Parcelles d'infini

Parcelles d'infini by Alain Nicolas, Belin, 2006, 183 pages

Alain Nicolas’s book (in French) is of a wide-ranging, multifaceted approach to (mostly) life-like tessellation. Throughout the book, there is a tutorial intent here, although this is not to say that this is the premise throughout. Various distinct aspects of tessellation are discussed, as listed below, and are discussed in detail further below.

Tessellations, all chapters

35 Isohedral types, Chapter 4, page 41

 ‘Picture stories’, Chapter 6, using the tessellations in the same manner as Escher did with his, 93–112.

‘Tessellating words’, an innovation of Nicolas’s devising, Chapter 7, pages 113–148.

Self-similar tilings, Chapter 9, page 167

 Overview
A pleasing aspect to the book is that, in contrast to most other tessellators, he gives explanations with both instructions and diagrams as to how some (but not all) of the tessellations were created. These include (numbers in brackets are numbers of examples): Pages 75 (3), 78 (4), 83 (1), 86 (4), 88 (4), giving a total of 16 explanations. Such a relatively high number thus permits a fair appraisal of his methods. Of note is that he invariably begins with a geometric tiling (i.e. of straight lines), of a polygonal base, and then, upon recognising a potential life-like creature, he refines this to a more ‘realistic’ motif, very much in the same way as Escher or myself. A frequent feature of these is that the initial tile is, surprisingly, reminiscent of nothing in particular. For example, the ‘seed’ tile for both of the Cowboy and Horse examples (Bucking Bronco) (pages 80–81) just appears to be arbitrary geometric shapes, with nothing a priori that could be said to be cowboy and horse-like. Only in hindsight, having seen the finished tessellation, can the resemblance to a particular motif can be seen. The same finding can be said for much like of the others. As such, the ability to extricate high-quality, recognisable motifs from what appears to be most unpromising beginnings reflects greatly on the artist. Most tessellators would simply dismiss these initial examples out of hand as unworthy of proceeding with (i.e. unsuitable for motifs).

 35 Isohedral Types
Of note is the concern with the 35 isohedral types, for which Nicolas provides all these with a bird-like tessellation (albeit varying in quality, likely to be expected, given the restrictions involved) in principle, as this is shown, regrettably, as just a single tile. Better would be to show these as complete tessellations, but perhaps, given the particular presentation, space for this was not available. Such a preoccupation is most gratifying, as this aspect of challenge is one that most tessellation artists ignore. Indeed, Andrew Crompton is the only other artist to have studied these, and this in a partial way. In contrast, Nicolas examines all possibilities.

 Picture Stories
Of note is a chapter on what I term ‘picture stories’, in which the tessellations are used much in the same manner as Escher did with his own. Of note here is that these are unifying, in that the motifs have a connection, either directly or as opposites. Also, the motifs are all of a ‘sensible’ orientation. A frequent occurrence with lesser artists is compositions of incongruent motifs, without any connection, rendering the composition as absurd, with unwise choices of symmetry, in which the motifs are upside down to each other.

Of particular note, and worthy of praise, is ‘Plane and Boat’, page 106. Aside from the inherent good quality of the motifs is the ‘type’ of tessellation here, in that he uses inanimate motifs, something that is rarely seen in other people's work, due to the difficulties involved, and so this is of more than interest than otherwise.

Tessellating Words
Another aspect of interest is words as tessellations. I am less qualified to judge on these, as I have not done anything in this field. However, it certainly looks very clever indeed, with much imagination and originality.

Self-Similar Tessellations
Examples of self-similarity are shown, largely of lower tariff motifs, of which for such types is largely a necessity.

 Multimorphic Tessellations
An interesting aspect to his oeuvre is tessellations, where, in simple terms, the motif is capable of being stacked in different ways. For this, Nicolas uses dog-like tiles, both which are somewhat contrived. However, of note is the construction underlying this, which appears to be new, at least as applied to tessellation.

Although the book is of considerable merit, I do have concerns as to secondary matters, such as the presentation. For example, the plane tilings are more or less scattered throughout the book, impinging on different subjects/chapters. Better would simply to have had a single chapter here. However, any perceived shortcomings in presentation are simply overridden by the sheer quality of the tessellations and their offshoots, the 35 isohedral tessellations, picture stories, word play and self-similar tilings.

In short, the book is a must for anyone who is interested in Escher-like tessellation, being either content with just looking at high-quality tessellations, and/or the creation process of life-like tessellations per se. It really is a delight and joy to behold, of quality and innovation throughout.

Critiques of the Individual Tessellations:
Due to there being so many tessellations, I don’t have the time to give an exhaustive appraisal as I would otherwise like; therefore, at present, the critiques below are an initial thought, pending subsequent addition. That said, the comments here should suffice to give a general indication of the merits of Nicolas’s tessellations. To quickly enable an overview, these are described initially with one-word descriptions, from six categories: Unacceptable, Poor, Reasonable, Good, Excellent, and Superlative, which speak for themselves. Occasionally, some are borderline between two categories; these I signify with a hyphen, such as ‘Good-Excellent’. These are then generally followed by explanatory discussions and comments. To clarify the titles, I have put a description in English of the respective tessellation.

 1. Reynards à la lune (Fox and Moon), page 15
Good. Has many fox-like elements.

2. Sorcier Condissant, page 16 and page 162
Good.

3. Karaté, page 17
Good-Excellent. The motif adopts a typical Karate pose, on bended knee, in typical Karate dress, with an arm raised as if ready for combat.

4. Fraternité (Man Running with Outstretched Arms), page 18
Excellent. Observe all the main elements of a human figure are clearly defined, head, body, arms and legs; Also, the figure has hands and feet, and in particular note the articulation of the hand, with thumbs. A delight.

5. Lucky Blanchepatte, mon Chien (Dog), page 19
Reasonable. Cartoon-like.

6. Birds, page 22 top
Good.

7. Birds, page 22 below
Reasonable.

8. Birds page, 23
Reasonable.

9. Birds page, 23
Reasonable.

10. Birds, page 24
Reasonable.

11. Colombes (Doves), page 27
Good.

12. Demi-tour de carte (Playing Card), page 28
Excellent. Of note here is the rarity of such a type of motif; a playing card detail (of the Queen of Diamonds) that no other artist has accomplished such a feat, and so this innovation is in itself worthy of the highest praise, never mind given the quality.

13. Octopus, page 29
Good. Again, another rare motif. Although a little stylised, the inherent quality should be obvious; in silhouette, all eight legs are clearly defined (contrast with Natalie Birett’s ‘octopus’, entirely of inferior surface decoration).

14. Birds, page 31
Reasonable.

15. L’athlete, page 32
Good-Excellent. Again, as with other human instances, the entire human-like elements of this runner are readily recognised in silhouette. A slight concern is the rear leg, which is slightly awkward, hence not quite assessed as excellent.

16. La Sirène (Mermaid) page 32
Good.

17. Le Lézard (Lizard), page 32
Good.

18. Le Chaton (Cat), pages 32 and 35
Reasonable.

19. L’oterie (Seal), page 33
Good.

20. Le Coq (Cockerel), page 33
Unassessed. As such, it is difficult to make out.

21. Le Chien (Dog), page 33
Reasonable. Although all dog-like elements are shown, there are perspective conflicts here

22. Le Gorille (Gorilla), page 33
Good-Excellent.

23. Le Papillon (Butterfly), page 34
Good. Observe how these butterflies have antennae as distinct entities, and how  the wings correctly taper (contrast with Escher's inferior butterfly)

24. Le Canard (Ducks), pages 34 and 37
Good.

25. Le Rainette (Frog 1), page 34
Good-Excellent. Observe the excellent articulation – all frog-like elements are clearly defined.

26. Le Puxxle du fou (Man with odd hat), page 39
Good. Although the articulation here is good, the anatomy and proportion of the figure are questionable. Also, the figure sports an odd hat. But even so, this still retains much merit.

27. Not titled. Boy in Vest, page 40
Good. Again, although the articulation here is good, the anatomy and proportion of the lower half figure are questionable. But even so, this still retains much merit.

28. D’Escher (Escher Portrait), page 40
Excellent. Although of a lower tariff motif, this still receives an excellent rating, in that it is portraying a specific instance of a head (rather than an easier generic instance), namely as a homage to Escher. As can be seen, the verisimilitude is superb.

29. Runner, page 74
Good-Excellent.

30. Salutations Respectueuses (Marcher), page 76
Good. An unusual pose, of a soldier marching and saluting, and such innovative poses are welcomed.

31. Montagne (Goat), page 77
Excellent. Innovative in different ways, being seen from above, of a three-quarter view. The quality is outstanding; observe all the goat-like elements

32. Indienes (Indians on Horseback, page 79
Good. It’s a little hard to assess this, given that the tariff is high. The horse is a little contrived, but that aside, the difficulties of such a higher degree of difficulty surely deserve praise, and so relative shortcomings can be overlooked.

33. Cow-boy (Bucking Bronco 1), page 80
Superlative. Perhaps better described as a rider and bucking bronco. This oozes with class, quality, and innovation. The confluence is superb, with a rodeo theme, of a cowboy and a ‘bucking bronco’, both motifs adopting typical poses, the rider with his arm raised, holding his hat, whilst the horse adopts the typical bucking pose, with an arched back and kicking action, all in proportion. The articulation of both motifs is superb, and in particular, the quality of the horse (given its challenging pose) deserves special praise, a difficult motif to undertake. As alluded to above, another pleasing factor to this is the innovation; no other artist has accomplished this particular pose, so again, high praise is warranted.
A highlight amongst many highlights here, and arguably the best of Nicholas’s work. Interestingly, upon correspondence with Nicolas, he told me that he regards this as his best work.

34. Rodéo, (Bucking Bronco 2), page 81
Superlative. Another instance of the theme of ‘Rider and Bucking Bronco’. Again, this has all the merits of ‘Cow-boy’ as described above, although here with a subtlety, or innovation all of its own. Note the innovation here, where the cowboy has ‘lost’ his hat (a typical situation in real life), serving to define the space between the horses’ neck and legs for the sake of better articulation. Great imagination; this is most innovative and impressive.

35. Emulation (Man with Guitar), page 82
Good-Excellent. I have a few concerns over the legs and general proportions, but that aside, the kernel of a high-quality motif remains.

36. Bears, page 83
Good. Cartoon-like, but still of high quality

37. Plongeon en eau trouble (Girl Diver), page 84
Superlative. A diving girl. The verisimilitude and articulation here are superb and are worthy of the highest praise. In this instance of the human motif, no concession is made to clothes (which can hide a multitude of tessellation sins), and so this instance is thus of a higher degree of tariff than with a clothed human (although clothed humans should not necessarily be decried, they have intrinsic challenges of their own). A delight.

38. Échec (Chess Knight), page 85
Good-Excellent. Of its type, quite superb in its quality, and innovative too. The verisimilitude is quite superb and is worthy of the highest praise. As alluded to above, praise is also due to its innovative motif, of which few tessellation artists have attempted.

39. Fish, page 86
Good. A typical quality fish, but of a lower tariff type.

40. Monkey, page 86
Good-Excellent.

41. Judo Player, page 87
Excellent. Superb articulations.

42. Lizard, page 88
Good. A typical lizard.

43. Frog 2, page 88
Excellent. All articulations are shown.

44. Gentil/Merchant (Two Heads), page 89
Curious. This appears to be based on the premise of optical illusions, but with a tessellation twist. As far as I am aware, a new concept in tessellation. Again, another instance of innovation from Nicholas.

45. Mimétisme (Fish), page 90
Good.

46. Puppet, page 92
Good. Innovative; I know of no other such instance of this motif.

47. Fish and Lizard, page 95
Reasonable-Good. A lower tariff of difficulty concerning the fish. Pleasing views of the respective motifs, both being consistent.

48. Rabbit and Leaves, page 96
Good. Cartoon-like rabbit

49. Regard d’Infant (Bird and Squirrel). page 108)
A nice, but not obvious, confluence; both motifs are found in trees.

50. Lizard, page 109
Good.

51. Léxards au Carré (Lizard), page 110
Reasonable-Good. However, although all the elements are recognisable, a little contrived, with anatomical distortions.

52. Rosace aux Léxards (Lizard), page 111
Good. The lizards here are in proportion.

53. Léxards (Lizards), page 112
Good. Four slightly different lizards, all in proportion.

54. Cascade (Flatfish), page 151
Reasonable, albeit of a lower tariff.

55. Bees, page 151
Excellent. Observe the articulation, with antennae and legs being clearly defined. Not only that, as I have discussed elsewhere, the inclusion of such fine detail, of essentially hair-like aspects, is of the utmost difficulty, and hence the success, as here, is a praiseworthy achievement.

56. Plouf (Frog), page 151
Excellent. Again, all elements are articulated. Of course, of necessity, the frog has been slightly stylised as regards the ends of its legs, but this is a necessity, as such exact detail in this instance is impossible.

57. Not titled (Lizards), page 163
Good.

58. Not titled (Dog), pages 168, 169
Reasonable. As such, this instance doesn’t really find favour, being a little too stylised for my liking. However,  a likely reason for this (rare instance) of lower quality motif is that Nicolas is attempting different ways of stacking the tile, and so, due to such circumstances, one must expect a decline in quality (as has occurred with a similar instance of my own). Also see 63, of the same premise

59. Flatfish, page 170
Reasonable. However, as a category, this type of motif doesn’t find favour; the motif is of a decidedly lower tariff, being so simple to accomplish, and lacks any challenge or artistic integrity.

60. Butterflies, page 173
Reasonable-Good. The butterflies are a little contrived here, with left and right wings of different sizes, for what is presumably an intended equal wing composition, and an awkward, overly large body.

61. Dog, page 178
Reasonable. As such, this instance doesn’t really find favour, being a little too stylised for my liking, but nonetheless retains much merit, in that the motif is largely articulated. However, a likely reason for this (rare instance) of lower quality motif is that Nicolas is attempting different ways of stacking the tile, and so, due to such circumstances, one must expect a decline in quality (as has occurred with a similar instance of my own). Also see 58, of the same premise.

Summary

His tessellations are mostly of a high quality, some excellent, and occasionally with some of a superlative nature. Particular highlights are the Cowboy and Horse (Bucking Bronco) and Girl Diver. Many others are worthy of considerable praise. For example, the human figures as a series in general. However, some are of questionable worth. In particular, I don’t find, for the greater part, favour with the ‘flatfish’ type, pages 68–69, 83, 95, 151, 170, these being somewhat reminiscent of Escher in style, further compounded in that as a category such examples are essentially to be ignored, on account of their atypical fish-like appearance, as well as their generally formless nature. I have concerns about the various dogs, which seem a little contrived, pages 33, 168–169 and 178–179, albeit here a concession seems to have been made to n-morphic tessellations of pages 168–169, 178–179. The lizards, pages 95, 109–112, 163, are somewhat alike in style to Escher’s, although I have less concerns here than with the flatfish type, as originality is indeed shown. Aside from the relative shortcomings above, though, I can find very little to fault here. Indeed, one could be accused of cavilling with the above comments – most other artists would be more than pleased with some of the examples here.

Agree/disagree? Email me.

13 June 2025. Improved text from Classic Sites.