What mathematical rules can we use to generate (single, double, triple) paradiddles? Perhaps even paradiddles with odd meters.
If you really want to go full math-rock, you could always put notes on the beats given by floor( sqrt(2) * n), for n = 1, 2, 3, ... This will generate notes on beats
1, 2, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 18, 19, 21, ...
X: 1 K: Cmaj M: L: 1/4 A A z A A z A A A z A A z A A A z A A z A
Mathematically, it can be proven that this pattern will never precisely repeat itself. It will never have two rests back-to-back. On average, there will be a note on about 1/sqrt(2) ≈ 70% of the beats.
Similar non-repeating patterns could be generated by replacing sqrt(2) with any irrational number greater than 1. A rational number would cause a pattern that repeated itself eventually, effectively acting as a polyrhythm where the number of the notes in the faster tuplet is given by the denominator of the rational number.