# Quantifying self-organization in cyclic cellular automata

@inproceedings{Shalizi2003QuantifyingSI, title={Quantifying self-organization in cyclic cellular automata}, author={Cosma Rohilla Shalizi and Kristina Lisa Shalizi}, booktitle={SPIE International Symposium on Fluctuations and Noise}, year={2003} }

Cyclic cellular automata (CCA) are models of excitable media. Started from random initial conditions, they produce several different kinds of spatial structure, depending on their control parameters. We introduce new tools from information theory that let us calculate the dynamical information content of spatial random processes. This complexity measure allows us to quantitatively determine the rate of self-organization of these cellular automata, and establish the relationship between…

## 32 Citations

### Phase Lengths in the Cyclic Cellular Automaton

- Computer Science
- 2019

An empirical method is provided for determining phase start and end points and the dependence of CCA phase lengths on k is described, finding that the length of each phase exhibits a distinctive power-law relation with k in a manner independent of lattice size.

### Elastic Dimer Automata : Discrete , Tunable Models for Complex Systems

- Computer Science
- 2012

A simple method for measuring self-organization in elastic dimer automata is presented which is used to aid in an exhaustive search for interesting rules in cellular automata, revealing simple rules for several interesting phenomena including multiple different types of wave phenomena.

### Towards a Formal Understanding of Bateson's Rule: Chromatic Symmetry in Cyclic Boolean Networks and its Relationship to Organism Growth and Cell Differentiation

- BiologyComplex Adaptive Systems
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### Morphogenesis and Growth Driven by Selection of Dynamical Properties

- Biology
- 2017

The focus here is on the relationship between organism homogeneity (or heterogeneity) and the dynamical properties of robustness, adaptivity, and chromatic symmetry, as well as the longterm, system-wide, and dynamical consequences of localized assumptions can be carefully explored.

### Asymptotic behaviour of the one-dimensional ``rock-paper-scissors'' cyclic cellular automaton

- Mathematics
- 2019

The one-dimensional three-state cyclic cellular automaton is a simple spatial model with three states in a cyclic ``rock-paper-scissors'' prey-predator relationship. Starting from a random…

### Self-organisation of evolving agent populations in Digital Ecosystems

- Computer ScienceInt. J. Internet Enterp. Manag.
- 2011

The self-organising behaviour of Digital Ecosystems is investigated and a definition for the diversity is investigated, relative to the selection pressures provided by the user requests, based upon convergence to an equilibrium distribution.

### Entropy-Based Complexity Measure for the Evolution-Based Self-Organisation of Agent Populations

- Computer Science
- 2004

A definition for self-organisation, based on statistical physics, is studied for evolving DBE service populations and an efficiency measure is presented for the organisational complexity present, relative to the maximum possible in the population, which is useful for detecting clustering.

### Optimal Nonlinear Prediction of Random Fields on Networks

- Computer ScienceDMCS
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The problem of optimal, nonlinear prediction of time-varying random fields is considered, showing from an information-theoretic perspective that it is formally identical to the problem of finding minimal local sufficient statistics.

### CCABC: Cyclic Cellular Automata Based Clustering For Energy Conservation in Sensor Networks

- Computer ScienceArXiv
- 2011

The simulation results establish that the cyclic cellular automata based clustering for energy conservation in sensor networks (CCABC) is more reliable than the existing schemes where clustering and CA based energy saving technique is used.

### Self-organised systems: fundamental properties

- Computer Science
- 2006

It is shown that, by overlooking it, the concept of self-organisation is not fulfilled, and two other salient aspects are identified: minimisation of local conflicts produces optimal evolutionarily stable self- Organisation and the hypothesis that complexity variations may distinguish living from non-livingSelf-organised systems.

## References

SHOWING 1-10 OF 33 REFERENCES

### Statistical mechanics of cellular automata

- Computer Science
- 1983

Analysis is given of ''elementary'' cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to p definite rules involving the values of its nearest neighbors.

### Cyclic Cellular Automata in Two Dimensions

- Computer Science
- 1991

Start by randomly populating each site of the two-dimensional integer lattice with any one of N types, labeled 0, 1,... ,N-1 (N ≥ 3). The type ζ(y) at site y can eat the type ζ(x) at neighboring site…

### On the nature and origin of complexity in discrete, homogeneous, locally-interacting systems

- Computer Science
- 1986

This work defines complexity as “logical depth,” a notion based on algorithmic information and computational time complexity, and examines the effects of dissipation, noise, and spatial and other symmetries of the initial conditions and equations of motion on the asymptotic complexity-generating abilities of statistical-mechanical model systems.

### Threshold-range scaling of excitable cellular automata

- Computer Science
- 1991

This paper describes a framework, theoretically based, but relying on extensive interactive computer graphics experimentation, for investigation of the complex dynamics shared by excitable media in a broad spectrum of scientific contexts by focusing on simple mathematical prototypes to obtain a better understanding of the basic organizational principles underlying spatially distributed oscillating systems.

### Causal architecture, complexity and self-organization in time series and cellular automata

- Computer Science
- 2001

This work develops computational mechanics for four increasingly sophisticated types of process—memoryless transducers, time series, transducers with memory, and cellular automata, and proves the optimality and uniqueness of the e-machine's representation of the causal architecture, and gives reliable algorithms for pattern discovery.

### Toward a quantitative theory of self-generated complexity

- Computer Science
- 1986

Quantities are defined operationally which qualify as measures of complexity of patterns arising in physical situations, and are essentially Shannon information needed to specify not individual patterns, but either measure-theoretic or algebraic properties of ensembles of pattern arising ina priori translationally invariant situations.

### Formative Processes. (Book Reviews: Self-Organization in Nonequilibrium Systems. From Dissipative Structures to Order through Fluctuations)

- Chemistry
- 1977

Conservation Equations. Thermodynamics of Irreversible Processes: The Linear Region. Nonlinear Thermodynamics. Systems Involving Chemical Reactions and Diffusion-Stability. Mathematical Tools. Simple…

### Thermodynamically reversible generalization of diffusion limited aggregation.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1999

A lattice gas model of cluster growth via the diffusive aggregation of particles in a closed system obeying a local, deterministic, microscopically reversible dynamics and shows that the relaxation to the maximum entropy state is initially a rapid nonequilibrium process, then subsequently it is a quasistatic process with a well defined temperature.

### Complexity of two-dimensional patterns

- Computer Science
- 2000

A complexity measure based on a mean information gain that does not require knowledge of the “maximal” entropy of the pattern, and at the same time sensitively accounts for the inherent correlations in the system.

### Turbulent Motion and the Structure of Chaos: A New Approach to the Statistical Theory of Open Systems

- Physics
- 1991

I.1. The Criteria of the Relative Degree of Order of the States of Open Systems.- I.2. Connection Between the Statistical and the Dynamic Descriptions of Motions in Macroscopic Open Systems. The…