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Glider-based computing in reaction-diffusion hexagonal cellular automata

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  • Adamatzky, Andrew
  • Wuensche, Andrew
  • De Lacy Costello, Benjamin

Abstract

A three-state hexagonal cellular automaton, discovered in [Wuensche A. Glider dynamics in 3-value hexagonal cellular automata: the beehive rule. Int J Unconvention Comput, in press], presents a conceptual discrete model of a reaction-diffusion system with inhibitor and activator reagents. The automaton model of reaction-diffusion exhibits mobile localized patterns (gliders) in its space–time dynamics. We show how to implement the basic computational operations with these mobile localizations, and thus demonstrate collision-based logical universality of the hexagonal reaction-diffusion cellular automaton.

Suggested Citation

  • Adamatzky, Andrew & Wuensche, Andrew & De Lacy Costello, Benjamin, 2006. "Glider-based computing in reaction-diffusion hexagonal cellular automata," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 287-295.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:2:p:287-295
    DOI: 10.1016/j.chaos.2005.03.048
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    References listed on IDEAS

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    1. De Lacy Costello, Benjamin & Adamatzky, Andrew, 2005. "Experimental implementation of collision-based gates in Belousov–Zhabotinsky medium," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 535-544.
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    Cited by:

    1. Aditya Tafta Nugraha & Ben J Waterson & Simon P Blainey & Frederick J Nash, 2021. "On the consistency of urban cellular automata models based on hexagonal and square cells," Environment and Planning B, , vol. 48(4), pages 845-860, May.
    2. Zhang, Liang & Adamatzky, Andrew, 2009. "Collision-based implementation of a two-bit adder in excitable cellular automaton," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1191-1200.
    3. Ko, Jing-Yuan & Hung, Yao-Chen & Ho, Ming-Chung & Jiang, I-Min, 2008. "Chaotic behavior in the disorder cellular automata," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 934-939.
    4. Xu, Junkang & Li, Erlin & Chen, Fangyue & Jin, Weifeng, 2018. "Chaotic properties of elementary cellular automata with majority memory," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 84-95.
    5. Adamatzky, Andrew, 2009. "Localizations in cellular automata with mutualistic excitation rules," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 981-1003.

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