Rendering this cost me 3°C of global warming.
4K images: https://blood2oo1.github.io/fractals/gallery/09/index.html

Revisitation of an old piece, Cinema 4D - Octane Vectron

Start with a rectangle in R^3. For each point in the rectangle, we start the Lorenz system up with that as the initial value, and color the point by the time it takes the system's x value to change sign. I added this one to the examples I distribute with MRaster:

https://github.com/richmit/mraster

You can find it in the examples/3da_frac_lorenz.cpp.

I swear, these things just pop up out of nowhere.

The time it takes for a particle starting at some point in R^3 to be "captured" by a strange attactor is reminiscent of the escape time function for the Mandelbrot set. Of course it's hard to tell when a solution to an IVP has been captured by the the attractor. For the Langford attractor all the trajectories eventually worm through the central "stalk" of the attactor. So we can measure the time required for a solution to hit the central part of this stalk region. The image in this post is colored by how long the attractor, starting from points in a rectangle in the y-z plane, take to cross the stalk.

Here is the code (which is probably easier to follow than my description above):

https://github.com/richmit/mraster/blob/master/examples/3da_frac_langford.cpp

I composited a modified Benesi Pine Fractal into Blender and made it breathe. Of course, the background, "heart" and silky fluid lines are of my own creation.