Chances are you've seen Conway's Game of Life. SmoothLife is one way to generalize conway's game of life to a continuous domain.
Lets start with Conway's game of life. We'll begin by defining the 'inner neighborhood' M, and the 'outer neighborhood' N. Next, let's define
m = M
n = ΣN.
We can write the Game of Life update rule as a function S(n,m) such that:
S(n,m) = 0 ; n < 2
S(n,m) = 0 ; n > 3
S(n,m) = 1 ; m = 1, 1 < n < 4
S(n,m) = 1 ; m = 1, n = 3
Generalization of Conway's "Game of Life" to a continuous domain - SmoothLife.