Minkowski's Question-Mark Function

Minkowski's question-mark function, denoted ?(x), maps the rational numbers to the dyadic rationals and irrational quadratic numbers to non-dyadic irrationals, built from the continued-fraction expansion of its argument. It is a continuous, strictly increasing, singular function, meaning its derivative is zero almost everywhere even though the function itself increases across its whole domain. The function provides a bridge between the Stern-Brocot tree's ordering of the rational numbers by continued fractions and the ordinary binary ordering of the real numbers on the unit interval.