Concept
Period doubling
A bifurcation at which a cycle loses stability and is replaced by one of twice its length.
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
The road paved with doublings
Turn one dial slowly and watch what a map settles into. It settles on a point, then on two points, then four, then eight — faster and faster, and the doublings run out at a parameter that is finite.
A constant that does not care which map
The gaps between successive period doublings shrink by a factor. Measure that factor for the logistic map and you get 4.669. Measure it for a completely different map and you get 4.669, and nobody expected that.
Named alongside it
The objects these essays reach for when they reach for this one.
BifurcationLogistic mapSelf similarityAttractorChaosConvergenceFeigenbaum constantPeriodic orbitRenormalisationScalingStabilityTransient