Definition:Conway Life

Definition

A cellular evolution deriving from a stencil shaped as:

$(1): \quad X := \Z^2$

$(2): \quad S_X := 2 := \set {0, 1}$

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

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

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

is called a Conway life.

Also see

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

Source of Name

This entry was named for John Horton Conway.