The 3D continuous cellular automata shown in the video are based on the 1D system by Stephen Wolfram in A New Kind of Science pp. 155-160:
https://www.wolframscience.com/nks/p155–continuous-cellular-automata
System details:
- Continuous cell states in [0, 1]
- Updated state = fractional part of (avg neighbor state + a constant)
- von Neumann neighborhood
- Cells with states below a threshold are not drawn.
After implementing and experimenting with this 3D threshold system I discovered that it has been previously studied by Richard Southwell, who used a threshold of 0.5 to construct an object for 3D printing.