Mandelbrot Set

The Mandelbrot set (black) within a continuously colored environment
Wikimedia Commons / Wolfgang Beyer / CC 3.0 GNU 1.2

The Mandelbrot set, named after Benoît Mandelbrot, is a famous example of a fractal. The Mandelbrot set is a mathematical set of points in the complex plane, the boundary of which forms a fractal. It begins with this equation: z_{n+1} = z_{n}^{2} + c. Starting with z_{0}=0, c is in the Mandelbrot set if the absolute value of z_{n} never exceeds a certain number (that number depends on c) however large n gets.
For example, if c = 1 then the sequence is 0, 1, 2, 5, 26,…, which goes to infinity. Therefore, 1 is not an element of the Mandelbrot set.
On the other hand, if c is equal to the square root of 1, also known as i, then the sequence is 0, i, (−1 + i), −i, (−1 + i), −i…, which does not go to infinity and so i belongs to the Mandelbrot set.
When graphed, the Mandelbrot set is very pretty and recognizable.
See also: Mandelbrot Set
Source: Wikipedia (All text is available under the terms of the Creative Commons AttributionShareAlike License)
