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.
An alternative proof for an aperiodic monotile
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abstract
We give an alternative simple proof that the monotile introduced by Smith, Myers, Kaplan and Goodman-Strass is aperiodic.
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2024 1verdicts
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On the long-range order of the Spectre tilings
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.