Because the number of possible values for these sequences are finite, both the formula_11 sequence, which is mod formula_3, and formula_9 sequence will eventually repeat, even though these values are unknown. If the sequences were to behave like random numbers, the birthday paradox implies that the number of formula_14 before a repetition occurs would be expected to be formula_15, where formula_16 is the number of possible values. So the sequence formula_9 will likely repeat much earlier than the sequence formula_11. Once a sequence has a repeated value, the sequence will cycle, because each value depends only on the one before it. This structure of eventual cycling gives rise to the name "Rho algorithm", owing to similarity to the shape of the Greek character ρ when the values formula_19, formula_20, etc. are represented as nodes in a directed graph.