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Lempel-Ziv complexity analysis of one dimensional cellular automata
E Estevez-Rams1, R Lora-Serrano2, C A J Nunes2
1Facultad de Física-Instituto de Ciencias y Tecnología de Materiales (IMRE), University of Havana, San Lazaro y L, CP 10400 La Habana, Cuba.
Chaos (Woodbury, N.Y.)
|January 3, 2016
Summary
The Lempel-Ziv complexity, a measure of string entropy, can now analyze cellular automata. This method reveals spatiotemporal dynamics and computational capabilities of these complex systems.
Area of Science:
- Complexity Science
- Information Theory
- Computational Science
Background:
- The Lempel-Ziv complexity is a metric used to quantify the entropy density of a string.
- It is defined by the number of factors in a string's production factorization.
Purpose of the Study:
- To extend the application of the Lempel-Ziv complexity measure.
- To analyze the spatiotemporal evolution of random initial configurations in cellular automata.
- To investigate information transfer and sensitivity to initial conditions.
Main Methods:
- Utilizing the normalized information distance alongside the Lempel-Ziv complexity.
- Studying information transfer between consecutive time configurations.
- Analyzing sensitivity to perturbed initial conditions in cellular automata.
Main Results:
- The Lempel-Ziv complexity, via normalized information distance, effectively studies cellular automata spatiotemporal dynamics.
- Information transfer and sensitivity to initial conditions were quantitatively assessed.
- Cellular automata rules exhibit diverse behaviors that resist single-class categorization.
Conclusions:
- The Lempel-Ziv complexity offers a powerful tool for understanding cellular automata.
- This approach is particularly suited for evaluating the computational processing capabilities of cellular automata rules.
- The study highlights the nuanced and varied nature of cellular automata rule behaviors.
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