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.