Forma, Vol. 13 (No. 2), pp. 81-97, 1998
Original Paper

A Local Painting Rule on Truncated Icosahedron to Generate a Soccer Ball Pattern

Takayuki Hirata

Faculty of Engineering, Department of Applied Physics, Fukui University, 3-9-1 Bunkyo, Fukui 910-8507, Japan

(Received November 1, 1994; Accepted June 14, 1995)

Keywords: Soccer Ball Pattern, Local Painting Rule, Information Gain, Closed Surface

Abstract. A local painting rule on the truncated icosahedron to generate a soccer ball pattern was examined by computer simulation: we will paint twelve faces of the truncated icosahedron and then rearrange the configuration of painted faces according to our local rule. A probabilistic cellular automata was used to model a local painting rule with repulsive interaction between painted faces. In order to measure the efficiency of our rule in achieving a soccer ball pattern, we use the information gain. The mean value of the number of iterations needed to achieve the goal pattern was 8,100.0 ± 8,075.7 (the standard deviation). Based on a simple assumption, we calculated the information gain I (P, ) due to our local painting rule: I (P, ) = 0.001645 bit.