Reversible cellular automata with memory: two-dimensional patterns from a single site seed

Standard cellular automata (CA) are ahistoric (memoryless), i.e., the new state of a cell depends on its neighborhood configuration only at the preceding time step. Historic memory of all past iterations can be incorporated into CA by featuring each cell by a weighted mean of all its past states. In this paper, a new kind of reversible CA, which incorporates memory, is introduced in a two-dimensional scenario.