A Probabilistic Cellular Automaton Model for Developing Spatio-Temporal Patterns

Takayuki Hirata¹*, Antonio M. Posadas², Atsushi Ogawa¹ and Yoshifumi Harada¹

¹Department of Human and Artificial Intelligent Systems, Fukui University, 3-9-1 Bunkyo, Fukui 910-8507, Japan
²Department of Applied Physics, Almeria University, 04120-Almeria, Spain
*E-mail address: d970062@icpc00.icpc.fukui-u.ac.jp

(Received October 29, 2001; Accepted February 13, 2002)

Keywords: Probabilistic Cellular Automaton, Black and White Pattern, Kullback-Leibler Information, Genetic Algorithms

Abstract. A new approach of modeling for developing spatio-temporal patterns by using a probabilistic cellular automaton is proposed. The developing spatio-temporal patterns is too complicated to describe it by a small number of parameters. In our model, two states, i.e. black and white, are used to represent the state of cells. Therefore, the spatio-temporal pattern is treated as the developing black and white patterns. Our model has three model parameters that characterize the nearest neighbor interaction. These model parameters can detect the change of mechanism that generate patterns, which is one of the strong points of our model for monitoring the change of mechanism. Artificial black and white patterns are generated for a given parameters, and then the optimal parameters of the probabilistic cellular automaton model are sought. Optimization of the parameters is carried out by using two genetic algorithms: classical one and more sophisticated one. The convergence of the model parameters by two genetic algorithms is discussed. The fitness between the model and the observation is measured based on the Kullback-Leibler information.