Optimization of 1 D and 2 D Cellular Automata for Pseudo Random Number Generator

In this paper we have implemented 1D binary cellular automata with wrap around at the edges (i.e. a ring). The default update rule used is rule 30 discovered by Stephen Wolfram. Rule 30 is an update rule that when applied to the CA will produce a class III, a periodic, chaotic behavior. The response with respect to rule 2 and rule 90 is also verified on Xilinx Spartan 3E FPGA and this can be applied for modeling PRNG. This paper also discusses the correlation between 1D and 2D cellular automata. Cellular automata concept was first introduced by von Neumann von Neumann for the proposal of modeling biological self-reproduction. The primary interest was to derive a computationally universal cellular space with self-reproduction configurations. Afterward, a new phase of activities was started by Wolfram who pioneered the investigation of Cellular automata as a mathematical model for self-organizing statistical systems. Wolfram was proved that the randomness of the patterns generated by maximum-length Cellular automata is significantly better than other widely used methods, such as linear feedback shift registers. The intensive interest in this field can be attributed to the phenomenal growth of the VLSI technology that permits cost-effective realization of the simple structure of local-neighborhood Cellular automata Wolfram.