Deltoid tangents with evenly distributed orientations and random tilings
Juan Garc\'ia Escudero
TL;DR
This paper explores the creation of plane tilings using deltoid tangents with evenly spread orientations, employing substitution rules and edge flips to generate random tiling ensembles.
Contribution
It introduces a novel method for constructing substitution tilings based on deltoid tangent configurations with evenly distributed orientations.
Findings
Development of substitution tilings from deltoid tangent simplicial configurations
Introduction of random tiling ensembles via edge flip rearrangements
New insights into the structure and diversity of plane tilings
Abstract
We study the construction of substitution tilings of the plane based on certain simplicial configurations of tangents of the deltoid with evenly distributed orientations. The random tiling ensembles are obtained as a result of tile rearrangements in the substitution rules associated to edge flips.
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Taxonomy
TopicsQuasicrystal Structures and Properties · Morphological variations and asymmetry · Cellular Automata and Applications