Skip to main content
Log in

Computing with planar toppling domino arrangements

  • Published:
Natural Computing Aims and scope Submit manuscript

Abstract

A method for implementing Boolean logic functions using arrangements of toppling dominoes is described. Logic functions are implemented using only lines of dominoes and fork junctions. Using a dual-rail representation for Boolean values, any desired combinational function can be implemented. Circuits constructed using this method have no timing or order constraints on their inputs and require no out-of-plane bridges for passing one line of dominoes over another. Since they are built using toppling dominoes, circuits can be used only once.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Adamatzky A (ed) (2002) Collision-based computing. Springer, London

    MATH  Google Scholar 

  • Dewdney AK (1979) Logic circuits in the plane. ACM SIGACT News 10(3):38–48

    Article  Google Scholar 

  • Fredkin E, Toffoli T (1982) Conservative logic. Int J Theor Phys 21(3):219–253

    Article  MathSciNet  MATH  Google Scholar 

  • Goles E, Margerstern M (1996) Sand piles as a universal computer. Int J Mod Phys C 7(2):113–122

    Article  MATH  Google Scholar 

  • Gorecka J, Gorecki J (2006) Multiargument logical operations performed with excitable chemical medium. J Chem Phys 124(8):084101

    Article  Google Scholar 

  • Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117(4):500–544

    Google Scholar 

  • Moore C (1997) Majority-vote cellular automata, Ising dynamics, and P-completeness. J Stat Phys 88(3–4):795–805

    Article  MATH  Google Scholar 

  • Moore C (2001) Computational complexity in physics. arXiv:cond-mat/0109010v1 [cond-mat.stat-mech]

  • O’Keefe S (2009) Implementation of logical operations on a domino substrate. Int J Unconv Comput 5(2):115–128

    Google Scholar 

  • Qian L, Winfree E (2011) Scaling up digital circuit computation with DNA strand displacement cascades. Science 332(6034):1196–1201

    Article  Google Scholar 

  • Sparsø J, Furber S (2001) Principles of asynchronous circuit design—a systems perspective. Kluwer, Boston

    Google Scholar 

  • Steinbock O, Kettunen P, Showalter K (1996) Chemical wave logic gates. J Phys Chem 100(49):18970–18975

    Article  Google Scholar 

  • Stevens WM (2008) Logic circuits in a system of repelling particles. Int J Unconv Comput 4(1):61–77

    Google Scholar 

  • Stevens WM (2012) Using transition systems to describe and predict the behaviour of structured excitable media. arXiv:1206.3026 [nlin.PS]

  • Stevens WM, Adamatzky A, Jahan I, De Lacy Costello B (2012) Time-dependent wave selection for information processing in excitable media. Phys Rev E 85(6):066129

    Google Scholar 

  • Toth R, Stone C, Adamatzky A, De Lacy Costello B, Bull L (2009) Experimental validation of binary collisions between wave fragments in the photosensitive Belousov–Zhabotinsky reaction. Chaos Soliton Fract 41(4):1605–1615

    Article  Google Scholar 

  • Von Neumann J (1956) Probabilistic logics and the synthesis of reliable organisms from unreliable components. In: Shannon C, McCarthy J (eds) Automata studies. Princeton University Press, Princeton, pp 43–98

    Google Scholar 

  • Wagon S, Pontarelli A, Briggs W, Becker S (2005) The dynamics of falling dominoes. UMAP J 26(1):35–47

    Google Scholar 

  • Zykov VS (2008) Excitable media. Scholarpedia 3(5):1834

    Article  Google Scholar 

Download references

Acknowledgments

Thanks to the anonymous reviewers of this paper for insightful comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to William M. Stevens.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stevens, W.M. Computing with planar toppling domino arrangements. Nat Comput 11, 665–672 (2012). https://doi.org/10.1007/s11047-012-9341-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11047-012-9341-x

Keywords

Navigation