01Mandelbrot set
c-plane · z₀ = 0 · the set of c for which z ← z² + c stays bounded
c = …
center −0.7500 + 0.0000 i · ×1.00
drag pan · wheel zoom · click seeds c →
02Julia set
z-plane · z₀ = pixel · parameter c = −0.8000 + 0.1560 i
z₀ = …
c = −0.8000 + 0.1560 i
The link
The Mandelbrot set is the table of contents of the Julia family. For every complex number c, the map z ← z² + c carves a Julia set Jc out of the plane — the boundary of the points that stay bounded. The Mandelbrot set is exactly the set of c for which Jc is connected. So the left panel is a map of the right one: click it, and the amber ring marks your c while the Julia set redraws itself. Inside the black set, Julia sets are whole; a hair's breadth outside, they dissolve into dust.
mapz ← z² + c, iterated from z₀
z₀0 for Mandelbrot · the pixel for Julia
escape|z| > 2 ⇒ diverges to ∞
colourμ = n + 1 − log₂ log|z| (continuous)
interiorn = max iter ⇒ black
canvasup to 900 × 900 px, device-scaled