Looking at that Wikipedia link for subdivision surface, the thing that jumped out to me was the visual example in the side bar. It says, āfirst three stepsā but the complexity seems to scale exponentially. However, the resulting 3D shapes are still distributing the flat surfaces evenly.
Because of the even distribution, I was thinking Euclidean divisions. But if a slider represents a subdivision amount, it is growing exponentially (2^n). So evenly spaced Euclidean subdivisions but when the slider goes from 1 to 2 to 3, the divisions would be divide-by-2, divide-by-4, divide-by-8, respectively.
I could see this being more useful in terms of performance and/or if you have some other modulation changing those subdivision amounts. Adjacent changes would have a more drastic effect than normal Euclidean.
Another interesting possibility would be to use two separate slider components (see the middle example in the clockalgo screenshot), the first for the base and second for the exponent. Again, modulate each slider value and the divisions could make rather big jumps and it could get into that chaotic territory with a lot of complexity (some parts seem random), but it is still deterministic.
