Symmetry In Cellular Automata And Mechanism Of Emergemce Of Complex Phenomena

Complex system exist in various fields widely,such as the system of origin of life, biological evolution, finance stock market, society, management, weather and so on. Emergence is the important phenomenon in complex system, It is signality to comprehend the complex system through the study of Mechanism of Emergemce.This paper researched the symmetry and the Mechanism of Emergemce in Elementary Cellular Automata, defined the degree of symmetry of cell truss, when the ECA rules evolve , calculate the degree of symmetry of every steps simultaneity, and then we can classify the 256 rules of ECA, there are steadily state,periodic state,chaotic state.This paper investigated the three facts, such as initial condition,the evolution steps,the cell of rule, which can affect the result of the ECA rules evolution, to adjust the classification. The result shows that the initial condition made a impact on a part of rules,which switchs between steadily state and periodic state; the evolution steps also made a impact on a part of rules, which translate the chaotic state to periodic state. So the adjusted classification is: steadily state,periodic state,transformation state,chaotic state. At the same time, we analyzed the classification deeply,finding out the rule is the key facts within initial condition , the evolution steps and rules, and the rules was affected by symmetry or asymmetry and fixed cell rule or changed cell rule.So the more symmetry of the cell rule of the bottom, the more stabilization of the evolution.