The same basic approach can be used to deduce the rule for an additive cellular automaton from vertical sequences.

Note (b) for More Cellular Automata…Algebraic forms [for cellular automaton rules] The rules here can be expressed in algebraic terms (see page 869 ) as follows: • Rule 22: Mod[p + q + r + p q r, 2] • Rule 60: Mod[p + q, 2] • Rule 105: Mod[1 + p + q + r, 2] • Rule 129: Mod[1 + p + q + r + p q + q r + p r, 2] • Rule 150: Mod[p + q + r, 2] • Rule 225: Mod[1 + p + q + r + q r, 2] Note that rules 60, 105 and 150 are additive, like rule 90.

Note (b) for Continuous Cellular Automata…Additive [continuous cellular automaton] rules In the case a = 0 the systems on page 159 are purely additive.

3D class 4 [cellular automaton] rules With a cubic lattice of the type shown on page 183 , and with updating rules of the form LifeStep3D[{p_, q_, r_}, a_List] := MapThread[If[ #1  1 && p ≤ #2 ≤ q || #2  r, 1, 0]&, {a, Sum[RotateLeft[ a, {i, j, k}], {i, -1, 1}, {j, -1, 1}, {k, -1, 1}] - a}, 3] Carter Bays discovered between 1986 and 1990 the three examples {5, 7, 6} , {4, 5, 5} , and {5, 6, 5} .

The picture at the top of the next page shows as a simple first example a cellular automaton which starts from a typical random initial condition, then evolves down the page according to the very simple rule that a cell becomes black if either of its neighbors are black.

Given a flat interface, the layer of cells immediately on either side of this interface behaves like the rule 150 1D cellular automaton. … The phenomenon of domains illustrated here is also found in various 2D cellular automata with 4-neighbor rather than 8-neighbor rules.

If the differences are computed modulo k then the difference table corresponds essentially to the evolution of an additive cellular automaton (see page 597 ).

But regardless of its origin, the effect itself can readily be captured just by setting up a two-dimensional cellular automaton with appropriate rules. … Evolution of simple two-dimensional cellular automata in which the color of each cell at each step is determined by looking at a weighted sum of the average colors of cells up to distance 3 away.

Konrad Zuse suggested that it could be a continuous cellular automaton; Edward Fredkin an ordinary cellular automaton (compare page 1027 ). And over the past few decades—normally in the context of amateur science—there have been a steady stream of systems like cellular automata constructed to have elements reminiscent of observed particles or forces.

The pictures below show what happens if the programs operate by applying elementary cellular automaton rules t times to 2t + 1 inputs.