Skip to content

README.md

Latest commit

 

History

History
50 lines (36 loc) · 3.25 KB

README.md

File metadata and controls

50 lines (36 loc) · 3.25 KB

Complex-System-Simulation-Project

Using cellular automata to model vegetation patterns in drylands

Team 15 Students: Emma van der Spek, Justus de Bruijn Kops, Lila Wagenaar

Project overview

Many arid and semi-arid regions exhibit large-scale vegetation patterns spanning multiple spatial scales. These patters suggest that ecosystems arise through self-organization rather than fine-tuned environmental conditions.

In this project, we implement and study a two-dimensional cellular automaton (CA) model based on Scanlon et al. (2007). The model uses probabilistic update rules combining local vegetation feedback and a global rainfall-dependent target, and seems to reproduces power-law cluster size distribution.

Our goal is to reproduce the results of Scanlon et al. (2007), as well as exploring the parameter space (rainfall, neighborhood radius, local/global weighting), study sensitivity and robustness of power-law scaling, and analyze percolation behavior.

Research questions

  • What ingredients in the CA model give rise to power-law clustering?
  • How do local and global contributions affect large-scale structure?
  • How sensitive is the power-law behavior to parameter changes?

Hypotheses (maybe to update a little bit?)

  • A combination of short and long-range interaction rules is necessary to generate structured vegetation patterns.
  • There are possibly several types of rules/methods in CA-based models that can give rise to certain behavior, i.e. some states (power-law clustering etc.) can be achieved in several different models.
  • To be able to reproduce the variety and statistics of real-life patterns, there is some probabilistic component necessary in the CA model.

Model description

In our model, each cell represents vegetation presence/absence. At every time step, cells update probabilitically based on:

  • A distance-weighted local vegetation density
  • A global rainfall-dependent target fraction

The model is implemented in src/CA_model.py with analysis tools in src/analysis.py and data management utilities in src/utils.py

Analysis & Experiments

The project includes:

  • Cluster size distribution analysis, including truncated power-law fitting
  • Percolation probability analysis, measuring connectivity across the grid
  • Parameter sweeps over rainall( true_frac ), neighborhood size (" k, M ), and local/global weight ( phi )
  • Visualization of equilibrium states for different parameter settings These analysis are primarily conducted in Jupyter notebookds in the notebooks/ directory, using saved simulation data to avoir recomputation.

Testing & Validation

To ensure correctness and robustness of the implementation, we included multiple assert statements and internal checks, in the core CA logic.

References

[1] Scanlon TM, Caylor KK, Levin SA, Rodriguez-Iturbe I. Positive feedbacks promote power-law clustering of Kalahari vegetation. Nature. 2007. [2] Pascual M, Guichard F. Criticality and disturbance in spatial ecological systems. Trends Ecol. Evol. 2005.

Notes

The simulations were computationally expensive; saved .npy files allow analysis without rerunning model. For some models, faster simulations are also available, with different parameters, but less precision.