Classifying CA Rules
K = # possible states of a cell
N = # cells considered to compute next state (“the neighborhood”)
S = KN = # possible neighborhood states.
KS = # possible CA rules. A rule defines one of K possible next states for each of the S possible neighbor state.
n = # neighbor states that map to a selected state, s* (e.g. 0)
l near 0 => most states map to s*
l near 1 => no states map to s*
l near (K-1) / K => even distribution of s* and other next states
Using rules from different l classes:
fixed points ---- cycles ----- complexity ---- chaos
(low l) (l = lc) (high l)