Ultra fractal buddhabrot8/3/2023 The Buddhabrot uses the same iteration rules as the Mandelbrot: Points are sampled on the complex plane, repeatedly transformed using a simple function, and filtered based on whether they escape to infinity or not. This emergent complexity seems to be a funky property of the complex plane, and many other fractals have been made using similarly simple rules over the complex numbers. The Mandelbrot fractal is fascinating, because it generates a point set of mind-boggling complexity from a few very simple rules. The points that do not escape become part of the set. The Wikipedia pages on the Mandelbrot and the Buddhabrot are a better resource, but briefly, the Mandelbrot set works by picking points on the complex plane, repeatedly transforming them with a simple formula and checking whether the points eventually escape outwards to infinity or not. The Buddhabrot is a curious fractal that produces wonderful images of cloudy and colorful nebulas, and is closely related to the Mandelbrot set. I am not convinced it was worth it, but I'm happy to finally put the project to rest :) A Buddhawhat? My poor GTX480 also ended up dying a fiery death at the hands of the fractal, and I had to borrow a computer to finish the job. Programming and camera setup took the better of two months, and rendering the final animation took more than 10 days. A lot of time went into careful importance sampling code and denoising methods to keep render costs in check. I was also set on rendering at 4K resolution, and render times shot through the roof. However, feature creep set in, and this ended up being a lot more complex to do than originally intended - a single camera pan was not interesting enough, and I started writing a lot of throw-away tools to setup 4D camera shots synchronized to music. The Buddhabrot lives in a 4D space, and rotating through different projections onto a 2D screen does better justice to its intricate shapes. Instead of rendering a single large image, I thought an animation sequence would be more interesting to look at. However, I don't like leaving things unfinished, and for the past few months I have been writing a modern GPU implementation of a Buddhabrot renderer to see where I could take it. I did not know a lot about writing fast code back then, and unsurprisingly that project was unsuccessful. Recently I have been digging through some old projects and rediscovered an old high school project of mine that attempted to render very large images of the Buddhabrot fractal. Rendering a Buddhabrot at 4K and Other Bad Ideas
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