This plugin draws 3D Mandelbrot fractals stacks.

Amaury CHABOD

a_chabod@yahoo.fr

2D Mandelbrot sets are (x+iy) points of plane where the iteration Z_p+1=Z_p²+(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 [ Z_p+1=Z_pⁿ + <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

“Mandelbulbe”.

http://en.wikipedia.org/wiki/Mandelbrot_set

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:

http://webscreen.ophth.uiowa.edu/bij/vr.htm

mandel_3d.class mandel_3d.java bulbe.class bulbe.java

This is an example of a 500X500X500 stack, with an 8-exponent and 25 iterations. 3D Rendering is the following: