A Mandelbox is a box shaped 3d object with a fractal surface and like the Mandelbrot set, a Mandelbox set is calculated by applying a formula repeatedly to every point in space.
The Mandelbrot equation is: z = z2 + c
The Mandelbox equation is: v = s * ballFold(r, f*boxFold(v)) + c
– v: 3d point
– 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]
– ballFold(r, v) means for v’s magnitude m:
if m < r m = m/r^2 else if m < 1 m = 1/m^2
The standard Mandelbox uses this formula with s=2, r=0.5 and f=1.