Introduction
The age-old question as to how best design a life-like tessellation often crops up, of which a variety of ways are given. These range from a ‘inverse’ tiling process (page 136), as in Kaplan’s Escherization, in which one begins with a predetermined motif in mind, and then ‘distorts’ this to a tessellating tile, to a ‘forward’ tiling process in which one uses one’s imagination to see a motif in a random tessellating shape, and then develop the tessellation from there to a recognizable motif. Another method, of my own devising, is of a stick figure method. Yet another design process, somewhat less generally used, is that of taking a motif bearing a resemblance in outline to a tessellating polygon, and 'adapting' it from there, of which this essay thus discusses. Here I examine the merits or otherwise of this procedure.

Seth Bareiss
One prominent exponent of this method is Seth Bareiss, who has written about this, of which I now examine his arguments to see if these are valid:

First among the shortcuts is, how to start. I familiarize myself with a few basic shapes that I know will tessellate: bricks, triangles, hexagons like chickenwire. Second, I look around for objects that roughly fit one of those shapes. For example, a sitting cat is roughly triangular, so stacking cats makes a good tessellation. Can you also see that a Buddha sitting Indian-style are roughly triangular?....

As can be seen, a tessellation of both a cat and Buddha are shown, and so at face value this method would appear to be valid. However, I believe that this method is decidedly restrictive, and is not conducive to good tessellation art. Firstly, one is restricted to very few suitable polygons (e.g. triangles of different types: equilateral, isosceles, scalene; quadrilaterals of different types, squares, rectangle, kites, and other polygons such as hexagons. Admittedly, the proportions of some of these can be varied, but in reality there is little variation, and so the number of suitable motifs that fit a given polygon must both be relatively few. Secondly, and of more importance, the process of forming the motif into a square, triangle or whatever is by its very nature is not conducive to a compelling silhouette. If it’s based upon a square, the silhouette will resemble a square. Likewise for others polygons, and so the silhouette is essentially atypical of the motif it is portraying. Certainly, it’s possible, but it’s lacking in intrinsic quality.

Underlying Polygon
More to the point, I believe that the type of underlying polygon as a premise is essentially inconsequential to a tessellating figure. For a specific example, see Birds* where these are all based upon a square, typically seen in an outstretched wing position, and yet no underlying square is ‘obvious’ from this. Furthermore, a variety of polygons can be used, all without their source being immediately obvious.

Summary
Therefore by the above explanations and arguments, I consider this method to be largely spurious. Certainly, one can be indeed use it to form tessellating motifs, but by its very nature it lacks a compelling silhouette and it is restricting, both of which are serious objections. Indeed, Bareiss gives just two examples. To solely use this would be to severely curtail the number of motifs possible by other means.

Agree/disagree? E-me.

Created: 9 August 2010