s′(i) = R[ 4·s(i−1) + 2·s(i) + s(i+1) ]
Each cell reads its left, centre and right neighbour as a 3-bit address 0–7 and looks up the answer in the rule's 8-bit table R. That one number, 0–255, is the whole physics.
rule—
binary—
hex—
λ (Langton)—
Wolfram class—
symmetry family — the same automaton
mirror (L↔R)—
complement—
mirror + complement—
Wolfram's four classes: I dies to uniform; II settles into stable or repeating structures; III is chaotic; IV is complex — localised structures that interact, the edge of chaos where Rule 110 turns out to be capable of universal computation.