Rewriting — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
![An L-system after 4 rewrites of two rules. X → F[+X]F[-X]+X and F → FF, walked by a turtle turning 22.5°. 130 segments, and not one of them knows anything about light, water or auxin.](/f/an-l-system-after-4-rewrites-of-two-rules-cf31ba72.svg)
L-systems describe, they do not explain
Two rewriting rules and a turtle produce something indistinguishable from a plant, and there is no plant in it — no light, no water, no auxin, no mechanics. That is worth demonstrating precisely because the output is so convincing.
A count set by a delay
An L-system describes a plant and forbids nothing, because none of its parameters is anything a plant has. One branching grammar is the exception: a mature apex makes a new bud every season, and a bud waits d seasons before it branches. Its counts grow at the root of x^(d+1) = x^d + 1, a delay of one season gives Fibonacci's numbers and nothing else does, and the fourth count already separates a one-season wait from every longer one. So a Fibonacci count in a branching plant is a measurement of how long its buds wait. It is also a fragile one: if one bud in ten waits two seasons instead, eleven counts in a row come out Fibonacci's three times in a thousand.
Named alongside it
The objects these essays reach for when they reach for this one.
BranchDescription versus mechanismL-systemsUnderdeterminationClaim testingEvidenceFalsifiabilityFibonacciHonest limitsPredictionSample sizeTurtle graphics