Elementary Cellular Automaton — Rule 110
Rule 110 is Turing-complete: complex structures emerge from a simple 3-cell local rule
Wolfram's elementary cellular automata evolve 1D binary rows by a 3-cell neighborhood rule. Rule 110 (proven Turing-complete by Cook 2004) produces gliders, eaters, and complex collisions from a simple seed. Rule 30 generates cryptographic-quality pseudorandom bits; Rule 90 creates Sierpinski triangle fractals.