Beebug


Tesselator

Author: Colin Cohen
Publisher: Addison-Wesley
Machine: BBC/Electron

 
Published in Beebug Volume 4 Number 2

Tesselator (Addison-Wesley)

Escher, whose picture of two hands drawing themselves popularized the idea of artistic tesselation, wrote "...later the designing of new motifs came with rather less struggle than in the early days, and yet this has remained a very strenuous occupation, a real mania to which I became enslaved and from which I can only with great difficulty free myself".

Even if you have only a passing interest in graphics (and none in programming or even computers) this program is addictive. The program more or less does for the would-be tessellator what Wordwise does for the writer. Neither will improve your talents if you have none, and neither intrudes more than the absolute minimum between your ideas and their execution by the computer.

Tessellations work on the mathematical principle that a variety of shapes or tiles can be made to interlock, leaving no gaps for a background colour between them, and is widely used in the production of textiles and wall/floor coverings. The term is now accepted as covering any shapes that repeat in regular order without gaps, and fall into two classes. The first class is the regular tessellation of equilateral triangles or regular hexagons, while the second is the semi-regular combination of regular polygons - for instance a hexagon with a square on each face and the space between them infilled with an isosceles triangle.

Tesselator

Clearly, hexagonal floor tiles tesselate (the term comes from the Latin tessala, for a small decorative tile) - but fish, birds and other irregular shapes? The answer is yes: if you are Escher it can be done only with blood, sweat and tears, while if you use this program it becomes an enjoyable process.

A series of basic shapes can be loaded, from squares to interlocking darts and kites, the latter introducing the user to the concept of using a pair of interlocking shapes which can be manipulated separately or as a pair. The shapes you want are created by loading the main program and using the cursor and other keys to distort or rotate the tile.

Having done the distortions (to get the outline one wants) pressing 'T' will cause the design to tesselate to the size chosen in a scale from 6.2 to 4.0. Then you can return to your shape to decorate and paint it (in monochrome, two or four colours, with a consequent lowering of the screen resolution) and re-tesselate in another scale to your heart's content.

The 78 page manual is among the better I have seen, and the program is sufficiently robust in fact for one to start before a thorough reading. However, it is still possible to be inadvertently taken back into Basic with a loss of current data. Regrettably, not all the single key commands are the same in each part of the suite - for instance there is no facility to save the data in the Patchwork section. However, this section is not only not protected, but is listed in the manual so you can work out your own dump. Clearly one cannot expect that an irregular tessellation saved from one part of the program can be loaded back into the regular part, but there is an Epson printer dump for those who need hard copy. Naturally the program cries out for a colour monitor - and printer.

Colin Cohen

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