Mandelbrot ↔ Julia Correspondence

Hover the Mandelbrot set to explore its Julia sets. Each point c in the Mandelbrot plane defines a Julia set J(fc).

Mandelbrot Set — hover to select c
Julia Set — J(z² + c)
c = 0.000 + 0.000i

The Mandelbrot set M is the set of c ∈ ℂ for which 0 does not escape under z ↦ z²+c. A point c ∈ M corresponds to a connected Julia set; c ∉ M gives a Cantor dust. The boundary of M has Hausdorff dimension 2 (Shishikura, 1998).