Optimization of 2D lattice cellular automata for pseudorandom number generation

This paper proposes a generalized approach to 2D CA PRNGs - the 2D lattice CA PRNG - by introducing vertical connections to arrays of ID CA. The structure of a 2D lattice CA PRNG lies in between that of ID CA and 2D CA grid PRNGs. With the generalized approach, 2D lattice CA PRNG offers more 2D CA PRNG variations. It is found that they can do better than the conventional 2D CA grid PRNGs. In this paper, the structure and properties of 2D lattice CA are explored by varying the number and location of vertical connections, and by searching for different 2D array settings that can give good randomness based on Diehard test. To get the most out of 2D lattice CA PRNGs, genetic algorithm is employed in searching for good neighborhood characteristics. By adopting an evolutionary approach, the randomness quality of 2D lattice CA PRNGs is optimized. In this paper, a new metric, #rn is introduced as a way of finding a 2D lattice CA PRNG with the least number of cells required to pass Diehard test. Following the introduction of the new metric #rn, a cropping technique is presented to further boost the CA PRNG performance. The cost and efficiency of 2D lattice CA PRNG is compared with past works on CA PRNGs.