Hover Mandelbrot to update Julia set in real time.
c = −0.7 + 0.27i
z_{n+1} = z_n² + c |z| → ∞ ⟺ point diverges
The Mandelbrot set M = {c ∈ ℂ : orbit of 0 is bounded}. Each point c in M defines a Julia set J_c = boundary of the filled Julia set. For c ∈ M, J_c is connected; for c ∉ M, J_c is a Cantor dust. The Mandelbrot set is a universal index of all Julia sets.