There are lots of cool patterns to the fibonacci sequence and its variants, with one of the main ones being that it can generate numbers that closely resemble squareroots, while not exactly being the same. This means you can use squareroots to directly generate numbers with some unpredictability (these numbers resemble squareroots, but aren't exactly the same and it makes it unpredictable). Using modified fibonacci sequences also add more "randomness" to this. The cool thing about this algorithm is that it will almost never repeat!
As far as I know, this is a cycle-free pseudo-random number generator. This is unproven, but I assume so considering it uses irrational numbers to generate the next thing in a sequence. If it does go in a cycle, it will stop every script. This is an open problem! If you find a proof that shows this is cycle-free, you're awesome! I'll be looking for my proof too, hehe. But here is some evidence so far: Testing shows that after 217,000 iterations, there has been no loop or cycle.
