  We consider multifractal random wavelet series built from Gibbs measures, and
study the singularity spectra associated with the graph and range of these
functions restricted to their iso-H\"older sets. To obtain these singularity
spectra, we use a family of Gibbs measures defined on a sequence of
topologically transitive subshift of finite type whose Hausdorff distance to
the set of zeros of the mother wavelet tends to 0.
