===== 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 Zp+1=Zp2+(x+iy) converges.
In the case of 3D, Daniel White uses the idea to create a pseudo-product using spherical coordinates:
n = rn
r=√(x²+y²+z²)
θ=atan(y/x)
φ=asin(z/r)
The iteration [ Zp+1=Zpn + ] 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|}}