Mandelbulb and Mandelbox fractals are similar to the Mandelbrot fractal in that they are all “escape” fractals. A point is or is not part of the set, based on whether or not it’s recursive function stays bounded, or runs off toward infinity. While the Mandelbrot images are 2D, Mandelbulb and Mandlebox images are 3D. The Mandelbulb is based on spherical coordinates (similar to polar coordinates) which are raised to some power. The Mandelbox, on the other hand, is based on a folding and scaling formula.
These images were produced with Mandelbulber, a free software 3D fractal generator and renderer.