# Compression-Based Investigation of the Dynamical Properties of Cellular Automata and Other Systems

@article{Zenil2009CompressionBasedIO, title={Compression-Based Investigation of the Dynamical Properties of Cellular Automata and Other Systems}, author={Hector Zenil}, journal={Complex Syst.}, year={2009}, volume={19} }

A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the compression-based approach classifies cellular automata (CA) into clusters according to their heuristic behavior, with these clusters showing a correspondence with Wolfram's main classes of CA behavior. A compression based method to estimate a characteristic exponentâ€¦Â

## 77 Citations

### Asymptotic Behavior and ratios of Complexity in Cellular Automata

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Using two different measures, Shannon's block entropy and Kolmogorov complexity, the latter approximated by two different methods (lossless compressibility and block decomposition), the trend of larger complex behavioural fractions is arrived at.

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A graph is computed showing which elementary cellular automata can be emulated by which and it is shown that certain chaotic automata are the only ones that cannot emulate any automata non-trivially.

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### Using compression to find interesting one-dimensional cellular automata

- Computer ScienceComplex & Intelligent Systems
- 2019

A new clustering algorithm has been designed and applied specifically for clustering 1D elementary cellular automata behaviour using the prediction by partial matching (PPM) compression scheme and it was discovered that the new algorithm was more effective in its ability to group interesting and unusual cellular Automata behaviours together.

### Lempel-Ziv complexity analysis of one dimensional cellular automata.

- Computer ScienceChaos
- 2015

It is shown that Lempel-Ziv complexity measure can be extended, by using the normalized information distance, to study the spatiotemporal evolution of random initial configurations under cellular automata rules, and the transfer information from time consecutive configurations is studied.

### A Measure for the Complexity of Elementary Cellular Automata

- Computer ScienceComplex Syst.
- 2019

A new measure for the complexity of elementary cellular automata (ECAs) is presented. This measure is based on the minimization of Boolean functions with three variables that represent the elementaryâ€¦

### On the Dynamic Qualitative Behavior of Universal Computation

- Computer ScienceComplex Syst.
- 2012

The main working hypothesis is that universality is deeply connected to the qualitative behaviour of a system, particularly to its ability to react to external stimulusâ€“as it needs to be programmedâ€“and to its capacity for transmitting this information.

### On the Dynamic Qualitative Behaviour of Universal Computation

- Computer ScienceArXiv
- 2012

The main working hypothesis is that universality is deeply connected to the qualitative behaviour of a system, particularly to its ability to react to external stimulus--as it needs to be programmed--and to its capacity for transmitting information.

### Dynamics and Complexity of Computrons

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It is shown that any finite-state machine can be represented as a computron and two novel set-theoretic concepts are developed: diversity space as a metric space that captures similarity of configurations on a given graph and basin complexity as a measure of complexity of partitions of the diversity space.

### Classification of Complex Systems Based on Transients

- Computer Science, MathematicsArXiv
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A novel classification method applicable to any class of deterministic discrete space and time dynamical systems is presented, which distinguishes between different asymptotic behaviors of a system's average computation time before entering a loop.

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