8 ms·
Because there are a finite number of states, it will always loop. An interesting question might be around how many distinct loops there are and whether there's
by cjg 3y ago
Because there are a finite number of states, it will always loop.
An interesting question might be around how many distinct loops there are and whether there's some pattern to the loop lengths.
- schwartzworld 3y ago> Because there are a finite number of states, it will always loop. No it wouldn't. The fact that it will pass through every state infinite times doesn't mean it will do it in the same order each time. Each digit of pi has only 10 possible states, but it never loops.
- tedsanders 3y agoIf 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.