An Application of Data-based Construction Method of Cellular Automata to Physical Phenomena
Akane Kawaharada and Makoto Iima
We introduce a statistical construction method of cellular automata based on observation data and confirm that this method is useful even to noisy observation data. Because variables and states of cellular automata should be discrete, we discretize the data. Under the given number of neighbors and states of a site, we estimate the rules of cellular automata by the statistic analysis. In this paper, we apply this method to the diffusion equation and the Burgers equation. Both deterministic and stochastic cellular automata, which have three neighbors and 2–8 states, are obtained. We compare the obtained cellular automata with that of the original equations and the ultra-discrete equations. Further, we show the robustness under noise contamination of this constructing method qualitatively.
Keywords: Constructing method of cellular automata, noisy observation data, the diffusion equation, the Burgers equation