Singular function emerging from one-dimensional elementary cellular automaton Rule 150
Dynamical Systems
2020-10-06 v2 Cellular Automata and Lattice Gases
Abstract
In this paper, we give a singular function on a unit interval derived from the dynamic of the one-dimensional elementary cellular automaton Rule 150. We describe properties of the resulting function, that is strictly increasing, uniformly continuous, and differentiable almost everywhere, and we show that it is not differentiable at dyadic rational points. We also give functional equations that the function satisfies, and show that the function is the only solution of the functional ones.
Keywords
Cite
@article{arxiv.2008.13217,
title = {Singular function emerging from one-dimensional elementary cellular automaton Rule 150},
author = {Akane Kawaharada},
journal= {arXiv preprint arXiv:2008.13217},
year = {2020}
}