MANDELBOX | Amine Akid

A Mandelbox is a box-like fractal object that shares several properties with the well known Mandelbrot set; it is a map of continuous, locally shape preserving Julia sets.
This means the object varies at different locations, since each area uses a Julia set fractal with a unique formula.

Like the Mandelbrot set a Mandelbox is calculated by applying a formula repeatedly to every point in space. That point v is part of a Mandelbox if it does not escape to infinity.
In fact it replaces the Mandelbrot equation z = z2 + c with:
v = s*ballFold(r, f*boxFold(v)) + c
where boxFold(v) means for each axis a:
if v[a]>1 v[a] = 2-v[a]
else if v[a]<-1 v[a] =-2-v[a]
and ballFold(r, v) means for v's magnitude m:
if m<r m = m/r^2
else if m<1 m = 1/m