** Authors:**
Ayşe GORBON, Ayşe ERZAN

** Abstract: **
The fractal dimension of the wrinkledness of a graph [1] of a
function is a measure of the smoothness or the seeming randomness of the
function considered. In this study, we introduce the generalized
dimensions of the graph, \beta(q), which are the scaling
exponents of the moments of the averaged graph length. These will have a
nonlinear dependence on the moments, q, if the wrinkledness is not equally
distributed. Moreover, the relation between the graph dimensions
and the scaling exponent of the 1^{st} order structure function [2] can
be generalized. To understand how the non--uniformity of the wrinkledness of the graph is
distributed, the generalized dimensions of the support,D(q), are introduced. These
dimensions are related with the generalized graph dimensions and the q^{th}
order structure functions. D(q) are related to \beta(q), and the scaling
exponents of the q^{th} order structure functions, \zeta_q. We have computed
\beta(q), \zeta_q, D(q) and the f(\alpha) spectrum for a number of
coupled map lattices [3,4], which may be thought as simple replacements for
non--linear partial differential equations [5]. We find that the graph of these CML
display multiscaling properties, with \beta(q) and D(q) depending weakly on q.

** Keywords: **