f_c(z) = z² + c. Click the Mandelbrot set (right) to pick c and see its Julia set (left).
Julia set J_c
Mandelbrot set M (click to pick c)
Parameter c
Re(c)-0.7269
Im(c)0.1889
|c|—
c in M?—
z₀ = 0, z_{n+1} = z_n² + c |c|≤2 boundary: Julia set c∈M: connected Julia set c∉M: Cantor dust (disconnected)
Presets
Render
Theory
Fatou set: stable (equicontinuous) Julia set: chaotic boundary ∂M = ∂{c: J_c connected} J_c has Hausdorff dim in (1,2] ∂M has dim = 2 (Shishikura 1998)