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Abstract: Limit periodic point sets are aperiodic structures with pure pointdiffraction supported on a countably, but not finitely generated Fourier modulethat is based on a lattice and certain integer multiples of it. Examples arecut and project sets with p-adic internal spaces. We illustrate this byexplicit results for the diffraction measures of two examples with 2-adicinternal spaces. The first and well-known example is the period doublingsequence in one dimension, which is based on the period doubling substitutionrule. The second example is a weighted planar point set that is derived fromthe classic chair tiling in the plane. It can be described as a fixed point ofa block substitution rule.



Author: Michael Baake, Uwe Grimm

Source: https://arxiv.org/



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