Quaternions and the Mandelbrot Set @FractalWoman

Uploaded June 2024 | Updated September 2026, 2 weeks ago

In this video, I demonstrate how to generate a 4D Mandelbrot Set using the 4x4 matrix version of quaternions. To visualize this 4D volumetric data, I use the 3D volumetric data visualizer that I use in the 3D ultrasound applications I develop for work. Although we can't visualize a 4D volume direction, we can visualize two 3D volumes as I show in the video.

Here is a link to my paper: The Mandelbrot Set as a Quasi-Black Hole

researchgate.net/publication/315381462_The_Mandelbrot_Set_as_a_Quasi-Black_Hole

Robitailles Biggest Blunder: On Boltzmanns Constant, Plancks Constant and Universality

$Popcorn All of the patterns in this video were generated by propagating two helix waves in opposite directions and looking at the interference pattern. The code never changes. Only the number of waves in in the forward vs the reverse wave (which can be a fraction). When the pattern looks simple, then the forward wave is a resonant frequency of the backward wave. There is so much complexity in these patterns and yet, the algorithm is so simple.$

$Fractal Flute Meditation Here is another fractal meditation video I created using some software I developed which allows me to fly through the fractal in real time. In this software, I record all of the motions in the flythrough, and then I generate all of the images in high resolution for the movie after the fact. It takes many hours to generate the images for each video.$