The Tessellations of Makiya Torigoe

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Makiya Torigoe’s Escher-like tessellations, in which he specifically focuses on a variety of dinosaurs and prehistoric fish, with other animals decidedly less so, can be described as very good indeed, if not superb, albeit typically, and unusually, without necessarily a convincing silhouette (which is generally the main attribute of a high-quality tessellation). Curiously, unlike most other artists, with a typically much broader range, he overwhelmingly restricts his tessellations to dinosaurs and prehistoric fish as part of his interest in them. (Alec Dixon is another, with a concerted dinosaur interest. Bruce Bilney of Australia is of another like type, although broader, who restricts his interest to indigenous Australian animals.) As a consequence, assessing his work, at least in terms of rating is not a straightforward task, as with the other artists here who include a much broader range of motifs. For instance, in variety, he would be marked down in comparison, as there are fewer other motifs, although he does indeed show variety, at least in relative terms. However, this downgrading could be argued as unfair, as other artists, with a broader range, are typically lacking in the inherent quality of Torigoe’s more focussed 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 nine, and arguably of all ten of the ten determining aspects of ability and understanding of the issues he scores heavily, with criteria as listed in the introduction:

(1) ✓x Recognisable in silhouette

(2) ✓ Showing the whole motif (excluding easier to achieve ‘heads’, except for special occasions, of a recognisable figure)

(3) ✓ True Tessellations: Excludes ‘inferior’ ‘breathing room’ or overlap

(4) ✓ The number of tessellations in the body of his work

(5) ✓ Variety of motifs

(6) ✓ A tendency to the more difficult to achieve motifs

(7) ✓ Best in Class

(8) ✓ Contrasting colouring of tessellations

(9) ✓ Finished rendering

(10) ✓ Borderline

It can be done; there is (tessellation) life after Escher…!

In more detail:

(1) Recognisable in Silhouette

In short, in particular of the dinosaurs, these are largely not recognisable in silhouette, but in this instance, this benchmark of quality has qualifications, in that the motif is clearly and unambiguously recognisable (a rare occurrence). However, assessing here is not straightforward - many dinosaurs shown here are known only to the expert, such as Troodon or Elmosaurus, and so to the typical viewer, without such an interest, the nuances are lost. Strictly, therefore, these are, or should be, marked down in silhouette, despite the motifs still being recognizable! On the face of it, these are thus at the same level with many inferior tessellators, but this is clearly not so! I shall fine-tune my criteria to allow for this, with simply recognisable, and accept these as equal merit with that of a convincing silhouette. In contrast, the animals mostly are recognisable in silhouette.

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

Torigoe’s tessellations, without exceptions, are a ‘complete’ motif (as preferred by the leading lights in the field). As an implied premise, the ‘head’ only type is excluded, as this category is lacking in any challenge of worth, being all too easy.

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: No Spaces, No Overlaps.

Torigoe’s tessellations are all instances of the ‘true’ type as defined by mathematicians, i.e. a tiling without spaces or overlaps and so exclude the leeway (inferior) ‘breathing room’ type.

Lesser artists frequently include ‘breathing room’ types, ranging from minor to 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

Torigoe has what can be described as a ‘reasonable’ number of tessellations, 55, but not all are published. Even so, he has more than most, albeit not of the vast output of others. For comparison, with his broad peer artists in quality, Sakuramederu has 1,200 (albeit some of these are ‘padded’ somewhat, with variations of the same tessellation, and some are simplified), Nicolas has 400, Nakamura has 268, and Escher 137. However, as I discuss elsewhere, quality, and not sheer number, is everything. Torigoe is a shining example.

Lesser artists typically 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

Although he undoubtedly focuses on dinosaurs and prehistoric fish, there is enough variety of his tessellations so that he reaches a more than an acceptable standard degree of variety. Indeed, there are no less than 14, all of the same high standard: Panda, Swallow, Killer Whale, Zebra, Skunk, Chameleon, Goldfish, Bat, Seahorse, Frog, Commerson’s Dolphin, Malayan Tapir, and Sun Bear.
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
This is difficult to assess! Are his (focused) dinosaurs and prehistoric fish as a motif to be regarded as challenging motifs such as human figures and insects? Yes and no. For certain, they are more difficult to achieve than birds and fish, although perhaps not quite as difficult as human figures and insects (although Sakuramederu has numerous instances of the latter and so in effect disproves this). As a category insects lack the obvious appeal of human figures, and so are thus generally neglected, but that is a different matter. All in all, I give a qualified yes to the dinosaurs and prehistoric fish as challenging motifs here. In any case, the other animals he shows can be considered challenging.

In general, dinosaurs as a motif are neglected (despite being a motif that is ‘popular’, especially with children), with few artists even attempting these. Curiously, Japan has displayed an interest more so than other countries, with two other artists of worth. Yasukiyo Yoshida (Sakuramederu) is especially prolific, albeit at the occasional expense of quality, whilst Makoto Nakumara also shows some good instances, but of a rather more stylized, non-specific nature. 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

Undoubtedly, ‘Best in Class’ is Torigoe’s strong point, with his focus on specific types of dinosaurs and prehistoric fish. Typically artists, when they deem to show dinosaurs and prehistoric fish (very few artists attempt these motifs) simply show generic instance if at all and in effect settle for that (and there’s nothing ‘wrong’ with that), but Torigoe (and his only serious rival Alec Dixon) goes beyond this, with specifics. These include well-known dinosaurs such as T. rex, Stegosaurus, Brontosaurus, and lesser ones too, such as with a Gorgosaurus and Rhamphorhynchus, and of the prehistoric fish, which are less well-known, such as Pikaika and Eusthenopteron. A highly desirable feature is that for this particular category of tessellation, in typical poses, the artist produces the leading examples. As can be seen, he is the leading practitioner by far, with no less than 32 instances to his name (Dixon has 16).

Lesser artists simply lack the ability to produce such instances.

(8) Contrasting Colouring of Tessellations

Torigoe’s tessellations are generally coloured in contrasting colours, albeit in muted, almost pastel-like colours. Ideally, I would like stronger, more saturated colours, but even so, the colouring is clearly contrasting. Unusually, his different categories are coloured in their own way:
Contrasting: Dinosaurs, Animal Mania 2, Yōkai, Prehistoric Fish, Others.
Non-Contrasting, i.e. all animals are coloured true-to-life: Animal Mania.
The explanation for the non-contrasting colours is that he desired the animal to retain its natural colouring, and so remain true-to-life. In such instances, contrast is thus impossible, and so I do not downgrade such examples here.

Lesser artists typically do not colour contrast their tessellations, and/or leave as wireframes, for no good reason (from which one can only conclude is that they do not understand the issues).

(9) Finished Rendering

Torigoe draws and colours his tessellations on the computer in the style, as regards finish, of a consistent manner throughout, favouring a degree of detail level as broadly espoused by Escher, of which I consider as the ideal. As a rule, generally, a ‘simplistic’ finish is to be preferred (as here), as against a photorealistic rendering, as too much detail hinders a clear interpretation of the motif.

Lesser artists, albeit with good intention, 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

Torigoe invariably adds a decided borderline, of which I favour. Unusually, his different categories have borderlines in their own way, as either black or white:
White: Dinosaurs, Animal Mania 2, Prehistoric Fish, Others.
Black: Yōkai.
Note that the inclusion or exclusion of a borderline cannot be said to be a fault as such, in that such matters is down to personal choice, depending on the circumstances of the tessellation. Sometimes the tessellations can be clearly defined by colour, and thus do not strictly require such a line. Undoubtedly, this aspect 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

Torigoe’s overall work as a general statement is of excellent quality that is deserving of the utmost praise, albeit qualified by the relatively few instances, at least in comparison to other leading lights. But even so, his output is still considerable, far more than most. Of course, the ideal is quality and numbers, of which it can be done; for instance, see Yasukiyo Yoshida (Sakuramederu), Makoto Nakamura and Alain Nicolas’ work. But that said quality (and not sheer numbers) is everything. A single high-quality instance is worth a thousand or more low quality. In particular, his instances of dinosaurs and prehistoric fish are quite outstanding, and of which he is the world leader. A pleasing feature here is the sheer variety of viewpoints; from above, front and back, in varying degrees, as well as different poses. No other artist shows such quality or variety in this field.

One curious aspect of his work though is that the silhouette is not always compelling. Typically, this results in an inferior motif. However, here, this is most emphatically not so! His work is outstanding. Therefore, the ‘silhouette test’, as I previously thought, with few exceptions, is not necessarily a precursor to quality, albeit it still acts as a general guideline.

Another pleasing feature is of what I term as ‘specifics’ (and furthermore not just on the odd occasion), in that not only is an animal clearly identifiable as a dinosaur, dolphin or whatever but has the additional aspect of a type or kind, such as above with an Allosaurus and Commerson’s Dolphin. Such additional matters add to the intrinsic value of the tessellation, of greater and greater degrees of refinement. In simple terms, stylisation is ‘acceptable’, recognisable is ‘good’, and specifics is ‘very good’.

Negatives

I am struggling to find anything that can be called negative here! The only drawbacks are the relative lack of variety of motif and number, although as he is purposefully focussing on dinosaurs and prehistoric fish this has to be qualified as to critique, in that he is not trying expressively for variety, although undoubtedly he could do so if he so decided to try. Even so, there are still more in number and variety than most.

Three Outstanding Tessellations

Of the work itself, I now select three outstanding tessellations to illustrate the points above, albeit a choice here is a somewhat invidious task, given the high quality overall; many others could equally have been used.

1. Gorgosaurus

Superb! This can be described as a typical dinosaur instance, of an aggressive action pose, of a three-quarter view seen from the front, albeit the specific dinosaur would likely be unfamiliar to most people. Although not effectively recognisable in silhouette, this is still unmistakably true-to-life.

Aside from the motif in general proportion, the articulations generally here are good, with a gaping mouth and distinct rear legs.