Computing by Programmable Particles

  • Joshua J. DaymudeEmail author
  • Kristian Hinnenthal
  • Andréa W. Richa
  • Christian Scheideler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11340)


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.


Programmable matter Self-organizing particle systems Distributed algorithms 



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.


  1. 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. 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)CrossRefGoogle Scholar
  3. 3.
    Baxter, R.J., Enting, I.G., Tsang, S.K.: Hard-square lattice gas. J. Stat. Phys. 22, 465–489 (1980)MathSciNetCrossRefGoogle Scholar
  4. 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).
  5. 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. 6.
    Bonato, A., Nowakowski, R.J.: The Game of Cops and Robbers on Graphs. AMS (2011)Google Scholar
  7. 7.
    Bonifaci, V., Mehlhorn, K., Varma, G.: Physarum can compute shortest paths. J. Theor. Biol. 309, 121–133 (2012)MathSciNetCrossRefGoogle Scholar
  8. 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. 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)CrossRefGoogle Scholar
  10. 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).
  11. 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.
  12. 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. 13.
    Das, S.: Mobile agents in distributed computing: network exploration. Bull. Eur. Assoc. Theor. Comput. Sci. 109, 54–69 (2013)zbMATHGoogle Scholar
  14. 14.
    Daymude, J.J., et al.: On the runtime of universal coating for programmable matter. Natural Comput. 17(1), 81–96 (2018)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Daymude, J.J., Gmyr, R., Hinnenthal, K., Kostitsyna, I., Scheideler, C., Richa, A.W.: Convex hull formation for programmable matter (2018).
  16. 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). Scholar
  17. 17.
    Daymude, J.J., Richa, A.W., Scheideler, C.: The amoebot model (2018).
  18. 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. 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. 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. 21.
    Derakhshandeh, Z., Gmyr, R., Richa, A.W., Scheideler, C., Strothmann, T.: Universal coating for programmable matter. Theor. Comput. Sci. 671, 56–68 (2017)MathSciNetCrossRefGoogle Scholar
  22. 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). Scholar
  23. 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. 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. 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).
  26. 26.
    Doty, D.: Theory of algorithmic self-assembly. Commun. ACM 55(12), 78–88 (2012)CrossRefGoogle Scholar
  27. 27.
    Feller, W.: An Introduction to Probability Theory and Its Applications, vol. 1. Wiley, New York (1968)zbMATHGoogle Scholar
  28. 28.
    Fomin, F.V., Thilikos, D.M.: An annotated bibliography on guaranteed graph searching. Theor. Comput. Sci. 399(3), 236–245 (2008)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Gmyr, R.: Distributed algorithms for overlay networks and programmable matter. Ph.D. thesis, Paderborn University (2017)Google Scholar
  30. 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. 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. 32.
    Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1), 97–109 (1970)MathSciNetCrossRefGoogle Scholar
  33. 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). Scholar
  34. 34.
    Jeanson, R., et al.: Self-organized aggregation in cockroaches. Anim. Behav. 69(1), 169–180 (2005)CrossRefGoogle Scholar
  35. 35.
    Lund, K., et al.: Molecular robots guided by prescriptive landscapes. Nature 465(7295), 206–210 (2010)CrossRefGoogle Scholar
  36. 36.
    Lynch, N.: Distributed Algorithms. Morgan Kauffman, Burlington (1996)zbMATHGoogle Scholar
  37. 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). Scholar
  38. 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)CrossRefGoogle Scholar
  39. 39.
    Omabegho, T., Sha, R., Seeman, N.C.: A bipedal DNA Brownian motor with coordinated legs. Science 324(5923), 67–71 (2009)CrossRefGoogle Scholar
  40. 40.
    Patitz, M.J.: An introduction to tile-based self-assembly and a survey of recent results. Natural Comput. 13(2), 195–224 (2014)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Pelc, A.: Deterministic rendezvous in networks: a comprehensive survey. Networks 59(3), 331–347 (2012)MathSciNetCrossRefGoogle Scholar
  42. 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). Scholar
  43. 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)CrossRefGoogle Scholar
  44. 44.
    Reid, C.R., Latty, T.: Collective behaviour and swarm intelligence in slime moulds. FEMS Microbiol. Rev. 40(6), 798–806 (2016)CrossRefGoogle Scholar
  45. 45.
    Reif, J.H., Sahu, S.: Autonomous programmable DNA nanorobotic devices using dnazymes. Theor. Comput. Sci. 410, 1428–1439 (2009)MathSciNetCrossRefGoogle Scholar
  46. 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)CrossRefGoogle Scholar
  47. 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). Scholar
  48. 48.
    Savoie, W., et al.: Phototactic supersmarticles. Artif. Life Robot. 23(4), 459–468 (2018)CrossRefGoogle Scholar
  49. 49.
    Schelling, T.C.: Models of segregation. Am. Econ. Rev. 59(2), 488–493 (1969)Google Scholar
  50. 50.
    Schelling, T.C.: Dynamic models of segregation. J. Math. Sociol. 1(2), 143–186 (1971)CrossRefGoogle Scholar
  51. 51.
    Shin, J.S., Pierce, N.A.: A synthetic DNA walker for molecular transport. J. Am. Chem. Soc. 126(35), 10834–10835 (2004)CrossRefGoogle Scholar
  52. 52.
    Strothmann, T.F.: Self-* algorithms for distributed systems: programmable matter & overlay networks. Ph.D. thesis, Paderborn University (2017)Google Scholar
  53. 53.
    Thubagere, A.J., et al.: A cargo-sorting DNA robot. Science 357(6356), eaan6558 (2017)CrossRefGoogle Scholar
  54. 54.
    Toffoli, T., Margolus, N.: Programmable matter: concepts and realization. Phys. D: Nonlinear Phenom. 47(1), 263–272 (1991)MathSciNetCrossRefGoogle Scholar
  55. 55.
    Vinković, D., Kirman, A.: A physical analogue of the Schelling model. Proc. Natl Acad. Sci. 103(51), 19261–19265 (2006)CrossRefGoogle Scholar
  56. 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)CrossRefGoogle Scholar
  57. 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)CrossRefGoogle Scholar
  58. 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. 59.
    Yim, M., et al.: Modular self-reconfigurable robot systems [grand challenges of robotics]. IEEE Robotics Automation Magazine 14(1), 43–52 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Joshua J. Daymude
    • 1
    Email author
  • Kristian Hinnenthal
    • 2
  • Andréa W. Richa
    • 1
  • Christian Scheideler
    • 2
  1. 1.Computer Science, CIDSEArizona State UniversityTempeUSA
  2. 2.Department of Computer SciencePaderborn UniversityPaderbornGermany

Personalised recommendations