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# Self-organized fractal river networks

## Details

**Authors** A. Rinaldo, I. Rodriguez-Iturbe, R. Rigon, E. Ijjasz-Vasquez, R. L. Bras

**Year** 1993

**Publisher** Physical Review Letters

**Kind of work** article

**Discipline** Hydrology

**Secondary disciplines** Geology

**Applied** false

[Read it at the publisher](https://doi.org/10.1103/PhysRevLett.70.822) 
10.1103/PhysRevLett.70.822

## In authors' words

### Abstract

Optimal channel networks (OCN's) obtained by minimizing the local and global rates of energy expenditure evolve automatically from arbitrary initial conditions to network configurations exhibiting fractal and multifractal statistics indistinguishable from those observed in nature. It is suggested that OCN's are spatial models of self-organized criticality and that natural fractal structures like river networks may arise as a joint consequence of optimality and randomness.

### What they set out to do (purpose)

To test whether the fractal, self-similar branching structure of real river networks can emerge from a simple local optimization principle rather than being externally imposed.

### Who or what was studied (sample)

Computationally simulated channel networks evolved on a lattice, compared against empirical statistics from real river networks.

### How they did it (methods)

Network configurations evolve from random initial states by minimizing local and global rates of energy dissipation; the resulting fractal, multifractal, and branching statistics are compared to those observed in nature.

### What they found (results)

Networks that minimize energy dissipation spontaneously self-organize into hierarchical branching configurations whose fractal and multifractal statistics are indistinguishable from those of real river networks.

## Commentary

### In short

The finding turns on Systems: a whole network's nested branching structure emerges from a local rule governing individual segments, and is not predictable from any single segment alone.

**Patterns it shows** S

**Added** 2026-09-26

**How to cite this** A. Rinaldo, I. Rodriguez-Iturbe, R. Rigon, E. Ijjasz-Vasquez, R. L. Bras (1993). Self-organized fractal river networks. Physical Review Letters.