PENROSE.SUBSTITUTION

This sketch uses a tile substitution method for constructing highly ordered aperiodic tilings. Each construction is made entirely from just two basic shapes. The shapes are triangles. Commonly called the ‘half-kite’ and ‘half-dart’ , they are derived from the pentagon and described in depth by Roger Penrose.

There are two substitution rules for each triangle. The two rules impose cardinality for the composition.

Variations in color and generation limits result in a near infinite number of unique arrangements.

Fractal tiling is achieved by varying the generation limits of different locale.

Alternate methods of drawing the triangles produce interesting effects.