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title
Geometry in color
description
hacking symmetries
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Geometry in color
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2026-02-15 19:01:40
raw text
Geometry in color | hacking symmetries Geometry in color hacking symmetries Skip to content Puzzles and Games Cellular automata Fractals Kaleidoscopes Quasiperiodic design Tilings programming ← Older posts Tilings of 5-Fold Rotational Symmetry: VI. Substitution at Diagonals Posted on January 27, 2023 by Peter Stampfli As we have seen previously, the substitution for a tiling puts a narrow child rhombus with its short diagonal at the border of the inflated parent rhombus. This cuts the rhombus into two triangles. One of them will be inside the parent rhombus. The other triangle belongs to a second parent rhombus that shares one of its sides with the first parent rhombus. Subsequent substitutions have to match across both parent rhombi. Thus the narrow rhombus must have a mirror symmetric substitution with its short diagonal as mirror axis. The same argument applies to the wide rhombus. It can have its long diagonal on the border of a parent tile. Thus ...
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