Skip to main content
SpringerLink
Log in

Computing by Programmable Particles

  • Chapter
  • First Online:
Distributed Computing by Mobile Entities

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11340))

Abstract

The vision for programmable matter is to realize a physical substance that is scalable, versatile, instantly reconfigurable, safe to handle, and robust to failures. Programmable matter could be deployed in a variety of domain spaces to address a wide gamut of problems, including applications in construction, environmental science, synthetic biology, and space exploration. However, there are considerable engineering and computational challenges that must be overcome before such a system could be implemented. Towards developing efficient algorithms for novel programmable matter behaviors, the amoebot model for self-organizing particle systems and its variant, hybrid programmable matter, provide formal computational frameworks that facilitate rigorous algorithmic research. In this chapter, we discuss distributed algorithms under these models for shape formation, shape recognition, object coating, compression, shortcut bridging, and separation in addition to some underlying algorithmic primitives.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Some papers refer to \(G_{\varDelta }\) as the equilateral triangular grid graph \(G_\text {eqt}\) or the triangular lattice \(\varGamma \).

  2. 2.

    A particle can only write into its own memory in the amoebot model’s publishing-based communication, so no conflicts of concurrent writes to the same memory location are possible.

  3. 3.

    An event occurs with high probability (w.h.p.) if the probability of success is at least \(1 - 1 / n^c\), where \(c > 0\) is a constant; in our setting, n is the number of particles.

  4. 4.

    In [16], the digits are chosen uniformly at random from \([0, r-1]\) where r is a fixed constant. The resulting identifiers are numbers with radix r.

  5. 5.

    For this presentation, we use a simplified scheme that results in a triangle with the seed at its center; the original scheme given in [19, 52] is significantly more complex and results in a triangle with the seed at one vertex.

  6. 6.

    The original publication on “universal” shape formation [20] claimed the algorithm could construct any shape with a constant number of faces. However, Gmyr corrected an oversight in this paper’s analysis in his Ph.D. thesis [29] and, as a result, the class of shapes had to be restricted to sequentially constructible shapes.

  7. 7.

    This definition of configuration connectivity is equivalent to that of system connectivity given in Sect. 2.2.

References

  1. Andrés Arroyo, M., Cannon, S., Daymude, J.J., Randall, D., Richa, A.W.: A stochastic approach to shortcut bridging in programmable matter. Nat. Comput. 17(4), 723–741 (2018)

    Google Scholar 

  2. Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distrib. Comput. 18(4), 235–253 (2006)

    Article  Google Scholar 

  3. Baxter, R.J., Enting, I.G., Tsang, S.K.: Hard-square lattice gas. J. Stat. Phys. 22, 465–489 (1980)

    Article  MathSciNet  Google Scholar 

  4. Blanca, A., Chen, Y., Galvin, D., Randall, D., Tetali, P.: Phase coexistence for the hard-core model on \(\mathbb{Z}^2\). Comb. Probab. Comput. 1–22 (2018). https://www.cambridge.org/core/journals/combinatorics-probability-and-computing/article/phase-coexistence-for-the-hardcore-model-on-2/9B652165B36865C568285FD7A37D8B59

  5. Blum, M., Kozen, D.: On the power of the compass (or, why mazes are easier to search than graphs). In: 19th Annual Symposium on Foundations of Computer Science, SFCS 1978, pp. 132–142 (1978)

    Google Scholar 

  6. Bonato, A., Nowakowski, R.J.: The Game of Cops and Robbers on Graphs. AMS (2011)

    Google Scholar 

  7. Bonifaci, V., Mehlhorn, K., Varma, G.: Physarum can compute shortest paths. J. Theor. Biol. 309, 121–133 (2012)

    Article  MathSciNet  Google Scholar 

  8. Borgs, C., et al.: Torpid mixing of some Monte Carlo Markov chain algorithms in statistical physics. In: Proceedings of the 40th Annual Symposium on Foundations of Computer Science, FOCS 1999, pp. 218–229 (1999)

    Google Scholar 

  9. Camazine, S., Visscher, P.K., Finley, J., Vetter, R.S.: House-hunting by honey bee swarms: collective decisions and individual behaviors. Insectes Soc. 46(4), 348–360 (1999)

    Article  Google Scholar 

  10. Cannon, S., Daymude, J.J., Gokmen, C., Randall, D., Richa, A.W.: Brief announcement: a local stochastic algorithm for separation in heterogeneous self-organizing particle systems. In: Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC 2018, pp. 483–485 (2018). https://arxiv.org/abs/1805.04599

  11. Cannon, S., Daymude, J.J., Randall, D., Richa, A.W.: A Markov chain algorithm for compression in self-organizing particle systems. In: Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, PODC 2016, pp. 279–288 (2016). A significantly updated journal version is in preparation. https://arxiv.org/abs/1603.07991

  12. Chirikjian, G.S.: Kinematics of a metamorphic robotic system. In: Proceedings of the 1994 IEEE International Conference on Robotics and Automation, ICRA 1994, vol. 1, pp. 449–455 (1994)

    Google Scholar 

  13. Das, S.: Mobile agents in distributed computing: network exploration. Bull. Eur. Assoc. Theor. Comput. Sci. 109, 54–69 (2013)

    MATH  Google Scholar 

  14. Daymude, J.J., et al.: On the runtime of universal coating for programmable matter. Natural Comput. 17(1), 81–96 (2018)

    Article  MathSciNet  Google Scholar 

  15. Daymude, J.J., Gmyr, R., Hinnenthal, K., Kostitsyna, I., Scheideler, C., Richa, A.W.: Convex hull formation for programmable matter (2018). https://arxiv.org/abs/1805.06149

  16. Daymude, J.J., Gmyr, R., Richa, A.W., Scheideler, C., Strothmann, T.: Improved leader election for self-organizing programmable matter. In: Fernández Anta, A., Jurdzinski, T., Mosteiro, M.A., Zhang, Y. (eds.) ALGOSENSORS 2017. LNCS, vol. 10718, pp. 127–140. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-72751-6_10

    Chapter  Google Scholar 

  17. Daymude, J.J., Richa, A.W., Scheideler, C.: The amoebot model (2018). https://sops.engineering.asu.edu/sops/amoebot

  18. Derakhshandeh, Z., Dolev, S., Gmyr, R., Richa, A.W., Scheideler, C., Strothmann, T.: Brief announcement: amoebot - a new model for programmable matter. In: Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2014, pp. 220–222 (2014)

    Google Scholar 

  19. Derakhshandeh, Z., Gmyr, R., Richa, A.W., Scheideler, C., Strothmann, T.: An algorithmic framework for shape formation problems in self-organizing particle systems. In: Proceedings of the Second Annual International Conference on Nanoscale Computing and Communication, NANOCOM 2015, pp. 21:1–21:2 (2015)

    Google Scholar 

  20. Derakhshandeh, Z., Gmyr, R., Richa, A.W., Scheideler, C., Strothmann, T.: Universal shape formation for programmable matter. In: Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2016, pp. 289–299 (2016)

    Google Scholar 

  21. Derakhshandeh, Z., Gmyr, R., Richa, A.W., Scheideler, C., Strothmann, T.: Universal coating for programmable matter. Theor. Comput. Sci. 671, 56–68 (2017)

    Article  MathSciNet  Google Scholar 

  22. Derakhshandeh, Z., Gmyr, R., Strothmann, T., Bazzi, R., Richa, A.W., Scheideler, C.: Leader election and shape formation with self-organizing programmable matter. In: Phillips, A., Yin, P. (eds.) DNA 2015. LNCS, vol. 9211, pp. 117–132. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21999-8_8

    Chapter  MATH  Google Scholar 

  23. Di Luna, G.A., Flocchini, P., Santoro, N., Viglietta, G., Yamauchi, Y.: Shape formation by programmable particles. In: 21st International Conference on Principles of Distributed Systems, OPODIS 2017, vol. 95, pp. 31:1–31:16 (2018)

    Google Scholar 

  24. Di Luna, G.A., Flocchini, P., Prencipe, G., Santoro, N., Viglietta, G.: Line recovery by programmable particles. In: Proceedings of the 19th International Conference on Distributed Computing and Networking, ICDCN 2018, pp. 4:1–4:10 (2018)

    Google Scholar 

  25. Dolev, S., Gmyr, R., Richa, A.W., Scheideler, C.: Ameba-inspired self-organizing particle systems (2013). Workshop paper at Biological Distributed Algorithms (BDA) (2013). https://arxiv.org/abs/1307.4259

  26. Doty, D.: Theory of algorithmic self-assembly. Commun. ACM 55(12), 78–88 (2012)

    Article  Google Scholar 

  27. Feller, W.: An Introduction to Probability Theory and Its Applications, vol. 1. Wiley, New York (1968)

    MATH  Google Scholar 

  28. Fomin, F.V., Thilikos, D.M.: An annotated bibliography on guaranteed graph searching. Theor. Comput. Sci. 399(3), 236–245 (2008)

    Article  MathSciNet  Google Scholar 

  29. Gmyr, R.: Distributed algorithms for overlay networks and programmable matter. Ph.D. thesis, Paderborn University (2017)

    Google Scholar 

  30. Gmyr, R., Hinnenthal, K., Kostitsyna, I., Kuhn, F., Rudolph, D., Scheideler, C.: Shape recognition by a finite automaton robot. In: 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018, pp. 52:1–52:15 (2018)

    Google Scholar 

  31. Gmyr, R., et al.: Forming tile shapes with simple robots. In: DNA Computing and Molecular Programming. DNA24, pp. 122–138 (2018)

    Google Scholar 

  32. Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1), 97–109 (1970)

    Article  MathSciNet  Google Scholar 

  33. Hoffmann, F.: One pebble does not suffice to search plane labyrinths. In: Gécseg, F. (ed.) FCT 1981. LNCS, vol. 117, pp. 433–444. Springer, Heidelberg (1981). https://doi.org/10.1007/3-540-10854-8_47

    Chapter  Google Scholar 

  34. Jeanson, R., et al.: Self-organized aggregation in cockroaches. Anim. Behav. 69(1), 169–180 (2005)

    Article  Google Scholar 

  35. Lund, K., et al.: Molecular robots guided by prescriptive landscapes. Nature 465(7295), 206–210 (2010)

    Article  Google Scholar 

  36. Lynch, N.: Distributed Algorithms. Morgan Kauffman, Burlington (1996)

    MATH  Google Scholar 

  37. Miracle, S., Randall, D., Streib, A.P.: Clustering in interfering binary mixtures. In: Goldberg, L.A., Jansen, K., Ravi, R., Rolim, J.D.P. (eds.) APPROX/RANDOM -2011. LNCS, vol. 6845, pp. 652–663. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22935-0_55

    Chapter  Google Scholar 

  38. Mlot, N.J., Tovey, C.A., Hu, D.L.: Fire ants self-assemble into waterproof rafts to survive floods. Proc. Natl Acad. Sci. 108(19), 7669–7673 (2011)

    Article  Google Scholar 

  39. Omabegho, T., Sha, R., Seeman, N.C.: A bipedal DNA Brownian motor with coordinated legs. Science 324(5923), 67–71 (2009)

    Article  Google Scholar 

  40. Patitz, M.J.: An introduction to tile-based self-assembly and a survey of recent results. Natural Comput. 13(2), 195–224 (2014)

    Article  MathSciNet  Google Scholar 

  41. Pelc, A.: Deterministic rendezvous in networks: a comprehensive survey. Networks 59(3), 331–347 (2012)

    Article  MathSciNet  Google Scholar 

  42. Porter, A., Richa, A.: Collaborative computation in self-organizing particle systems. In: Stepney, S., Verlan, S. (eds.) UCNC 2018. LNCS, vol. 10867, pp. 188–203. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-92435-9_14

    Chapter  MATH  Google Scholar 

  43. Reid, C.R., Lutz, M.J., Powell, S., Kao, A.B., Couzin, I.D., Garnier, S.: Army ants dynamically adjust living bridges in response to a cost-benefit trade-off. Proc. Natl Acad. Sci. 112(49), 15113–15118 (2015)

    Article  Google Scholar 

  44. Reid, C.R., Latty, T.: Collective behaviour and swarm intelligence in slime moulds. FEMS Microbiol. Rev. 40(6), 798–806 (2016)

    Article  Google Scholar 

  45. Reif, J.H., Sahu, S.: Autonomous programmable DNA nanorobotic devices using dnazymes. Theor. Comput. Sci. 410, 1428–1439 (2009)

    Article  MathSciNet  Google Scholar 

  46. Restrepo, R., Shin, J., Tetali, P., Vigoda, E., Yang, L.: Improving mixing conditions on the grid for counting and sampling independent sets. Probab. Theory Relat. Fields 156, 75–99 (2013)

    Article  Google Scholar 

  47. Şahin, E.: Swarm robotics: from sources of inspiration to domains of application. In: Şahin, E., Spears, W.M. (eds.) SR 2004. LNCS, vol. 3342, pp. 10–20. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30552-1_2

    Chapter  Google Scholar 

  48. Savoie, W., et al.: Phototactic supersmarticles. Artif. Life Robot. 23(4), 459–468 (2018)

    Article  Google Scholar 

  49. Schelling, T.C.: Models of segregation. Am. Econ. Rev. 59(2), 488–493 (1969)

    Google Scholar 

  50. Schelling, T.C.: Dynamic models of segregation. J. Math. Sociol. 1(2), 143–186 (1971)

    Article  Google Scholar 

  51. Shin, J.S., Pierce, N.A.: A synthetic DNA walker for molecular transport. J. Am. Chem. Soc. 126(35), 10834–10835 (2004)

    Article  Google Scholar 

  52. Strothmann, T.F.: Self-* algorithms for distributed systems: programmable matter & overlay networks. Ph.D. thesis, Paderborn University (2017)

    Google Scholar 

  53. Thubagere, A.J., et al.: A cargo-sorting DNA robot. Science 357(6356), eaan6558 (2017)

    Article  Google Scholar 

  54. Toffoli, T., Margolus, N.: Programmable matter: concepts and realization. Phys. D: Nonlinear Phenom. 47(1), 263–272 (1991)

    Article  MathSciNet  Google Scholar 

  55. Vinković, D., Kirman, A.: A physical analogue of the Schelling model. Proc. Natl Acad. Sci. 103(51), 19261–19265 (2006)

    Article  Google Scholar 

  56. Walter, J.E., Tsai, E.M., Amato, N.M.: Algorithms for fast concurrent reconfiguration of hexagonal metamorphic robots. IEEE Trans. Robot. 21(4), 621–631 (2005)

    Article  Google Scholar 

  57. Wickham, S.F., et al.: A DNA-based molecular motor that can navigate a network of tracks. Nat. Nanotechnol. 7(3), 169–173 (2012)

    Article  Google Scholar 

  58. Woods, D., Chen, H.L., Goodfriend, S., Dabby, N., Winfree, E., Yin, P.: Active self-assembly of algorithmic shapes and patterns in polylogarithmic time. In: Proceedings of the 4th Conference on Innovations in Theoretical Computer Science. pp. 353–354 (2013)

    Google Scholar 

  59. Yim, M., et al.: Modular self-reconfigurable robot systems [grand challenges of robotics]. IEEE Robotics Automation Magazine 14(1), 43–52 (2007)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

Our warmest gratitude belongs to all of our wonderful collaborators, both past and present, without whom this research would not have been possible. We would like to thank Robert Gmyr, Thim Strothmann, and Zahra Derakhshandeh for their trailblazing work on self-organizing particle systems during their Ph.D. studies. We would especially like to thank Robert for letting us use materials from his Ph.D. thesis for this chapter (in particular, his excellent images). To Dana Randall and Sarah Cannon, thank you for leading us into a new paradigm by showing us just how much one can do with a whole lot of randomness. To Irina Kostitsyna and Dorian Rudolph, thank you for all your work in developing hybrid programmable matter. Finally, to our undergraduate research assistants, especially Alexandra Porter: thank you for your enthusiasm, energy, and effort.

Author information

Authors and Affiliations

  1. Computer Science, CIDSE, Arizona State University, Tempe, AZ, USA

    Joshua J. Daymude & Andréa W. Richa

  2. Department of Computer Science, Paderborn University, Paderborn, Germany

    Kristian Hinnenthal & Christian Scheideler

Authors
  1. Joshua J. Daymude
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kristian Hinnenthal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andréa W. Richa
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Christian Scheideler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joshua J. Daymude .

Editor information

Editors and Affiliations

  1. University of Ottawa, Ottawa, ON, Canada

    Paola Flocchini

  2. University of Pisa, Pisa, Italy

    Giuseppe Prencipe

  3. Carleton University, Ottawa, ON, Canada

    Nicola Santoro

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Daymude, J.J., Hinnenthal, K., Richa, A.W., Scheideler, C. (2019). Computing by Programmable Particles. In: Flocchini, P., Prencipe, G., Santoro, N. (eds) Distributed Computing by Mobile Entities. Lecture Notes in Computer Science(), vol 11340. Springer, Cham. https://doi.org/10.1007/978-3-030-11072-7_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-11072-7_22

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11071-0

  • Online ISBN: 978-3-030-11072-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation