This plugin draws 3D Mandelbrot fractals stacks.
2D Mandelbrot sets are (x+iy) points of plane where the iteration Zp+1=Zp2+(x+iy) converges.
In the case of 3D, Daniel White uses the idea to create a pseudo-product using spherical coordinates:
<x,y,z>n = rn <cos(nθ)cos(nφ),sin(nθ)cos(nφ),sin(nφ)>
r=√(x²+y²+z²) θ=atan(y/x) φ=asin(z/r)
The iteration [ Zp+1=Zpn + <x,y,z> ] converges inside a 3D fractal area.
Paul Nylander makes experiments with exponants higher than 2. The best result is obtained with exponant 8 and is named
The Mandel_3D plugin contains two java class files.
3D rendering is assumed using VolumeJ IMAGEJ plugin:
This is an example of a 500X500X500 stack, with an 8-exponent and 25 iterations. 3D Rendering is the following: