mandelbrot set

mandelbrot set

Buddhabrot Grand Tour

2w ago
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Description

This is a detailed and technical tour of the Buddhabrot. The zooms and rotations are slow to give the viewer a chance to see the details and relationships between the different parts of the fractal which become noticeable as it's rotated. The Buddhabrot is an alternate rendering of the well known Mandelbrot Fractal. Rather than the traditional method of coloring pixels based on the number of iterations, you plot the trajectories of each iteration to draw the Buddhabrot. The result is a cloudy, nebulous form that resembles the Mandelbrot set as well as a Buddha sitting in meditation if you rotate it 90 degrees. This fractal is extremely computationally intense to render because for any given region you want to look at, the points that draw it come in from source points all over the place. Looking at smaller and smaller areas becomes exponentially more difficult to compute. The traditional methods of random sampling or the Metropolis-Hastings method for finding source points to draw this fractal didn't seem to have enough performance or resolve very much detail. So I started from scratch and worked out my own moderately high performance methods which allowed me to produce this entire animation on two Core2Duo laptops using my own software written in C++ on Linux & OS X. My software is CPU based since it's approach is not GPU friendly. Quick stats: Computation method: CPU (multi-threaded, C++, Linux & OS X) Frame size: 1280x720 Iterations: 2000i-10,000i (variable) Deepest zoom: approx 3.3 million x Number of frames: approx 7,800 Frame computation time: 30sec - 3hrs per frame (variable) -William Milberry