Here's the mandelbrot generalized to 4 dimensions.
It's based on the idea that the complex plane arises
from the real number line. The new (imaginary) axis
is derived from the real axis by taking the square root
of the negative unit of the real axis. The generalization
introduces a third axis derived from the imaginary axis
by taking the square root of the negative unit of the
imaginary axis: root(-i). Maths in this volume reveals
a fourth axis: root(i).
Here's the mandelblob in 4D. the third dimension is
held at zero and the fourth dimension (time) is seen
in the animation
This is my first lisp program