CA Perfect Hash function?

gistfile1.txt

input = "0 1 0"   # example input bits

neighborhood_w = len(input) # 3

possible_states = 2^len(input)

# rule = neighbor-count mapped to indexes of original input [0,1,0], thus f(0) = input[0], etc
#        edges do not wrap, padded w/ 0s

neighbor_count = "1 1 1"

hash = 1 1 1

# more pairs:
101, 121, 101
100, 110, 110
001, 011, 011
110, 221, 001

000, 001, 010, 011, 100, 101, 110, 111
000, 011, 111, 122, 110, 121, 211, 232
000, 011, 111, 100, 110, 101, 011, 0?0
      ^------------------------^    ^----indexOutOfBounds
             collision