Fast marching to branching morphologies
Many living systems self-organize into tree-like hierarchical branching patterns. How the function of these systems is shaped by their morphology, and whether it reflects optimization of any resource or cost draws a sustained interest. Applications in computational biology and biomimetics require tools to generate branching morphologies across a wide range of feature space. Here we propose a simple framework to build branching structures as converging gradient-descent paths in travel-time maps, computed with fast-marching algorithm over a stochastic speed field, with a structure- dependent feedback on local speed and path targets. We demonstrate the effects of speed field profile, feedback properties and seed density and sampling order on the resulting morphologies and their transport properties. The main utility of the framework is in its simplicity and the ability to generate realistic standalone structures in 2D in 3D, as well as tiling networks resembling astrocyte syncytium in the brain.