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# Density-conserving affine continuous cellular automata solving the relaxed density classification problem

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Abstract
The focus of this paper is on the density classification problem in the context of affine continuous cellular automata. Although such cellular automata cannot solve this problem in the classical sense, most density-conserving affine continuous cellular automata with a unit neighborhood radius are valid solutions of a slightly relaxed version of this problem. This result follows from a detailed study of the dynamics of the density-conserving affine continuous cellular automata that we introduce.
Keywords
:cellular automata, density classification, density conservation, RULES, 2-STATE

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## Citation

Chicago
Wolnik, Barbara, Marcin Dembowski, Witold Bołt, Jan Baetens, and Bernard De Baets. 2017. “Density-conserving Affine Continuous Cellular Automata Solving the Relaxed Density Classification Problem.” Journal of Physics A-mathematical and Theoretical 50 (34).
APA
Wolnik, B., Dembowski, M., Bołt, W., Baetens, J., & De Baets, B. (2017). Density-conserving affine continuous cellular automata solving the relaxed density classification problem. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 50(34).
Vancouver
1.
Wolnik B, Dembowski M, Bołt W, Baetens J, De Baets B. Density-conserving affine continuous cellular automata solving the relaxed density classification problem. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2017;50(34).
MLA
Wolnik, Barbara, Marcin Dembowski, Witold Bołt, et al. “Density-conserving Affine Continuous Cellular Automata Solving the Relaxed Density Classification Problem.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 50.34 (2017): n. pag. Print.
```@article{8535682,
abstract     = {The focus of this paper is on the density classification problem in the context of affine continuous cellular automata. Although such cellular automata cannot solve this problem in the classical sense, most density-conserving affine continuous cellular automata with a unit neighborhood radius are valid solutions of a slightly relaxed version of this problem. This result follows from a detailed study of the dynamics of the density-conserving affine continuous cellular automata that we introduce.},
articleno    = {345103},
author       = {Wolnik, Barbara and Dembowski, Marcin and Bo\unmatched{0142}t, Witold and Baetens, Jan and De Baets, Bernard},
issn         = {1751-8113},
journal      = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
language     = {eng},
number       = {34},
pages        = {18},
title        = {Density-conserving affine continuous cellular automata solving the relaxed density classification problem},
url          = {http://dx.doi.org/10.1088/1751-8121/aa7d86},
volume       = {50},
year         = {2017},
}

```
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