The space-filling property of the vascular system is quantified by the fractal dimension (D), which falls between two topological integer dimensions. A. A Euclidean three-dimensional space (i.e. a cube) can contain a branching structure (i.e. the vascular system) without this entirely filling its internal space. B. Two-dimensional sectioning of the vascular network makes it possible to identify a variable number of vessels depending on the geometrical complexity of the system at any particular level of sectioning. C. The geometrical complexity of a 2-D section (s
) of the vascular network depends in the number of sectioned vessels and their distribution pattern.