Algorithm 3.

Model 2. The algorithm is embedded in Alg. 1, line 7. Parameter: branching probability $p_{\mathit{ba}}$, resource consumption R, elongation speed v, weights $w_{1,2,3}$, external gradient $\mathrm{\nabla }\varphi$, resource threshold $r_{min}$, start resource $r_0$Agent Attributes: resource r , if agent is tip s (boolean), start point ${\mathbf{x}}_s$, end point ${\mathbf{x}}_e$, length l.