Penrose Triangle 1


The Robinson Triangle substitution is just one out of several possibilities to play with the triangle versions of the Penrose tilings. Another one is the Tübingen Triangle substitution. Here is an example where the obtuse triangle is the smaller prototile, and the acute triangle is the larger one. Reflecting the entire supertile, or reflecting single tiles in the supertile, leads to many distinct substitution rules. Some of them generate the same tilings, many of them differ. The different tilings may or may not be mdl (mutually locally derivable). The Robinson Triangle tilings are indeed the ones among all these possibilities that are mld to the original Penrose Rhomb tilings.

Substitution Rule

Rule Penrose Triangle 1


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