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.
- Download it
- Copy the files Mandel_3D.class and bulbe.class to your ImageJ plugins folder or subfolder (please observe the uppercase characters in the class name)
- Restart ImageJ or go to Help>Update Menus
- The plugin can be accessed through the ImageJ plugins menu as /plugin/Folder/Mandel_3D. This plugin needs any input 8-bytes image to run (File/new image).
3D rendering is assumed using VolumeJ IMAGEJ plugin: