  We introduce the concept of Minkowski normality, a different type of
normality for the regular continued fraction expansion. We use the ordering \[
\frac{1}{2},\quad \frac{1}{3}, \frac{2}{3},\quad \frac{1}{4},
\frac{3}{4},\frac{2}{5}, \frac{3}{5},\quad \frac{1}{5}, \cdots \] of rationals
obtained from the Kepler tree to give a concrete construction of an infinite
continued fraction whose digits are distributed according to the Minkowski
question mark measure. To do this we define an explicit correspondence between
continued fraction expansions and binary codes to show that we can use the
dyadic Champernowne number to prove normality of the constructed number.
Furthermore, we provide a generalised construction based on the underlying
structure of the Kepler tree, which shows that any construction that
concatenates the continued fraction expansions of all rationals, ordered so
that the sum of the digits of the continued fraction expansion are
non-decreasing, results in a number that is Minkowski normal.
