This applet calculates and displays the Mandelbrot Set, one of the most famous of chaos fractals. A fractal is defined by having infinite resolution and being self-similar. Examples can be found all around. A tree, for instance, has a trunk that splits into branches which further split into smaller branches which split into twigs and on and on...Yet all the while the structure of a branch remains the same.

The Mandelbrot fractal lies in imaginary space and is the result of the recursive equation: z = z^2 + c, where c is the complex equation, x + yi. As you iterate this function, the value of z will take on new values, either diverging quickly or converging to a limit. It is the rate of divergence/convergence that decides which color pixel is chosen for the point (x,y). The Mandelbrot Set is called a chaos fractal because small changes in the intial starting point (x,y) can lead to wildy varying rates of convergence/divergence. There is also another possibility, besides converging or diverging, the function can bounce around endlessly, becoming essentially cyclic in nature. The set of points that do this lie between points of convergence and divergence and are known as the Julia Set of the fractal.

This applet is computationally intensive and will take a while to draw. You can use your mouse to zoom in on a particular area of the fractal. Just click over the area you wish to enlarge. The black area is where the function coverges. Refresh the page to start anew. If you zoom in far enough, you will eventually reach the limit of the precision of Java's double type.

Launch Mandelbrot applet.