Marangoni Flow Driven Maze Solving

  • Kohta Suzuno
  • Daishin Ueyama
  • Michal Branicki
  • Rita Tóth
  • Artur Braun
  • István LagziEmail author
Part of the Emergence, Complexity and Computation book series (ECC, volume 23)


Algorithmic approaches to maze solving problems and finding shortest paths are generally NP-hard (Non-deterministic Polynomial-time hard) and thus, at best, computationally expensive. Unconventional computational methods, which often utilize non-local information about the geometry at hand, provide an alternative to solving such problems much more efficiently. In the past few decades several chemical, physical and other methods have been proposed to tackle this issue. In this chapter we discuss a novel chemical method for maze solving which relies on the Marangoni flow induced by a surface tension gradient due to a pH gradient imposed between the entrance and exit of the maze. The solutions of the maze problem are revealed by paths of a passive dye which is transported on the surface of the liquid in the direction of the acidic area, which is chosen to be the exit of the maze. The shortest path is visualized first, as the Marangoni flow advecting the dye particles is the most intense along the shortest path. The longer paths, which also solve the maze, emerge subsequently as they are associated with weaker branches of the chemically-induced Marangoni flow which is key to the proposed method.


Surface Tension Short Path Solution Path Surface Tension Gradient Fatty Acid Molecule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Authors acknowledge the financial support of the Hungarian Scientific Research Fund (OTKA K104666). A.B. is grateful for financial support from the Swiss National Science Foundation project no\(^{\circ }\) #200021-137868. R. T. is grateful for financial support from the Swiss National Science Foundation Marie Heim Vögtlin Fellowship No. PMPDP2-139689/1. K.S., D.U. and I.L. gratefully acknowledge the financial support of the National Research, Development and Innovation Office of Hungary (TÉT_12_JP-1-2014-0005).


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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Kohta Suzuno
    • 1
  • Daishin Ueyama
    • 1
  • Michal Branicki
    • 2
  • Rita Tóth
    • 3
  • Artur Braun
    • 3
  • István Lagzi
    • 4
    Email author
  1. 1.Graduate School of Advanced Mathematical SciencesMeiji UniversityTokyoJapan
  2. 2.School of MathematicsUniversity of EdinburghEdinburghUK
  3. 3.Laboratory for High Performance CeramicsEmpa, Swiss Federal Laboratories for Materials Science and TechnologyDübendorfSwitzerland
  4. 4.Department of PhysicsBudapest University of Technology and EconomicsBudapestHungary

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