Symmetropy and Self-Organized Criticality
K. Z. Nanjo, Hiroyuki Nagahama, Eiji Yodogawa · Forma · 2001
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.