Fractal Analysis of Aggregates : Correlation between the 2d and 3d Box-Counting Fractal Dimension and Power Law Fractal Dimension

Fractal dimension ( ) has been extensively used for many years to characterize the morphological properties of aggregate systems. There are two main methods to estimate the fractal dimension of aggregates, namely the box-counting (BC) and power law (PL) methods. However, the relationship between the BC fractal dimension ( ) and PL fractal dimension ( ) has not been discussed yet. In this work, a series of three-dimensional aggregates with different input parameters ( and the number of primary particles) is generated by a tunable aggregation model. Then, the fractal dimensions ( ) of all the aggregates are estimated by the 3D BC method. The relationship between and is investigated. We found that is greater than when 2.5. However, the situation is reversed when 2.5. Further, a novel projection method is proposed and applied to all the 3D aggregates to obtain their 2D projection images. In this projection method, the minimum projection overlapping area of all the primary particles in the aggregate is considered. Then, the fractal dimensions ( ) of 2D projection images are estimated using the 2D BC method. Finally, correlations between and with are established