# Growth of a tree with allocations rules: Part 1 Kinematics

## TL;DR

This paper introduces a non-local model for the growth of tree-like transportation networks, analyzing how resource allocation rules influence network viability, with analytical and numerical insights into different growth outcomes.

## Contribution

It presents a novel non-local model for tree growth based on resource transport and allocation rules, with analytical and numerical analysis of network viability.

## Key findings

- Viability depends on resource allocation and maintenance costs.
- Different growth outcomes are identified through analytical and numerical methods.
- Model extensions are discussed for future research.

## Abstract

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.