Saturday, June 5, 2010

Julia sets and more fractals

Following on from my last post on the Mandelbrot set I've created a Julia set generator. Julia sets are a similar sort of fractal to the Mandelbrot set. The Julia sets I am showing are all generated using the function zn+1 = zn2+c. Thus for every possible value of c we get a different Julia set. In this viewer the Julia sets are shown in red. There are many other types, but these are the classic Julia sets that led to the development of the Mandelbrot set.

The Julia sets come in two varieties; connected and disconnected sets. Either all the points in the Julia set are connected to each other (forming a single central entity) or all the points are disconnected (forming a Cauchy set, also called Fatou dust). The Mandelbrot set is generated from this fact, basically the Mandelbrot set is all the values of c such that the generated Julia set. In fact the Mandelbrot set forms a pictographic index of all the connected Julia sets. If you zoom in enough into the Mandelbrot set you will eventually find a copy of every conceivable Julia set. Which is pretty cool.

Some of the Julia sets form incredibly beautiful shapes, while others can be pretty mundane, I have put a list of some interesting sets below the viewer, just click on the links and the values will load into the viewer. Otherwise please explore the space and try your own values. If you find a combination of values that looks particularly impressive please leave the values as a comment for other people to try. The instruction for use are the same as the previous Mandelbrot viewer with the addition of being able to change the values for c by giving the real and the imaginary parts.


Some interesting sets

Click links to load:

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