Abstract: Formation of multifractal structure is simulated.Through a contrastive analysis on analytic,multifractal spectrum of structure and calculated multifractal spectrum with partition function,it is found that multifractal spectrum can describe structure growth pattern in a certain scale-free zone.It is found that all structure scale-free zones exhibit value of research.Since traditional multifractal analysis method can not make full use of the data in a structure,we propose a new method to calculate multifractal spectrum based on several scale-free zones.

Key words: multifractal, partition function, scale