Today the father of fractal geometry turns 83. Benoît Mandelbrot is known for the Mandelbrot set, a set of points in the complex plane that forms a fractal. To see if a point c belongs to the Mandelbrot set start with z_{0} = 0 and generate the sequence z_{1}, z_{2}, z_{3},.. by iterating the function z_{n+1} = z_{n}^{2} + c. If the value z remains close to the origin, the value c belongs to the Mandelbrot set. If it runs away to infinity, it doesn’t. Plotting the set of points in the complex plane gives you this picture.

The picture is the result of running a small program I wrote on the TI-83+ calculator. You can download it from here. The program runs for several hours. The zip-file also includes two of my other TI-Basic fractal programs. A Julia fractal and the Sierpinski triangle.