Self-Organized Construction in Sparse Random Arrays of Conway’s Game of Life (original) (raw)

New Constructions in Cellular Automata, 2003

Abstract

The construction problems and techniques described in this chapter arose out of a single problem: . . . What happens in very low density infinite random arrays of Conway’s Game of Life? . . . However, the work reported has wider implications, briefly discussed in the final section. Conway’s Game of Life (henceforth GoL) is a deterministic cellular automaton (CA), which is binary (a cell has two possible states: 0 and 1) and runs on an infinite two-dimensional grid of cells. A deterministic CA cell’s state at time step t is determined, according to a transition rule, by those of a set of in-neighbors at step t — 1, and its own state at step t — 1 can affect the state of i out-neighbors at t. In GoL, in-neighbors and out-neighbors coincide, and include the cell itself. The neighborhood is a 3 x 3 square of cells. GoL’s transition rule specifies that a cell is in state 1 at step t if and only if either of the following held at t - 1. 1. The cell and either two or three other cells in i...

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