Julia Set Morphing

Continuous journey through the parameter space of Julia sets

Iterations 100 Orbit speed 0.15 Orbit r 0.70 Colormap

c = ... Click canvas to pin c parameter

The Julia set J_c = {z ∈ ℂ : |f_c^n(z)| remains bounded}, where f_c(z) = z² + c. As c varies continuously, the Julia set undergoes a phase transition at the Mandelbrot boundary: connected (c inside M) → Cantor dust (c outside M). The "morphing" traces a closed orbit in c-space, passing through a variety of topologically distinct Julia sets.