The frantic frog function, denoted \(S(n)\) or \( ext{FF}(n)\), 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. While first discussed by Tibor Radó, the name "frantic frog" was given by James Harland, as part of his "Zany Zoo" Turing machine research project.