# On the optimal form of branching supply and collection networks

## TL;DR

This paper explores the optimal design of branching supply and collection networks, revealing fundamental limits on sink density scaling and implications for biological and geological systems.

## Contribution

It introduces a simple volume minimization argument to determine limits of sink density scaling in branching networks, linking it to biological and geomorphological phenomena.

## Key findings

- Identifies limits to sink density scaling in branching networks
- Links network volume minimization to biological and landscape scaling laws
- Provides insights into organismal metabolism and landscape erosion patterns

## Abstract

For the problem of efficiently supplying material to a spatial region from a single source, we present a simple scaling argument based on branching network volume minimization that identifies limits to the scaling of sink density. We discuss implications for two fundamental and unresolved problems in organismal biology and geomorphology: how basal metabolism scales with body size for homeotherms and the scaling of drainage basin shape on eroding landscapes.