Andrew Crompton


The Tessellations of Andrew Crompton



Andrew Crompton’s tessellations are of a degree of magnitude above most other people in the field, although in terms of ability I put him below the leading light, Makoto Nakamura. Unfortunately, a drawback in assessing Crompton’s total oeuvre is that over the years some examples have been omitted from his website. However, these are included in the discussions below, and where this occurs I simply state ‘omitted’. Therefore, not all of the tessellations below are readily available to view.

On seven of the nine 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)

(2) Showing the whole motif (excluding ‘heads’)

(3) X The number of tessellations in the body of his work

(4) Variety of motifs

(5) X A tendency to the more difficult to achieve motifs

(6) Coloured or shaded tessellations (excluding wireframes)

(7) Map colouring of tessellations

(8) Degree of finished rendering

(9) Borderline


Pleasingly, Crompton’s tessellations possess seven of the nine 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 Crompton’s tessellations are immediately recognisable in silhouette, for the most part these are indeed readily discernible, of which by implication he must thus strive for such examples. Some notable examples include elephants, dolphins, and dogs, with many more of equal or near equal worth.

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 with a recognisable exterior outline.


(2) Shows the Complete Motif  

Crompton’s tessellations, bar one, are in all instances of a ‘complete’, whole body motif, (like Bailey, Bilney, Escher, and Nakamura). The ‘head’ only type per se is excluded, as this category is lacking in any challenge of worth, being all too easy. The exception here is ‘permissible’, in that he does not show just an arbitrary head (as with most other people), but of a specific instance of portraiture, namely that of ‘Sherlock Holmes’ (omitted), and so my objections to this type are waived in this instance.

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) The Number of Tessellations
Crompton shows 40 examples, of which although reasonably high is just below the arbitrary benchmark figure of 50 and above as regards the highest standards. Escher (137) and Nakamura (268) show considerably more. Given such a reasonably high number, one might expect that these would not all of the same highest quality. However, this is not so, and by far the overwhelming majority show true worth.

Typically, lesser artists will show a large number of inferior examples, and consider that such large numbers outweighs quality.


(4) Variety of Motifs

Crompton shows 25 different motifs, of which although relatively high is noticeably below Bilney (39), Escher (32) and Nakamura (39). Although the commonly to be found bird motifs occur (which accounts for approximately a third of his output), he does nonetheless show creatures and motifs not usually shown, such as badgers, countries, hedgehogs, seals, and shrimps, and so such variety is welcomed.

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.


(5) Challenging Motifs – Human Figures

The more challenging and interesting human figure is essentially ignored, with only one example, and furthermore this is only in conjunction with an elephant in a Penrose tiling (omitted). However, many other examples of a challenging motif can be seen, notably with badgers and elephants, and so he scores relatively heavily here, despite having only the one human figure. However, without more human-like figures, I fail his tessellations in this category.

Generally artists, for other reasons than the desire not to repeat themselves, shy away from such challenging motif examples (on account of their degree of difficulty).


(6) Coloured or Shaded tessellations

All of Crompton’s tessellations are shown coloured (like Bailey, Bilney, Escher, and Nakamura). 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).


(7) Map Colouring of Tessellations

All of Crompton’s tessellations are shown with map colouring, one of the few artists who do so (like Bailey).

Lesser artists frequently disregard this aspect, for no good reason (from which one can only conclude is that they do not understand the issues). Perhaps surprisingly, of note is that other leading tessellators, such as Nakamura and Bilney also disregard this aspect on more occasions than I would like.


(8) Finished Rendering

Crompton’s style, as regards finish, is of a consistent approach, with just the right amount of detail, with little if any variation of note. Generally, he uses single ‘strong’ colours without any pretence of three-dimensional shading. As a rule, generally a simplistic finish is to be preferred (as here), as too much detail i.e. a photorealistic rendering hinders a clear interpretation of the motif.

Lesser artists frequently disregard this aspect, with a rendering that is too real, that although well intentioned, is to the overall detriment of identifying the motif/s of the tessellation.


(9) Borderline

Crompton generally uses both a decided borderline, and where not he uses a self-defining colouration, 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.

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:

A pleasing feature of Crompton’s tessellations is a concern with more ‘involved’ tilings, devised by mathematicians, such as with isohedral types, the Penrose tilings, Voderberg spiral, Trimorphic tiles, and the 17 plane symmetry types. (The first, I believe, to present the latter as a concerted grouping.) As such, he obviously sets himself the challenging task to use these for arguably more ‘interesting’ tilings (as above), in addition to the more normal procedure of using underlying, squares, triangles, hexagon. By and large he succeeds in this task, as the quality of the tessellations of this more ‘involved’ kind is indistinguishable from his more ‘normal’ ones.

Aside from the animal-like tessellations are a handful of non-living motifs, such as numbers, countries, flying books. As such, a pleasing addition to the life-like motifs



One particular innovation of his (or at least rarely attempted), that I like is that of a series of countries, namely with the UK, France, Australia, and USA. These are quite pleasing (The UK one is very good indeed), albeit not particularly significant as a category. (Bilney also shows his own country, Australia). Pleasing for its sheer simplicity is that of rarely attempted motifs, such as Badgers and Hedgehogs. Other motifs worthy of praise include Swim and Kiss (Dolphins), Elephants, and Scotty Dogs.

In general, he is concerned with the quality issue, in that noticeably inferior examples are simply not shown. (Escher has many such inferior examples.) Indeed, it is hard to find any inferior ones; they are all of a good or exemplary standard.



However, although I am very positive on Crompton’s tessellations, this is not to say that a few don’t have some shortcomings, in that some examples I have reservations with. For example, Journey to the Outer Planets and Mystery of the Sphinx. However, this is a very rare occurrence, much less than with just about any other tessellator.

As detailed above, the near exclusion of human figures (omitted) is somewhat to the detriment of the oeuvre here, as ideally he would show many more. However, shortcomings per se are very much in the background, with his work typically being of good quality, whatever the motif.



Crompton is a very good tessellator. As detailed above, he understands the various issues underpinning the composing of inherent quality of tessellations. Furthermore, he mostly composes challenging motifs (albeit generally not of human figures), or at least rarely shown, with creatures such as elephants, hedgehogs, and lobsters.

Is he better than Escher? I’d put him below Escher, but not noticeably so. The examinations below should show this:

Roughly equal in the ‘silhouette test’ with Escher

Less number of tessellations than Escher, broadly of generally comparable quality, 40 against 137 (albeit Escher’s are padded somewhat by unacceptable examples, whilst Crompton’s are not)

Less variety of motifs than Escher, 25 against 32

Less challenging motifs (i.e. human figures) than Escher, 1 against 4

Although most of his tessellations pass the above criteria tests, these are of a markedly lower degree of quality as when compared to Nakamura. In particular, there is a decided absence of the more challenging human figures, with only one example (and furthermore that is in conjunction with another motif).

However, even while not of the highest standards, then these are still generally of a much 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, such as with the desire to compose life-like examples for the ‘mathematical tilings’ as detailed above, of which few, if any, artists have turned their attention to.

Last Updated: 16 April 2010