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arXiv · 1003.2898

Algorithm for determining pure pointedness of self-affine tilings

Shigeki Akiyama·Jeong-Yup Lee
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Abstract

Overlap coincidence in a self-affine tiling in $\R^d$ is equivalent to pure point dynamical spectrum of the tiling dynamical system. We interpret the overlap coincidence in the setting of substitution Delone set in $\R^d$ and find an efficient algorithm to check the pure point dynamical spectrum. This algorithm is easy to implement into a computer program. We give the program and apply it to several examples. In the course the proof of the algorithm, we show a variant of the conjecture of Urbański (Solomyak \cite{Solomyak:08}) on the Hausdorff dimension of the boundaries of fractal tiles.

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Shigeki Akiyama, Jeong-Yup Lee. 2010-03-15. Algorithm for determining pure pointedness of self-affine tilings. https://arxiv.org/abs/1003.2898

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