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cyclic_cellular_automata

by Juan Ignacio Perotti (Submitted: 11/01/2010)

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WHAT IS IT?

This is a cyclic cellular automata (CCA). CCA are caricatures of pattern formation in chemical oscillators and other exitable media.

HOW IT WORKS

This section could explain what rules the agents use to create the overall behavior of the model.

Each site in a square two-dimensional lattice is in one of 4 colors. A cell of color k will change its color to (k+1) mod 4 if there are already T cells of that color in its neighborhood (its 4 nearest neighbors plus its 4 second nearest neighbors). Otherwiaw, the cell retains its current color. All cells update their color in parallel.

HOW TO USE IT

First select a value for T. Then click on "setup". Finally click on "go". Depending in the value assigned to T, different patterns will appear. It is possible to change T during the evolution of the system.

THINGS TO NOTICE

The CCA has three generic forms of long-term behavior, depending on the size of the threshold T. At high thresholds, the CCA forms homogeneous blocks of solid color, wich are completely static (so called fixation behavior). At very low thresholds, the entire lattice eventually oscillates periodically; sometimes the oscillation takes the form of a large spiral waves wich grows to engulf the entire lattice. There is an intermediate range of thresholds where incoherent traveling waves form, propagate for a while, and then disperse (a kind of turbulence).

THINGS TO TRY

Try to start for each value of T from a random position (clicking "setup" before "go").
Then try to switch from one behavior/threshold to another meanwhile running.

EXTENDING THE MODEL

A basic extension is to let the system evolve under tresholds higer than T=4.
It can be seen that T=5,6,7,8 lead to the same behavior than T=4.

Also, the model can be extended to incorporate more (less) neighbors that influence each cell. For example nearest neighbors only.

NETLOGO FEATURES

I think that NetLogo is an easy environment where to implement this model. It might also point out places where workarounds were needed because of missing features. It took no more than 44 lines of code to implement the model.

RELATED MODELS

I don't know about related models.

CREDITS AND REFERENCES

I pick this model from the following paper:

Cosma Rohila Shalizi and Kristina Lisa Shalizi,
"Quantifying self-organization in cyclic cellular automata",
Arxiv preprint nlin/0507067, (2005)

Download the paper from here:
http://arxiv.org/abs/nlin/0507067

PROGRAM DETAILS

Author: J. I. Perotti
E-mail: juanpool@gmail.com
Date of this version: November 2010
NetLogo version: 4.1.1

I pick some text of the original paper in order to explain the properties of the model.

Any errors/mistake/missunderstanding are almost certain of my own making.

I apologize for my english.

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