Tool

Julia Explorer

For each complex parameter c, the Julia set is the set of starting points z whose iteration z ← z² + c stays bounded. Pick c by clicking the Mandelbrot atlas on the right, or dial it in with the sliders.

Click on Julia: zoom in · Shift+click: zoom out · Drag: pan0 ms

c (real): -0.7000

c (imag): 0.2702

Max iterations: 200

Pick c from the Mandelbrot atlas:

c = -0.7000 + 0.2702i

Iteration rule

z_{n+1} = z_n² + c   with   z_0 = (Re pixel, Im pixel)
c = -0.7000 + 0.2702 i  (fixed for the whole image)
escape test: stop when |z_n| > 2

Each pixel is the starting value z₀. The filled Julia set K_c is the set of starting points whose orbit stays bounded.

What to try

Pick c inside the Mandelbrot set (the black region) for a connected Julia set.
Pick c outside for a Cantor-dust Julia set (totally disconnected).
Move c along the Mandelbrot boundary, the Julia set deforms smoothly between connected and disconnected.
Click the preset chips for classic c values (Douady rabbit, dendrite, basilica, San Marco dragon).

FAQ