Definition:Conway Life

Definition
A cellular evolution deriving from a stencil shaped as:


 * $(1): \quad X := \Z^2$


 * $(2): \quad S_X := 2 := \set {0, 1}$


 * $(3): \quad \map S 0 \in \paren {\Z^2 \to 2}$


 * $(4): \quad \Delta := \tuple {\tuple {0, 0}, \tuple {0, 1}, \tuple {1, 1}, \tuple {1, 0}, \tuple {1, -1}, \tuple {0, -1}, \tuple {-1, -1}, \tuple {-1, 0}, \tuple {-1, 1} }$


 * $(5): \quad \map \delta {m, n_1, n_2, n_3, n_4, n_5, n_6, n_7, n_8} := \tuple {m, \displaystyle \sum_{i \mathop = 1}^8 n_i} \in \set {\tuple {0, 3}, \tuple {1, 2}, \tuple {1, 3} } ? 1 : 0$

is called a Conway life.

Also see

 * Conway's Game of Life is Turing Complete
 * Hashlife Algorithm Speeds Up Conway Life Computations