Perturbation Theory and the Mandelbrot set

I've recently been following the well-worn path of Mandelbrot set computation and rendering in my onoing development of Very Plotter. In my last blog post, I mentioned how fast floating point math was used for more "zoomed out" images, and slower arbitrary precision math was used otherwise. In this post I'll discuss the breakthrough of Perturbation theory, which allows fast floating point math to continue to be used as we dive deeper into the set.

By applying perturbation theory to the Mandelbrot set problem, images that would normally take days to calculate can be completed in minutes!

The Mandelbrot set on Very Plotter

I've added the Mandelbrot set to Very Plotter.

This was a fun project, especially doing various tests and enhancements to improve calculation speed. I wrote my own arbitrary precision code, based on the new-ish JavaScript BigInt class.

It was also a worthwhile challenge, I think, to get the site usable on mobile (tested on iOS) devices, where most interactive JavaScript Mandelbrot viewers I've seen do not work so well on iPhones/iPads.

Very Plotter

This is definitely not just any old quick project to plot and view points from mathematical sequences. This is Very Plotter.

Remembering Steve Jobs Ten Years Later

I took this screenshot of apple.com 10 years ago this month. It's remained on my desktop ever since.

Publishing Permanent Photo Signatures with Blockchains

I really don’t like copyright notices and logos on images. I wanted a way to digitally (cryptographically) sign my photos before publishing them, so I came up with my own method. I also want my signatures to be public and impossible to corrupt, modify, or delete. How is this possible? "Groan," you say, "don't say with a blockchain". Yes, I am using blockchains (oh no!).