Random Number Generation by Cellular Automata With Memory

Abstract

This paper considers an extension to the standard framework of cellular automata which implements memory capabilities by featuring cells by elementary rules of its last three states. A study is made of the potential value of elementary cellular automata with elementary memory rules as random number generators.

Elementary Cellular Automata with Minimal Memory and Random Number Generation

“…Rules without memory fail to pass the tests. Their low P-values are given in [20]. It seems that the regularities, the triangular features appreciated in their spatio-temporal patterns, are translated into some kind of tendencies that the tests for randomness detect.…”

“…This may be the origin of the weakness of the studied rules regarding randomness. This does not happen when keeping parity memory of the three last states as reported in [20], or moreover of the last four states as shown in Figure 7, in which case the space seems conveniently filled with scattered points. Table 2 shows how the probability parameters in this parity of the last four states' memory scenario turn out to be close to 0.5, that is, a genuine random sequence.…”

“…One hundred windows of size 50, from sites @1, 50D up to @100, 150D, were sampled. (This mechanism differs from the one followed in the general study on proper CA as RNGs made in [20]. There, the 100 simulations were obtained starting from 100 different, and notably wider, initial random configurations.…”