Spatiotemporal chaos in two-dimensional dynamic coupled map lattices system based on elementary cellular automata

This paper proposes a two-dimensional dynamic coupled map lattices system (2D DCML) based on elementary cellular automata (ECA). In this system, the two-dimensional coupled map lattices are iterated simultaneously with the ECA, and the dynamic coupling methods and perturbations for each lattice are obtained according to the iterative results of the ECA. We analyze various properties of the proposed system: the Kolmogorov-Sinai entropy, the bifurcation diagram, the return map, the time-domain analysis, the correlation coefficient, and the NIST SP800-22 statistical test. Theoretical analysis and experimental results demonstrate that the proposed system possesses superior chaotic properties and wider parameter space than other two-dimensional coupled map lattices systems, such as the two-dimensional nonlinear coupled map lattices system and the two-dimensional mixed pseudo-random coupling PWLCM-Sin map lattices system. Furthermore, the output sequences of the proposed system exhibit better ergodicity, uniformity, and randomness. These outstanding properties demonstrate the promising application of the 2D DCML system in the field of cryptography.