Investigating Transformational Complexity: Counting Functions a Region Induces on Another in Elementary Cellular Automata

Table 1

Classification of the rules into four classes, corresponding to the analysis of our results.

Type	Number	Rules
Class A (monotonic and quasi-constant)	31	0, 1, 2, 3, 4, 5, 8, 10, 12, 15, 19, 29, 30, 32, 34, 37, 41, 42, 50, 51, 54, 62, 76, 106, 108, 110, 132, 138, 170, 200, 204
Class B (monotonic and not quasi-constant)	43	7, 9, 11, 13, 14, 18, 22, 23, 24, 25, 28, 33, 35, 36, 38, 43, 44, 45, 46, 58, 60, 72, 73, 77, 78, 94, 104, 122, 126, 134, 136, 140, 142, 146, 152, 154, 156, 164, 168, 172, 178, 184, 232
Class C (exhibit local maxima and not exceptional)	14	6, 26, 27, 40, 56, 57, 74, 128, 130, 160, 162
Class D (exceptional)	3	90, 105, 150