See this post for my previous explorations of Root-Finding Fractals.
A while back I implemented a Custom Formula Editor in Visions of Chaos. The Custom Formula Editor allows users of Visions of Chaos to program their own fractal formulas which run on their GPUs for much faster performance than when using the CPU for calculations.
One of my hopes for coding the custom editor was that users of Visions of Chaos would make their own formulas and share them with me to include in future releases.
Recently I was contacted by Dr Bernd Frassek who was working with Root-Finding Fractals. See here for more of Dr Frassek’s information about these root-finding methods. For an English version see this Google translated version. Being much more of a mathematician than I am, he was able to implement a lot more root-finding methods that I had never experimented with or even heard of. The total count of methods for finding roots went from 4 in my previous version to 23 in the new mode.
With some more testing and a bit of back and forth emails we were able to get the code working and the end result is a new GPU accelerated Root-Finding Fractals mode in Visions of Chaos. You can find this new mode under “Mode->Fractals->Root-Finding Fractals 2”. All of the formulas, methods, coloring and orbit trap settings from the older Root-Finding Fractals mode have been migrated to the new mode.
If you are interested in coding these sort of fractals yourself you can see the latest GLSL shader source code (as of the 8th of March, 2021) by clicking here.
You can also check the “Show shader code” checkbox in the Root-Finding Settings dialog which will cause Visions of Chaos to show you the generated shader code before rendering the fractal image.
Here is a sample movie showing some results from the new mode.
This next movie uses orbit traps.
If you have any other formulas or root-finding methods that you would like to see implemented let me know. The structure of the shader allows new formulas and root-finding methods to be added relatively easily.