Minkowski's Question Mark Function
Minkowski's question mark function is a purely singular odd function of a real argument. If is the simple continued fraction representation of the positive number , then . The value of the question mark function on the integers, rationals, or irrational quadratic numbers is rational. This Demonstration visualizes Minkowski's question mark function on the interval .
The Minkowski question mark function is quasi-periodic: . Also, for all , it satisfies the self-similarity relations: and .