Fractal analysis of tree figures

Two methods for calculating fractal dimensions, the cover method and the method of gyration radius, are discussed. The cover method is applicable to both tree-type tree patterns and aegagropila-type tree patterns. The method of gyration radius is also applicable to aegagropila-type patterns but those fractal dimensions take slightly different values depending on how the center of the gyration radius is put in the pattern. This method was not very applicable to the three-type tree patterns. The multifractal dimension of tree-type tree patterns is also discussed. The dimensions are calculated by the cover method. The multifractal dimension of the tree-type tree patterns gradually increases from 0.6 to 1.84, in the average, when the moment order increases from -4 to 8, though the dimension generally decreases depending on the moment order