Two elementary cellular automata with a new kind of dynamic

Finite elementary cellular automata (ECAs) are studied, considering periodic and the four types of fixed boundary conditions. It is shown that two of these automata, rules 26 and 154, have particularly interesting dynamics. Both these rules are in Wolfram’s class 2 when subject to periodic boundary conditions but have chaotic dynamics, typical of Wolfram’s class 3, when we consider fixed boundary conditions a ℓ = 1 and a r = 0. The same rules, when fixed null boundary conditions a ℓ = 0 and a r = 0 are used, show complex dynamics with a mixture of order and disorder completely different from the one identified with Wolfram’s class 4: it grows in complexity in order to reach, in just a few time steps, an extremely simple, almost homogeneous configuration, from which the complexification starts again.