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

Abstract

We report on a peculiar effect regrading 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 trying two different 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. We conjecture on an analytical condition for reproducing the particular effect based on Carleman linearization as well as on the possibility of certain continuous Langevin diffusion process that could reproduce similar behavior for appropriate noise source. We discuss the possibility oft further experiments with supercomputers further corroborating these results.