Complex variables and fractals
This semester, Professor Cartwright's class is exploring the mathematics behind the generation of fractal patterns. A typical example is the Mandelbrot set shown above.
The process uses complex numbers, which correspond to points in the plane. A series of values is produced according to the rule: z0 = 0, zi+1 = zi2 + c. The behavior of the series varies depending on the complex number c. The picture shows as black the values of c for which the series stays close to the origin. For other values of c, the colors show how fast the series goes away from the origin.