Changing the Neighborhood of Cellular Automata

Reversibility of Ca-150 With Symmetry Local Structure

“…Morita and Harao (1989) and Morita (1995) showed the computational universality of reversible cellular automata and proposed a method for constructing a reversible cellular automaton that simulate an irreversible cellular automaton. Nishio (2006) and Nishio (2007) investigated how the global behavior of cellular automata changes by changing not only their local functions but also their neighborhood, and proves that the reversibility and the neighborhood are independent for six 1-dimensional 2-state 3neighborhood cellular automata whose reversibilities are shown by Wolfram (2002). It is also proved that the surjectivity (injectivity) does not depend on the neighborhood in the linear cellular automata on a cell array where the Garden of Eden theorem holds.…”