The geometry of optimally collecting networks is investigated. The object is to find the geometry of a network that collects over a terrain, as a consequence of a cost function and constraints. The resulting configurations are called optimally collecting networks. A discrete lattice is used to represent the network and the terrain over which collection takes place. A cost function is set up and optimized configurations are found using Monte Carlo and simulated annealing. The methods can also be applied to collection networks over nonuniform terrains. © 1989 IOP Publication Ltd.