Self-similar Discrete Rotation Configurations and Interlaced Sturmian Words

Abstract

Rotation configurations for quadratic angles exhibit self-similar dynamics. Visually, it may be considered as quite evident. However, no additional details have yet been published on the exact nature of the arithmetical reasons that support this fact. In this paper, to support the existence of self-similar dynamic in 2d-configuration, we will use the constructive 1-d substitution theory in order to iteratively build quadratic rotation configurations from substitutive Sturmian words. More specifically : the self-similar rotation configurations are first shown to be an interlacing of configurations that are direct product of superposition of Sturmian words.

DOI: 10.1007/978-3-540-79126-3_23

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@inproceedings{Nouvel2008SelfsimilarDR, title={Self-similar Discrete Rotation Configurations and Interlaced Sturmian Words}, author={Bertrand Nouvel}, booktitle={DGCI}, year={2008} }