Natural Computing

, Volume 15, Issue 2, pp 279–295 | Cite as

Physarum in silicon: the Greek motorways study

  • Michail-Antisthenis I. Tsompanas
  • Georgios Ch. SirakoulisEmail author
  • Andrew I. Adamatzky


Physarum polycephalum has repeatedly, during the last decade, demonstrated that has unexpected computing abilities. While the plasmodium of P. polycephalum can effectively solve several geographical described problems, like evaluating human–made transport networks, a disadvantage of a biological computer, like the aforementioned is directly apparent; the great amount of time needed to provide results. Thus, the main focus of this paper is the enhancement of the time efficiency of the biological computer by using conventional computers or even digital circuitry. Cellular automata (CA) as a powerful computational tool has been selected to tackle with these difficulties and a software (Matlab) CA model is used to produce results in shorter time periods. While the duration of a laboratory experiment is occasionally from 3 to 5 days, the CA model, for a specific configuration, needs around 40 s. In order to achieve a further acceleration of the computation, a hardware implementation of the corresponding CA software based model is proposed here, taking full advantage of the CA inherent parallelism, uniformity and the locality of interconnections. Consequently, the digital circuit designed can be used as a massively parallel nature inspired computer for real–time applications. The hardware implementation of the model needs six orders of magnitude less time than the software representation. In this paper, in order to develop a proof of concept and depict the applicability of the proposed hardware oriented CA approach, the topology of Greece is used as an input of the biological computer. The network formed by the in vitro experiments, along with the one designed by the CA model and implemented in hardware are compared with the real motorways and the proximity graphs of the topology.


Unconventional computing Slime mould Cellular automata Hardware Motorway networks Biological computer 


  1. Adamatzky A (1994) Identification Of Cellular Automata. Taylor & Francis Group,  LondonzbMATHGoogle Scholar
  2. Adamatzky A (2007) Physarum machine: implementation of a Kolmogorov-Uspensky machine on a biological substrate. Parallel Processing Letters 17:455–467MathSciNetCrossRefGoogle Scholar
  3. Adamatzky A (2010) Physarum Machines: Making Computers from Slime Mould. World Scientific, SingaporeGoogle Scholar
  4. Adamatzky A, Alonso-Sanz R (2011) Rebuilding Iberian transports with slime mould. Biosystems 105:89–100CrossRefGoogle Scholar
  5. Adamatzky A, Jones J (2010a) Programmable reconfiguration of physarum machines. Natural Computing 9(1):219–237MathSciNetCrossRefzbMATHGoogle Scholar
  6. Adamatzky A, Jones J (2010) Road planning with slime mould: If Physarum built transports it would route M6/M74 through Newcastle. Int J Bifurcation and Chaos 20:3065–3084MathSciNetCrossRefGoogle Scholar
  7. Adamatzky A, Prokopenko M (2012) Slime mould evaluation of Australian transports. Int J Parallel Emergent Distributed Systems 27(4):275–295CrossRefGoogle Scholar
  8. Adamatzky A, Martinez GJ, Chapa-Vergara SV, Asomoza-Palacio R, Stephens CR (2011) Approximating Mexican transports with slime mould. Natural Computing 10:1195–1214MathSciNetCrossRefGoogle Scholar
  9. Aono M, Hirata Y, Hara M, Aihara K (2011) Greedy versus social: resource-competing oscillator network as a model of amoeba-based neurocomputer. Natural Computing 10(4):1219–1244MathSciNetCrossRefzbMATHGoogle Scholar
  10. Dennunzio A, Fats N, Formenti E (2013) Foreword: asynchronous cellular automata and applications. Natural Computing 12(4):537–538MathSciNetCrossRefzbMATHGoogle Scholar
  11. Gabriel KR, Sokal RR (1969) A new statistical approach to geographic variation analysis. Systematic Zoology 18:259–278CrossRefGoogle Scholar
  12. Georgoudas IG, Kyriakos P, Sirakoulis GC, Andreadis IT (2010) An FPGA implemented cellular automaton crowd evacuation model inspired by the electrostatic-induced potential fields. Microprocessors and Microsystems 34(7):285–300CrossRefGoogle Scholar
  13. Gunji YP, Shirakawa T, Niizato T, Haruna T (2008) Minimal model of a cell connecting amoebic motion and adaptive transport networks. Journal of Theoretical Biology 253(4):659–667CrossRefGoogle Scholar
  14. Halbach M, Hoffmann R (2004) Implementing cellular automata in FPGA logic. In: Parallel and Distributed Processing Symposium, 2004. Proceedings. 18th International, IEEE, p 258.Google Scholar
  15. Hellenic Statistical Authority (ELSTAT) (2013)
  16. Houbraken M, Demeyer S, Staessens D, Audenaert P, Colle D, Pickavet M (2013) Fault tolerant network design inspired by physarum polycephalum. Natural Computing 12(2):277–289MathSciNetCrossRefGoogle Scholar
  17. Jaromczyk JW, Toussaint GT (1992) Relative neighborhood graphs and their relatives. Proc IEEE 80:1502–1517CrossRefGoogle Scholar
  18. Jendrsczok J, Ediger P, Hoffmann R (2009) A scalable configurable architecture for the massively parallel gca model. International Journal of Parallel, Emergent and Distributed Systems 24(4):275–291MathSciNetCrossRefzbMATHGoogle Scholar
  19. Jones J (2009) Approximating the behaviours of physarum polycephalum for the construction and minimisation of synthetic transport networks. In: Calude CS, Costa JF, Dershowitz N, Freire E, Rozenberg G (eds) UC, Springer, Lecture Notes in Computer Science, vol 5715, pp 191–208.Google Scholar
  20. Jones J, Adamatzky A (2013) Computation of the travelling salesman problem by a shrinking blob. Natural Computing pp 1–16.Google Scholar
  21. Kalogeiton VS, Papadopoulos DP, Sirakoulis GC (2013) Implementation of a novel physarum-inspired and ca-based single-camera slam method. In: Workshop Unconventional Approaches to Robotics, Automation and Control Inspired by Nature, UARACIN 2013, of IEEE International Conference on Robotics and Automation, ICRA 2013, Karlsruhe, Germany, 6–10 May 2013, IEEE, pp 1–3.Google Scholar
  22. Kalogeropoulos G, Sirakoulis G, Karafyllidis I (2013) Cellular automata on FPGA for real-time urban traffic signals control. The Journal of Supercomputing 65(2):664–681CrossRefGoogle Scholar
  23. Liu L, Song Y, Ma H, Zhang X (2012) Physarum optimization: A biology-inspired algorithm for minimal exposure path problem in wireless sensor networks. In: INFOCOM, 2012 Proceedings IEEE, pp 1296–1304.Google Scholar
  24. Matula DW, Sokal RR (1984) Properties of Gabriel graphs relevant to geographical variation research and the clustering of points in the same plane. Geographical Analysis 12:205–222CrossRefGoogle Scholar
  25. Murtaza S, Hoekstra AG, Shot P (2007) Performance modeling of 2d cellular automata on FPGA. In: Field Programmable Logic and Applications, 2007. FPL 2007. International Conference on, IEEE, pp 74–78.Google Scholar
  26. Nakagaki T, Yamada H, Ueda T (2000) Interaction between cell shape and contraction pattern in the physarum plasmodium. Biophysical Chemistry 84:195–204CrossRefGoogle Scholar
  27. Nakagaki T, Yamada H, Toth A (2001) Path finding by tube morphogenesis in an amoeboid organism. Biophysical Chemistry 92:47–52CrossRefGoogle Scholar
  28. Nesetril J, Milkova E, Nesetrilova H (2001) Otakar Boruvka on minimum spanning tree problem. Discrete Mathematics 233:3–36MathSciNetCrossRefzbMATHGoogle Scholar
  29. Porter R, Frigo J, Conti A, Harvey N, Kenyon G, Gokhale M (2007) A reconfigurable computing framework for multi-scale cellular image processing. Microprocessors and Microsystems 31(8):546–563CrossRefGoogle Scholar
  30. Progias P, Sirakoulis GC (2013) An FPGA processor for modelling wildfire spread. Mathematical and Computer Modeling 57(5–6):1436–1452MathSciNetCrossRefGoogle Scholar
  31. Schumann A, Adamatzky A (2011) Physarum spatial logic. New Mathematics and Natural Computation 07(03):483–498MathSciNetCrossRefzbMATHGoogle Scholar
  32. Shirakawa T, Adamatzky A, Gunji YP, Miyake Y (2009) On simultaneous construction of Voronoi diagram and Delaunay triangulation by Physarum polycephalum. Int J Bifurcation and Chaos 9:3109–3117CrossRefGoogle Scholar
  33. Sirakoulis GC, Karafyllidis I, Thanailakis A, Mardiris V (2001) A methodology for VLSI implementation of cellular automata algorithms using VHDL. Advances in Engineering Software 32:189–202CrossRefzbMATHGoogle Scholar
  34. Sirakoulis GC, Karafyllidis I, Thanailakis A (2003) A CAD system for the construction and VLSI implementation of cellular automata algorithms using VHDL. Microprocessors and Microsystems 27:381–396CrossRefGoogle Scholar
  35. Song Y, Liu L, Ma H (2012) A physarum-inspired algorithm for minimal exposure problem in wireless sensor networks. In: Wireless Communications and Networking Conference (WCNC), 2012 IEEE, pp 2151–2156.Google Scholar
  36. Tero A, Kobayashi R, Nakagaki T (2007) A mathematical model for adaptive transport network in path finding by true slime mold. Journal of Theoretical Biology 244(4):553. doi: 10.1016/j.jtbi.2006.07.015 MathSciNetCrossRefGoogle Scholar
  37. Toffoli T (1984) Cellular automata as an alternative to (rather than an approximation of) differential equations in modeling physics. Physica D: Nonlinear Phenomena 10(1–2):117–127MathSciNetCrossRefzbMATHGoogle Scholar
  38. Toussaint GT (1980) The relative neighborhood graph of a finite planar set. Pattern Recognition 12:261–268MathSciNetCrossRefzbMATHGoogle Scholar
  39. Tsompanas MA, Sirakoulis G, Adamatzky A (2013) Evolving transport networks with cellular automata models inspired by slime mould. IEEE Transactions on Cybernetics p submitted.Google Scholar
  40. Tsompanas MAI, Sirakoulis GC (2012) Modeling and hardware implementation of an amoeba-like cellular automaton. Bioinspiration & Biomimetics 7(036):013Google Scholar
  41. Tsuda S, Aono M, Gunji YP (2004) Robust and emergent physarum logical-computing. Biosystems 73:45–55CrossRefGoogle Scholar
  42. von Neumann J (1966) Theory of Self-reproducing Automata. University of Illinois Press, UrbanaGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Michail-Antisthenis I. Tsompanas
    • 1
  • Georgios Ch. Sirakoulis
    • 1
    Email author
  • Andrew I. Adamatzky
    • 2
  1. 1.Laboratory of Electronics, Department of Electrical and Computer EngineeringDemocritus University of ThraceXanthiGreece
  2. 2.Unconventional Computing CentreUniversity of the West of EnglandBristolUK

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