This is a plot of the Newton basin of z⁴ - 1, which has four roots, i, -i, 1 and -1. Each pixel represents a point of the complex plane, and the value corresponding to each pixel in turn is taken as the initial value Zo.

Then Newton's method for finding the roots of a function with a continuous derivative is applied, using the iteration scheme Zn+1 = Zn - f(Zn) / f '(Zn). In this case f(z) = z⁴ - 1, and f '(z) = z³.

Each pixel is then coloured according to which of the four roots it converges to.