# Vegetation pattern formation in a sinuous free-scale landscape

## TL;DR

This paper extends Hardenberg's biomass pattern model to non-flat landscapes, introduces a stability analysis, and develops a cellular automata version to simulate realistic vegetation patterns.

## Contribution

It generalizes the original model to varied terrains and presents a cellular automata approach for realistic pattern simulation.

## Key findings

- Stability analysis around fixed points shows predictable vegetation patterns.
- A relationship among dynamical variables at stable points is established.
- Cellular automata reproduce realistic stable spatial vegetation patterns.

## Abstract

The original Hardenberg's model of biomass patterns in arid and semi-arid regions is revisited to extend it to more general non flat regions. It is proposed a technique to study these more generalized (non-flat) regions using both a conservation criterion and a explicit spatial dependent function $\nu (x)$. In this paper a study of dynamical stability around system's fixed points made. Under the idea of predictability via air images a fitted relationship among dynamical variables at stable fixed points is stablished. Also, is presented a discrete version of the model, in the form of Cellular Automata techniques, that allows to neglect the spatial scale and reproduces realistic stable spatial patterns.