Co-dimenion function c(g)
The singularities
are defined , we focus on their theoretical probability laws through the concept of the co-dimension function
. In the genral case , the probability distribution function and the distribution function depend on the scale ratio
. In the case of multifractal , they take a particular form.
a process is called multifractal if the function
follows the law described by:

According to the figure in the above section, one can write:

can be obtained by plotting the above equation in log-log plot.

It represents the logarithm of the probability of exceeding singularities and integrates information at all scales.