Julia sets

One of the most basic fractal types is the family of Julia sets, discovered by the French mathematician Gaston Julia during the first World War. Julia sets are created by a simple formula with one complex parameter called c or seed. This parameter can be varied to create many variations. Here are a few examples.

Ultra Fractal juliabasic Julia sets Ultra Fractal julia2 Julia sets Ultra Fractal julia3 Julia sets

Julia sets are also self-similar, as illustrated by the following zooms into the last image above. The first zoomed image shows the top of the original. Further zooms are illustrated by the small red rectangles in the images.

Ultra Fractal julia3zoom1 Julia sets Ultra Fractal julia3zoom2 Julia sets Ultra Fractal julia3zoom3 Julia sets

The same spiral-like shape is repeated over and over again.

It can be difficult to find good values of the c parameter. Fortunately, the Mandelbrot set, which is discussed next, can help you with that.

Next: The Mandelbrot set

See Also
What are fractals?

Julia sets