Maximum shifts function

The frantic frog function, denoted \(S(n)\) or \(\text{FF}(n)\), is a cousin of the busy beaver function. \(S(n)\) is defined as the maximum number of state transitions made by an n-state, 2-color Turing machine before halting, given blank input. The name "frantic frog" was given by James Harland.

Like \(\Sigma(n)\), \(S(n)\) also eventually dominates all Turing-computable functions.