Wanderer (reflections)

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This Wanderer tiling is the first of an infinite series of substitution tilings by Joan Taylor based on paper-folding sequences. It uses a single square tile with four distinct rotations and two distinct reflections. Here we use colours to distinguish left-handed (brown) from right-handed (white) tiles. In the substitution rule the orientation of the tiles is indicated by a line in the interior of the tiles. In the large patch below these lines and all edges are omitted since the interesting feature are the patterns produced by white resp. brown squares.

A relative of this tiling is the Wanderer (rotations), where tiles are not coloured according to left- vs right-handedness, but according to horizontal vs vertical.

Substitution Rule

Rule Wanderer (reflections)


Patch Wanderer (reflections)