Minkowski's question-mark function

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In mathematics, Minkowski's question-mark function, denoted ?(x), is a function with unusual fractal properties, defined by Hermann Minkowski in 1904.^[1] It maps quadratic irrational numbers to rational numbers on the unit interval, via an expression relating the continued fraction expansions of the quadratics to the binary expansions of the rationals, given by Arnaud Denjoy in 1938.^[2] It also maps rational numbers to dyadic rationals, as can be seen by a recursive definition closely related to the Stern–Brocot tree.