Of interest are the various ways and means of designing life-like tessellations. As such, it is all too easy to become stuck in a rut with one’s own ideas, and seeing other people’s procedures may offer up new thoughts and ideas. I begin with a brief discussion as to the two main ways, albeit with leeway as to procedures within any one category, followed by an open question as to which is the best. This is then followed by some examples of the design process from other contemporary artists.

Mathematical Premise
Beginning with a recognisable tiling polygon, such as a square or triangle, one makes changes, or deforms, to the straight lines, as according to tiling rules. This is the method most commonly used. For example, if a square is deformed of its opposite sides, this is guaranteed to tessellate. This procedure was used extensively, and notably, by M. C. Escher, indeed to the exclusion of others. As such, this can be described as ‘hit and miss’, in that upon beginning one does not necessarily have a pre-determined motif in mind, and frequently the resulting deforms, despite additional adjustments, still remain recalcitrant in forming life-like tiling worthy of the name, hence the description above.

A Motif Already in Mind
Another approach to the above largely ‘hit and miss’ approach is to begin with a motif already in mind, with a picture taken from a book. This has the advantage that the initial motif is automatically lifelike and so can be of the highest quality, but this shape will invariably fail to tessellate. However, by making certain adaptations, one can ‘force’ this into a tiling. Andrew Crompton is an advocate of this method, with examples of this work below. A variation on this procedure is to take a motif, and in effect ‘plug’ it into a computer and let the computer find a tiling for this. Craig Kaplan has done the pioneering work on this with his ‘Escherization’ process, with much interesting results. However, still as yet, these do not match in quality to the best of today’s tessellators, of whichever method they use.

An open question is to which of the methods above can be described as the best. Certainly, the mathematical premise will always guarantee a tessellation, but typically, not always of a high standard in terms of life-likeness. Furthermore, and although not necessarily, it has a tendency to lead to bird and fish motifs, of which these can be described of a lower tariff, being easier to design. More challenging would be other motifs, such a human figures, or quadrupeds. The other method of the motif ‘already in mind’ has the advantage of a lifelike outline, but then the question (at least by hand) of how to adapt this as a tessellation arises, with the resultant compromises in outline; much additional work is typically needed. This though has the advantage in that more exotic motifs can be tried rather than the lower tariff bids and fish, as detailed above. Both methods have advantages and disadvantages that roughly equal out in terms of designing time require for a given tessellation. Below I show some advocates of the design procedures above:

Andrew Crompton (motif already in mind)

Sherlock Holmes

Created 14 February 2014