The Mandelbrot Set
The Mandelbrot set was developed by Benoit Mandelbrot. To generate a Mandelbrot set each point in the complex number plane is tested to determine its "stability". Points within the set have stable behavior and are able to pass the test many times (shown in deep red). Points outside the set rapidly increase to infinity in few iterations exhibiting unstable behavior (shown in blue). The points on the boarder of the set are in transition and are displayed in colors.
A simple Matlab program was created to generate a Mandelbrot sets below. The mouse was clicked to highlight a small portion of the first plot (small white box) and a second plot (middle) was generated showing the zoomed section. By clicking on the second plot, the third plot was generated. The Mandelbrot set may be thought of as a "basin of stability". Notice that the system has an irregular boarder and it show self similarity as the scale is decreased.
Matlab Code:
Code is freely available for download: Mandelbrot
Have Fun and Enjoy!!!