An interesting new way of displaying mandelbrot set imagery was recently developed by Melinda Green.

Coined 'Buhhdabrots' by Lori Gardi, the technique is a different way of displaying mandelbrot images. Points which escape wander the complex plane between -2 ... +2 (before escaping). The buddhabrot technique creates a density plot of all the points that escape, but only within the region being viewed on the complex plane. A density plot esentially gives each point a color based on the number of times it's 'visited' by escaping points. Generally the brighter the color the greater number of times it's been visited.

'Classic' mandelbrot set images are usually colored based on the number of iterations a point had to go through before 'escaping'. The buddhabrot technique is thus a totally different, yet equally valid, way of displaying mandelbrot images. The classic rendering technique makes no attempt to evaluate the underlying orbits of the points which escape, which is what the buddhabrot method does.

I added buddhabrot functionaliy to my program, and this gallery represents my first images. I really like the ghostly quality of the images, as well as the many bizarre and freaky patterns in them. The small copies of the mandelbrot set (islands) are where the most interesting buddhabrots are found, and that's where most of the images in the gallery are from. If you look at a larger copy of any of the thumbnails, there's a link which will take you to a 'classic' version of the buddhabrot image. It's interesting to compare the two.

Because of the way buddhabrot images are created, there's a limit to how far one can zoom in and still get an interesting image. Because escaping points wander the entire complex plane between -2 ... +2, while the buddha method only looks at the area of the complex plane being viewed (which gets smaller and smaller as one zooms in) it takes greater numbers of iterations to create an interesting plot. Also, certain areas are more interesting than others. I found the islands along the negative real axis to be the most interesting. The plots were tighter and less vaporous than most other areas, and the symmetry about the imaginary (y) axis creates interesting patterns.

Hope you enjoy the gallery, I had a lot of fun putting it together.

-Eric Bazan