Progress has been made in developing manufacturing technologies which enable the fabrication of artificial vascular networks for tissue cultivation. However, those networks are rudimentary designed with respect to their geometry. This restricts long-term biological functionality of vascular cells which depends on geometry-related fluid mechanical stimuli and the avoidance of vessel occlusion. In the present work, a bioinspired geometry optimization for branchings in artificial vascular networks has been conducted. The analysis could be simplified by exploiting self-similarity properties of the system. Design rules in the form of two geometrical parameters, i.e., the branching angle and the radius ratio of the daughter branches, are derived using the wall shear stress as command variable. The numerical values of these parameters are within the range of experimental observations. Those design rules are not only beneficial for tissue engineering applications. Moreover, they can be used as indicators for diagnoses of vascular diseases or for the layout of vascular grafts.