Estimating the Fractal Dimensions of Vascular Networks and Other Branching Structures: Some Words of Caution

Branching patterns are ubiquitous in nature; consequently, over the years many researchers have tried to characterize complexity of their structures. Due hierarchical nature and resemblance fractal trees, they often thought properties; however, non-homogeneity (i.e., lack strict self-similarity) is ignored. In this paper we review examine use box-counting sandbox methods estimate dimensions branching We highlight fact that these rely on an assumption self-similarity not present structures due non-homogeneous nature. Looking at local slopes log–log plots used by reveals problems caused non-homogeneity. Finally, role canopies (endpoints or limit points) estimation dimensions.