Evolution and extinction of families in cellular automata
György Szabó, István Borsos · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1994
In a large class of cellular automata a unique ``parent'' particle of the previous state can be assigned to each particle of the present state. This allows us to define families and study their evolution and extinction in one-dimensional cellular automata. The size density of families is found to tend towards a universal function for large times. The evolution of the average family size, proportional to \ensuremath{\surd}t , is strongly related to the ordering mechanism found by Grassberger [Phys. Rev. A 28, 3666 (1983)].