Concept
Basin of attraction
The set of starting points whose orbits all end up at the same place. Iterating a map divides the space into basins, one for each attractor, and the boundaries between them can be extremely intricate.
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
One c, one picture
The same iteration, with the parameter held still and the starting point varied instead. Every complex number gets its own picture, and moving the parameter a hair can shatter it into dust.
Where Newton's method goes instead
An algorithm designed to find roots, run from every starting point at once. Three roots, three basins, and a boundary at which all three are arbitrarily close — so a rule with no randomness in it has starting points whose answer cannot be predicted.
Named alongside it
The objects these essays reach for when they reach for this one.
Complex numbersFractalIterationConnectednessConvergenceDerivativeEscape-timeJulia setMandelbrot setNewtons methodOrbitRoot-finding