Wolfram's Rule 110 is Turing-complete (Cook 2004) via tag system embedding
Rule 110: A 1D elementary CA where cell state depends on left, center, right neighbors. Among 256 possible rules, Rule 110 was proved Turing-complete by Matthew Cook (2004) using a reduction to cyclic tag systems — a minimal form of Tag system. The proof constructs gliders and their collisions in Rule 110 spacetime to simulate any computation. Rule bits: 01101110₂ = 110.