The Buddhabrot Set is a re-visualization of the familiar Mandelbrot Set using a technique invented by Melinda Green. Instead of selecting points on the real-complex plane, initial points are selected at random from the image region. The point is iterated through the function, z = zˆ2 + c, where z has components in both the real and imaginary planes.
If the particle escapes (exits the viewing area with high speed), its path is reiterated, exposing its position onto the image surface with each step. In this fashion, areas of dense particle travel appear bright white. The result is an amazing universe of structure, spirituality, and mathematical intrigue.
When I originally wrote this program in 2004, it took my fastest computer six days to complete the final rendering. With some optimizations to the code and executing on my current fastest computer, it took 15 minutes.
Magnifying and exploring the heart of the Buddhabrot.
Each image represents multiple bailout values for the iteration limits so post-processed compositing is not required.
A new feature allows dynamic rendering and exposure limits for the traveling particles.
Programmed in Processing
In Albuquerque, New Mexico, USA
Around 8:08pm February 6, 2020
Originally published in 2004 at Complexification