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Deltoid tangents with evenly distributed orientations and random tilings. (English) Zbl 1523.52030

Author’s 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. Special types of random tilings for Euclidean, spherical and hyperbolic three-manifolds are also considered.

MSC:

52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)
52C23 Quasicrystals and aperiodic tilings in discrete geometry
52C30 Planar arrangements of lines and pseudolines (aspects of discrete geometry)
60D05 Geometric probability and stochastic geometry
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