Natural Computing

, Volume 9, Issue 1, pp 219–237 | Cite as

Programmable reconfiguration of Physarum machines



Plasmodium of Physarum polycephalum is a large cell capable of solving graph-theoretic, optimization and computational geometry problems due to its unique foraging behavior. Also the plasmodium is a unique biological substrate that mimics universal storage modification machines, namely the Kolmogorov–Uspensky machine. In the plasmodium implementation of the storage modification machine data are represented by sources of nutrients and memory structure by protoplasmic tubes connecting the sources. In laboratory experiments and simulation we demonstrate how the plasmodium-based storage modification machine can be programmed. We show execution of the following operations with the active zone (where computation occurs): merge two active zones, multiply active zone, translate active zone from one data site to another, direct active zone. Results of the paper bear two-fold value: they provide a basis for programming unconventional devices based on biological substrates and also shed light on behavioral patterns of the plasmodium.


Physarum polycephalum Kolmogorov–Uspensky machine Pattern formation Morphogenesis Graph theory 


  1. Adamatzky A (2007a) Physarum machine: implementation of a Kolmogorov–Uspensky machine on a biological substrate. Parallel Process Lett 17:455–467CrossRefMathSciNetGoogle Scholar
  2. Adamatzky A (2007b) Physarum machines: encapsulating reaction-diffusion to compute spanning tree. Naturwisseschaften 94:975–980CrossRefGoogle Scholar
  3. Adamatzky A (2008a) Growing spanning trees in plasmodium machines. Kybernetes: Int J Syst Cybern 37: 258–264Google Scholar
  4. Adamatzky A (2008b) Developing proximity graphs by Physarum polycephalum: does the plasmodium follow the Toussaint hierarchy? Parallel Process Lett 19:105–127CrossRefMathSciNetGoogle Scholar
  5. Adamatzky A, De Lacy Costello B, Asai T (2005) Reaction-diffusion computers. Elsevier, AmsterdamGoogle Scholar
  6. Adamatzky A, De Lacy Costello B, Shirakawa T (2008) Universal computation with limited resources: Belousov-Zhabotinsky and Physarum computers. Int J Bifurc Chaos 18:2373–2389CrossRefGoogle Scholar
  7. Aono M, Hara M (2007) Amoeba-based nonequilibrium neurocomputer utilizing fluctuations and instability. In: Lecture Notes in Computer Science 4618, p 41Google Scholar
  8. Blass A, Gurevich Y (2003) Algorithms: a quest for absolute definitions. Bull Eur Assoc TCS 81:195–225MathSciNetMATHGoogle Scholar
  9. Jones J (2008, in press) The emergence and dynamical evolution of complex transport networks from simple low-level behaviours. Int J Unconv ComputGoogle Scholar
  10. Knuth DE (1968) The art of computer programming, vol. 1: fundamental algorithms. Addison-Wesley, ReadingMATHGoogle Scholar
  11. Kolmogorov AN (1953) On the concept of algorithm. Uspekhi Mat Nauk 8(4)175–176Google Scholar
  12. Nakagaki T (2001) Smart behavior of true slime mold in a labyrinth. Res Microbiol 152:767–770CrossRefGoogle Scholar
  13. Nakagaki T, Yamada H, Ueda T (1999) Modulation of cellular rhythm and photoavoidance by oscillatory irradiation in the Physarum plasmodium. Biophys Chem 82:23–28CrossRefGoogle Scholar
  14. Nakagakia T, Yamada H, Ueda T (2000) Interaction between cell shape and contraction pattern in the Physarum plasmodium. Biophys Chem 84:195–204CrossRefGoogle Scholar
  15. Nakagaki T, Yamada H, Toth A (2001) Path finding by tube morphogenesis in an amoeboid organism. Biophys Chem 92: 47–52CrossRefGoogle Scholar
  16. Nakagaki T, Kobayashi R, Nishiura Y, Ueda T (2004) Obtaining multiple separate food sources: behavioural intelligence in the Physarum plasmodium. Proc Roy Soc B 271:2305–2310CrossRefGoogle Scholar
  17. Nakagaki T, Makoto I, Ueda, T, Nishiura T, Saigusa T, Tero A, Kobayashi R, Showalter K (2007) Minimum-risk path finding by an adaptive amoebal network. Phys Rev Lett 99:68104CrossRefGoogle Scholar
  18. Schönhage A (1973) Real-time simulation of multi-dimensional Turing machines by storage modification machines. Project MAC Technical Memorandum 37. MITGoogle Scholar
  19. Schönhage A (1980) Storage modification machines. SIAM J. Comput 9:490–508CrossRefMathSciNetMATHGoogle Scholar
  20. Shirakawa T, Gunji Y (2007) Emergence of morphological order in the network formation of Physarum polycephalum. Biophys Chem 128:253–260CrossRefGoogle Scholar
  21. Shirakawa T, Adamatzky A, Gunji Y-P, Miyake Y (2008, submitted) On simultaneous construction of Voronoi diagram and Delaunay triangulation by Physarum polycephalum Google Scholar
  22. Takamatsu A (2007) Mobiligence in an amoeboid cell, plasmodium of Physarum polycephalum. In: Second international symposium on mobilgence. Awaji, Japan, pp 48–51Google Scholar
  23. Tarjan RE (1977) Reference machines require non-linear time to maintain disjoint sets. STAN-CS-77-603, March 1977Google Scholar
  24. Tsuda S, Aono M, Gunji Y (2004) Robust and emergent Physarum logical-computing. BioSystems 73: 45–55CrossRefGoogle Scholar
  25. Uspensky VA (1992) Kolmogorov and mathematical logic. J Symb Logic 57: 385–412CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.University of the West of EnglandBristolUK

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