Multiscaling of the graph length in Coupled Map Lattices

We consider generalized scaling exponents for the graph of a scalar function to allow for multiscaling of the graph length. These generalized exponents are related to the moments of the distribution of roughness over the support of the graph. We report numerical computations of these exponents for the graphs of Coupled Map Lattices exhibiting phase transitions between laminar and turbulent behaviour. We observe multiscaling of the graph in the transition region. Furthermore, the generalized-dimensions D(q) are computed for a conserved measure of graph roughness.