| Title: |
Discontinuous Riemann integrable functions emerging from cellular automata |
| Authors: |
Kawaharada, Akane |
| Publication Year: |
2021 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Dynamical Systems, 26A30, 28A80, 37B15, 68Q80 |
| More Details: |
This paper presents discontinuous Riemann integrable functions on the unit interval $[0, 1]$ 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 $[0, 1]$ and demonstrate the relationship between them.
Comment: 18 pages |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2103.02256 |
| Accession Number: |
edsarx.2103.02256 |
| Database: |
arXiv |
