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arXiv · 2108.07712

Persistent order in Schramm-Loewner Evolution driven by the primes last digit sequence

Theophanes Raptis·Alberto Fraile
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Abstract

We report on a peculiar effect regarding the use of the prime's last digit sequence which is equivalent to a quaternary symbolic sequence. This was used as a driving sequence for the recently introduced Schramm-Loewner Evolution after using two different classes of possible binary encodings. We report on a clear deviation from the standard space-filling curves normally expected from such a process. We also contrast this behavior with others produced via a symbolic dynamics applied on standard noise sources as well as deterministic sequences produced by simple automata. Our findings include the well known, Morse-Thue sequence as the simplest model exhibiting such behavior apart from some strongly biased Levy walks.

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Theophanes Raptis, Alberto Fraile. 2021-08-06. Persistent order in Schramm-Loewner Evolution driven by the primes last digit sequence. https://arxiv.org/abs/2108.07712

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