Investigation of the Relationship between the 2D and 3D Box-Counting Fractal Properties and Power Law Fractal Properties of Aggregates

The fractal dimension Df has been widely used to describe the structural and morphological characteristics of aggregates. Box-counting (BC) power law (PL) are most common methods calculate However, prefactor k, as another important property, received less attention. Furthermore, there is no relevant research about BC (kBC). This work applied a tunable aggregation model generate series three-dimensional aggregates with different input parameters (power properties: Df,PL kPL, number primary particles NP). Then, projection method obtain 2D information generated properties (kBC Df,BC) estimated by both, for 3D methods. Next, relationships between box-counting investigated. Notably, easier achieved than data in real processes, especially made nanoparticles. Therefore, correlations PL potentially high importance established present work. Finally, comparison these previous one (not considering k) performed, results show that new more accurate.