Abstract
The main goal of this work is to develop a robust framework for an exhaustive description of essential properties of a fractal object. For this purpose, the inherent features of fractal sets are scrutinized. The topological, metrological, morphological, and topographical attributes of fractal systems are delineated. The criteria of the fractal connectedness are established. The characteristics of the fractal connectivity and ramification are ascertained. The index of the fractal loopiness is introduced. The quantifications of the fractal heterogeneity, lacunarity, and anisotropy are briefly sketched out. A set of key attributes which enable a proper characterization of fractal system are suggested.
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