\begin{definition}[Definition:Conway Life]
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'''.
\end{definition}