The Tessellations of Jinny Beyer

Designing Tessellations. The Secrets of Interlocking Patterns

(No website of tessellations)

Jinny Beyer’s tessellations are of the opposite end to the spectrum of the other people detailed here. These are, in the strictest sense, essentially worthless (as I will demonstrate below). As such, these seem to be very much secondary to her main interest, in quilting. Normally, I would not deign to discuss or include such examples, but in this instance I have decided to include these as a single example of decidedly inferior tessellations of the type to avoid doing, by means of contrast with the superior examples of the other people as detailed.
As such, the inclusion of Beyer’s work is open to merit here, in that her book is mostly concerned with the creation of tessellations per se, rather than life-like tessellations. Therefore, one could query the appropriateness of her work for this discussion. Indeed, the creating Escher-like chapter is only a relatively small part of the book, a single chapter out of eleven. I could easily as have chosen other people. For example, Patrick Murphy, in Modern Mathematics Made Simple; and Chris De Cordova, in the Tessellations File Escher-like efforts leaves me speechless! Other, like poor examples can be found on the web, with many children’s efforts, all of which I could have chosen to comment upon. However, what arouses my ire and separates Beyer and the above is that her tessellations are shown in a sumptuously produced book, with the impression that her tessellations are given from a position of authority on the subject. Further ‘credence’ to this is giving by the author stating ‘Thank you … to Doris Schattschneider for [her] advice’ (hopefully this was for the other, non-Escher chapters). Aside from this, external factors, such as the books’ review on Amazon, where it is given 5-star reviews, thus further contributes to this impression. Therefore, on the face of it, this is a book of undoubted substance and worth. This being so, one has a right to expect the contents to live up to its production and billing, which sadly is not the case. The tessellations are quite frankly execrable, and show a complete lack of understanding of the issues. This sorry state of affairs simply cannot be allowed to remain unchallenged. Therefore, I thus select this book (or more precisely, the relevant chapter, Chapter 10 ‘Creating Representational Tessellations’) as the one source to discuss of as inferior standards in tessellation.

Assessing at–a-Glance:
On only three of the nine determining aspects of ability and understanding of the issues does she score (and these are of the lesser important by far art aspects), with criteria as listed in the introduction:

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. Here Beyer shows little understanding of this issue, with many examples unrecognisable. I struggle to find a single example that I am entirely happy with. Of these, the only one of worth is Sport (a horse head), but this is of the lower category of difficulty of motif here, a head only. At a pinch, one could also include Tessellating Sue (a cat). Those aside, nothing else. This is simply not good enough, and so I fail her here.
Lesser artists, like Beyer, 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
Beyer’s tessellations are mostly of ‘complete’, whole body motifs, albeit some supposedly ‘whole’ motifs lack fundamental parts. These include birds without bodies, houses without floors, trees without trunks, and so one cannot truly say that this is a complete motif. A few incomplete head examples are also included, such as an eagle head, a horses head. Although the majority of hers are indeed of the whole body, in percentage terms the ratio to ‘whole body’ and ‘parts’ is too high, and so I thus fail her here.
Lesser artists, like Bayer, 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. Contrast this with Bailey, Bilney, Crompton, Escher, and Nakamura.

(3) The Number of Tessellations
Beyer shows 20 examples, which is far 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 low number, one might expect that these would be of quality, on the basis of quality, not quantity. However, this is not so, as these do not show true worth, as detailed above. Such paucity is unacceptable, and so I thus fail her here.
Typically, lesser artists, like Beyer, will show a large number of inferior examples, and consider that such large numbers outweighs quality. Beyer, thankfully, does not at least present even more…

(4) Variety of Motifs
Beyer shows just 10 different motifs, which is noticeably below Bilney (39), Escher (32), Nakamura (39) and Crompton (25). Very few of the motifs are of interest as regards inherent interest, such as the ‘rarity’ aspect, of creatures not commonly seen (which is Bilney’s speciality). Such few numbers in variety are unacceptable, and so I thus fail her here.
Lesser artists, like Beyer, frequently shy away from undertaking variety, showing simpler to achieve birds and fish (I exclude her from this) 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 ignored in its entirety. Aside from this, to perhaps try and ‘rectify’ this omission, with other examples of a challenging motif these are not shown (contrast this with Bilney). Therefore again, I fail her tessellations in this category.
Generally artists, as with Beyer, 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 Beyer’s tessellations are shown coloured (like Bailey, Bilney, Crompton, Escher, and Nakamura). No inferior wireframe examples are shown. Therefore, I pass her tessellations of this aspect. However, this should not be thought to be a case for undue celebration, as this point is not concerned with the all important design aspect, but rather of presentation, and is very simple to achieve, requiring no further skills beyond colouring in.
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
Most of Beyer’s tessellations are shown with map colouring, the exceptions being Birds (page 217) and Endangered Species. Therefore, I pass her tessellations of this aspect. However, again, as above, this is not a cause of undue celebration, in that one simply uses contrasting colours, requiring no further skills beyond colouring in.
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
Assessing the rendering is a little difficult, as it is not clear as to who exactly produced these. The book credits Kandy Petersen as the illustrator. Therefore, although it would appear strictly that Beyer did not do these per se, they were likely executed supplied from drawings under her watch. Therefore, below I refer to ‘her’ tessellations, in the sense of as by Beyer.
Beyer’s style, as regards finish, is of a consistent approach, with just the right amount of detail, with little if any variation of note. These are drawn and rendered by computer. Generally, she 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. Therefore, I pass her tessellations of this aspect.
Lesser artists frequently disregard this aspect, with a rendering that is too real, too photorealistic, in that although well intentioned, such rendering is to the overall detriment of identifying the motif/s of the tessellation.

(9) Borderline
Beyer shuns the use of a decided borderline, with the outlines of the same thickness as of the interior detail. Normally, I would prefer a decided borderline in such circumstances However, the use of self-defining colouration, with ‘strong’ colours, as here, does not necessarily require a borderline. Even so, in such instances, I consider a borderline ideal, but not a necessity. Therefore, I give her a weak failure of this aspect.
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:
Beyer’s tessellations have little or nothing to recommend them. Throughout, her tessellations have been examined and found to be wanting in the all important design aspects, criteria 1-5. Only in the lesser important art aspects, 6-8, is there a satisfactory outcome.

Positives:
Unfortunately, I cannot say a single positive word as to her tessellations. Even her best tessellation, Sport, is merely of a lower difficulty head type.