Growth of a tree with allocations rules: Part 1 Kinematics

A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some general results are given on the viability tree-like networks that produce an amount of resource based on its amount of leaves while having a maintenance cost for each node. Some analytical studies and numerical surveys of the model in "simple" situations are made. The different outcomes are discussed and possible extensions of the model are then discussed.