Julia Sets Explorer

The Julia set for a complex number $c$ is the boundary between points that escape to infinity and those that remain bounded under iteration of:

$$z_{n+1} = z_n^2 + c$$

Each value of $c$ produces a different fractal. Connected Julia sets correspond to points inside the Mandelbrot set; disconnected “dust” fractals come from points outside.

Controls: Click the Mandelbrot set (left) to choose $c$. Drag to pan, scroll to zoom the Julia set.

The coloring uses smooth iteration count to avoid banding:

$$\text{smooth}_i = i - \log_2(\log_2|z_n|)$$

Try these interesting values:

Code