Concept
Cobweb
A staircase drawn between a map's graph and the diagonal, which traces an orbit on the picture of the map itself.
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
The staircase that shows the whole orbit
Take a number, feed it to a rule, feed the answer back in. There is a way of drawing that on the rule's own graph which turns the entire future of a starting point into a shape — and the shape is legible.
A point that pulls, and a point that pushes
Every crossing of a curve with the diagonal is a value the rule leaves alone. Whether anything ever arrives there is decided by one number — the slope at the crossing — and the picture makes the reason obvious.
Named alongside it
The objects these essays reach for when they reach for this one.
Fixed pointIterationLogistic mapOrbitAttractorContractionConvergenceDerivativeLinearisationPeriodic orbitSelf similarityStability