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

TL;DR

This paper investigates how the prime's last digit sequence influences Schramm-Loewner Evolution, revealing unique space-filling deviations and contrasting behaviors with other symbolic sequences and noise sources.

Contribution

It introduces the use of prime last digit sequences as driving signals in Schramm-Loewner Evolution and characterizes their distinct geometric properties.

Findings

Prime last digit sequence causes deviation from standard SLE curves.

Morse-Thue sequence exhibits similar behavior to prime last digit sequence.

Different symbolic sequences produce varied geometric patterns in SLE.

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.