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arXiv · 1709.09325

Self-Similar Tilings of Fractal Blow-Ups

Michael F Barnsley·Andrew Vince
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Abstract

New tilings of certain subsets of $\mathbb{R}^{M}$ are studied, tilings associated with fractal blow-ups of certain similitude iterated function systems (IFS). For each such IFS with attractor satisfying the open set condition, our construction produces a usually infinite family of tilings that satisfy the following properties: (1) the prototile set is finite; (2) the tilings are repetitive (quasiperiodic); (3) each family contains self-similartilings, usually infinitely many; and (4) when the IFS is rigid in an appropriate sense, the tiling has no non-trivial symmetry; in particular the tiling is non-periodic.

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Michael F Barnsley, Andrew Vince. 2017-09-27. Self-Similar Tilings of Fractal Blow-Ups. https://arxiv.org/abs/1709.09325

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