One-sided multifractal analysis and points of non-differentiability of devil's staircases

We examine the multifractal spectra of one-sided local dimensions of Ahlfors regular measures on R. This brings into a natural context a curious property that has been observed in a number of instances, namely that the Hausdorff dimension of the set of points of non-differentiability of a self-affine 'devil's staircase' function is the square of the dimension of the set of points of increase.