Julia sets

Fix c and shade every starting point z by whether z ↦ z² + c keeps it bounded. Each c gives a different set: connected when c lies in the Mandelbrot set, a scattered dust when it does not. In the first variant c walks around a circle and the set breathes.

zₙ₊₁ = zₙ² + c, c fixed

On mathcurve.com as Ensembles de Julia