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

@article{Zenil2010CompressionBasedIO, title={Compression-Based Investigation of the Dynamical Properties of Cellular Automata and Other Systems}, author={Hector Zenil}, journal={Complex Syst.}, year={2010}, 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

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## References

SHOWING 1-10 OF 35 REFERENCES

### Kolmogorov complexity and cellular automata classification

- Computer ScienceTheor. Comput. Sci.
- 2001

### Chaotic Properties of the Elementary Cellular Automaton Rule 40 in Wolfram's Class I

- Computer ScienceComplex Syst.
- 2007

It is shown that the dynamical system defined by rule 40 is Devaney chaos on a class of configurations of some particular type and has every periodic point except prime period one, four, or six.

### Time-space pattern and periodic property of elementary cellular automata â€” Sierpinski gasket and partially Sierpinski Gasket â€”

- Computer Science
- 2001

It is logically prove that the time-space patterns of rule 180 are those cut off from theTime-space pattern of rule 90, and then prove the conjecture of Braga et al.

### Complex Chaotic Behavior of a Class of Subshift Cellular Automata

- PhysicsComplex Syst.
- 1993

A new class of cellular auto mata is identified that is characterized by shift like dynamics (simple and complex subshift rules); these cellular automata correspond to t he asymmet ric sit uations and they are chaotic dynamical syst ems.

### Generalized Sub-Shifts in Elementary Cellular Automata: The "Strange Case" of Chaotic Rule 180

- PhysicsTheor. Comput. Sci.
- 1998

### A new kind of science

- Computer Science
- 2002

A New Kind of Science, written and published by Stephen Wolfram, is the outcome of the studies he conducted systematically upon cellular automata, a class of computer model which may be visualized as a set of memory locations, each containing one bit.

### Undecidability of CA Classification Schemes

- Computer ScienceComplex Syst.
- 1988

It is shown that it is undecidable to which class a given cellula r automaton belongs, even when choosing only between the two simp lest classes.