Thank you for sharing this

[unphased]

I made a Mandelbrot renderer as a WebGPU Hello World experiment today, and it led me down one of the nicest rabbit holes I've ever been on. I went to look for prior art eventually to help debug my perturbation implementation, and someone on reddit linked to this implementation of yours. Now this is a jaw dropping implementation and leaves the thing that I made (that I thought was pretty cool) in shambles.

Years ago I had a h264 video someone pre-rendered running it for months on a CPU zooming into the mandelbrot set. I thought that was cool. Now you show us this multithreaded and also WebGPU accelerated mandelbrot renderer with effectively UNLIMITED zoom. This is true black magic wizardry on display here. I thought we would need to layer on ever more complex hacks just to get each couple orders of magnitude out.

It looks like your exponent augmentation method leads to basically no scalability limit for zooming. I love how smooth the iteration boundaries are at any zoom (I've zoomed in to 200 orders of magnitude and it's starting to be a slog!)

[bertbaron]

Thanks for your feedback!

I was also impressed by the perturbation algorithm and how much it improves on the rendering time. I must admit I had a hard time understanding the math behind it, but managed to implement it using the information on Wikipedia. Once I understood that the new limit for zooming was due to the limited scale of floating point numbers but not their precision, I came up with the 'extended float'. In the javascript implementation a function to 'predict' this extra exponent but to be honest I don't think this function is entirely correct, it just seems to work well enough for any reasonable zoom level. In the WebGPU implementation this trick isn't used but the exponent is simply updated when needed because I'm afraid that the limitation will become clear with float32 numbers. This is a bit more costly though.

The WebGPU can render up to 10^1500 with decent performance, but only with a limited number of iterations (something like 10000). The wiki also mentions series approximation and interpolation which could help to go even further, but I haven't tried to implement these yet. So if you're up for a challenge, feel free to give it a go!