Multifractal approach to inhomogeneous fractals

Vicsek et al. have shown that DLA can be described as a geometrical multifractal by defining the mass Mi within box i normalized to the object's total mass M0 as the measure μi = Mi/M0. This measure shows its multifractal property by the dependence of the generalized dimensions Dq on q. Recently, we have shown that the arterial blood vessels, which are fat fractals, are also geometrically multifractal. We have examined the origin of multifractality of thin and fat fractals and give a new classification of thin and fat monofractals and multifractals.