Makoto Nakamura

The Tessellations of Makoto Nakamura

http://makoto-nakamura.sakura.ne.jp/home.index.html


Makoto Nakamura’s tessellations 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) The inherent quality of the motif (silhouette and articulation)
(2) Showing the whole motif (excluding ‘heads’)
(3) Excludes ‘breathing room’ tessellations
(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) Coloured or shaded tessellations (excluding wireframes)
(8) Contrasting colouring of tessellations
(9) Finished rendering
(10) Borderline

Pleasingly, Nakamura’s tessellations posses all ten desired attributes. It can be done; there is (tessellation) life after Escher…!

In more detail:

(1)  Recognisable in Silhouette
The aspect of recognisably of the motif, as seen in silhouette is fundamental to the premise of a quality tessellation. Although not all of Nakamura’s tessellations are immediately recognisable in silhouette, for the most part these are indeed readily discernable. The articulation is quite superb, not just of individual motifs but in number as well. Indeed, on only two occasions can lower quality surface embellishment be seen.
    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 a exterior outline that is articulated.

(2) Shows The Complete Motif
Nakamura’s tessellations in all instances are of a ‘complete’ motif (like Escher, Bailey, and Bilney). 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) Excludes ‘Breathing Room’ Tessellations
Nakamura’s tessellations are in all instances of the ‘true’ type as defined by mathematicians, i.e.  a tiling without spaces or gaps.
    Lesser artists frequently include ‘breathing room’ types (on account of their less challenging aspect), and unfortunately delude themselves as to equating these with the more challenging ‘true’ type.

(4) The Number of Tessellations
Nakamura shows no less than 268 examples, of which he is without peer in this aspect. Of note is that his output by far outweighs any other individual artist (indeed, it almost doubles). Note that Escher has only 137 numbered drawings. Given such a large number, one might expect that these would not all of the same highest quality. However, although the quality is occasionally questionable, by far 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 outweighs quality.

(5) Variety of Motifs
A pleasing aspect to these is the sheer variety of motif, which is again amongst the highest of other tessellation artist (albeit here he has more peers); with no less than 39 different motifs (Bilney has 39, Escher has 32). Frequently, these are of creatures not usually shown, including many of worth that even Escher did not attempt, such as Cats, Bison, Chameleons, Chickens, Deer, Dolphins, Dragons, Elephants, Foxes, Gazelles, Lions, Lobsters, Martens, Monkeys, Penguins, Rabbits, Rats, Sharks, Sheep, and Wild Boars.
    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
Prominent amongst Nakamura’s tessellations are human figures, and indeed, these are the most numerous of all, despite the inherent difficulty of producing examples of true worth. Indeed, he shows no less than 70, although not all are of a single motif (some are in combination with other motifs), which when compared to Escher's paltry 4 is worthy of the utmost praise.
    As such, the impression given by this is that human figures are ‘easy’, indeed, the easiest of all, on account of their 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.
    However, although he has a pleasing number of motifs, not all of these are of the same high quality, indeed, he includes many examples that are of debatable worth, with many possessing anatomical inconsistencies, such as unnatural ‘bendy’ arms, arms without hands. Are such examples worthy of inclusion? This is a moot point. Certainly, Bilney would not entertain any examples of this sort. However, whether these are of worth is to a degree a matter for the artist’s conscience. Permitting a degree of artistic licence, I don’t mind examples of this kind too much. However, distinctions should be made that these are of a lower degree of difficulty than a truly anatomically correct figure.
    Lesser artists frequently shy away from such examples (on account of their challenging aspect), preferring the simpler to achieve birds and fish.

(7) Coloured or Shaded Tessellations
All of Nakamura’s tessellations are shown coloured (like Bailey, Bilney, Crompton, Escher, and Nicolas). No inferior wireframe examples are shown.
    Lesser artists frequently show wireframe examples, for no good reason (from which one can only conclude is that they do not understand the issues).

(8) Contrasting Colouring of Tessellations
Although overwhelmingly his tessellations show contrast, on a few occasions there is the odd exception to this feature. Normally, this would be considered a failing, but Nakamura shows enough desired colourings that he plainly understands the issues. Why, therefore, does he use this type of colouring? Frequently, it will be seen that where this feature occurs, it is relatively minor, in which the contiguous region is in comparison to the motif relatively small. Likely, he has decided to use this for the sake of a better presentation. For example, rather than using three colours, he uses two, to echo the orientations.

(9) Finished Rendering
Nakamura’s style, as regards finish, varies considerably, from no detail whatsoever to relatively detailed (albeit none of these is rendered to a photorealistic degree) and all types in between. However, that said, he tends towards the simplistic, and indeed the minimalist, albeit there is no clear direction as to what his preferred choice is, if any. For example, many of his possess an eye only, sometimes in addition with some other minor interior detail. There is an occasional more detailed example, but these are relatively few and far between. Presumably, such a ‘Spartan’ approach is purposeful. Speculating, perhaps the reason for this is that the motif generally stands out by the silhouette alone, and so does not require additional interior detail to identify the motif. Generally, he uses single ‘strong’ colours without any three-dimensional shading.
    As a rule, generally a simplistic finish is to be preferred, as too much detail hinders a clear interpretation of the motif.

(10) Borderline
Nakamura generally disregards a decided borderline, but does, on occasions, use this feature. In his work, Nakamura generally uses a colouring scheme that is self-defining, with ‘strong’ colours that do not require a borderline. Other, fewer tessellations have what I term as an ‘incidental’ borderline, of which although this is discernable, is negligible, on account of its essentially hair-like nature that is not an intrinsic feature of the tessellation. Only occasionally is a decided borderline used.
    Occasionally, some of his tessellations suffer as a result of not having a decided borderline, as the motif is not readily identifiable. Particularly, this includes some of the human figures, such as Wind 1 and Children 3, 5 which would especially benefit from this. Other motifs include Dogs 3.
    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.

General Comments:

Positives
Nakamura, in contrast to most other tessellators, has so many tessellations of good quality that one scarcely knows where to begin. The all-important aspect of recognisable in silhouette extends to mostly his entire work. Indeed, very few fail this test. Not only are these recognisable is silhouette, but their articulation is invariably very good indeed. In particular, his human figurers are quite superb. 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. Contrast this with other people’s human figures which lack this, which are generally wholly surface embellishment. Many of his tessellations are of a themed nature, in that the motifs have a natural confluence to each other, either directly, as in bird-fish, or as opposites, rabbit-eagle (hunter/prey). Likely, he must be striving for such confluences. In contrast, other tessellators have enough trouble coming up with any two motifs, never mind with confluences. A feature throughout is a natural confluence of the individual motifs, with the motifs possessing all the elements (animal motifs, e.g. a dog, with head, stop, ears, body, legs, and tail) or accoutrements (e.g. human-like, such as with Santas, with hats, sacks, sleigh, and reindeer) of the motifs they are representing. Again, such attention to what might at first thought be petty detail simply adds to the inherent quality of the tessellation. Say if a dogs’ ear can be articulated, then make it so, rather than just surface embellishment, as favoured by lesser artists. 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 features.
    To ease the discussion below, I discuss as according to his grouping on the website, although the grouping is not always ideal, in that some groups would be better amalgamated, such as Horses and Pegasus, and some example would have their own separate section for certain groupings, for example ‘Fish and Seahorses’, which is filed under fish. However, rather than being selective here, I simply discuss as according to Nakamura’s grouping.
    Rather than an individual comment each time, I broadly assess the tessellation as according to a series of simple descriptions, with their merit increasing:

1. Very pleasing. A tessellation that is very pleasing, in that although it may have the occasional shortcoming, in that certain aspects may be a little contrived, it still retains much of merit
2. Especially pleasing. A tessellation that is especially pleasing, of undoubted quality, with only the most minor of shortcomings, of considerable merit
3. Superlative. A tessellation that is superlative, with no shortcomings whatsoever.
    The superlative listing includes what I term as aesthetic and non-aesthetic examples. Note that this is not a commentary on the motifs themselves, as it indeed appears to be at first sight, but is instead refers to the motifs orientation, as regards a sensible as against a disjoint appearance. Simply stated, aesthetic is with the motif all upright, and so sensible, and non-aesthetic is where the motifs are in an upright and upside down orientation, and so disjoint, as this is a unnatural view. Essentially, aesthetic examples have added value by default.
    Most artists struggle to compose any of a superlative nature. In contrast, Nakamura has abundance. Indeed, I could have added a few more to this category with justification, but decided against, so spoilt was I for choice.

FISH

Fish 1-19 1-19
Many pleasing examples of fish can be seen, albeit as a category of motif this hardly poses a challenge at times. Naturally, with a fish motif being relatively easy to accomplish, there are many examples of this motif.
    One aspect of note is the complete absence of any of the flatfish type (as particularly favoured by Escher who inexplicably included many examples of this type). A weakness in Nakamura’s oeuvre? No. This is omission is most gratifying, as the flatfish as a type is essentially worthless, being an ambiguous shape, and lacks any challenge whatsoever. By its omission, Nakamura thus shows understanding of the issues, and simply does not demean himself with any examples of this lower type.
    Note that the fish motifs are also combined with birds, but these are filed in a category of Birds and Fish.
    Fish 1, 3, 5 are arguably the best.
    Fish 13, although somewhat of a misnomer, as it is in conjunction with a Seahorse, is particularly pleasing per se, with veracity of outline, and furthermore the motifs have an obvious confluence.

Lobsters 20 20
This is a most trying motif to achieve of its type, as it possesses spindly legs, and so such features, of broadly a very thin line cause considerable difficulty for the tessellator. Indeed, most artists either ignore motifs of this type, or take the easier option of ‘breathing space’, in which the restrictions of the premise of tessellation are relaxed, as favoured to a large extent by John Osborn and to a lesser degree Bruce Bilney. In contrast, Nakamura rose to the challenge and shows a superior ‘complete’ tessellation.
    Although only a single lobster example is shown, this is of note for its sheer quality, albeit with a curious protuberance from the head. Note how each of the pairs of legs are articulated, rather than of surface embellishment, as so often happens with lesser artists.

Frogs 1-4 21-24
The frogs are shown in a variety of poses, from ‘standing’, sideways, and leaping.
    Particularly pleasing is 2, whilst 4 is portrayed in a typical leaping position.

BIRDS
Birds 1- 33 25-57
Many pleasing examples of birds can be seen, albeit as a category of motif this hardly poses a challenge at times. Naturally, with a bird motif being relatively easy to accomplish, there are many examples of this motif.
    Many of Nakamura’s birds are not just good as a generic bird (as most people settle for), but are of specific types, i.e. an obviously harder degree of difficulty to accomplish. Most other tessellators have enough trouble with composing generic birds, without reference to different types.
    Many of the birds can be seen with serrated wing feathers. All this is to simply improve the articulation of the motif, and noticeably in all instances where feasible (where the wings are in contact) Nakamura invariably does so. Again, yet another instance of understanding the issues.
    In addition to just the single bird motif, this is combined with others as well, of both a connected and unconnected nature, with fish, flowers, leaves, stars, and children, of which I discuss these as under their respective groupings.
    Particularly pleasing are Toucan, 7 31, Swan, 8 32, Eagle 9 33, Flamingo 16, 40, are all being of a specific type, rather than just generic bird.
    As alluded to above, most pleasing are Birds 1, 2, 3, 4, 7, 8, 22, 27, and 29, as these .all display serrated wings, thus showing the understanding of these issues.

Chickens 1- 2 58-59
Both of the chicken motifs are very good, with notable articulation, such as combs and feet.

Penguins 1 60
Very pleasing, with good articulation. Note that another penguin is in Birds 26.

Bats (and Stars) 1 61

Birds and Flowers 1-7 62-68
Many pleasing examples of this natural confluence are shown, and furthermore Nakamura shows not just the one, but a whole series of this theme. Particularly pleasing is Birds-Flowers 1, where Nakamura show a specific bird, namely a hummingbird, this being associated directly with flowers.

Birds-Leaves 1 69

Birds-Stars 1-2 70-71
No obvious confluence.

Birds-Fish 1-6 72-77
Many pleasing examples of this natural connection are shown, where he shows not one the one example, but a whole series based on this theme.
    Pleasing are Birds-Fish 2 and 4.

Birds-Children 1-2 78-79
Although there is no natural confluence between these two motifs, the quality is most pleasing per se, although against that is the scale of the two motifs, which are nonsensical. Be that as it may, although ideally the scale would be commensurate, this objection is cavilling, and any other tessellators would be more than pleased to have composed these.
    Although classified as Children, there is nothing particularly suggestive of a child in No. 2. Better would have been to place this with ‘Mankind’.

ANIMALS

Horses 1-4 80-83
Very pleasing is Nakamura’s horses, of which although a most trying motif to accomplish to a satisfactory degree, primarily due to long, spindly legs, he more or less succeeds here. Of note is that all the horses adopt an ‘action’ pose, rather than standing. This is to overcome the difficulties posed by spindly legs per se. Although these are somewhat stylised at times, these are not so much so distorted as to be considered as unacceptable.
    Particularly pleasing is the articulation of the mane and legs, on all four examples (Horses 1-4). 
    1 and 2 are the best, with 3 and 4 a little contrived
In addition to just the single horse motif, this is combined with others as well, of unconnected nature, with birds, of which I discuss as under their respective groupings. Incidentally, these are also of the same ‘action’ pose.

Horse-Birds 1-3 84-86
Although there is no natural confluence between these two motifs, the quality is most pleasing. That said, 2 is a little contrived. Particular highlights are Horse-Birds 1 and 3, with 3 being regarded as a superlative. Both motifs are in proportion. The articulation of the horse is quite superb, with all the elements, readily discernable, namely the head, neck, body, legs and tail.

Pegasus 1-2 87-88

Cats 1-19 89-107
Although his cat motifs are particularly weak, two of pleasing note is Cats 19, albeit in a frontal position rather than the more typical (and ideal) sideways view, and Cats 12 is also quite pleasing.
    In addition to just the single cat motif, this is combined with others as well, of both a connected and unconnected nature, with fish, birds, rats, of which I discuss as under there respective groupings.

Cats-Fish 1-5 108-112
Much, much better are his cats in combination with other motifs, rather than as single cats. Also, this particular combination of motifs makes a natural confluence.
    Pleasing are Cats-Fish 1-3, 5.

Cats-Bird 1-9 113-121
Again the cats in combination with other motifs are much better than his single cats.  Also, this particular combination of motifs makes a natural confluence.
    Pleasing is Cats-Birds 2-3, 6

Cats-Rats 1-10 122-131
Again the cats in combination with other motifs are much better than his single cats.  Also, this particular combination of motifs makes a natural confluence.
    Pleasing is Cats-Rats 3, 6

Rabbits 1-17 132-148
Very good for the most part are his rabbit motifs, with good articulation. Of note is that the rabbits adopt a series of different poses, such as standing, walking, or action. The most noticeable identifier of a rabbit, namely the long ears and bob tail is readily discerned.
    1, 6, 7, 13, 15 are pleasing, although some are a little contrived. Nonetheless, most are instantly recognisable as rabbits.
    3 is a superlative, where this adopts an action pose, in that it as portrayed leaping, with all its elements readily discernable, namely long ears, body, four legs, and bob tail. Furthermore, this is aesthetic, in that the motifs remain in a ‘sensible’ orientation, i.e. upright, rather than a ‘disjoint’ upright and upside down
    Again, these are combined with other motifs, such as eagles, of which I discuss in that particular grouping.

Rabbits-Eagles 1-2 149-150
Very good are the rabbit-eagle motifs, with a natural contrasting confluence (hunter/prey), with good articulation.
    1 is worthy of especial praise. The degree of articulation is quite outstanding. The elements of both motifs are readily discernable, with for the rabbit, namely long ears, body, four legs, and bob tail, whilst for the eagle, namely talons, hooked beak, ’oversize’ wings. A superlative.

Reindeer 1 151
Of praise especially is 1. The degree of articulation concerning the antlers is quite outstanding, albeit the legs are somewhat contrived. Nonetheless, the motif is still readily recognisable in silhouette.

Deer 1 152
Of praise especially is 1, in an action pose. The degree of articulation is quite outstanding. The elements of the motif are readily discernable, with antlers, head and neck, Legs leaping, as does a typical deer, body and  tail. A superlative.

Gazelles 1-2 153-154
Of praise especially is 2, in an action pose. The degree of articulation is quite outstanding. The elements of the motif are readily discernable, with antlers, head and neck, Legs leaping, as does a typical gazelle, body and tail. A superlative.

Dogs 1-8 155-162
Many pleasing dogs, and not just of a single pose, but of different ones, with various actions, running, with legs outstretched, and standing.
    In addition to just the single dog motif, this is combined with others as well, of both a connected and unconnected nature, with rabbits and birds, of which I discuss as under there respective groupings.
    Particularly good are 2 and 4.
    Of praise especially is 1 and 7. The articulation is superb. The elements of the motif are readily discernable, with head, ears, stop, neck, body, legs and tail leaping/running, as does a typical dog. Also, the orientation is aesthetic in both instances. Both superlatives.

Dogs-Rabbits 1-2 163-164
Of praise especially is 1. The degree of articulation is quite outstanding. The elements of the respective motifs are readily discernable. For the dog, with head, ears, stop, neck, body, legs and tail leaping/running, as does a typical dog. For the Rabbit, head, long ears, bob tail, portrayed leaping, as does a typical rabbit. Also, the orientation is aesthetic in both instances. A superlative.

Dogs-Birds 1-2 165-166
Of praise especially is 1. The degree of articulation is quite outstanding.

Squirrels 1-4 167-170

Rats 1-4 171-174
Rats are shown in different poses, of pleasing quality. These could also be classified as mice.
Of praise especially is 1 and 4. The degree of articulation is very good, with head, ears, body, legs and long tail.

Fox 1-3 175-177
Of praise especially is 3. The degree of articulation is very good, with the motifs identifier, a bushy tail, prominent.

Foxes-Rats 1 178

Martens 1 179

Sheep 1-2 180-181
Of praise especially is 1. The degree of articulation is very good, with its identifying feature, a horn, clearly shown.

Monkeys 1-6 182-187
Of a pleasing nature, especially 1-5.
    1 is pleasing. The degree of articulation is very good, with head, legs, arms, body, and long curly tail.
    6 is clever, in that it uses a double purpose. One interpretation is of a monkey carrying a ball, or balancing it on his knee. The latter interpretation is preferred, as then the arm is better articulated.

Wild Boar 1-3 188-190
2-3 are quite pleasing.

Lions 1 191
1 is worthy of especial praise. The degree of articulation is quite outstanding, with the general build of a lion, and head, ears, body, tail. A superlative.

Dolphins 1-2 192-193

Elephants 1-3 194-196
1 and 2 are somewhat stylised, but still relatively pleasing.
  3 is worthy of utmost praise. The articulation is superb, with all the elements readily discerned, such as trunk, large ears, large body, and sturdy legs. On the borderline of superlative.

Bison 1 197
1 is worthy of praise especially. The degree of articulation is very good, with typical bison horns and build. Very pleasing.

DINOSAUR

Dinosaurs 1-7 198-204
Very pleasing as a category, with many fine examples.
2 is worthy of praise where a most pleasing nuance is shown, with spurs on the legs.
4 is pleasing, notably of the ‘unusual’ pose, in that the motif is turning away from the viewer.
5 is pleasing, with fine detail (articulation) in the form of teeth.

Chameleons 1 205
Very pleasing.
1 is most pleasing, with much fine detail. Observe the subtlety of front foot, which closely resembles a chameleon’s real life type. Also fine detail of the back.

Dragon 1 206

Lizards 1-3 207-209
A somewhat ambiguous category, with a wide discrepancy of quality,
    No. 3 is quite pleasing.

INSECT

Insects 1-9 210-218
Insects in particular cause untoward difficulties to the tessellator, with many hair-like line features that are for the most part most trying to accommodate in a tessellation. Nonetheless, Nakamura rises to the challenge and shows some pleasing examples, and does not resort to the ‘breathing room’ type as espoused by Osborn.
1 is pleasing, although of a generic nature
2 is very pleasing, in that here we have a specific type of insect, namely a Praying Mantis with all the elements associated with this insect
3 is very pleasing, a spider
4 is pleasing, a beetle

MANKIND

Human-like
Of particular note, and worthy of the utmost praise, not just of quality but number as well, are his human-like tessellations, these being broadly categorised as ‘Mankind’. Again, as well as single motifs, these are in conjunction with other animals. These adopt a series of poses, such as running, dancing, hunting, swimming, and soccer playing, to name but a few. Again, such specificality is worthy of praise, rather than of ‘just’ a generic human.

Marathon (Running Figure) 1-3  219-221
There are very good indeed, and are articulated in all three instances, with very little degree of contriveness. In particular note No. 1 and 3, which has feet and hands.

Runner1  222
This is very good indeed, and are articulated.

Coexists 1 (Warrior with club and Shield)  223
Very pleasing, fully articulated, and with all the accruements of a warier, namely a club and shield.

Soccer (Soccer player with ball) 1-4 224-227
Very pleasing, in that the motif is portrayed as a sportsman, with accoutrements i.e. a soccer ball. Perhaps some people may gripe with the generally larger size of ball, at least of 1-3, than is normally to be seen with a soccer player, but I think this is acceptable, in that the premise is one of association, rather than a true representation per se. In any case, No. 4 is indeed broadly proportional. Although No.2 is a decidedly contrived, this is still nonetheless of a more than acceptable tessellation.
    Also see Ballplay and Volleyball for a like theme.

Ballplay 1 228
Very pleasing, fully articulated again, the same idea as with the soccer player is evident.

Volleyball 1 229
Very pleasing, fully articulated again, the same idea as with the soccer player is evident.

Dance 1-8 230-237
A popular pose of Nakamura’s is of dancing, with no less than eight examples. All are very pleasing, fully articulated.
Of particular note are 6 and 8.
1 and 5 are superlative.

Mikoshi 1 238

Very pleasing, fully articulated

Hunting 1-5 239-243
By Nakamura’s own high standards, these are a little contrived, but even so, the quality here is unmistakeable. 1 is particularly good.

Ice Skate 1 244
Very pleasing, fully articulated. Note the innovative use made of a bobble hat, where the bobble serves as the inner arm. Also, to overcome the club-like nature of the feet, Nakamura has now given the figure ice skates, to better overcome this. Note how consistent the figure is, with all the accoutrements of an ice skater. Borderline superlative.

Skiing 1-2 245-246
Both are very pleasing, fully articulated. Note the innovative use is made of a bobble hat in 2. Also rather than a most ungainly shape at the bottom of the tile, Nakamura has given his figure a ski board. Lesser tessellators would simply show this as waste space. Note how consistent the figure is, with all the accoutrements of a skier.

Skate 1 (with Bird) 247
Very pleasing, fully articulated. In combination with a bird. Note the innovative usage made of the tie, which serves to define the inner legs.

Snowball fight 1 248
Very pleasing, fully articulated.

Rush Hour 1-2 249-250
Both are very pleasing, fully articulated. Note the innovative usage made of the of the figure, a city gent, with all the accoutrements with newspaper and briefcase, of the tie serves to define the lower leg and foot 1, and the inner legs 2.

Fisherman 1 251
Consistent themed motifs.

Shark and Woman 252
Exceptionally pleasing, both the woman and shark are fully articulated, and a natural confluence.  A superlative.

Swimming 1-4 253-256
The swimming series (of which I include ‘Shark and Woman’, and ‘Mermaids’) is particularly impressive. All are of a very pleasing, fully articulated nature.  A highlight amongst highlights, with the motifs adapting typical swimming poses.
    1 is quite superb, fully articulated. The motifs are in a aesthetically pleasing orientation. A superlative.
    3 is quite superb, fully articulated. A superlative. The swimmers appear in tow orientations, of which such an appearance is normally somewhat jarring. However, here, one could say that this objection can be overruled, in that the motifs appear to be doing the front crawl and backstroke, and so appear ‘normal’. Most inventive.
    4 is quite superb, fully articulated. The swimmer is accompanied by dolphin. Again, a natural confluence.  A superlative.

Mermaids (and Dolphin) 1 257
Very pleasing, fully articulated. Again, a natural confluence, of mermaids with dolphins .– observe the subtlety of the dolphin, with the typical bottle nose. Again, a natural confluence. A superlative.

Children 1-5 258-262
Perhaps by Nakamura’s own high standards, a little contrived at time especially Children 3, but most people would be pleased with these if they could do them. These are in some instances accompanied with other motifs.
    2 is very pleasing, fully articulated with a child, dog and oversize soccer ball, likely on the theme of play.
    4 a unicyclist, a most unusual combination, and so worthy for rarity.
    5 has a pleasing innovation, one again concerning the bobble hat, in that this also serves as the dogs’ collar. A very pleasing ‘recycling’. The only drawback here is the symmetry arrangement, which thus causes the motifs to be upside down to each other, and so is a little jarring. However, this is not a fault per se, as it is simply the mathematics which dictates such an outcome. Nonetheless, aesthetically better would have been with both motifs in the same orientation.

Girls-Rabbits 1 263
1 is not just very pleasing, but quite superb, with both motifs fully articulated, and furthermore in an aesthetically pleasing same orientation. Although there is no obvious confluence, and a slightly discordant scale, the sheer quality of the motifs in a sense overrides this cavil. A superlative.

Nurse (and child) 1 264
As such, a relative low point in his work, in that although of a pleasing confluence, the child is decidedly contrived, and is little more than surface embellishment.

Cultivation 1 265
Quite what the figure is holding is unclear, but even so one can see the idea of ‘cultivation’ taking place, even if the figure is decidedly out of proportion to the implement.
    A little contrived by Nakamura’s standards, but still better than with most other people.

War (and Peace?) 1 266
A very pleasing confluence, of war and peace, represented by a soldier and dove, with all the accoutrements of a war, namely holding an gun and olive branch respectively.

Wind 1-3 267-269
1 is very pleasing. Observe the subtly of the high heel of both of the shoes, which serves as the head and neck. The billowing skirt is a typical feature of a female human figure.
2 is pleasing, with the premise of a hat blowing away.
3 is pleasing, albeit weakened slightly by an oversize hat. Still, most of other people would regard this as a highlight in their work.

Santa 2-3 271-272
Santa 2 is especially pleasing, where this not just of a Santa on his own, but is in conjunction with all the accoutrements of a Santa, namely hat, sack, cloak, and boots, along with a sledge and a reindeer. Observe the articulation of the reindeer. The confluence is quite superb. A superlative.
Santa 3 is pleasing, with all the accoutrements of a Santa, namely hat, sack, cloak, and boots.

 
Thieves 273
Although not particularly suggestive of thieves, the figure per se is most pleasing.

Witches 274
Very pleasing, with superb confluences, with all the accoutrements of a witch, namely aside a flying broomstick and witches hat.

Devil 275

Angels 276

Pierots (with ball) 277

Men-Dogs 278
Quite pleasing

Listing Superlatives:
Rabbits 3 134 Aesthetic
Rabbits-Eagles 1 149 Aesthetic
Deer 1 152 Aesthetic
Gazelles 2 154 Aesthetic
Dogs 1 155 Aesthetic
Dog 7 161 Aesthetic
Dogs-Rabbits 1 163 Aesthetic
Lions 1 191 Aesthetic
Dance 1 230 Aesthetic
Dance 5 234 Aesthetic
Shark and Woman 252 Aesthetic
Swimming 1 253 Aesthetic
Swimming 3 255 Aesthetic
Swimming 4 256 Aesthetic
Mermaids 257 Aesthetic
Girls-Rabbits 1 263 Aesthetic
Santa 2 272 Non-Aesthetic

Negatives
However, although I am overwhelmingly positive on Nakamura’s 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 his cats, of which such examples are of a noticeable inferior quality to the rest of his oeuvre. Certainly, they have cat-like features, but generally have anatomical inconsistencies, with strictly different viewpoints. Such an example is Cats 1, 89 with multiple viewpoints, of (presumably not desired) a cubist-like painting appearance. Other examples of this type, detailed without discussion, include Cats 3, 4, 5, 7, 13, 15, and 16. Furthermore, many of these have their tail emanating awkwardly from the back, rather than the rear. Typically, these also have awkward, stilted poses. For unclear reasons, he seems to have had a desire to produce numerous cats without undue regard as to inherent quality. Additionally to this, he combined cats with other motifs, such as fish and rats, of which although these are of a better portrayal, some remain of a like contrived nature.
    Aside from the shortcomings of the cats though, I can find very little to fault here. Indeed, one could be accused of cavilling with the following – most other artists would be more than pleased with some of the examples below.
    One could argue that some human-like examples lack hands and feet, and so cannot be said to be life-like. However, I consider this point to be in the extreme. The composing of human figures, to a worthy degree, i.e. recognisable in silhouette and ideally fully articulated, is most difficult. Most tessellation artists show human figures with considerable distortions, such as legs of different thicknesses, and odd proportions such as longer arms than are appropriate for the rest of the body, and so are noticeable at a glance. In contrast, although Nakamura’s on occasions omits hands and feet, this is barely noticeable, in that they form a relatively minor part of the overall figure. Most tessellations are compromises, to greater or lesser degrees. Look at Escher’s birds – do these have, for the most part, legs? No. Look at Escher’s human figure, No 21, with most awkward, ‘clunky’ legs and feet. These are most unlife-like. But is this not acceptable? Therefore, the occasional omission of hands and feet and odd proportions in Nakamura’s work should not be thought of as a stick of which to be him with. Ideally, yes of course they would be included, but due to the nature of tessellation this is not always possible.
    Some examples I have reservations with as regards portrayal. Some are arguably too ambiguous, in that that creature stated could have a different interpretation. That said though, frequently these are still well articulated, and so remain life-like, albeit not particularly reminiscent of a specific motif. For example, Dogs 6 160, Sheep 2 181
    Some examples are arguably are a little too ‘cartoony’. For example, Fish 6 6 and 15 15, Birds 19 43, Cats 6 94, Monkeys 5 186
    Some examples are of minor, ‘cheap’ ‘in-filling’, such as Bats 1 61, Birds–Stars 1 70 Birds–Stars 2 71, Cats 2 90
    Some examples can be said to be ‘extreme’ in their features, such as fish with large, oversize fins. For example, Birds–Fish 5 76
    Some examples occasionally have perspective concerns. For example, Birds 1 25
    Some examples are portrayed with an anatomically incorrect tail, in that it emanates from the back for example. For example, Cats 3 91, Cats 5 93, Cats-Birds 7 119, Rabbits 9 140, Squirrels 2 168
    Some examples occasionally lack articulation. For example Elephants 1 194, Lizards 1 207
    Some examples are a little contrived. For example, Fish 2 2, Fish 4 4
    However, shortcomings per se are very much in the background, with his work, aside from the cats’ examples, typically being of outstanding quality, whatever the motif.

Summary
Nakamura is a superb tessellator, with his tessellations occasionally being of a superlative nature. Even when not, then these are still generally of a higher quality than with other people. As detailed above, he understands the various issues underpinning the composing of inherent quality of tessellations. Furthermore, he introduces some innovations of his own, or at least rarely shown, with the extended leg pose, as well as the motif placement on vertices. Is he better than Escher? Can I say it… dare I say it , but yes. The examinations below should show this:
More tessellations than Escher, of generally comparable quality, indeed if not better, 268 against 137
More variety of motifs than Escher, 39 against 32
More challenging motifs (i.e. human figures) than Escher, 70 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 from is worthy of the utmost praise. Indeed, without Escher, how many people, including Nakamura, 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 of a like mind have now followed him through, some, but not many, with innovations of their own to contribute. Escher did not do everything.

Last updated: 21 May 2010

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