About Mandelbrot and Julia Sets

The Mandelbrot and Julia Sets are among the most well known of all fractals. Countless breathtaking shapes and curves hide within their depths, beautifully displaying the concept of self-similarity that can be found in many fractals. Zooming into the edges of the "apple man" will expose many more "apple men" with very similar details as the outer one. Julia Sets can be generated for points on the Mandelbrot Set. Interesting Julia Sets can be found at places where the Mandelbrot Set exhibits interesting details as well. The pattern of the Julia Set for a particular point of the Mandelbrot Set is typically quite similar to an enlargement of the Mandelbrot Set at the given point and adds a different kind of beauty to the pattern.

Interactive Explorer

The following is a generator for Mandelbrot and Julia Sets that allows for interactive exploration of the depth and beauty of both sets. The program is written as a Java Applet and should work with Microsoft's Internet Explorer and Netscape's Navigator. Simply press the button below to start. Enjoy your journey through the fractal world of Mandelbrot and Julia Sets!

The following iterated equation produces both the Mandelbrot and Julia Sets:

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