Fractals are just plain amazing. This demo explores, in particular, the Mandelbrot Set, a very well-known fractal. It exists near the origin on the complex plane of numbers, and is, naturally, an infinitely complex fractal. I use the Escape Time Algorithm for drawing, which, while not the best algorithm for drawing the set, is reasonably easy to implement.

This is defined mathematically on Wikipedia as, "the set of complex c-values for which the orbit of 0 under iteration of the complex quadratic polynomial xn+1 = xn2 + c remains bounded". The aforementioned Escape Time Algorithm performs an iterations over the sequence that this creates, and based on whether it "appears" to be bounded, draws a grayscale pixel of brightness dependent on "how bounded" it seems to be. While simple, it creates some obvious banding in the colouring, and limits how 'far' one can zoom in to.

Controls are: the arrow keys will pan the camera across the plane, and Page Up/Down will zoom the camera in and out.

Windows
Download Mandelbrot Explorer (.zip) [~360 KB]