Growth And Time Evolution Behavior Of Helical Cellular Automata And Its Application

In present, the study of nonlinear phenomena is a focal field, which scientists pay close attention to, and Cellular Automata (CA) is an important means and tool of studing Nonlinearity.In this thesis, the main principle of CA and the construct mothod of several tapical CA have been reviewed. The pattern formation in a helical cellular automaton (HCA) model is studied by computer simulations. It is found that the evolutions of the HCA are sensitive not only to the circumference of the helix but also to the initial seeds. The long-term growth behavior is determined by the circumulate of helix while the local behavior is determined by the periodic seed configuration with fixed circumference. The model generates a series of novel patterns, including Sierpinski triangle gasket, compound patterns consisting of regular and random structures, compound pattern array, layer pattern, two-phase, and so on. With increasing height of the patterns (increasing growth time), the model also exhibits periodic, abrupt, and gradual growth behaviors for different seed configurations, respectively. Fractal dimension analysis is used to characterize these different evolution processes quantitatively. Subsequently, the occupancy value of time evolution behavior is calculated and found to be close to 0.334 after abrupt oscillation.Some applications of HCA have been studied also in this paper. It is found that the curve of time evolution where p is equal to a positive integer power of 2 is similar to weibull distribution curve, which used to describe the relationship of environmental pullution and economic growth. Finally, according to the chaos behavior in our HCA model, a sample of pseudorandom number generator was designed as another example of applications of the HCA.