Six Iterations Towards the Mandelbrot Set

Posted: 2006-10-16

This applet shows six iterations of the complex function that in the limit of infinite iterations, determines the Mandlebrot set. Click on points in the applet to see variations from the standard Mandelbrot function. By clicking on points you are changing the initial complex value that the iterated function is applied to. For the standard Mandelbrot set this value is 0.

The complex function is displayed by mapping complex numbers to colors using the HSV (hue, saturation, value) colorspace described here: The Mandelbrot Dazibao—The HSV Colorspace. (This actually differs a little from the usual definition of the HSV colorspace.) A complex number is mapped to a color by mapping its magnitude (absolute value) to value (brightness), and by mapping its angle (complex argument) to hue. Saturation is clamped to the maximum possible for a given value and hue. Zero is white, and as magnitude increases, the colors fade to black. The hue is red at 0° (the positive real line) and it is green at 120° and it is blue at 240°.