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