Julia

Many fractal types, the Mandelbrot set for instance, have a related set of fractals called Julia sets. These Julia set fractals use the same equation as their non-Julia counterparts, but the equations are evaluated differently.

For each type of fractal that has Julia sets, there are an infinite number of Julia sets. Each one is uniquely defined by a seed location, which is a point on the fractal from which they are derived. This seed location is set in the Set Julia Seed window.

Julia sets have their own distinct style and visual appeal but, despite their differences, they maintain a certain similarity to the fractal which they are based upon. In fact, if you zoom in on a Julia set, and at the same time zoom in on the corresponding non-Julia fractal in the area of the Julia seed, the Julia and non-Julia fractals become more and more similar -- an odd thing considering their radically different appearances when zoomed out.

For an example of this similarity, try out the Finding order in chaos exercise.