Discontinuous Riemann integrable functions emerging from cellular automata
Dynamical Systems
2021-03-04 v1
Abstract
This paper presents discontinuous Riemann integrable functions on the unit interval derived from the dynamics of two-dimensional elementary cellular automata. Based on the self-similarities of their orbits, we write down the numbers of nonzero states in the spatial and spatio-temporal patterns and obtain discontinuous Riemann integrable functions by normalizing the values. We calculate the integrals of the two obtained functions over and demonstrate the relationship between them.
Keywords
Cite
@article{arxiv.2103.02256,
title = {Discontinuous Riemann integrable functions emerging from cellular automata},
author = {Akane Kawaharada},
journal= {arXiv preprint arXiv:2103.02256},
year = {2021}
}
Comments
18 pages