In this paper, we investigate number-conserving cellular automata with up to five inputs and two states the goal of comparing their dynamics diffusion. For purpose, introduce concept decompression ratio describing expansion configurations finite support. We find that a large number rules exhibit abrupt change in when density initial pattern is increasing, somewhat analogous second-order phase t...

Abstract Let G be a group and A set equipped with collection of finitary operations. We study cellular automata $$\tau :{A^G} \to {A^G}$$ that preserve the operations induced componentwise from . show τ is an endomorphism if only its local function homomorphism. When entropic (i.e. all are homomorphisms), we establish EndCA( G;A ), consisting such endomorphic automata, isomorphic to direct limi...

For a d-dimensional cellular automaton with d $\ge$ 1 we introduce rescaled entropy which estimates the growth rate of at small scales by generalizing previous approaches [1, 9]. We also define notion Lyapunov exponent and proves Ruelle inequality as already established for = in [16, 15]. Finally generalize formula 1-dimensional permutative automata [18] to higher dimensions. This last result e...