2020/08/30 by Akane Kawaharada, Kawaharada, Akane · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Mathematical Dynamics and Fractals #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2008.13217
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.