The Hausdorff measure functions: A new way to characterize fractal sets

摘要

We introduce a new method based on Hausdorff measure spectrum function (HMSF) which provides a more precise way for tracing the geometrical organization of a fractal set. The HMSF does carry a huge amount of information about the set to likely be explored in a chosen way. Depending on the nature of the set, we propose two ways to extract this information. We apply these methods to typical fractals as well as to synthetic models of porous media. This results in a complete distinction between same fractal dimension sets.