3D fractal dimension of fat crystal networks

The relationship between the 2D and 3D fractal dimensions of a self-similar fractal object is addressed through both theoretical analysis and experimental study. The common approach to obtain the 3D fractal dimension of a self-similar fractal object by adding one to its corresponding 2D fractal dimension is found to be inappropriate. A 3D box-counting, particle-counting and mass fractal dimension must be determined through image analysis of 3D volume elements of the fractal object.