While hash functions are not periodical in the mathematical sense it is possible to create and manipulate hash behaviors in order to predict what values the hash will follow like truncating it. This is where Floyd’s cycle-finding (rho) algorithm comes in. By repeatedly hashing a value with the same hash you will eventually create a cycle with a period around square root of n of the size of the hash. What happens with current hashes is that they are too big and these calculations take too much time to be found, they are infeasible. So SHA(1) SHA(2) etc. wont be periodical but u can indeed find that mentioned periodicity if u did SHA(fn), SHA(SHA(fn) etc.