What are the Cellular Automata and its randomness rules?

Cellular Automata can discrete dynamical system with simple construction but complex self-organizing behavior. This behavior is completely specified in terms of local relations who at each step each cell computes its new state from that of its close neighbors. Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes. Three classes exhibit behavior analogous to limit points, limit cycles and chaotic attractors. The fourth class is probably capable of universal computation, so that properties of its infinite time behavior are undecided. The different classes of cellular automaton behavior allow different levels of prediction of the outcome of cellular automaton evolution from particular initial states. In the first class, the outcome of the evolution is determined (with probability 1), independent of the initial state. In the second class, the value of a particular site at large times is determined by the initial values of sites in a ...  more