One row of cells, one dumb rule: a cell’s next state depends only on itself and its two neighbours. Rule 110 is the simplest rule proven Turing-complete — a universe that can compute anything, from a lookup table eight entries long. Slide to grow the space-time and watch structure crawl out of nothing.
The rule is a table: for each of the 8 possible (left,centre,right) patterns, the new centre bit is (110 >> pattern) & 1, i.e. 111→0, 110→1, 101→1, 100→0, 011→1, 010→1, 001→1, 000→0. The instrument evolves a real row under exactly that table. A fail-loud self-check throws unless the eight table outputs match 110’s binary AND a deterministic evolution reproduces bit-for-bit. Rule 110’s Turing-completeness (Cook, 2004) is why ‘simple local rule’ does not mean ‘simple behaviour’.
The Turing-completeness is cited (Cook 2004), not re-proved here; what is exact is the rule table and the evolution. Boundaries wrap (a torus) — a finite stand-in for the infinite line.