GSDEMO: Orbits of the Starship Mandelbrot, in 3D

[Alan Richmond]

This program is a novel view of the Mandelbrot Set, showing the orbits projected out into 3D. Orbits are the sequences of the iterated function z^2 + c, where c is the point in the complex plane being tested for membership of the M-set, and z starts at 0+0j. Those that stay bounded are in the set, those that shoot off are not. If you draw several of them in the complex plane it soon gets cluttered, so I flip out either the x-coordinate around the orbit's origin, or the y-coordinate. If you plot the orbit of every point c selected the picture still gets crowded, so I select from a grid of sub-points, shown in the display by red balls (as opposed to white). The user can select the grid size and offsets. A small grid size may slow the program noticeably! They can also select which coordinate to flip. Tip: zoom in close!

There is a little more information and a gallery of pictures at http://fractalart.gallery/the-orbits-of-starship-mandelbrot-in-3d/ I plan to add panning or dragging (grab the thing & move it) in a future version. Comments & suggestions welcome!