Generator

basins

A generator in the dynamics library, called 0 times across 0 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.

basins is one function. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page — so a figure here is the same figure a reader meets in an essay, and if the generator changes, this page changes with it.

At its defaults

The basins of Newton's method on z³ = 1The complex plane coloured by which cube root of one Newton's method converges to from each starting point.root 1root 2root 3each point coloured by which of the three roots Newton's method takes it tothe boundary is not three sectors: every point of it has all three basins arbitrarily close by

What it checks while it draws

Collected by running the family and listening to lib/verify.js, not written here. The count is how many separate times this build put that claim to the test.

The whole library · What the figures prove