4 ms·
If the state evolution: (a) is deterministic (b) depends only on the current state, and (c) can only occupy a finite number of states then it will loop. Pi
by tedsanders 3y ago
If the state evolution:
(a) is deterministic
(b) depends only on the current state, and
(c) can only occupy a finite number of states
then it will loop.
Pi digits do not satisfy this because while the digit space is finite (10), the next digit depends on more than just the prior digit.
Related (but not the same): https://en.wikipedia.org/wiki/Poincaré_recurrence_theorem https://en.wikipedia.org/wiki/Poincaré_recurrence_theorem
- BriggyDwiggs42 3y agoOoh that’s cool I’ve never seen that before.
- bobsmooth 3y agoThe speed of the balls are changed by a small random amount when they hit a tile, so it's not deterministic.
- Scarblac 3y agoIf it's a deterministic RNG then it just means the state space is very large.