The Cellular Automata Studying Of Complex System

For the development of the future science, it is an accepted fact in scientific community that science is at the turning point at present, where complexity science is blooming. The research object of complexity science mainly faced to complex system and complexity. Complex system possesses a great deal of essential characteristics different from simple system, such as emergence, self-organization, self-adaption, self-similarity, and so on. It is the key issue for complexity science research to open out the inherent law and the evolutionary mechanism in complex system.Cellular automata are the computational models for vast parallelism devised by von Neumann, and it can be looked as the prototype of the new generation of computer. On the one hand, cellular automata have so rich dynamical behaviors that it can be used to simulate theoretically any complicated phenomenon, on the other hand, cellular automata are so simple that it is very convenient to study the complex system's essential characterics. This thesis focuses on cellular automata. Based on many boffin's research work and a mass of computer experiment, the radical viewpoint was proposed: the basal evolutionary mechanism of complexity was the simple repetition, and the complex phenomenon of complex system was resulted from the repletion caused by simple interreaction among the components. The unity of opposites between simplicity and complexity in the complex system was emphasized in this viewpoint, which was helpful to explore the inherent law and the mechanism of evolution in complex system. Moreover, this view results in that the cellular automata are the most efficient approach to study the complex system and complexity.Though lots of studies have been carried on the application of cellular automata, its theoretical basis is serious lacking why the classical methods based on the continuum hypothesis are not fit to deal with cellular automata. The combination of large-scale computer experiments and modern mathematical approach are necessary to studying cellular automata. A program of one-dimensional cellular automta has been implemented for the computer experiment based on Borland C++ Builder 6. Large-scale computer experiments are carried, and a few especial rules were analyzed whose evolutionary patterns are comparatively cramped. And then cellular automata's evolutionary patterns has characterized quantificationally for the first time by the means of power spectrum, and the results indicate that the power spectrum of cellular automta evolutionary configures can be used to distinguish wolfram's class-IV from other classes.The structure of cellular automata rule space is the center issue of theoretical research for cellular automta. Walsh orthogonal transform are introduced to cellular automta's rules, and a parameterδis proposed to characterize the rule space, according to which the phase transform and criticality in elementary cellular automta rule space can be better interpreted when compared with the parameterλproposed by Langton.It is one of the most key pace for the modeling complex system that cellular automta is applied in modeling life phenomena. Cellular automata model of microorganism growth is set up firstly, and then life's self-reproduction is simulated in cellular automata, which is evolutionary based on unsheathed-loop. In addition, self-replication structure's emergence spontaneously from random initial conditions is investigated and implemented in the evolutionary model.In a word, by the studies systematically for cellular automata in this thesis, such conclusions are followed: computer experiment is important for finding new problem, methods and results in the research of cellular automta and complexity, then cellular automta is effective for complexity research, and the combination of computer experiment and modern mathematic approach should be one of the most appropriate approach for cellular automata and general complex system.