Single Bridge Formation in Self-Organizing Particle Systems

Authors Shunhao Oh , Joseph L. Briones , Jacob Calvert , Noah Egan, Dana Randall , Andréa W. Richa



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Author Details

Shunhao Oh
  • School of Computer Science, Georgia Institute of Technology, Atlanta, GA, USA
Joseph L. Briones
  • School of Computing and Augmented Intelligence, Arizona State University, Tempe, AZ, USA
Jacob Calvert
  • School of Computer Science, Georgia Institute of Technology, Atlanta, GA, USA
Noah Egan
  • School of Computer Science, Georgia Institute of Technology, Atlanta, GA, USA
Dana Randall
  • School of Computer Science, Georgia Institute of Technology, Atlanta, GA, USA
Andréa W. Richa
  • School of Computing and Augmented Intelligence, Arizona State University, Tempe, AZ, USA

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Shunhao Oh, Joseph L. Briones, Jacob Calvert, Noah Egan, Dana Randall, and Andréa W. Richa. Single Bridge Formation in Self-Organizing Particle Systems. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 34:1-34:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.DISC.2024.34

Abstract

Local interactions of uncoordinated individuals produce the collective behaviors of many biological systems, inspiring much of the current research in programmable matter. A striking example is the spontaneous assembly of fire ants into "bridges" comprising their own bodies to traverse obstacles and reach sources of food. Experiments and simulations suggest that, remarkably, these ants always form one bridge - instead of multiple, competing bridges - despite a lack of central coordination. We argue that the reliable formation of a single bridge does not require sophistication on behalf of the individuals by provably reproducing this behavior in a self-organizing particle system. We show that the formation of a single bridge by the particles is a statistical inevitability of their preferences to move in a particular direction, such as toward a food source, and their preference for more neighbors. Two parameters, η and β, reflect the strengths of these preferences and determine the Gibbs stationary measure of the corresponding particle system’s Markov chain dynamics. We show that a single bridge almost certainly forms when η and β are sufficiently large. Our proof introduces an auxiliary Markov chain, called an "occupancy chain," that captures only the significant, global changes to the system. Through the occupancy chain, we abstract away information about the motion of individual particles, but we gain a more direct means of analyzing their collective behavior. Such abstractions provide a promising new direction for understanding many other systems of programmable matter.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Self-organizing particle systems
  • programmable matter
  • bridging
  • jump chain

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References

  1. M. Andrés Arroyo, S. Cannon, J.J. Daymude, D. Randall, and A.W. Richa. A stochastic approach to shortcut bridging in programmable matter. Natural Computing, 17(4):723-741, 2018. URL: https://doi.org/10.1007/S11047-018-9714-X.
  2. S. Camazine, K.P. Visscher, J. Finley, and S.R. Vetter. House-hunting by honey bee swarms: Collective decisions and individual behaviors. Insectes Sociaux, 46(4):348-360, 1999. Google Scholar
  3. S. Cannon, J.J. Daymude, C. Gökmen, D. Randall, and A.W. Richa. A local stochastic algorithm for separation in heterogeneous self-organizing particle systems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM), pages 54:1-54:22, 2019. Google Scholar
  4. S. Cannon, J.J. Daymude, D. Randall, and A.W. Richa. A Markov chain algorithm for compression in self-organizing particle systems. In Proceedings of the ACM Symposium on Principles of Distributed Computing (PODC), pages 279-288, 2016. Google Scholar
  5. J. Daudelin, G. Jing, T. Tosun, M. Yim, H. Kress-Gazit, and M. Campbell. An integrated system for perception-driven autonomy with modular robots. Science Robotics, 3(23):eaat4983, 2018. URL: https://doi.org/10.1126/scirobotics.aat4983.
  6. J.J. Daymude, A.W. Richa, and C. Scheideler. The canonical amoebot model: Algorithms and concurrency control. CoRR, abs/2105.02420, 2021. URL: https://arxiv.org/abs/2105.02420.
  7. Z. Derakhshandeh, S. Dolev, R. Gmyr, A.W. Richa, C. Scheideler, and T. Strothmann. Brief announcement: Amoebot - a new model for programmable matter. In Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 220-222, 2014. Google Scholar
  8. R.L. Dobrushin, R. Kotecky, and S.B. Shlosman. The Wulff Construction: a Global Shape from Local Interactions. American Mathematical Society, Providence, 1992. Google Scholar
  9. S. Greenberg, D. Randall, and A.P. Streib. Sampling biased monotonic surfaces usijng exponential metrics. Combinatorics, Probability and Computing, 29:672-697, 2020. URL: https://doi.org/10.1017/S0963548320000188.
  10. R. Jeanson, C. Rivault, J.L. Deneubourg, S. Blanco, R. Fournier, C. Jost, and G. Theraulaz. Self-organized aggregation in cockroaches. Animal Behaviour, 69(1):169-180, 2005. Google Scholar
  11. E. Karzbrun, A.M. Tayar, V. Noireaux, and R.H. Bar-Ziv. Programmable on-chip DNA compartments as artificial cells. Science, 345(6198):829-832, 2014. URL: https://doi.org/10.1126/science.1255550.
  12. S. Li, B. Dutta, S. Cannon, J.J. Daymude, R. Avinery, E. Aydin, A.W. Richa, D.I. Goldman, and D. Randall. Programming active cohesive granular matter with mechanically induced phase changes. Science Advances, 7(17):eabe8494, 2021. URL: https://doi.org/10.1126/sciadv.abe8494.
  13. A. Lioni, C. Sauwens, G. Theraulaz, and J.-L. Deneubourg. Chain formation in Oecophylla longinoda. Journal of Insect Behavior, 14(5):679-696, 2001. Google Scholar
  14. N. Madras and D. Randall. Markov chain decomposition for convergence rate analysis. Annals of Applied Probability, 12(2):581-606, 2002. Google Scholar
  15. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller. Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21:1087-1092, 1953. Google Scholar
  16. N.J. Mlot, C.A. Tovey, and D.L. Hu. Fire ants self-assemble into waterproof rafts to survive floods. Proceedings of the National Academy of Sciences, 108(19):7669-7673, 2011. Google Scholar
  17. S. Oh, J.L. Briones, J. Calvert, N. Egan, D. Randall, and A.W. Richa. Single bridge formation in self-organizing particle systems. ArXiv preprint http://www.arxiv.org/abs/2408.10830, 2024. Google Scholar
  18. N.T. Ouellette and D.M. Gordon. Goals and limitations of modeling collective behavior in biological systems. Frontiers in Physics, 9, 2021. URL: https://doi.org/10.3389/fphy.2021.687823.
  19. C.R. Reid, M.J. Lutz, S. Powell, A.B. Kao, I.D. Couzin, and S. Garnier. Army ants dynamically adjust living bridges in response to a cost-benefit trade-off. Proceedings of the National Academy of Sciences, 112(49):15113-15118, 2015. Google Scholar
  20. E. Şahin. Swarm robotics: From sources of inspiration to domains of application. In Swarm Robotics, pages 10-20, 2005. Google Scholar
  21. W. Savoie, S. Cannon, J.J. Daymude, R. Warkentin, S. Li, A.W. Richa, D. Randall, and D. I. Goldman. Phototactic supersmarticles. Artificial Life and Robotics, 23(4):459-468, 2018. URL: https://doi.org/10.1007/S10015-018-0473-7.
  22. B. Wei, M. Dai, and P. Yin. Complex shapes self-assembled from single-stranded DNA tiles. Nature, 485(7400):623-626, 2012. URL: https://doi.org/10.1038/nature11075.
  23. A. Yadav. Stochastic maze solving under the geometric amoebot model. Master’s thesis, Rutgers University, 2021. URL: https://rucore.libraries.rutgers.edu/rutgers-lib/65707/.
  24. H. Zeng, J. Briones, R. Avinery, S. Li, A. Richa, D. Goldman, and T. Sasaki. Fire ant pontoon bridge: a self-assembled dynamic functional structure. In Integrative and Comparative Biology, volume 62, pages S341-S342, 2023. Google Scholar
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