  Conway's Game of Life is the best-known cellular automaton. It is a classic
model of emergence and self-organization, it is Turing-complete, and it can
simulate a universal constructor. The Game of Life belongs to the set of
semi-totalistic cellular automata, a family with 262,144 members. Many of these
automata may deserve as much attention as the Game of Life, if not more. The
challenge we address here is to provide a structure for organizing this large
family, to make it easier to find interesting automata, and to understand the
relations between automata. Packard and Wolfram (1985) divided the family into
four classes, based on the observed behaviours of the rules. Eppstein (2010)
proposed an alternative four-class system, based on the forms of the rules.
Instead of a class-based organization, we propose a continuous high-dimensional
vector space, where each automaton is represented by a point in the space. The
distance between two automata in this space corresponds to the differences in
their behavioural characteristics. Nearest neighbours in the space have similar
behaviours. This space should make it easier for researchers to see the
structure of the family of semi-totalistic rules and to find the hidden gems in
the family.
