Background: In the laws of niddah there is something called a vesst haflaga, which is a period that occurs at some consistent interval. If a woman establishes a pattern for some amount of consecutive periods, there are various halachic stringencies and leniencies that result from assuming that this pattern will continue.
The most straightforward occurrence of such a pattern would be if a woman had her period at equidistant times, i.e. day 1, 31, 61, 91 (30 days apart). However, it can follow more complicated patterns, such as an incrementally increasing pattern (1, 30, 60, 91 ...) (S.A. Y.D. 189:5). The pattern can also consist of a repeating series, such as 25 - 26 - 27 - 25 - 26 - 27 - 25 - 26 - 27, in which the pattern of 25 days later, followed by 26 days later, followed by 27 days later is repeated 3 times, and that whole series becomes the assumed pattern (Y.D. 189:8).
My question is, how complicated can such a pattern be? Can it be a Fibonacci Sequence? Can it be ascending perfect squares? Do the numbers need to be mappable by a polynomial function (as opposed to, say, the set of prime numbers*)?
*I'm not so interested in debating the mathematical claim