Symmetropy and Self-Organized Criticality

Kazuyoshi Nanjo¹, Hiroyuki Nagahama² and Eiji Yodogawa³

¹Earthquake Research Institute, University of Tokyo, Bunkyo-ku, Tokyo 113-0032, Japan
²Institute of Geology and Paleontology, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
³Department of Computer Science and Communication Engineering, Kogakuin University, Shinjuku-ku, Tokyo 163-8677, Japan

(Received September 17, 2001; Accepted October 12, 2001)

Keywords: Symmetropy, Self-Organized Criticality, Complex System, Symmetry Breaking

Abstract. Curie symmetry principle (CSP) states that the effects may occasionally have the same or a higher symmetry than the causes, and is often a powerful constraint for setting a bound on the symmetries of the causes or the effects. In this paper, the validity of CSP in a complex system is investigated. The concept of "symmetropy" that can measure the amount of symmetry and entropy of an object is introduced, and the symmetropies evaluating the causes and the effects in a cellular-automaton system with self-organized criticality are examined. During sub-critical states, the symmetropies satisfy CSP, but not always at the criticality (the edge of chaos). Our results show that symmetry breaking can occur without an anisotropy interaction between elements in a cellular-automaton model and without a special tuning parameter in bifurcation process.