The Tessellations of Alain Nicolas

tessellations-nicolas.com

Alain Nicolas’ Escher-like tessellations can only be described as magnificent, the very epitome of the art. Although there can be said to be some good tessellators, and some excellent, they are still left trailing in his wake; Nicolas is one of the few people (Makoto Nakamura is another) who can be said to truly understand and have mastered the art, and his works transcend that of his contemporaries. His tessellations simply ooze class and quality. Not only does he outscore his contemporaries on intrinsic quality, and ‘best in class’ unique tessellations, but on the sheer variety and the high number of works (300), without any dilution in quality, is quite remarkable. His work is full of innovation, elegance and grace. And not only that, his work in ambigrams is of like outstanding nature, but this is outside of the discussion here.
How does he do it? I asked him, and upon beginning with traditional means, of pen and paper, he has in relatively recent years moved on to computer aid, notably with Kevin Lee’s ‘TesselManiac’, for the initial designing, before moving the artwork onto Illustrator for the finished work.

I now more formally examine his tessellations as according to a set of ten criteria. As alluded to above, these are of a degree of magnitude above other people in the field. On each of the ten determining aspects of ability and understanding of the issues he scores heavily, with criteria as listed in the introduction:

(1) ü Recognisable in silhouette
(2) ü Showing the whole motif (excluding easier to achieve ‘heads’, except for special occasions, of a recognisable figure)
(3) ü True Tessellations: Excludes ‘inferior’ ‘breathing room’ or overlap
(4) ü The number of tessellations in the body of his work
(5) ü Variety of motifs
(6) ü A tendency to the more difficult to achieve motifs
(7) ü Best in Class
(8) ü Contrasting colouring of tessellations
(9) ü Finished rendering
(10) ü Borderline

Pleasingly, Nicholas’ tessellations show all ten of the desired attributes. It can be done; there is (tessellation) life after Escher…!

In more detail:

(1) Recognisable in Silhouette
Just about all of Nicolas’ tessellations are immediately recognisable in silhouette, the benchmark for quality. The articulation is quite superb, with so many subtleties and nuances permeating throughout his work. Indeed, only rarely can lower quality surface embellishment be seen.
The aspect of recognisably of the motif in silhouette is fundamental to the premise of a quality tessellation.
Lesser artists struggle with this concept (inexplicably so, given its simple premise), and fail to recognise its importance and unfortunately delude themselves as to equating interior life-like interior detail surface detail with an exterior outline that is articulated.

(2) Shows the Complete Motif
Nicolas’ tessellations, with just two exceptions, are a ‘complete’ motif (as preferred by the leading lights in the field). As a premise, the ‘head’ only type is excluded, as this category is lacking in any challenge of worth, being all too easy. The exceptions here are shown with a specific aim in mind, namely of a recognisable portrait (of Escher), and an invertible head, and so examples of this type are indeed acceptable (in contrast to a generic head of no particular recognition).
Lesser artists frequently do not understand the difference between the two types and undertake such ‘head’ only examples (on account of their less challenging aspect), and unfortunately, delude themselves as to equating these with the more challenging whole body motif.

(3) True Tessellations: Excludes Inferior ‘Breathing Room’ or Overlap
Nicolas’ tessellations and are in nearly all instances of the ‘true’ type as defined by mathematicians, i.e. a tiling without spaces or overlaps and essentially exclude the ‘breathing room’ type. That said, he does on just two occasions employ what I term as ‘inconsequential’ breathing room, of a slight ‘rounding off’, which to all extents and purposes is of the ‘no breathing room’ type. Examples of this include birds, pages 22 and 23. As such, I have no qualms about this whatsoever, and so these are thus regarded as a bona fide tessellation.
Lesser artists frequently include ‘breathing room’ types, if not vast, wide swathes of open space (on account of their less challenging aspect), and or ‘overlaps’ and unfortunately delude themselves as to equating these with the more challenging ‘true’ double contour type.

(4) The Number of Tessellations
The sheer number of his tessellations is most impressive, now 350. Of note is that his output is the highest of any other artist. For comparison, Nakamura has 268, and Escher 137, albeit both of these are ‘padded’ somewhat, with lesser works, in contrast to Nicolas, which are all of invariable high quality. Given such a relatively large number, one might expect that these would not all of the same highest quality. However, although the quality is very occasionally questionable, in percentage terms the overwhelming majority show true worth, and so he is not simply producing average or poorer quality examples with the aim of just large numbers of tessellations primarily in mind.
Typically, lesser artists will show a large number of inferior examples, and consider that such large numbers outweigh quality. Unfortunately for them, this is not so!

(5) Variety of Motifs
A pleasing aspect to these is the sheer variety of motif, which he is again higher than of other tessellation artists, with no less than * different motifs (For comparison, has, Escher has *). Frequently, these are of creatures or motifs not usually shown, including many of worth that even Escher did not attempt, such as Bucking Broncos, Diver, Playing Cards, Octopuses, Gorillas, Goats, and Chess Knights.
Lesser artists frequently shy away from undertaking such variety, showing simpler to achieve birds and fish to the exclusion of variety, and unfortunately delude themselves as to equating these with the more praiseworthy variety of motifs.

(6) Challenging Motifs – Human Figures, Insects
Prominent amongst Nicolas’ tessellations are human figures (the merits of which I have previously discussed in my series of essays), despite the inherent difficulty of producing examples of true worth. Indeed, he shows no less than 54, and of which although this is a little lower than Nakamura’s 70, the latter is ‘padded’ by many inferior examples (such as unnatural ‘bendy’ arms, arms without hands). In contrast, Nicolas’s are far more worthy, with nearly of all inherent high quality throughout. When compared to Escher's paltry 4, this is worthy of the utmost praise. There are so many here of true worth. Highlights include: ‘Waiter ... Champagne, Please!’, ‘Mexico: The Vaquero’, ‘The musicians: Guitarist’, ‘Flamenco & Castanets’, ‘And Clap Your Hands’. (The last two are of the Cairo Tiling). I could add much more!
Also shown are insects, of which due to their many prominences and indentations are a most difficult motif to achieve, and so are generally neglected by artists. Although these as a category lack the obvious appeal of human figures, and so are thus generally neglected, those by Nicolas are most impressive.
As such, the impression given by this is that human figures in proportion with articulations are ‘easy’, because of their relative frequency here. However, this is to the contrary, as these are amongst the most difficult motifs to achieve. As such, he must be purposefully striving for such motifs, of which aside from the challenging aspect appeal on the human-interest level.
Lesser artists frequently shy away from such examples (on account of their challenging aspect), or when shown are best described as mutants, with disjoint, out of proportion elements, such over long arms or legs, or anatomical inconsistencies, preferring the simpler to achieve birds and fish.

(7) Best in Class
A highly desirable feature is what I term as ‘best in class’, in that for any particular category of tessellation, such as with human figures in specific poses, and dogs, cats, etc in typical poses, the artist produces the leading example. As can be seen, he is the leading practitioner with no less than * to his name. In contrast, the next person, * has *.
Lesser artists simply lack the ability to produce such instances.

(8) Contrasting Colouring of Tessellations
Nicolas’ tessellations as a premise are coloured in contrasting colours. Although overwhelmingly his tessellations show contrast, on a few occasions there is the odd exception to this feature. For example, Frogs, page 88, Heads, page 89, where rather than colouring in an artificial way, such as with red, blue, yellow etc, he chooses to have contiguous colouring. Likely, he has decided to use this for the sake of a more natural presentation, of which such instances are justified.
At first glance, the human figure diver tessellation, page 84, may appear to be of no contrast, but this has subtleties of flesh colour, of darker and lighter regions, where rather than colouring in an artificial way, such as with red, blue, yellow etc, he chooses to have contiguous flesh colouring. Likely, he has decided to use this for the sake of a more natural presentation, of which such instances are justified.
Lesser artists frequently show do not colour contrast their tessellations, and leave as wireframes, for no good reason (from which one can only conclude is that they do not understand the issues).

(9) Finished Rendering
Nicolas’ style, as regards finish, is of a consistent manner throughout, favouring a degree of detail level as espoused by Escher, although he uses a different medium to Escher’s use of watercolour. Rather than hand-drawn, these are all computer rendered, with Illustrator, to a very pleasing, high-quality standard. Again, he has also mastered the medium here, too. As such, he strikes the ideal balance between too simple (although this has its strengths) and too detailed. As a rule, generally, a simplistic finish is to be preferred (as here), as too much detail hinders a clear interpretation of the motif.
Lesser artists sometimes render the motifs in too much detail, as in a photograph, believing this to be superior to a more simplistic rendering. However, such instances make for a most trying viewing, with the viewer struggling to identify the individual motifs. Sometimes less is indeed more, as here.

(10) Borderline
Nicolas generally adds a decided borderline, but does, on occasions, have lines of unit thickness. Generally, strong colours are used that don’t strictly require a borderline. Even so, even in such instances, he nonetheless uses this feature.
However, the omission of a borderline cannot be said to be a fault as such, in that the inclusion or exclusion is down to personal choice, depending on the circumstances of the tessellation. Undoubtedly, this is secondary to the tessellation itself, and so of less importance to other, more fundamental issues, as detailed above.
Lesser artists invariably omit this feature, not understanding the reasons for its general desirability, namely that of aid in discerning the motifs.

General Comments:

Positives
Nicolas, in contrast to most other tessellators, has so many tessellations of good or excellent quality that is deserving of the utmost praise. The all-important aspect of being recognisable instantly in silhouette extends to mostly his entire work. Indeed, very few fail this test. Not only are these recognisable in silhouette, but their articulation is invariably very good indeed. In particular, his human figures are very good. Furthermore, his motifs do not have just the single, most typical viewpoint, but strike different poses (typically of an ‘action’ pose, such as leaping), all the while retaining their inherent quality. Note that many have true articulation, in that the head, body, arms (and ideally hands), and legs (and ideally feet) are readily discernable. And on occasion even further finer detail, with thumbs or with heels of shoes. Contrast this with other people’s human figures which lack this finery, and are either clunky or are generally wholly or mostly inferior surface embellishment.
Many of his two-motif tessellations are of a themed nature, in that the motifs have a natural confluence to each other, as in a bucking bronco with a cowboy, a magician and rabbit and so. Such types, due to the conditions imposed, are much more than a generic two-motif tessellation. Without a doubt, he must be striving for such confluences. In contrast, other tessellators have enough trouble coming up with any two motifs, never mind with confluences. Inferior artists often have to accept their motifs with disjoint features that bear no relation to the motif e.g. a dog carrying a box on its back, which obviously lacks any unifying feature. A feature throughout is a natural confluence of the individual motifs, with the motifs possessing all the elements or accoutrements (e.g. human-like, such as a singer with guitar, or a karate player adopting a karate-like pose in a karate suit. Again, such attention to what might at first thought be petty detail simply adds to the inherent quality of the tessellation. Say if a hand can be articulated, then make it so, rather than just surface embellishment, as favoured by lesser artists.

Yet another outstanding feature is that of choosing ‘special’ tiles, such as the Penrose tiles or Cairo tiling, to name but two, and using these as the underlying framework. Of course, due to the restrictions on choice, this is more difficult to achieve. Furthermore, as to be expected, these are of the higher standards, with the lines meeting the vertices. Although it is possible to relax the conditions and let the lines ‘wander’ from the vertices, I consider this sharp practice. Why do I critique instances of this type of presentation? It’s simply that so doing (using ‘wandering lines’) the artist has more chance of success of forming a motif with the additional leeway/latitude. In short, the inferior types is based ON the Cairo tiling but is not OF it. I am a stickler on this! In a like manner, I even take Roger Penrose to task on his Birds and Chickens! These use ‘wandering’ lines, and so depart from the vertices. Of the higher standards, see ‘And Clap Your Hands’ Cairo tiling and his Penrose tiling ‘Pentagonal Rose with Birds’ (Kites and Darts) of birds, both superb pieces of art, ‘And Clap Your Hands’ (detailed below), in particular; the nuances are a delight. It can be done!

Further to the special tiles, he also designs as according to symmetry concerns as well, with the 35 isohedral tilings. Most artists disregard a complete listing by symmetry concerns.

Negatives
I am struggling to find anything that can be called negative! I have to examine these in minute detail to say anything in a negative sense. However, although I am overwhelmingly positive on Nicolas’ tessellations, this is not to say that his don’t have some shortcomings. However, ‘shortcomings’ here are in relative terms, as many people would be more than happy to compose anything like his ‘inferior’ examples. 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. Even so, they are still ‘good’ art of their type. And that’s about it! Indeed, one could be accused of cavilling with the above comments.

Highlights
Where to begin, I am spoiled for choice! Although nearly all are of a like high standard, some are indeed worth singling out in particular for praise, of which I detail below:

‘And Clap Your Hands’ (of the Cairo tiling)
Superb! Aside from the clapping man being in general proportion, the articulations here are quite superb; not just of the figure overall, with head, body, arms and legs, all in proportion, but with the finer articulations, of the hand, with thumb and fingers differentiated as well as the heel of the shoe. Further, this is of the Cairo tiling, and so this, being a special tile, only adds even more value to the tessellation.

‘Mexico: The Vaquero’
The proportion of the horse and rider are quite superb. Contrast this with Escher's much-lauded Horseman (periodic drawing 45). His horse and rider is considerably out of proportion, and yet Escher is universally praised, whilst so far as I am aware of no recognition is given to Nicolas’ far superior instance. Also, see the tail; Nicolas’ is distinct, whilst Escher’s is merely surface decoration.

Waiter ... Champagne, Please!’ (Self Portrait)
A self-portrait of Nicolas seated, reading his book, requesting a glass of (well-deserved) champagne at an open-air restaurant. Praiseworthy as an unusual pose, and with all the usual high standards.

Dog (Oxo)
Superb! Aside from the dog being in general proportion, with all four legs distinct, a most difficult pose (many artists portray the legs merged, on account of difficulty), the number of articulations is quite staggering. Every part of the dog, where possible, is articulated.

Escher Comparison
Is Nicolas better than Escher? Can I say it, dare I say it … but YES! Not just subjectively, but the examinations below should show this:
Much better in the ‘silhouette test’ with Escher
More tessellations than with Escher, not just a few, but by a substantial degree of magnitude, more than doubling Escher’s output (Escher’s 137 being padded to some extent, whilst Nicolas’ 350 are not), of generally better quality
More variety of motifs with Escher, * against 32
More challenging motifs (i.e. human figures) than Escher, 54 against 4

Admittedly, Escher was, to all intents and purposes, the first tessellator (negating Koloman Moser’s examples), and so all the kudos of inventing/discovering a new type of art form is worthy of the utmost praise. Indeed, without Escher, how many people, including Nicolas, would have the wit and invention to do this? Probably none. Therefore, Escher stands alone here. However, that said, why should the person who makes the breakthrough in a certain field be regarded as having the field to himself, with other people’s contributions neglected or ignored? As Escher himself stated, he himself opened the garden gate of tessellation and wandered around. Other people, like Nicolas, of a like mind, have now followed him through the gate, and some, but not many, with ideas and innovations of their own to contribute, and indeed, in this case far exceed Escher. The facts and figures bear this out. Escher did not do everything.

Summary
Nicolas is quite simply the tessellator par excellence. Only Makoto Nakamura can even remotely approach him in standard. Who is the best is a moot point. However, I now consider Nicolas to be the No. 1. Quite simply, his work has everything, recognisable silhouettes, most ‘best in class’, articulations, superlatives, quality, variety, number, innovation, emphasis on human figures, special tiles, no padding, and all rendered to a most pleasing standard of finish. Bravo, Alain!

Created 26 June 2010. Last Updated: 11 October 2017. Notably expanded in places, and with wholesale new text, rewrites, substantial revisions, as well as minor corrections.