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Orbit separation dimension as complexity measure for primitive inflation tilings

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arxiv 2311.03541 v2 pith:WD33JGLM submitted 2023-11-06 math.DS

Michael Baake (Bielefeld) , Franz Gähler (Bielefeld) , Philipp Gohlke (Lund) This is my paper · ORCID
classification math.DS
keywords complexitysystemsdimensiondynamicalinflationmeasureorbitprimitive
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Orbit separation dimension (OSD), previously introduced as amorphic complexity, is a powerful complexity measure for topological dynamical systems with pure-point spectrum. Here, we develop methods and tools for it that allow a systematic application to translation dynamical systems of tiling spaces that are generated by primitive inflation rules. These systems share many nice properties that permit the explicit computation of the OSD, thus providing a rich class of examples with non-trivial OSD.

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  1. On the long-range order of the Spectre tilings

    math.DS 2024-11 conditional novelty 7.0 of 10

    The Spectre tiling and all Spectre-like tilings have pure point diffraction and are MLD to reprojections of a cut-and-project model set, with the smallest possible first Čech cohomology.

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