## Complex patterns generated by next nearest neighbors cellular automata (1989)

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Venue: | Computer & Graphics |

Citations: | 3 - 1 self |

### BibTeX

@ARTICLE{Li89complexpatterns,

author = {Wentian Li},

title = {Complex patterns generated by next nearest neighbors cellular automata},

journal = {Computer & Graphics},

year = {1989},

volume = {13},

pages = {531--537}

}

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### Abstract

included Abstract. A greater number of complicated patterns can be produced by cellular automata rules with next nearest neighbors in the updating, than those with only nearest neighbors couplings. Some patterns can be identified as gliders moving on the background, while other rules have more intriguing configurations called “creatures ” which move irregularly on the background. Sometimes, even the distinction between creatures and the background disappear, and the patterns look strikingly similar to those generated by probabilistic rules, even though the rules used are strictly deterministic. The question of how the complicated behaviors of biological systems can be explained in terms of the simple laws of physics motivated Von Neumann and Ulam to propose the use of cellular automaton [1], a fully discretized dynamical system with local couplings. It is indeed found that some specially designed 2-dimensional cellular automata can mimic the least selfreproduction behaviors [2]. Although we lack the general criteria on what types of cellular automata rules can produce what behaviors, it is widely appreciated nowadays that simple rules can lead to complex dynamics [3, 4]. The simplest type of cellular automata are on a 1-dimensional lattice with 2 state values at each site, and with nearest neighbors couplings: a t+1 i = f(ati−1,ati,ati+1) (0.1) where a t i is the state value on site i at time t, and f() is some kind of function, usually in a tabular form, with the state values at previous time step on nearest sites as the variables. These cellular automata are thoroughly studied, and their spatial-temporal patterns can be found in the Appendix

### Citations

560 |
Theory of Self-Reproducing Automata
- Neumann
- 1966
(Show Context)
Citation Context ...ic. The question of how the complicated behaviors of biological systems can be explained in terms of the simple laws of physics motivated Von Neumann and Ulam to propose the use of cellular automaton =-=[1]-=-, a fully discretized dynamical system with local couplings. It is indeed found that some specially designed 2-dimensional cellular automata can mimic the least selfreproduction behaviors [2]. Althoug... |

55 |
Cellular Automata as Models of Complexity
- Wolfram
- 1984
(Show Context)
Citation Context ...aviors [2]. Although we lack the general criteria on what types of cellular automata rules can produce what behaviors, it is widely appreciated nowadays that simple rules can lead to complex dynamics =-=[3, 4]-=-. The simplest type of cellular automata are on a 1-dimensional lattice with 2 state values at each site, and with nearest neighbors couplings: a t+1 i = f(ati−1 ,ati ,ati+1 ) (0.1) where a t i is the... |

34 |
Chaos - Making a New Science. Viking
- Gleick
- 1987
(Show Context)
Citation Context ...aviors [2]. Although we lack the general criteria on what types of cellular automata rules can produce what behaviors, it is widely appreciated nowadays that simple rules can lead to complex dynamics =-=[3, 4]-=-. The simplest type of cellular automata are on a 1-dimensional lattice with 2 state values at each site, and with nearest neighbors couplings: a t+1 i = f(ati−1 ,ati ,ati+1 ) (0.1) where a t i is the... |

30 | Transition phenomena in cellular automata rule space
- Li, Packard, et al.
- 1990
(Show Context)
Citation Context ...nerated tends to have a lot of 0’s which can hardly be an interesting situation. The same argument can be applied to the situation with too many 1’s. A more quantitative study has been carried out in =-=[6, 7]-=-, which shows the optimal filling density in the rule table for interesting rules is not actually 0.5, and this optimal density moves away from 0.5 when more and more neighbors are included in the cou... |

3 |
Self-reproduction in cellular automata. In: Cellular Automata
- Langton
- 1984
(Show Context)
Citation Context ...utomaton [1], a fully discretized dynamical system with local couplings. It is indeed found that some specially designed 2-dimensional cellular automata can mimic the least selfreproduction behaviors =-=[2]-=-. Although we lack the general criteria on what types of cellular automata rules can produce what behaviors, it is widely appreciated nowadays that simple rules can lead to complex dynamics [3, 4]. Th... |

1 |
Pretty pictures generated by two-state five-neighbor cellular automata
- Li
- 1988
(Show Context)
Citation Context ...e table from 0 to 1. (It is rule (195,188,227,146).) Comparing the two patterns, we see little similarities. Some other pictures generated by next nearest neighbors cellular automata are collected in =-=[8]-=-. I saw even more patterns on the computer screen but I didn’t have the chance to print them out. I wish more wonderful “cellular automata arts” to appear in the future. Acknowledgements This paper ha... |