Cellular Automata Automatically Constructed from a Bioconvection Pattern

Kawaharada, Akane; Shoji, Eita; Nishimori, Hiraku; Awazu, Akinori; Izumi, Shin-ichi; Iima, Makoto

doi:10.1007/978-4-431-55429-5_2

Cited by 4 publications

(2 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Burgers' equation is a nonlinear example that possesses both characteristics of advection and diffusion. The previous studies supposed the number of states is less than or equal to eight ( [4], [5], [2], [6], and [3]), and we have used k = 8 in this study, which is far from the limit k → ∞. Nevertheless, a stochastic CA obtained by the minimal method reproduces qualitative feature of the corresponding difference equation in each case.…”

Section: Burgers' Casmentioning

confidence: 99%

“…They attempted to find a CA model for some phenomenon whose governing equation is unclear. They applied it to a pattern formation of Euglena gracilis and reproduced some features of the original pattern [6]. Throughout this paper, we call their method the experimental method, as it is based on observation data collected by an experiment to generate the local rules.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of a method for constructing a cellular automaton from a continuous system

Kawaharada

Miyaji

Nakano

2016

IJNC

Self Cite

View full text Add to dashboard Cite

A method of constructing a cellular automaton (CA) from numerical solutions of a given partial differential equation (PDE) is considered. It consists of two parts, namely, collecting spatiotemporal data numerically and finding local rules of a CA that appear most frequently.In this paper, we analyze the method mathematically to examine its selectivity and its robustness of the derived local rules so that we can ensure validity of the resultant CA model. In particular, we investigated two limit cases: (a) the number of states of CA goes to infinity and (b) the number of spatiotemporal data goes to infinity. In the former case, we prove that the resultant CA converges to the difference equation where numerical solutions of a PDE are collected. In the latter case, through mathematical analysis, we derive conditions that the resultant CA is uniquely determined when the method of constructing a CA is applied to the diffusion equation. Our study can be a theoretical foundation of empirical CA modeling methods to create a reasonable CA which can somehow reproduce the original behavior of datasets under consideration.

show abstract