Determinism
Named by 6 essays across one field — each of them below, with the objects they name alongside it.
A difference too small to draw
Two starting points a ten-thousandth apart, under the same rule, with nothing random anywhere. Within forty steps they have nothing in common — and the rule was not doing anything to them that it does not do to everything.
Eight rules and a triangle
A row of cells, each one deciding its next state from the three above it. Eight cases, one bit of output each — a rule that fits in a byte, and 256 of them in total. One of those bytes draws Pascal's triangle.
The obstacle that makes a table chaotic
Put one round post in the middle of a square table and every trace of order goes. Two paths that start a hundred-thousandth of a degree apart end up on opposite sides of the table, and the reason is that a wall curving outwards multiplies a gap where a flat one only adds to it.
A road where nobody overtakes
Rule 184 moves every 1 one cell to the right whenever the cell ahead is empty. It is one of only five elementary rules that never change the number of 1s, and that single property turns it into a model of traffic with an exact transition: below half density every jam dissolves, above it jams can never all clear and drift backwards against the flow.
No local rule can count the votes
A ring of cells, each holding 0 or 1, has to agree on whichever value is in the majority — every cell seeing only its neighbours. The best-known rule gets it right most of the time and wrong near a tie; no rule of any radius gets it right always. Yet two rules run one after the other do, on every ring, and the first of them is the traffic rule.
A rule that remembers one row back
Only six of the 256 elementary cellular automata can be run backwards, and all six are trivial: shifts, copies and complements. Every interesting rule forgets. But make the new row depend on the row before the current one as well — combine the rule's output with it cell by cell — and every rule, rule 30 included, becomes exactly reversible: run forwards, swap the last two rows, run the same rule again, and the starting row comes back cell for cell. Nothing is lost, and yet the patterns still look as disordered as ever.
Named alongside it
The objects these essays reach for when they reach for this one.
Cellular automatonLocalityInvariantIterationState spaceChaosSensitive dependenceBilliardsBinaryComputationCounterexampleCurvature