The picture you see is the Mandelbrot set, probably the most famous of all fractals. 
This odd shaped image is created with an extremely simple formula: Z = Z * Z + C. 



Odd facts about the Mandelbrot set: 


The area of the Mandelbrot set is unknown, but it\'s fairly small. 


The length of the border is known - it\'s infinite!

 
The barnacle covered pear shape that you see occurs an infinite number of times in the Mandelbrot set. 
Rotated, distorted and shrunken, but quite recognizeable. 


All of the black areas of the Mandelbrot set are connected together. 


Every band of colour around the Mandelbrot set (not shown on this image) goes all the way around, 
without breaking, and without crossing any other colour bands. Think about that when looking at some 
of the more complex areas! 


The Mandelbrot set can be used as a very inefficient way to calculate PI. 


The Mandelbrot set is named after its discoverer, Benoit B. Mandelbrot. 


The Mandelbrot set has infinite detail - you can keep zooming in forever. 


How can such a simple formula create such incredible complexity? Because it is used in a feedback loop.


 The equation is calculated dozens, or even millions of times for each pixel. Each time through the loop, 


the result of one calculation is used as the input for the next calculation. It is this feedback loop that gives 
the Mandelbrot set, and many other fractals, their complex behaviour.
The Sierpinski Triangle
An  application of fractals and chaos is in music. Some music, including that of Back and Mozart, 
can be stripped down so that is contains as little as 1/64th of its notes and still retain the essence of the composer. 
Many new software applications are and have been developed which contain chaotic filters, similiar to those 
which change the speed, or the pitch of music. 
 Fractal Generator
 Link to lots of Pretty Fractals