from cellular automata, 1968.
neumann’s rules:
- An infinite plane is divided up into squares.
- Each square contains a copy of the same finite automaton (the square together with this automaton is called a cell).
- Associated with each cell is its neighborhood, consisting of itself together with its four immediate, nondiagonal neighbors.
- The state of a cell at time t + 1 is uniquely determined by its neighborhood state at time /, together with the transition function / of the finite automaton which is associated with every cell.
- The finite automaton associated with each cell possesses a distinguished state v0 called the quiescent state, such that f(v09 v0,…9 v0) = v0.
- At each time step all but a finite number of cells are in the quiescent state.
- The number of distinct states for the finite automaton associated with each cell is 29.
- A particular transition function / is specified and shown to yield certain computation and construction properties discussed below.