This ended up being much more popular than I thought it would be. It's a model of the number of iterations before confirmed escape of Mandelbrot set, namely the equation Z_(n+1) = (Z_n)² + C where Z is the coordinate mapped to a complex number. What I did was increase the value of two (the power) on an interpolation between one and eight, using OSL, just to see how it looked. The result was a little boring, but the progression was amazing. (And yes, it is one through eight—each power of N has N-1 spires; with two having one spire and being the traditional Mandelbrot, one being a boring circle, and eight having seven spires.)
The funny thing about the Mandelbrot set, which I intend to render in a future video, is that while it's clearly of finite area, it is of literally unlimited perimeter. The further you zoom in, the squirrlier it gets. I'll check on this later on as part of my book.
The whole thing was done in OSL in Blender, back on version 2.79 I think. Maybe 2.80. I think the majority of the confusion is in how I managed to work with complex numbers in a language that inherently does not support them; but if you want to see how it's done, you'll just have to purchase "The Warrior Poet's Guide to OSL" when it comes out and read it until close to the end. I promise you'll be a much better graphics-ninja for it.
I was a little hesitant about including this, as to be fair I rendered it, I didn't "design" it. No one did. The Mandelbrot set has been called "the fingerprint of God", and has been zoomed in by an absurd amount without ever finding an orderly repeating pattern or an end. However, I did think to render the number of iterations of N before it escaped as a color value; and in fact also did it as a blackbody glow temperature but never got around to uploading it. I think the result is charming.
The camera was kept in orthographic mode at a consistent distance from the plane that the rendering was on; with the OSL script piped to an emissive value in an otherwise dark and endless environment. 3D software, after all, would be a lot harder if we didn't master the first two! In all seriousness, I'm considering zooming the camera in along a logarithm for my next rendering; so it will forever be getting closer to the image but never quite reaching it. I think I can bring out the incredible weirdness of the Mandelbrot meta-shape.