$z_{n+1} = z_n - \frac{p(z_n)}{p'(z_n)}$ where $p(z) = z^3 - 1$

In other words, we are iterating Newton's algorithm to solve $z^3=1$.

But there are multiple solutions : $\exp\left(i\frac{2kπ}{3}\right), ∀k∈\{0,1,2\}$ so we render for each $z_0$ (that is set to pixel coordinate) what complex value it reaches. The angle is plotted in color Hue and the absolute value as intensity (we always converge to something of norm $1$ so it's bright everywhere)

For fun, I messed up $p$ a little bit with mouse coorinate, so it's more like $p(z) = z^k - 1$ where $k=3$ when the mouse is at the center of the image