Minkowski's Question Mark Function

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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 .

Contributed by: Oleksandr Pavlyk (March 2011)
Open content licensed under CC BY-NC-SA


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Details

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



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