Writing discrete "differentials" to simulate totalistic CA
Posted: August 16th, 2022, 2:17 pm
let's say we have a set of 1s and 0s that take up a 3 dimensional plane. A(x,y,t) is a function that give us the state of a cell with coordinates x,y at t generations. To condense everything, a will be the sum of all neighboring points in the x-y plane of generation t. B and S are sets, and they represent the birth and survival states. B⊆{0...8},S⊆{0...8}. Using Boolean logic, A(x,y,t+1)=(A(x,y,t)∧a∈S)∨(Ā(x,y,t)∧a∈B).
In other words, If A(x,y,t)=1 and a is within the set of survival states, or A(x,y,t) is 0 and a is within the set of birth states, then A(x,y,t+1) is 1, otherwise A(x,y,t) is 0. For example, cgol's sets are, B={3} and S={2,3}.
In other words, If A(x,y,t)=1 and a is within the set of survival states, or A(x,y,t) is 0 and a is within the set of birth states, then A(x,y,t+1) is 1, otherwise A(x,y,t) is 0. For example, cgol's sets are, B={3} and S={2,3}.