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===== Introduction =====

This plugin draws 3D Mandelbrot fractals stacks.

===== Author =====

Amaury CHABOD

[[a_chabod@yahoo.fr|a_chabod@yahoo.fr]]

===== Description =====


2D Mandelbrot sets are (x+iy) points of plane where the iteration Z<sub>p+1</sub>=Z<sub>p</sub><sup>2</sup>+(x+iy) converges.

In the case of 3D, Daniel White uses the idea to create a pseudo-product using spherical coordinates:

<x,y,z><sup>n</sup> = r<sup>n</sup> <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<sub>p+1</sub>=Z<sub>p</sub><sup>n</sup> + <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
===== Installation =====

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

===== Download =====

{{:plugin:3d:3d_mandelbrot_fractals:mandel_3d.class|}}
{{:plugin:3d:3d_mandelbrot_fractals:mandel_3d.java|}}
{{:plugin:3d:3d_mandelbrot_fractals:bulbe.class|}}
{{:plugin:3d:3d_mandelbrot_fractals:bulbe.java|}}

===== Examples =====

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

{{:plugin:3d:3d_mandelbrot_fractals:rendering_bulbe_exp8.gif|}}