Statistical Complexity of Boolean Cellular Automata with Short-Term Reaction-Diffusion Memory on a Square Lattice

Abstract

Memory is a ubiquitous phenomenon in biological systems, in which the present system state is not entirely determined by the current conditions but also depends on the time evolutionary path of the system. Specifically, many phenomena related to memory are characterized by chemical memory reactions that may fire under particular system conditions. These conditional chemical reactions contradict the extant approaches for modeling chemical kinetics and have increasingly posed significant challenges to mathematical modeling and computer simulation. Along these lines, we can imagine a memory module contributing to cell therapy or the synthetic differentiation of certain cells in a certain fashion after experiencing a brief stimulus. We demonstrate that information processing properties of cellular automata (CAs) can be controlled by a signal composed of excitation pulses. We discuss how cellular memory can be incorporated into more complex systems like CAs to understand the controlling of information processing performed by a medium with the use of a pulse signal propagated from a number of control cells. In this paper, we also investigate the potential application of cellular computation for constructing pseudorandom number generators (PRNGs). Furthermore, the PRNG scheme based on CAs with reaction-diffusion memory is proposed for its capability of generating ultrahigh-quality random numbers. However, the quality bottleneck of a practical PRNG lies in the limited cycle of the generator. To close the gap between the pure randomness generation and the short period, we propose and implement a memory algorithm based on a reaction-diffusion process in a chemical system for Boolean CAs. This scheme is characterized by a tradeoff between, on one hand, the rate of generation of random bits and, on the other hand, the degree of randomness that the series can deliver. These successful applications of the memory modeling framework suggest that this innovative theory is an effective and powerful tool for studying memory processes and conditional chemical reactions in a wide range of complex biological systems. This result also opens a new perspective to apply CAs as a computational engine for the robust generation of pure random numbers, which has important applications in cryptography and other related areas. © 2019, Complex Systems Publications, Inc. All rights reserved.