The Mandelbrot Set Spring 2009

• Explore the set by clicking on a region to zoom in.
• Each click will center the viewing window on the point you clicked on and magnify by a factor controlled by the Scale slider.
• The Resolution slider controls how many iterations are executed to decide if a point is in the set or not; the more iterations, the more detailed the image.
• Your cursor’s coordinates are listed at the bottom.

In my senior year of high school I hacked together this Java applet. It lets you explore the Mandelbrot Set, an incredibly fascinating and beautiful mathematical object.

I first came across it when I read Chaos by James Gleick in 10th grade. Right after that, I read Hofstadter’s Gödel, Escher, Bach (like every other introspective nerd). This was my first glimpse of real mathematics. I had always thought I hated math, but after seeing this I realized that what I hated was math class.

The Mandelbrot Set is just the set of complex numbers $$c$$ for which the orbit of $$0$$ remains bounded under iteration of this beautifully simple equation:

$z_{n+1} = z^2_n + c$