MinkowskiQM.m

Given x from 0 to 1, compute ?(x), where ? is the Minkowski question mark function.

Description

Given x from 0 to 1, this program computes ?(x), where ? is the Minkowski question mark function, defined by

?(0)=0, ?(1)=1, and ?((a+b)/(c+d))=
(?(a/c) + ?(b/d))/2, where a/b and c/d are consecutive terms in the Farey sequence. ?(x) is continuous but nowhere differentiable. ?(x) is rational whenever x is rational or a quadratic irrational. If x is rational, the denominator of ?(x) is a power of 2, otherwise it is not.

• MATLAB release: MATLAB 6.0 (R12)