrate how the parquet deformation of Ref. 17 can be generated

...Fig. 4. The parquet deformation …

Wikipedia

An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar. An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial "axiom" string from which to begin construction, and a mechanism for translating the generated strings into geometric structures.

Obviously advanced. Unlikely to be of any real interest.

1991 (4)

Jablokov, Alexander. ‘Living Will’. Isaac Asimov's Science Fiction Magazine, Davis Publications, Dozois, Gardner (ed). June 1991, Vol. 15, Issues 7–9, p. 64.

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Full text at Internet Archive:

The bathroom was clean tile with a wonderful claw-footed bathtub. The floor was tiled in a colored parquet-deformation pattern that started with ordinary bathroom-floor hexagons near the toilet, slowly modified itself into complex knotted shapes in the middle and then, by another deformation, returned to hexagons under the sink. It had cost him a small fortune and months of work to create this complex mathematical tessellation. It was a dizzying thing to contemplate from the throne and it now turned the ordinarily safe bathroom into a place of nightmare. Why couldn’t he have picked something more comforting?

Kappraff, Jay. Connections. The Geometric Bridge Between Art and Science. McGraw-Hill Inc. 1991

Parquet deformation pp. 190–194, within Chapter 5, ‘Tilings with Polygons’:

5. 10. 5 ‘One-dimensional parquet deformations’,

This is mostly merely excerpted from Huff’s article (1983), as the author credits. ‘Consternation’ is shown.

Kreutzer, Wolfgang and ‎Bruce McKenzie. Programming for Artificial Intelligence: Methods, Tools, and Applications. Addison-Wesley, 1991

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P. 650 Parquet deformations: a subtle, intricate art form. In: [Hofstadter (1985), 191 - 212 ] …

Appears to be merely a bibliographic reference.

Talley, Charles (Editor). Surface Design Journal - Volumes 16-17. United States: Surface Design Association, pp. 8–10, 1991. Neither author nor article title is given.

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Quotes (with spelling mistake) Hofstadter's Metamagical Themas Questing for the Essence of MInd and Matter.

P. 8. Another off-beat book with fresh ideas that apply to quilts is Metamagical Themes [sic] Questing for the Essence of Mind and Matter based on a series of columns written for Scientific American by Douglas R. Hofstadter. One particular relevant chapter is devoted to “Parquet Deformations,” a “subtle, intricate art form” developed by William Huff, a professor of architecture through assigned student studies)

And

P. 10. The incremental pace of change in a parquet deformation is rather like that of days moving one season to the next. Hofstadter notes its temporal character, equating a parquet deformation to visible music. The underlying principle seems to be …

1992 (0)

1993 (0)

1994 (3)

Bigalke, Hans-Günther. Reguläre Parkettierungen. Mit Anwendungen in Kristallographie, Industrie, Baugewerbe, Design und Kunst. BI Science Publisher, 1994

Translated: Regular tilings: With applications in Crystallography, industry, construction, design and art.

P. 232 illustration and Huff mention. A ‘Square to double basketweave to Cairo deform’, with an Alhambra transition not seen before (in ‘Square to double basketweave’ section), with the designer not credited. Seems to be only a single page study.

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2Ähnliche "parquet deformations" sind z . B . von S . HUFF , Department of Architecture , Carnegie Institute of Technology , Pittsburgh / Pennsylvania , oder von M . C . ESCHER , Z . B . in seinen " Metamorphosen " von 1939 und 1967 …

Wikipedia:

Hans-Günther Bigalke (born February 23, 1933 in Celle ; † April 19, 2019 there) was a German mathematician and university professor. He was one of the pioneers of didactics of mathematics in Germany and co-founder of the Society for Didactics of Mathematics.

Huff 1994 see

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In scientific terms, such a progressive, step-by-step alteration is known as a parquet deformation. But in Studstill's case, the principle of incrementally graduating tones was not soley [sic] based on scientific or color theory, but also intuited …

HathiTrust: Published on occasion of the exhibition held at the Renwick Gallery, National Museum of American Art, Smithsonian Institution, Washington, D.C., Feb. 25-April 17, 1994.

Introduction briefly describes the history of the Renwick Gallery of the National Museum of American Art which specializes in American crafts and decorative arts. The rest of the book concerns the donation of the American craft collection from KPMG Peat Marwick. Includes a background of corporate collecting in America in the past century, reproductions of many works in the collection, and biographies on the artists.

https://americanart.si.edu/artist/pamela-studstill-6283

As the eye moves from top to bottom, Quilt #17 undergoes a subtle but definitive transformation in color and light. Gradually, almost imperceptibly, lighter color values change into darker ones. “Each of my quilts,” the artist writes; “is a study in light.” Surface paint helps ease the transition from one color to another. In scientific terms, such a progressive, step-by-step alteration is known as a parquet deformation. But in Studstill’s case, the principle of incrementally graduating tones was not soley [sic] based on scientific or color theory, but also intuited from the experience of her Texas Hill Country surroundings. “I am inspired,” she writes; “by landscape views and vistas, fields of [all kinds] … and changes in my local landscape.”

N.B. Quilt #17, 1982, is not a parquet deformation as such!

1995 (1)

Hofstadter, D. R. Fluid Concepts and Creative Analogies. Computer Models of the Fundamental Mechanisms of Thought. Harvester Wheatsheaf 1995, and Allen Lane The Penguin Press 1997, 501 pp.

A single page discussion on parquet deformations, albeit without diagrams, p. 477. A heavyweight tome, of largely of an academic nature, although readable, but obscure, with numerous essays, albeit invariably of limited interest, way beyond my understanding. And an interesting tidbit on Amazon, below the main discussion!

P. 477. For me, what Lenat and Chamberlain did for their programs is strongly reminiscent of the role that is played by William Huff, an architecture professor, with respect to students in his design courses. Huff has a long-standing tradition of assigning his design students the challenge of creating "parquet deformations" - tilings of the plane that gradually metamorphose in an Escher-like manner as they move across the plane (many examples are given and discussed in Chapter 10 of Hofstadter, 1985). To get the idea across to the students in each successive class, Huff shows a portfolio consisting of what he considers to be the best examples from previous years. Thereby inspired, the current crop of students then produces a large set of new parquet deformations, most of which are not great, but usually at least a few of which are novel and exciting. As one would expect, Huff applies his own keen artistic judgment to the latest harvest, pruning the weak ones out and adding his favorites to the growing portfolio to be shown to subsequent classes. In this way, a process of evolution takes place, with Huff playing the role of natural selection, letting artistically weak specimens die and strong ones survive, and then propagating the "most fit genes" by exhibiting the survivors to his class the next year. Over a period of some twenty or more years, Huff has managed to direct the course of evolution of parquet deformations in a very interesting way.

The question naturally arises as to the authorship of all these pieces. Huff has a practice of labeling each piece, when they are exhibited in a museum or gallery, "from the studio of William Huff", with no further information. However, when I decided to publish a small selection of these beautiful studies, I felt that Huff's labeling practice was too one-sided, and so for each piece I listed both Huff's name and the student's name. I felt this was fairer. But I certainly could see two sides of this question. There was no doubt in my mind that Huff deserved a large portion of the credit. Whether it was less or more than 50 percent remains an unresolved but fascinating question in my mind.

Wikipedia

Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought is a 1995 book by Douglas Hofstadter and other members of the Fluid Analogies Research Group exploring the mechanisms of intelligence through computer modeling. It contends that the notions of analogy and fluidity are fundamental to explain how the human mind solves problems and to create computer programs that show intelligent behavior. It analyzes several computer programs that members of the group have created over the years to solve problems that require intelligence. It was the first book ever sold by Amazon.com.

https://s3.amazonaws.com/arena-attachments/669097/a6e33859f5f6677f20615f14fdbf52fa.pdf

1996 (1)

Huff, William S. ‘The Landscape Handscroll and the Parquet Deformation’, In Katachi U Symmetry. Tohru Ogawa, ‎Koryo Miura, ‎and Takashi Masunari. Tokyo: Springer-Verlag 1996, pp. 307–314.

Of fundamental interest, and a must-read in the field. Huff compares the Landscape Handscroll and the Parquet Deformation with the Sino-Japanese right-left viewing and the Western left to right, and more, including temporality, off-shoots of D'Arcy Thompson and Escher. An excellent all-round overview, with all aspects considered. This being so, I thus detail this article more extensively than others. The main substance is Chapter 2. The article includes:

1 The Aesthetics of the Parquet Deformation: Canons and their Afterimage

1.1 Do East and West Share the Same Sense of Drama?

1.2 Spatial versus Temporal Art Forms

1.3 Temporal Visual Art, Experienced through Channeled "Serial Images"

1.4 How Are Handscrolls and Parquet Deformations Composed?

2 The Mathematics of the Parquet Deformation: Constraints of Symmetry and

Topology

2.1 Parquet Patterns, a Recent Diversion in Geometry

2.2 Designing Novel Parquet Patterns and Deforming One into Another

2.3 Influence of D'Arcy Thompson; Comparisons with M. C. Escher

The article has seven parquet deformations from Huff’s studio, with works by, in sequential order, Liou Jiunn-liang (Romeo and Juliet, 1993), Fred Watts (Fylfot Flipflop, 1963), Pamela McCracken (Cloisonné, 1990), Loretta Fontaine (Seven of One Make Three, 1991), Vincent Marlowe (Clearing the Thicket, 1979), Alexandria Gelencser (Swizzle Stick Twirl, 1986), Bryce Bixby (They Come, They Go, 1991). All are from Buffalo, save for the Watts (Carnegie-Mellon) instance. However, perhaps a little oddly, there is no discussion (or even a reference) of these in the text. Likely, these serve for generic illustrative purposes.

Of note, in detail:

2.1 Parquet Patterns, a Recent Diversion in Geometry

Essentially, the background to tiling, titled ‘parquet’ by Huff. Mentions of Thomás Maldonado (HfG), Martin Gardner (Scientific American column), and Branko Grünbaum (definition of monohedral tiling). Mentions ‘improper’ parquets.

2.2 Designing Novel Parquet Patterns and Deforming One into Another

The title here suggests a tutorial, but this is not so. Rather, it discusses matters of Bravais lattices and rotational symmetry.

Chapter 2.3 Influence of D’Arcy Thompson; Comparisons with M. C. Escher.

Of note here in the first line is:

The intriguing possibility of the incremental deformability of one parquet pattern into another came to our attention in 1960 when it was recognized in one student's designs of several very different

looking patterns that there were underlying, but far from obvious morphological relationships

between them.

The unnamed student is Peter Hotz, derived from Huff’s notes for a SEMA talk (2003). Mentions D’Arcy Thompson’s, On Growth and Form and his chapter ‘On the Theory of Transformations’, and Escher's comparable work. Also detailed is, in so many words, ‘permissible’ and ‘non-permissible’ parquets (not illustrated), the intricacies of which (without visual aid) I am at a loss to understand. Much here is taken from Hofstadter's 1983 article.

In the references, Huff quotes four people, including Walther Lietzmann, Anschauliche Topologie and P. A. MacMahon, New Mathematical Pastimes. However, I’m not sure why. In particular, Lietzmann only has a small four-page chapter on tilings, and these are the basics of a school-level introduction. He mentions the MacMahon book elsewhere in general for his tiling interest.

1997 (0)

1998 (1)

Inconsequential. Brief mention (not illustrated) of parquet deformations (in Hofstadter's Metamagical Themas) on pp. 48–49 in the context on dance.

Pp. 48–49. In terms of the relation of figure and space, the patterns of such choreography reveal a similarity with the designs that are known as "parquet deformations" (Hofstadter 1985:195-218): gradually developing transformations of divisions of the plane, or tessellations, which, through the lengthening or rotating of a line or through the introduction of a hinge, result in a complete distortion or regrouping-like a type of ornamental morphing.

MIT

TDR traces the broad spectrum of performances, studying performances in their aesthetic, social, economic, and political contexts. With an emphasis on experimental, avant-garde, intercultural, and interdisciplinary performance, TDR covers performance art, theatre, dance, music, visual art, popular entertainments, media, sports, rituals, and the performance in and of politics and everyday life.

1999 (0)

2000 (1)

Kaplan, Craig S. and David H. Salesin. ‘Escherization’. SIGGRAPH '00: Proceedings of the 27th annual conference on Computer graphics and interactive techniques, July 2000 pp. 499–510

A brief mention on parquet deformations in passing (not illustrated), p. 510:

...This research suggests many future directions, including generalizing our algorithms to handle multihedral and aperiodic tilings, parquet deformations [13, Chap. 10], or tilings over non-Euclidean domains, such as the hyperbolic plane [7]....

The reference quotes Hofstadter’s Metamagical Themas.

Note a similar titled paper by both authors, ‘Dihedral Escherization’, of 2004, does not contain any references to parquet deformation or Huff.

https://static.aminer.org/pdf/PDF/000/593/525/escherization.pdf

2001 (0)

2002 (2)

A major writing, of 18 references to parquet deformation. Many references to parquet deformations in Chapter 3.4.1 ‘Islamic parquet deformations’ pp. 57–58 and Chapter 5.4, ‘Deformations and metamorphoses’, pp. 187–194. Also see p. 212. A select few references:

P. 57

Parquet deformations are a style of ornamental design created by William Huff, a professor of architectural design, and later popularized by Hofstadter in Scientific American [83, Chapter 10]. They are a kind of “spatial animation,” a geometric drawing that makes a smooth transition in space rather than time. Parquet deformations are certainly closely related to Escher’s Metamorphosis prints, though unlike Escher’s work they are purely abstract, geometric compositions. They will be discussed in more detail in Section 5.4. Hankin’s method can be used as the basis for a simple but highly effective method of constructing Islamic patterns in the spirit of parquet deformations. I lay out a strip of the template tiling and then run a modified inference algorithm where the contact angle at every contact point is determined by the location of that point in the strip. Smoothly varying the contact angle results in a gently changing geometric design that is still recognizably Islamic. The construction process is illustrated in Figure 3.7; two more examples appear in Figure 3.8. These parquet deformations occupy an interesting place in the world of Islamic geometric art. They have enough overall structure and balance to satisfy the Islamic aesthetic, but they would not have been produced historically because very little repetition is involved. The effort of working out the constantly changing shapes by hand would have tested the patience of any ancient designer.

P. 58

Figure 3.7 The construction of an Islamic parquet deformation based on Hankin’s method. The top rows shows the effect of continuously varying the contact angle of a ray depending on the x position of the ray’s starting point in the design. When the process is carried to all other tiles, the design in the second row emerges.

Figure 3.8 More examples of Islamic parquet deformations based on Hankin’s method.

P. 190

Figure 5.2 Examples of parquet deformations.

Presumably, a one-to-one correspondence is established between the tiles of T1 and T2, and as a parameter t moves from 0 to 1, each individual tile gradually deforms from its T1 shape to its T2 shape. The transition might be carried out spatially as in Escher’s art, or even temporally as a smooth animation from T1 to T2.

As was mentioned in Section 3.4.1, the parquet deformations of William Huff are a kind of spatial animation. Huff was inspired directly by Escher’s Metamorphoses. He distilled the style down to an abstract core, considering only interpolation transitions, and favouring abstract geometry rendered as simple line art to Escher’s decorated animal forms. As reported by Hofstadter [83, Chapter 10], Huff decided further to focus on the case where T1 and T2 are “directly monohedral,” in the sense that every tile is congruent to every other through translation and rotation only. We may also assume he had only periodic tilings in mind. Finally, he asked that in the intermediate stages of the deformation the tile shapes created could each be the prototile of a monohedral tiling (Hofstadter amends this rule, pointing out that some deformation might be necessary to make the intermediate shapes tile). Inspired by parquet deformations and by Escher’s interpolation transitions, we may pose the

P. 191

related problem of finding a smooth transition between any pair of isohedral tilings. A solution to this problem might then be expanded to encompass Escher’s work (by considering a k-isohedral extension) or parquet deformations (by introducing the restrictions mentioned above). In any case, the isohedral problem is sufficiently interesting, and the results sufficiently attractive, that it can be fruitfully studied in isolation....

P. 193

As long as any pair of Laves tilings is joined via a path of base cases, we should be able to move between any two isohedral types. I have found topological transitions that obey all the restrictions of parquet deformations and that unify all the Laves tilings except for (4.6.12).

P. 194

Figure 5.3 A collection of parquet deformations between the Laves tilings

https://cs.uwaterloo.ca/~csk/other/phd/kaplan_diss_full_screen.pdf

Kinsey, L. Christine and Teresa E. Moore. Symmetry, Shape and Space: An Introduction to Mathematics. Key College Publishing, 2002. Hardcover Wiley 2008, 494 pp.

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N.B. I have a like titled book by the same authors Symmetry, Shape and Space with the Geometer's Sketchpad, 169 pp., which is notably different. I think I thought I was getting the original material and the new sketchpad material when I ordered the latter!

P. 108. Chapter 4 Tesselations [sic]

Parquet Deformations

In 1937 the Dutch graphic artist M. C. Escher began to experiment with the metamorphosis of his tiling patterns…

P. 113. A later development of the idea of transforming tiling took place in the architecture studios of William Huff, at Carnegie Mellon and SUNY-Buffalo. He coined the phrase parquet deformation and dictated two rules (quoted from Hosftadter)

Wikipedia

Laura Christine Kinsey is an American mathematician specializing in topology. She is a professor of mathematics at Canisius College.

2003 (3)

Dawson, Robert J. MacG (probably). ‘Crooked Wallpaper’. Journal of Graphics Tools. Volumes 8–9, A. K. Peters, 2003, pp. 33–46

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p. 43 seen in the “parquet deformation" of Figure 10, which shows seven tilings (a–g), all with the same periodicity. Applying stretch to any tiling (except the right - most) yields the one immediately to its right; the shaded fundamental domain …

Wikipedia

The Journal of Graphics Tools (JGT) was a quarterly peer-reviewed scientific journal covering computer graphics. It was established in 1996 and published by A K Peters, Ltd., now part of Taylor & Francis. From 2009-2011 the journal was published as the Journal of Graphics, GPU, & Game Tools. In 2012, a large part of the editorial board resigned to form the open access Journal of Computer Graphics Techniques (JCGT). The Journal of Graphics Tools continued with a new editorial board. The last editor-in-chief is Francesco Banterle (Istituto di Scienza e Tecnologie dell'Informazione). Previous editors-in-chief have been Andrew Glassner, Ronen Barzel, Doug Roble, and Morgan McGuire. The final volume was released in 2013 and the journal formally ceased with its final issue in 2015.

Can’t find with ease. Available at Taylor & Francis?

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From SEMA website:

SEMA is the acronym for the Society of Morphological Studies of Argentina. Our society summons those who investigate, teach and produce forms in different disciplinary fields in order to build a common territory. SEMA tries to be a meeting space for architects, artists, designers, mathematicians, musicians, poets, philosophers, biologists ... and for all those genuinely interested in the territory of Form.

We founded SEMA in December 1996 in Buenos Aires, Argentina. Since then, we have held eleven biannual congresses (eight of them international), published publications and organized numerous artistic and scientific conferences and meetings throughout the Argentine territory... SEMA has become a rich space for meeting, working and exchanging knowledge between people and institutions from all over the country and related groups from all over the world.

The SEMA website does not appear to have archives, and I could not find this publication on Bookfinder. Although not seen, from prepared notes, this paper is likely of fundamental importance, in terms of historical developments. The perceived wisdom is that Huff devised the concept. However, this now appears not to be strictly so! Rather, it came from one of his students, Peter Hotz, arising from a plane tiling study (parquets). Interestingly in revisiting old emails (2003), he in effect told me this, but without mentioning Hotz’s name! I seem not to have realised the significance at the time, and with the passing of time I forgot about it. The revelation in the notes hit me like a bombshell! I have since found Hotz, and more detail in a general sense on his work is forthcoming.

Inkpen, Kori and ‎Michiel Van de Panne. Graphics Interface 2003, A K Peters/CRC Press, 2005, pp. 179–181

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1 Islamic parquet deformations Parquet deformations are a style of ornamental design created by William Huff, and later popularized by Douglas Hofstadter (16, Chapter 10 ]. They are a kind of “ spatial animation, ”a geometric drawing that …

On Kaplan’s Islamic deformations.

Wikipedia

The Graphics Interface (GI) conference is the oldest continuously scheduled conference devoted to computer graphics, and human–computer interaction. GI was held biannually between 1969 and 1981, and has been held annually since then. Prior to 1982, the conference was called Canadian Man-Computer Communications Conference (CMCCC)...

2004 (0)

2005 (3)

Comptes Rendus - Interface Graphique. National Research Council of Canada, 2005

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P. 177. We show how this method can be adapted to construct Islamic designs reminiscent of Huff's parquet deformations. Finally, we introduce a geometric transformation on tilings that expands the range of patterns accessible using our method.

Bibliographic detail is scanty here. Although not stated, the text is taken from Kaplan’s

‘Islamic star patterns from polygons in contact’.

I have not been able to find out more on this Canadian journal.

Inkpen, Kori and ‎Michiel Van de Panne. Graphics Interface 2003, A K Peters/CRC Press, 2005 pp. 179–181

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On Kaplan’s Islamic deformations.

Wikipedia

Kaplan, Craig S. ‘Islamic star patterns from polygons in contact’. Proceedings of Graphics Interface 2005, pp. 177–185

Islamic designs reminiscent of Huff's parquet deformations. ... in the style of Huff's parquet deformations [16, Chap- ... book also appear in a recent paper [4].

2006 (0)

2007 (1)

Horstadter, Douglas R. I Am a Strange Loop. Basic Books, 2007 Hardback, 2008 Paperback, 412 pp.

One true mention. A marvelous pen-and-ink “parquet deformation” drawn in 1964 by David Oleson (below) illustrates this idea not only graphically but also via a pun, for it is entitled “I at the Center”:

David Oleson I at the Center parquet deformation discussion in Chapter 1, ‘How We Live in Each Other’, pp. 241–258. The premise of the book, detailed below, thus makes David Oleson's work here an obvious choice for inclusion. Note that Hofstadter here is making a point in his writing, and is not a discussion as to the parquet deformation in general, as with his Scientific American 1983 piece.

Page 252. All of this suggests that each of us is a bundle of fragments of other people’s souls, simply put together in a new way. But of course not all contributors are represented equally. Those whom we love and who love us are the most strongly represented inside us, and our “I” is formed by a

complex collusion of all their influences echoing down the many years. A marvelous pen-and-ink “parquet deformation” drawn in 1964 by David Oleson (below) illustrates this idea not only graphically but also via a pun, for it is entitled “I at the Center”:

[Image]

Here one sees a metaphorical individual at the center, whose shape (the letter “I”) is a consequence of the shapes of all its neighbors. Their shapes, likewise, are consequences of the shapes of their neighbors, and so on. As one drifts out toward the periphery of the design, the shapes gradually become more and more different from each other. What a wonderful visual metaphor for how we are all determined by the people to whom we are close, especially those to whom we are closest!

Wikipedia

I Am a Strange Loop is a 2007 book by Douglas Hofstadter, examining in depth the concept of a strange loop to explain the sense of "I". The concept of a strange loop was originally developed in his 1979 book Gödel, Escher, Bach...

In the end, we are self-perceiving, self-inventing, locked-in mirages that are little miracles of self-reference.

— Douglas Hofstadter, I Am a Strange Loop p. 363

http://digitalphysics.ru/pdf/Kaminskii_A_V/I_Am_a_Strange_Loop--Douglas_Hofstadter.pdf

2008 (1)

Kaplan, Craig S. ‘Metamorphosis in Escher’s Art’. In Bridges 2008: Mathematical Connections in Art, Music and Science, pp. 39–46

Eight mentions. First mention; In addition to Escher’s art, we can also turn to William Huff’s parquet deformations as a source of inspiration.

Within an Escher framework of transitions, has much on parquet deformations, pp. 42–45.

http://archive.bridgesmathart.org/2008/bridges2008-39.pdf

2009 (2)

Bosch, Robert and Andrew Pike. Map-Colored Mosaics. Proceedings of the 2009 Bridges Banff Conference, held in Banff, Canada. Edited by Craig S. Kaplan and Reza Sarhangi, pp. 139–146

P. 142: Once we have created a map-colored mosaic that pleases us, we can modify it by replacing its square tiles with other tiles that behave like squares. By doing this, we obtain images that are reminiscent of Escher-like tessellations [6,10] or Huff-like parquet deformations [7,9] when viewed from up close, yet still look like familiar images when viewed from a distance. See Figures 5 and 6.

http://archive.bridgesmathart.org/2009/bridges2009-139.pdf

Andrew Pike (LinkedIn)

Experienced Researcher with a demonstrated history of working in the e-learning industry. Skilled in Cell Culture, Science, Western Blotting, Laboratory Skills, and Protein Expression. Strong human resources professional with a PhD focused in Molecular Microbiology and Immunology from Johns Hopkins Bloomberg School of Public Health.

Kaplan, Craig S. Introductory Tiling Theory for Computer Graphics. Morgan and Claypool Publishers, 2009

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P. 53. 13. Write a program to create parquet deformations: patches of tiles that slowly evolve…Parquet deformations were devised by Huff… My Bridges 2008 paper discusses methods for drawing parquet deformations based on isohedral tilings.

Brief mention of Huff and parquet deformation.

2010 (3)

Ellison, Elaine K. and John Sharp. ‘Tiled Torus Quilt with changing tiles’. Bridges 2010, pp. 67–74

P. 68: Huff used the idea which he called "parquet deformation" as an exercise to develop visual thinking in his students. He was inspired by Escher's woodcut Night and Day. In July 1983 Douglas Hofstadter, writing about these ideas in his Scientific American column [3], explained the basics of one-dimensional parquet deformation. He subsequently published his column articles in book form [4] and they form chapter 10 there. John Sharp produced many designs at this time as he describes below. The Hofstadter article also inspired Craig S. Kaplan who included it in his paper titled Metamorphosis in Escher’s Art at the 2008 Bridges Conference in Leeuwarden, Netherlands. Robert Bosch and Andrew Pike also presented a paper Map-Coloured Mosaics at the 2009 Bridges Conference in Banff, Canada which refers to Huff's work through Hofstadter's book.

Mostly John Sharp-inspired parquet deformations.

Huff, William S. ‘Simulacra of Nonorientable Surfaces—Experienced through Timing’. In Spatial Lines, (Líneas espaciales) Patricia Muñoz, compiler. Buenos Aires: De la Forma, 2010, 128 pp.

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See Chapter 4. One paragraph of reference to parquet deformations amid a Möbius Band premise:

The Experience of Timing

On previous occasions, I gave oral and written accounts of a type of design, regularly assigned in my basic design studio—the parquet deformation—which disposes time to participate as an integral third dimension, thus dynamizing the two-dimensional spatial content of the design. Commentary on the aesthetic potential of the parquet deformation was presented at the Katachi 2 conference (Huff 1994: 219-222), and commentary on its geometric requisites was presented at the SEMA 4 conference (Huff 2003: 9). I liken the parquet deformation to a remarkable art form, the Chinese handscroll, which, in its most exceptional, but younger genre, the landscape handscroll, goes back a thousand years. Time unfolds as the scroll is synchronously unrolled and rolled—pleasurable frame by pleasurable frame—not dissimilarly to how music flows. Time is engaged, however, in a different manner in respect to compositions whose three dimensions are all spatial.

Oddly, the pdf is not paginated, despite the contents being so! The likely reason is that the images are omitted in the pdf.

Background of the compiler: Professor Patricia Muñoz, Industrial Designer, Doctor UBA

From http://edicionesdelaforma.blogspot.com/

This book has several authors. Some are part of a research group at IEHU, Laboratory of Morphology, FADU, University of Buenos Aires. Others are part of the teaching team that brought this topic to the classroom at the Industrial Design Career, FADU, UBA. In addition, three guests make a significant contribution from other areas. Roberto Doberti refers to the interdisciplinary nature of this work, saying: It is no less important that the book be a product of various hands, none of which loses its particular tenderness in the caress of these forms. In turn, Claudio Guerri points out that this production: unites temporal extremes turning them into spatial neighborhoods, by exploring a theme that links ancient Greek developments with contemporary design practice.

http://www.documentosplm.com.ar/downloads/englishtextonly.pdf

http://edicionesdelaforma.blogspot.com/2010/05/lineas-espaciales.html

31 mentions of parquet deformation!

Abstract

In this paper, I consider the question of how to carry out aesthetically pleasing evolution of the curves that make up the edges in a parquet deformation.

Some most impressive, highly advanced (in concept) parquet deformations.

http://archive.bridgesmathart.org/2010/bridges2010-95.pdf

Schattschneider, Doris. ‘The Mathematical Side of M. C. Escher’. Notices of the American Mathematical Society. Volume 57, Number 6, June/July 2010, pp. 706–718

A brief discussion on parquet deformation in the context of the overall mathematical side of Escher:

P. 716: Metamorphosis, or topological change, was one of Escher’s key devices in his prints. His interlocked creatures often began as parallelograms, squares, triangles, or hexagons, then seamlessly morphed into recognizable shapes, preserving an underlying lattice, as in his visual demonstration in Plate I in [19]. At other times the metamorphosis of creatures changed that lattice, as occurs in his Metamorphosis III. William Huff’s design studio produced some intriguing examples of “parquet deformations” that preserve lattice structure [30], and, more recently, Craig Kaplan has investigated the varieties of deformation employed by Escher [34].

https://www.ams.org/notices/201006/rtx100600706p.pdf

2011 (1)

Anceschi, Giovanni. New Basic Design a Venezia e Basic Design a Ulm, ISIA Urbino, Self Published on Issuu January 19, 2011, 72 pp.

Two mentions, simply captioned ‘Parquet Deformation’. Conference by Giovanni Anceschi, Reference teacher Nunzia Coco.

Three untitled parquet deformations, by Watts, Holtz and Lane, p. 58; David Oleson’s The I at the Center, p. 64.

https://issuu.com/giovannianceschiteoria/docs/2.2-newbasic-e-basic

2012 (5)

Hann, Michael. Structure and Form in Design: Critical Ideas for Creative Practice. Bloomsbury Academic, 2012

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Three references, p. xviii, p. 104, 179 (index)

P. 104 Craig Kaplan ‘fractal’.

Huff, William S. ‘Defining Basic Design as a Discipline’. In Symmetry: Art and Science, Vol. 2 (new series) Numbers 1–4, 2012, pp. 91–98

One mention, p. 91:

Publications: “Ordering Disorder after K. L. Wolf,” in: Forma, 15, Tokyo (2000), 41-47; “The Landscape Handscroll and the Parquet Deformation,” in: Katachi U Symmetry, Tokyo: Springer-Verlag (1996), 307-314;

Parquet deformation is only mentioned once, in passing, as a reference in his list of publications, on the first page.

https://www.yumpu.com/en/document/read/12301640/symmetryart-and-science-sint-lucas

Laparidis, Stavros. ‘The Role of Allusion in Ligeti's Piano Music’. Dissertation, 2012, P. 22.

19 Example 5. Étude 9: Vertige, opening seemingly static but constantly changing type

of music as “parquet deformation,” a very insightful term to describe this compositional design…

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Only a part-preview is available on ProQuest, of which just the first 13 pages are viewable.

Although likely of a mention in passing, of considerable interest due to one of the few music links.

Pitici, Mircea. The Best Writing on Mathematics 2011. Princeton University Press, 2012

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P. 148 D. Hofstadter, Parquet deformations: Patterns of tiles that shift gradually in one dimension, Scientific American (July 1983): 14–20. Also in Metamagical Themas: Questing for the Essence of Mind and Pattern, Basic Books, New York, 1985.

Princeton University Press.

This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2020 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday aspects of math, and take readers behind the scenes of today’s hottest mathematical debates.

Seemingly the series began in 2010.

Simmi, Simone (ed?). Eredità, 19 Nov 2012. 16 pp.

Inconsequential. Article by Anceschi?

Bill Huff svilupperà questa tematica intitolandola “Parquet deformations”

= Bill Huff will develop this theme entitled "Parquet deformations"

eredità = heredity

An obscure publication in Italian, with much uncertainty. Minor mention of Huff and parquet deformations, p. 9.

https://issuu.com/simonesci/docs/ulm

2013 (2)

A brief mention essentially in passing of a fabricated(?) Craig Kaplan parquet deformation upon the opening of the museum.

P. 545. Art and math are interwoven within the very fabric of the Museum. A parquet deformation designed by Craig Kaplan surrounds the front façade (Fig. 5).

Figure 5: Parquet deformation (C. Kaplan)

Disappointingly, Fig. 5 is in close up, rather than the parquet deformation in context with its surroundings.

http://archive.bridgesmathart.org/2013/bridges2013-547.pdf

Olmsted, Zachary T., Tim D. Riehlman, Carmen Branca, Andrew G. Colliver, Adam M. Winnie, Janet L. Paluh. ‘Metamorphic Pattern Formation and Deformation: In Vivo and In Vitro Mechanisms’. Biophysical Journal, January 2013, p. 142a

...Our goal is to apply insights on patterning biological polymers in vivo to development of hybrid biosynthetic systems capable of utilizing microtubules in self-assembling metamorphic patterns including parquet deformation behavior.

I’m not too sure what the brief text is; an article, a note or...? As such, it is more of a note. The text is academic. Whatever, a single mention in passing.

2014 (5)

Anon. ‘In Brief. Awards and Announcements’. B/a+p. News from the School of Architecture and Planning University at Buffalo, Spring 2014

Text, p. 4:

Basic Design: An Exhibition of Works by Students of William S. Huff

The works of students of William S. Huff, professor emeritus of architecture, were featured in “Basic Design,” a recent exhibition at the Ulm Museum in Ulm, Germany. An internationally noted scholar, Huff studied at the Ulm School of Design and Yale University and then taught at Carnegie-Mellon University before joining the faculty of the Buffalo School in 1974. Over the years, Huff has amassed a collection of material documenting design theory, from the Bauhaus to the HfG/Ulm to the latest methods in design education. Huff has gradually donated much of this material, including the results of many Buffalo School student design assignments, to the HfG/Ulm Archive. “Basic Design” features 40 graphic works and 20 study models from this collection, highlighting Huff’s experimentation with symmetry (programmed design), black & white and color rasters (grid manipulation), congruent sectioning of space, effecting color in pigments as color in light, and the deformation of parquet patterns. Huff’s fundamental doctrine has impacted basic design teaching around the world.

Nicholas Bruscia is also mentioned, but not in the context of parquet deformation.

https://ap.buffalo.edu/content/dam/ap/3-News---Events/BapMagazine/BAP-Magazine-Spring2014-sm.pdf

Artist’s Page. Mutahir Arif. Crossing Disciplines – Scope: (Art & Design), 9, 2014

P. 86. Untitled (2014) was inspired by Islamic parquet ‘deformations’ created by Craig Kaplan. Kaplan’s work was based on research by William Huff, and was later popularised by Douglas Hofstadter who in turn had been influenced by M.C. Escher’s Metamorphosis series.²

I extended Kaplan’s spatial animation work by applying the animation principles, known to most professional animators, to the star forms of Islamic patterns. Although Kaplan was successful in rendering his Islamic star patterns by way of an inference algorithm written as a standalone and executable Java application, he conceded that “(t)he construction of Islamic parquet deformations requires many separate invocations of the inference algorithm, and [was] currently too slow to run interactively.”³ To solve this problem, I adopted a more traditional approach by constructing the parquet deformations animation the old-fashioned way by using a more basic technique, frame-by frame animation. The drive to realise Kaplan’s vision of “a gently changing geometric design that is still recognizably Islamic” was inspired by the fact that nobody had attempted this approach before, owing to the painstaking nature of the undertaking. Changing shapes by hand and then executing the application was very time-consuming.⁴ Even in today’s digital age, achieving such a result is no mean feat…

Inconsequential. Oddly, the work Untitled, Fig. 3, although said to be parquet deformation related, is not a parquet deformation as such, and is merely a typical Islamic repeat tiling! Further, Figure 1 and Figure 2 are not (or appear to be) parquet deformations!

Background

I am not too sure as to what exactly ‘Crossing Disciplines’ is. It may be an off-shoot of the New Zealand-based ‘Scope’: Scope: Contemporary Research Topics is peer-reviewed and published annually in November by Otago Polytechnic/Te Kura Matatini ki Otago, Dunedin, New Zealand.

It's unclear as to how to cite this. I will place it under ‘Artist’s Page’.

https://www.thescopes.org/assets/Uploads/ed703b16df/009-86-Ariff-11-14.pdf

Bellos, Alex. ‘Crazy paving: the twisted world of parquet deformations’. The Guardian, 9 September 2014 (N.B. Online only)

Nine mentions. First: In the 1960s an American architecture professor, William Huff, coined the term ‘parquet deformation’ to mean a regular pattern of tiles that transforms as you go from left to right whilst maintaining the regularity of the tiling.

Essentially a substantial feature on Craig Kaplan’s work rather than a general discussion on the subject, and all mightily impressive and is of required reading. Of a cross-section of his work, in which he brings his full range of computer scientist/mathematical abilities to the premise, leaving lesser mortals far behind. Most of these are simply impractical without the aid of a computer. Bellos captions these as: Grid-based parquet deformation, Funky tiles, Iteration deformations, Organic labyrinth growth, Islamic tiling, 2D parquet deformation, and Circular deformation.

Unusually, these are shown coloured. Kaplan is one of the few who use colour (others include de Villiers), of both flat and graduated colours.

https://www.theguardian.com/artanddesign/alexs-adventures-in-numberland/2014/sep/09/crazy-paving-the-twisted-world-of-parquet-deformations

Schaffer, Karl. ‘Dancing Deformations’. Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture, pp. 253–260

On the analogies of dance with parquet deformation. Not illustrated with Huff-type examples. Also see a like later paper of his, ‘Dichromatic Dances’, of 2017. Such comparisons are rare. Also see Gabriele Brandstetter and Marta Ulvaeus on the same theme.

P. 253:

Abstract

The performing art of dance employs symmetry in a variety of ways. Often choreographers blur the lines between symmetries or seamlessly morph from one symmetry type to another. This may be seen to be similar to parquet deformations, visual images in which one tiling deforms seamlessly into another…

Parquet Deformations. The artist M.C. Escher created a number of works in which one tessellation morphs into another. Later in the 1960s the architect William Huff investigated these designs with his students, and received wider attention when explored and written about by Douglas Hoffstadter [4]. Recently Craig S. Kaplan has presented his investigations of them at Bridges [6]. These visual designs usually change seamlessly in a horizontal direction through several tiling patterns. Dance choreographers often utilize similar deformations, in both time and space.

P. 260:

[4] Douglas R. Hofstadter, “Parquet Deformations: Patterns of Tiles that Shift Gradually in One Dimension,” Scientific American, 1983.

[6] Craig S. Kaplan, “Curve Evolution Schemes for Parquet Deformations,” Bridges Proceedings, 2010, pp. 95-102.

https://archive.bridgesmathart.org/2014/bridges2014-253.pdf

Schattschneider, Doris. M. C. Escher: Visions of Symmetry. W. H. Freeman, 2004

A brief discussion (not illustrated):

P. 281: At least one professor of design, W. S. Huff, found inspiration in Escher continuous deformations of interlocked motifs in his metamorphosis works, and explored various possibilities for these with his students. Some of this work is reported in the article, “Parquet Deformations: Patterns of Tiles That Shift Gradually in One Dimension" by Douglas Hofstadter.

P. 362: (bibliography, Hofstadter article, as above).

2015 (6)

‘BAD’ (Built by Associative Data). By ‘MUQ’?, ‘Computation Coding/Recoding Islamic Patterns’. Self Published on Issuu March 13, 2015, 102 pp.

The construction of an Islamic parquet deformation based on Hankin’s [Method]

See p. 91. Three Islamic-style parquet deformations, of the more computer (Grasshopper?) ‘intricate’ type. Quite who the designer is for this is unclear - ‘Muq’?

https://issuu.com/akabbara/docs/bad_profile_selected_projects

Lamm, Dan. Material Systems, MIT Media Lab, 2015. Self Published on Issuu October 31, 2015, 169 pp.

See pp. 80-81.

Prepared for admission into the Mediated Matter research group in the Media Lab at MIT.

The first part of this project was to select and analyze a hand-drawn parquet deformation with no computational ...

N.B. I Looked for ‘Dan Lamm parquet deformations’ separately, but without success.

https://issuu.com/dlamm4/docs/mit_portfolio_-_reduced

Lee, Kevin. ‘Algorithms for Morphing Escher-Like Tessellations’. Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture pp. 483–48

Abstract

Inspired by the way M.C. Escher combined metamorphosis and regular division in his art, I explore linear and nonlinear algorithms that automatically morph tiles from the base polygon to a final shape. The morphing can be visualized as an animation or as a parquet deformation...

References

[2] Craig S. Kaplan. Curve Evolutions Schemes for Parquet Deformations. In Bridges 2010: Mathematical Connections in Art, Music and Science, pages 95-102, 2010.

Inconsequential (as good as the paper may be in morphing aspects), of just two mentions in passing. Mostly on morphing Bruce Bilney’s elephant tessellation.

https://archive.bridgesmathart.org/2015/bridges2015-483.pdf

Plender, Richard (ed.). Issues in International Migration Law. Brill - Nijhoff, first edition 2015

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David Oleson's 'parquet deformation', created at Carnegie-Mellon in....

pp. 107, 109

Google Scholar:

My special thanks also go to David Oleson, for kind permission to reproduce his 'Parquet Deformation' design on p. 109

£120 Bookfinder. Discussion on David Oleson, pp. 108–109.

Yao, Szu-An. Portfolio 2015. ‘Deformative Space Space Frame Structure by Adaptation of Parquet Patterns’. Self Published on Issuu, January 7, 2016, pp. 56

See pp. 54–55.

Parquet deformations are an abstract form of ornament first introduced by Willliam Huff as an exercise for his Architecture students, and later popularized by Douglas Hofstadter in his Scientific American column.….

Arguably the best on Issuu. A discussion, with five references to ‘parquet deformation’ and 16 to ‘parquet’. Mention of Huff and Hofstadter. Uses Escher's Sky and Water I.

https://issuu.com/annannyao/docs/0106portfolio_nocv.compressed

Ying, Fu. Portfolio. ‘Landscape Mosque’. Self Published on Issuu April 8, 2015, 37 pp.

See p. 28.

...This idea is similar to the idea of parquet deformation that the roof is a single piece, but the geometries are varied.

Alludes to parquet deformation, rather than showing any.

https://issuu.com/fuying5211/docs/fuying-port-page

2016 (0)

2017 (6)

Bonner, Jay, with contributions by Craig Kaplan. Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Construction. Springer, 2017

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Front Matter work, designs with diminishing scale, parquet deformations as per the work of Craig Kaplan…

Table of Contents …568 4.6 Extensions 568 4.6.1 Parquet Deformations

Page 569 references with additional information. 4.6.1 Parquet Deformations Th… (illustrated)

Page 570 I name such designs “Islamic Parquet Deformations,” after the … Huff…

Index ... Parquet deformation, 569–570.

Llonardi, Giulia. Portfolio. Self Published on Issuu May 19, 2017, 16 pp.

See p. 13 Parquet deformation (no other text or reference to Huff!)

Four, or three, depending on interpretation, parquet deformations, of varying adherence to the Huff model. Includes a (black and white) houndstooth instance.

N.B. I Looked for ‘Giulia Llonardi, parquet deformations’ separately, but without success.

https://issuu.com/giuliaiallonardi/docs/portfoliopdf

Şehir Çekmeköy, Tarih, Toplum ve Gelecek

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In short, a Turkish symposium, on, surmising on the translated text, ‘city history society future’?

P. 28. Two parquets illustrated:

Şekil 11. William Huff, 1979. The Parquet Deformation-iki örnek

Trans. According to Huff, it is a harmonious change of shapes (Figure 11).

P. 29 Quotes Huff in a list of references:

Huff, William. 1979. The Parquet Deformation. McGinty, T. (der). Best Beginning Design Projects Volume 1. Milwaukee: University of Wisconsin. S.30-33.

ŞEHİR TARİH TOPLUM GELECEK

Trans. CITY HISTORY SOCIETY FUTURE

https://www.cekmekoy.bel.tr/uploads/geneldosya/i-cekmekoy-sempozyumu-kitabi-1307-d.pdf#page=18

On the analogies of dance with parquet deformation. Not illustrated with Huff-type examples.

P. 291

Abstract

...This paper investigates danced two-colored or dichromatic symmetry patterns, and continues an earlier investigation on how such danced symmetry patterns may be seamlessly morphed from one symmetry type to another, in a manner similar to visual parquet deformations...

Introduction

....In this paper, I extend to two-colored or “dichromatic” patterns an exploration into danced parquet deformations [9], in which symmetric patterns of dancers morph from one pattern to another without breaking symmetry.

P. 292

… The earlier paper [9] examined how this may allow parquet like deformations from one symmetric dance formation to another.

P. 293

Figure 3 shows a “parquet deformation” sequence of positions for 4 dancers from a recent dance by the author titled “Blacks and Whites,” using possible two colorings of the one-color designs from Figure 2…

https://archive.bridgesmathart.org/2017/bridges2017-291.pdf

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This work resonates to the “Parquet Deformation” studio taught by William Huff at Carnegie Mellon in 1966, when, without using computers, such adaptive design concepts were already thought of and exercised [13] …

Quotes Huff.

13. Huff, W.S.: What is basic design? In: Crowell, R.A. (ed.) Intersight One. State University of New York, Buffalo (1990)

N.B. 2017 published

13 references to ‘parquet deformation’ and 52 to ‘parquet’. The first:

In his later writings, Huff redefines the exercise from different perspectives. For example, he compares the examples of Parquet Deformations with ancient Sino-Japanese landscape handscrolls while discussing the meaning and importance of temporal and spatial variation in different visual cultures (p. 307).

Broadly written from an architecture viewpoint. A major subpiece on ‘William Huff and the Parquet Deformation’.Tuğral (who I have corresponded with previously on parquet deformations, and who has studied these extensively on his Design Coding website), here presents his (first?) paper on them. However, I don’t quite know what to make of this, as the writing and explanations are somewhat technical. It is essentially a study of Huff student-inspired works and in particular ‘Trifoliate’ by Glen Paris. Other Huff-related works include ‘Crossover’, by Richard Long and ‘I at the Center’ by David Oleson. Further, his own students' works are included as well. Extensive use is made of the computer plug-in Grasshopper, much beyond my understanding, or indeed interest, as good as it may be in the right hands.

Mentions of myself, p. 254, and in the acknowledgements, p. 265.

Gives a good and extensive bibliography, although many of the references are peripheral, and/or not readily found to those without academic access.

Whatever, my perceived views, an article of substance, and required reading.

https://www.academia.edu/search?utf8=%E2%9C%93&q=parquet+deformations

Click on download, Tugral.

2018 (1)

Kitchen, Paul. Portfolio. Student Architectural Portfolio. Self Published on Issuu March 5, 2018, 23 pp.

See pp. 8–9, 18–19

Two references:

Pp. 8–9. Exploration of William Huff’s parquet deformations began with a series of hand-made physical models. These models transformed a rotated square into a rectangle. Parquet deformations limited the transformation to a single direction and two dimensional system…

For unclear reasons (in error?) the text repeats on pp. 18-19, on a section on climate change…

Three instances of sorts. Goes from 1-dimension to 2-dimensions and then (ostensibly) to 3-dimensions. He states he uses Grasshopper.

N.B. I looked for Paul Kitchen, parquet deformations separately, but without success.

https://issuu.com/pkitchen/docs/issuu_upload

2019 (6)

Bosch, Robert. Opt Art: From Mathematical Optimization to Visual Design. Princeton University Press, 2019.

NOT SEEN, GOOGLE BOOKS REFERENCE

See pp. 149–150, 187 (index)

From Mathematical Optimization to Visual Design. Figure 10.6 displays four versions—with squares, fans, square rings, and a parquet deformation…

A square to Shepherd’s Check parquet deformation, in his series of Frankenstein-themed ideas. Also, Vermeer’s ‘Girl with a Pink Earring’, p. 154.

Hann, Michael. The Grammar of Pattern. CRC Press, 2019, 229 pp.

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Three minor references. Page number is odd on Google Books, with page 4–17, 6–163, 6–164 (index)! Quotes Kappraff. Seems inconsequential.

...and one-dimensional parquet deformation (Kappraff, 1991, p. 184).

Book

The Grammar of Pattern describes characteristics of textile and other surface patterns, and identifies, illustrates, and reviews a wide range of pattern types including spotted, striped, checked, tessellating and other types of all-over patterns with original drawings and images.

Biography

Professor Michael Hann (BA, MPhil, PhD, FRSA, FRAS, FTI) holds the Chair of Design Theory at the University of Leeds. He is also Director of ULITA – an Archive of International Textiles, an important international archive (and, in the context of this book, a source of illustrative material). He has published across a wide range of subject areas, has made numerous keynote addresses at international conferences, and is an acknowledged international authority on the geometry of design. Recent book publications include: Hann, M (2012). Structure and Form in Design (London: Berg); Hann, M. (2013), Symbol, Pattern and Symmetry (London: Bloomsbury) and Hann, M. (2015), Stripes, Grids and Checks (London: Bloomsbury). He has held adjunct, visiting or invited professorships at institutions in Belgium, Taiwan, Hong Kong, Korea and the Peoples’ Republic of China.

Hoeydonck, Werner Van. ‘William Huff’s Parquet Deformations: A Viennese Experiment’.

Abstract

My presentation in Kanazawa aims to bring a renewed interest and a new nexus of activities around William Huff’s work, especially as an exercise in transformational thinking in the field of architectural education. After his retirement, professor Huff donated a beautiful collection of his students’ work to the HfG-Archiv in Ulm, Germany, which inspired us at the Institute of Art and Design in Vienna to conduct a semester assignment for 450 students around the topic of Parquet

Deformations (P.D.). The open search for strategies to transfer the spatiotemporal idea

of a planar P.D. into 3D led to fascinating results. Hereby we discovered a field of

formal research that opened the students’ eyes for two and three-dimensional

relationships and made them enthusiastic and sensitive for spatial transformations. This

is a brief report on how we conducted the exercise, as a fruitful exercise for the basic

design education of young architects and designers.

Includes a recreation of ‘Leather of the Lesser Gator’, by Thomas C. Davies, 1964. Also includes a modern-day work by Kim Ye-ryum, 2017, but no others. It is not a tutorial as such. My website gets a mention.

https://www.academia.edu/42758497/WILLIAM_HUFFS_PARQUET_DEFORMATIONS_A_VIENNESE_EXPERIMENT

Kaplan, Craig S. ‘Animated Isohedral Tilings’. In Bridges 2019 Conference Proceedings, pp. 99-106.

A brief discussion. There are other implied parquet deformations in the context of the animations.

Escher was a master of this form; as I have explained elsewhere [3], he used a number of visual “metamorphosis” devices to draw tilings that change spatially. Inspired by Escher, the architect and designer William Huff developed “parquet deformations” [2], which were designed to be more abstract and geometric exercises. I have explored several techniques for drawing parquet deformations [3, 5], some of which are relevant here. Temporal animations of tilings are arguably easier to construct than spatial animations, because in the latter case the tiles are changing their shapes in the same dimension in which they are trying to interlock.

http://archive.bridgesmathart.org/2019/bridges2019-99.pdf

Leone, Francesca. Portfolio Progettazione Grafica. Self Published on Issuu July 14, 2019, 68 pp.

In Italian.

P. 14. Parquet deformation o trapposo di forme. Bill Huff… parquet deformation

Ostensibly on parquet deformation, but in reality not. Gives Escher’s Day and Night. https://issuu.com/frleone97/docs/portoflio

Reddy, Hasitha. Architecture, Interiors and Urban Design Portfolio. Self Published on Issuu February 21, 2019. 58 pp.

See pp. 50–51

Robots and Architecture, Deformation, Art with Kuka Robot

Weak premise.

N. B. I looked for ‘Hasitha Reddy, parquet deformations’ separately, but without success.

https://issuu.com/hasithareddy/docs/portfolio_hvalmeti

2020 (3)

Fathauer, Robert. Tessellations: Mathematics, Art, and Recreation. A K Peters/CRC Press, 2020

Chapter 19, Tessellation Metamorphoses and Dissections pp. 301–307. Parquet deformation amid a chapter on tiling metamorphosis in general, including Escher-like art. ‘Morphs’ is his preferred title. Regarding parquet deformation, includes a discussion on Metamorphosis II. Also shows an Islamic-type isometric instance of his own. Has a brief discussion of Huff’s work, p. 302:

… Linear geometric morphs were explored by Williams S. Huff in the 1960s. He called them “parquet deformations” and had his architecture students design them [Hofstadter1986]. Craig Kaplan has developed schemes to allow parquet deformations to be generated by computer [Kaplan 2010].

————. ‘William Huff’s Parquet Deformations: Two Viennese Experiments’. Bridges 2020 Conference Proceedings, pp. 383–386.

Abstract

This paper aims to bring a new nexus of activities around architect and educator William Huff’s work, presented here as an experimental design assignment in architectural education. After his retirement, professor Huff donated a collection of his students’ work to the HfG Archive in Ulm, Germany, which inspired us, at the Institute of Art and Design in Vienna to give a semester assignment focusing on parquet deformations (PD). The open search for strategies to transfer the idea of planar PDs into 3D led to fascinating results. We discovered a field of formal research that broadened the students’ horizons concerning 2 and 3-dimensional relationships enthusing them considerably by making them aware of the unlimited possibilities of spatial transformation. This is a brief report of a fruitful project in basic design education for architects and designers.

Includes a work by Tobias Dirsch, 2017 and an anonymous designer but no others. Mostly the concern is 3D. My website gets a mention.

https://archive.bridgesmathart.org/2020/bridges2020-383.pdf

Moradzadeh, Sam and Ahad Nejad Ebrahimi. ‘Islamic Geometric Patterns in Higher Dimensions’. Nexus Network Journal Vol. 22, 11 May 2020, pp. 777–798

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Springer snippet: William Huff, an American architecture professor, used the term “parquet deformation” in the 1960s and later Douglas Hofstadter developed this…

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