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 .


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The Minkowski question mark function is quasi-periodic: . Also, for all , it satisfies the self-similarity relations: and .
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