Linguofreak
Well-known member
The Mandelbrot set is the set of points c on the complex plane such that when you start with z=0 and perform repeated iterations of z=z^2+c, z remains bounded.
Most color visualizations of the set color the exterior (the points not in the set) according to the escape time (the number of iterations required to reach since distance from the origin). However it seems like it should be possible to color the interior: any point that does not go to infinity should have either a limit that it goes to or at least some sort of average value over many iterations of the sequence. And every point that does not go to infinity remains within a circle of radius 2. So it seems that we could color the set using a fairly common scheme for visualizations of complex functions: assign the complex phase to the hue component of an HSV color, set full saturation, and set the value according to magnitude, with black for zero and V=1/2 of full for a magnitude of two. Then color the exterior of the set white. Has anyone seen a Mandelbrot set visualization with that sort of coloring scheme?
Most color visualizations of the set color the exterior (the points not in the set) according to the escape time (the number of iterations required to reach since distance from the origin). However it seems like it should be possible to color the interior: any point that does not go to infinity should have either a limit that it goes to or at least some sort of average value over many iterations of the sequence. And every point that does not go to infinity remains within a circle of radius 2. So it seems that we could color the set using a fairly common scheme for visualizations of complex functions: assign the complex phase to the hue component of an HSV color, set full saturation, and set the value according to magnitude, with black for zero and V=1/2 of full for a magnitude of two. Then color the exterior of the set white. Has anyone seen a Mandelbrot set visualization with that sort of coloring scheme?
