Julia Set

f(z) = z² + c — drag to change c, scroll to zoom

Parameters

c = -0.745 + 0.113i

About

For each pixel z₀, iterate z → z² + c. Color by how many iterations before |z|>2 (escape). Points that never escape form the Julia set J_c. At c=0, J_c is the unit circle. As c varies, J_c changes — connected when c is inside the Mandelbrot set, totally disconnected (Cantor dust) when outside. Drag on the canvas to move c, or use sliders. Try c = -0.4+0.6i (dendrite), c = 0.285+0.01i (rabbit), or c = -0.7269+0.1889i (San Marco).