Forma, Vol. 13 (No. 3), pp. 179-197, 1998
Original Paper

A Mathematical Modeling of Pattern-Generation in Rock Textures and Its Application to Natural Rock Textures

Ritsuo Morishita

Graduate School of Science and Technology, Kumamoto University, Kurokami 2-39-1, Kumamoto 860-8555, Japan

(Received November 15, 1997; Accepted July 24, 1998)

Keywords: Cellular Automata, Phase Transition, Digital Image Processing, Symplectite

Abstract. This paper proposes a new mathematical model of pattern generation in the rock texture. This model has two parameters—a critical parameter and an interaction parameter. These parameters decide the cell activity which corresponds to chemical potential. The simulation repeats random exchange of cell pairs. First the model for two species system has two critical parameters is discussed. Various patterns appear as the values of the critical parameters change. All patterns can be categorized into regular patterns and two special patterns, i.e. nucleation & growth type and spinodal type. All regular patterns can be classified into four classes. Next the model for three species system with three critical parameters and three interaction parameters is discussed. Finally, the generated textures will be compared with a natural symplectite texture consisting of three minerals: spinel, orthopyroxene, and clinopyroxene. The model quantifies successfully the textural feature of the symplectite, by employing spatial correlation function and size distribution of minerals.