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Physical Maze Solvers. All Twelve Prototypes Implement 1961 Lee Algorithm

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Emergent Computation

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 24))

Abstract

We overview experimental laboratory prototypes of maze solvers. We speculate that all maze solvers implement Lee algorithm by first developing a gradient of values showing a distance from any site of the maze to the destination site and then tracing a path from a given source site to the destination site. All prototypes approximate a set of many-source-one-destination paths using resistance, chemical and temporal gradients. They trace a path from a given source site to the destination site using electrical current, fluidic, growth of slime mould, Marangoni flow, crawling of epithelial cells, excitation waves in chemical medium, propagating crystallisation patterns. Some of the prototypes visualise the path using a stream of dye, thermal camera or glow discharge; others require a computer to extract the path from time lapse images of the tracing. We discuss the prototypes in terms of speed, costs and durability of the path visualisation.

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Notes

  1. 1.

    See http://cyberneticzoo.com/mazesolvers/.

References

  1. Abelson, H., Di Sessa, A.: Turtle Geometry: The Computer as a Medium for Exploring Mathematics. MIT Press (1986)

    Google Scholar 

  2. Adamatzky, A.: Cellular automaton labyrinths and solution finding. Comput. Graph. 21(4), 519–522 (1997)

    Article  Google Scholar 

  3. Adamatzky, A.: Hot ice computer. Phys. Lett. A 374(2), 264–271 (2009)

    Article  Google Scholar 

  4. Adamatzky, A.: Slime mold solves maze in one pass, assisted by gradient of chemo-attractants. IEEE Trans. NanoBiosci. 11(2), 131–134 (2012)

    Article  Google Scholar 

  5. Adamatzky, A.: Towards plant wires. Biosystems 122, 1–6 (2014)

    Article  MathSciNet  Google Scholar 

  6. Adamatzky, A., de Lacy Costello, B.: Collision-free path planning in the Belousov-Zhabotinsky medium assisted by a cellular automaton. Naturwissenschaften 89(10), 474–478 (2002)

    Google Scholar 

  7. Adamatzky, A., de Lacy Costello, B., Melhuish, C., Ratcliffe, N.: Experimental implementation of mobile robot taxis with onboard Belousov-Zhabotinsky chemical medium. Mater. Sci. Eng. C 24(4), 541–548 (2004)

    Google Scholar 

  8. Adamatzky, A., Teuscher, C. (eds.): From Utopian to Genuine Unconventional Computers. Luniver Press (2006)

    Google Scholar 

  9. Agladze, K., Magome, N., Aliev, R., Yamaguchi, T., Yoshikawa, K.: Finding the optimal path with the aid of chemical wave. Physica D 106(3), 247–254 (1997)

    Article  Google Scholar 

  10. Aleliunas, R., Karp, R.M., Lipton, R.J., Lovasz, L., Rackoff, C.: Random walks, universal traversal sequences, and the complexity of maze problems. In: FOCS, vol. 79, pp. 218–223 (1979)

    Google Scholar 

  11. Ayrinhac, S.: Electric current solves mazes. Phys. Educ. 49(4), 443–446 (2014)

    Article  Google Scholar 

  12. Babula, M.: Simulated maze solving algorithms through unknown mazes. In: Organizing and Program Committee, p. 13 (2009)

    Google Scholar 

  13. Ban, T., Yamagami, T., Nakata, H., Okano, Y.: pH-dependent motion of self-propelled droplets due to Marangoni effect at neutral pH. Langmuir 29(8), 2554–2561 (2013)

    Google Scholar 

  14. Blum, M., Kozen, D.: On the power of the compass. In: Proceedings of 19th Annual Symposium on Foundations of Computer Science, pp. 132–142 (1978)

    Google Scholar 

  15. Bugmann, G., Taylor, J.G., Denham, M.: Route finding by neural nets. Neural Networks 217–230 (1995)

    Google Scholar 

  16. Čejkova, J., Novak, M., Stepanek, F., Hanczyc, M.: Dynamics of chemotactic droplets in salt concentration gradients. Langmuir 30(40), 11937–11944 (2014)

    Google Scholar 

  17. Connolly, C.I., Burns, J.B., Weiss, R.: Path planning using Laplace’s equation. In: IEEE International Conference on Robotics and Automation. Proceedings, pp. 2102–2106. IEEE (1990)

    Google Scholar 

  18. Dubinov, A.E., Maksimov, A.N., Mironenko, M.S., Pylayev, N.A., Selemir, V.D.: Glow discharge based device for solving mazes. Phys. Plasmas (1994–present) 21(9), 093503 (2014)

    Google Scholar 

  19. Fuerstman, M.J., Deschatelets, P., Kane, R., Schwartz, A., Kenis, P.J.A., Deutch, J.M., Whitesides, G.M.: Solving mazes using microfluidic networks. Langmuir 19(11), 4714–4722 (2003)

    Google Scholar 

  20. Goss, S., Aron, S., Deneubourg, J.-L., Pasteels, J.M.: Self-organized shortcuts in the Argentine ant. Naturwissenschaften 76(12), 579–581 (1989)

    Article  Google Scholar 

  21. Goss, S., Beckers, R., Deneubourg, J.-L., Aron, S., Pasteels, J.M.: How trail laying and trail following can solve foraging problems for ant colonies. In: Behavioural Mechanisms of Food Selection, pp. 661–678. Springer (1990)

    Google Scholar 

  22. Gourtzelidis, P., Tzagarakis, C., Lewis, S.M., Crowe, D.A., Auerbach, E., Jerde, T.A., Uğurbil, K., Georgopoulos, A.P.: Mental maze solving: directional fMRI tuning and population coding in the superior parietal lobule. Exp. Brain Res. 165(3), 273–282 (2005)

    Google Scholar 

  23. Haist, T., Osten, W.: Wave-optical computing based on white-light interferometry. DGaO Proc. (2008)

    Google Scholar 

  24. Huang, L.-D., Wong, M.D.F.: Optical proximity correction: friendly maze routing. In: Proceedings of the 41st Annual Design Automation Conference, pp. 186–191. ACM (2004)

    Google Scholar 

  25. Hwang, Y.K., Ahuja, N.: A potential field approach to path planning. IEEE Trans. Robot. Autom. 8(1), 23–32 (1992)

    Google Scholar 

  26. Kemeny, S.E., Shaw, T.J., Nixon, R.H., Fossum, E.R.: Parallel processor array for high speed path planning. In: Proceedings of IEEE Custom Integrated Circuits Conference, vol. 6, pp. 1–5 (1992)

    Google Scholar 

  27. Khan, G.M., Miller, J.F.: Solving mazes using an artificial developmental neuron. In: ALIFE, pp. 241–248 (2010)

    Google Scholar 

  28. Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Robot. Res. 5(1), 90–98 (1986)

    Article  Google Scholar 

  29. Kolobov, V.I.: Advances in electron kinetics and theory of gas discharges. Phys. Plasmas (1994–present) 20(10), 101610 (2013)

    Google Scholar 

  30. Lagzi, I., Soh, S., Wesson, P.J., Browne, K.P., Grzybowski, B.A.: Maze solving by chemotactic droplets. J. Am. Chem. Soc. 132(4), 1198–1199 (2010)

    Google Scholar 

  31. Lee, C.Y.: An algorithm for path connections and its applications. IRE Trans. Electron. Comput. 3, 346–365 (1961)

    Article  MathSciNet  Google Scholar 

  32. Lovass, P., Branicki, M., Tóth, R., Braun, A., Suzuno, K., Ueyama, D., Lagzi, I.: Maze solving using temperature-induced Marangoni flow. RSC Adv. 5(60), 48563–48568 (2015)

    Article  Google Scholar 

  33. Lumelsky, V.J.: A comparative study on the path length performance of maze-searching and robot motion planning algorithms. IEEE Trans. Robot. Autom. 7(1), 57–66 (1991)

    Google Scholar 

  34. Lumelsky, V.J., Stepanov, A.A.: Path-planning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shape. Algorithmica 2(1–4), 403–430 (1987)

    Google Scholar 

  35. Nair, A., Raghunandan, K., Yaswant, V., Pillai, S.S., Sambandan, S.: Maze solving automatons for self-healing of open interconnects: modular add-on for circuit boards. Appl. Phys. Lett. 106(12), 123103 (2015)

    Google Scholar 

  36. Nakagaki, T., Yamada, H., Toth, A.: Path finding by tube morphogenesis in an amoeboid organism. Biophys. Chem. 92(1), 47–52 (2001)

    Article  Google Scholar 

  37. Narendra, A.: Homing strategies of the Australian desert ant Melophorus bagoti I. Proportional path-integration takes the ant half-way home. J. Exp. Biol. 210(10), 1798–1803 (2007)

    Article  Google Scholar 

  38. Okabayashi, Y., Isoshima, T., Nameda, E., Kim, S.-J., Hara, M.: Two-dimensional nonlinear Fabry-Perot interferometer: an unconventional computing substrate for maze exploration and logic gate operation. Int. J. Nanotechnol. Mol. Comput. (IJNMC) 3(1), 13–23 (2011)

    Article  Google Scholar 

  39. Pavlov, V.V., Voronin, A.N.: The method of potential functions for coding constraints of the external space in an intelligent mobile robot. Sov. Autom. Control 17(6), 45–51 (1984)

    MATH  Google Scholar 

  40. Pershin, Y.V., Di Ventra, M.: Solving mazes with memristors: a massively parallel approach. Phys. Rev. E 84(4), 046703 (2011)

    Google Scholar 

  41. Pimienta, V., Antoine, C.: Self-propulsion on liquid surfaces. Curr. Opin. Colloid Interface Sci. 19(4), 290–299 (2014)

    Article  Google Scholar 

  42. Qin, J., Wheller, A.R.: Maze exploration and learning in C. elegans. Lab Chip 7(2), 186–192 (2007)

    Google Scholar 

  43. Rambidi, N.G., Yakovenchuk, D.: Chemical reaction-diffusion implementation of finding the shortest paths in a labyrinth. Phys. Rev. E 63(2), 026607 (2001)

    Article  Google Scholar 

  44. Reyes, D.R., Ghanem, M.M., Whitesides, G.M., Manz, A.: Glow discharge in microfluidic chips for visible analog computing. Lab Chip 2(2), 113–116 (2002)

    Google Scholar 

  45. Reynolds, A.M., Dutta, T.K., Curtis, R.H.C., Powers, S.J., Gaur, H.S., Kerry, B.R.: Chemotaxis can take plant-parasitic nematodes to the source of a chemo-attractant via the shortest possible routes. J. R. Soc. Interface 8(57), 568–577 (2011)

    Google Scholar 

  46. Ricigliano, V., Chitaman, J., Tong, J., Adamatzky, A., Howarth, D.G.: Plant hairy root cultures as plasmodium modulators of the slime mold emergent computing substrate Physarum polycephalum. Front. Microbiol. 6 (2015)

    Google Scholar 

  47. Rubin, F.: The Lee path connection algorithm. IEEE Trans. Comput. 100(9), 907–914 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  48. Scherber, C., Aranyosi, A.J., Kulemann, B., Thayer, S.P., Toner, M., Iliopoulos, O., Irimia, D.: Epithelial cell guidance by self-generated EGF gradients. Integr. Biol. 4(3), 259–269 (2012)

    Google Scholar 

  49. Shannon, C.E.: Presentation of a maze-solving machine. In: 8th International Conference of the Josiah Macy Jr. Found. (Cybernetics), pp. 173–180 (1951)

    Google Scholar 

  50. Stan, M.R., Burleson, W.P., Connolly, C.I., Grupen, R.A.: Analog VLSI for robot path planning. Analog Integr. Circ. Sig. Process. 6(1), 61–73 (1994)

    Google Scholar 

  51. Steinbock, O., Tóth, Á., Showalter, K.: Navigating complex labyrinths: optimal paths from chemical waves. Science-New York Then Washington-, 868–868 (1995)

    Google Scholar 

  52. Stratton, L.O., Coleman, W.P.: Maze learning and orientation in the fire ant (Solenopsis saevissima). J. Comp. Physiol. Psychol. 83(1), 7 (1973)

    Google Scholar 

  53. Tarassenko, L., Blake, A.: Analogue computation of collision-free paths. In: IEEE International Conference on Robotics and Automation, Proceedings, pp. 540–545. IEEE (1991)

    Google Scholar 

  54. Tarassenko, L., Brownlow, M., Marshall, G., Tombs, J., Murray, A.: Real-time autonomous robot navigation using VLSI neural networks. In: Advances in Neural Information Processing Systems, pp. 422–428 (1991)

    Google Scholar 

  55. Tero, A., Kobayashi, R., Nakagaki, T.: Physarum solver: a biologically inspired method of road-network navigation. Physica A 363(1), 115–119 (2006)

    Article  Google Scholar 

  56. Turner, C.H.: The homing of ants: an experimental study of ant behavior. J. Comp. Neurol. Psychol. 17(5), 367–434 (1907)

    Article  Google Scholar 

  57. Wallace, R.A.: The maze solving computer. In: Proceedings of the 1952 ACM National Meeting (Pittsburgh), pp. 119–125. ACM (1952)

    Google Scholar 

  58. Willardson, D.M.: Analysis of micromouse maze solving algorithm. In: Learning from Data (2001)

    Google Scholar 

  59. Wyard-Scott, L., Meng, Q.-H.M.: A potential maze solving algorithm for a micromouse robot. In: IEEE Pacific Rim Conference on Communications, Computers, and Signal Processing, 1995. Proceedings, pp. 614–618. IEEE (1995)

    Google Scholar 

  60. Yokawa, K., Derrien-Maze, N., Mancuso, S., Baluška, F.: Binary decisions in maize root behavior: Y-maze system as tool for unconventional computation in plants. Int. J. Unconv. Comput. 10 (2014)

    Google Scholar 

  61. Zhang, H.M., Peh, L.S., Wang, Y.H.: Study on flood-fill algorithm used in micromouse solving maze. In: Applied Mechanics and Materials, vol. 599, pp. 1981–1984. Trans Tech Publications (2014)

    Google Scholar 

  62. Zhang, S., Mizutani, A., Srinivasan, M.V.: Maze navigation by honeybees: learning path regularity. Learn. Mem. 7(6), 363–374 (2000)

    Google Scholar 

  63. Zhao, M., Marquez, A.G.: Understanding humans’ strategies in maze solving. arXiv:1307.5713 (2013)

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Adamatzky, A. (2017). Physical Maze Solvers. All Twelve Prototypes Implement 1961 Lee Algorithm. In: Adamatzky, A. (eds) Emergent Computation . Emergence, Complexity and Computation, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-319-46376-6_23

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  • DOI: https://doi.org/10.1007/978-3-319-46376-6_23

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