PROBE FOR MORPHOLOGY AND HIERARCHICAL CORRELATIONS IN SCALE-INVARIANT STRUCTURES

A correlation technique is developed to characterize the distribution of fractal structures. This method generalizes the concept of lacunarity to a scaling function and is naturally suited to distinguish between fractal structures with similar fractal dimensions for already small systems. We therefore propose it as a convenient tool to quantify the vaguely defined concept of morphology. Our lacunarity function is sensitive to logarithmic periodicities and we conjecture that its asymptotic behavior yields information on corrections to scaling in simpler measurements. The formalism we use can be generalized to analyze multifractal structures.