I am just beginning to study cellular automata and I am having trouble understanding the so called Garden of Eden states. How can a deterministic algorithm wind up in a state that has no pre-image, this seems impossible to me?
2026-02-23 08:43:03.1771836183
Garden of Eden States in Cellular Automata
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Not every state is guaranteed to be possible in cellular automata, so it can never end in a Garden of Eden state.
The Garden of Eden Theorem states that iff an automaton has twins, that is iff it's possible to replace one state with another without changing the future states, then there can be a Garden of Eden state. For sufficiently large sizes of grids the number of potential predecessors (that do not contain a twin pattern) is smaller than the number of future states.