The Mandelbox - a 3D version of a Mandelbrot Set was discovered in 2010 and is producing some interesting video.
A trip into a Mandelbox with (relatively) constant zoom.
There are a lot of Mandelbox videos if you look.
And a good old-fashioned Mandelbrot Set - Constant Zoom.
Because someone will ask.
In mathematics the Mandelbrot set, named after Benoît Mandelbrot, is a set of points in the complex plane, the boundary of which forms a fractal. Mathematically the Mandelbrot set can be defined as the set of complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1 = zn2 + c remains bounded.