Developing proximity graphs by physarum polycephalum: Does the plasmodium follow the toussaint hierarchy?

Parallel Processing Letters

Volumn 19, Issue 1, 2009, Pages 105-127

  Adamatzky, Andrew ^a  

^a UNIVERSITY OF THE WEST OF ENGLAND   (United Kingdom)

Author keywords

Natural computation; Parallel computing; Plasmodium; Proximity graphs

Indexed keywords

DELAUNAY TRIANGULATIONS; FORAGING BEHAVIORS; GABRIEL GRAPHS; MINIMAL SPANNING TREES; MINIMUM SPANNING TREES; NATURAL COMPUTATION; NEAREST NEIGHBOURS; PARALLEL COMPUTING; PHYSARUM POLYCEPHALUM; PLASMODIUM; PROXIMITY GRAPHS; RELATIVE NEIGHBORHOOD GRAPHS;

NUTRIENTS; PARALLEL PROCESSING SYSTEMS;

TREES (MATHEMATICS);

EID: 59649100669     PISSN: 01296264     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129626409000109     Document Type: Article

References (35)

1. Adamatzky A. Neural algorithm for constructing minimal spanning tree. Neural Network World, 6 (1991) 335-339.
2. Adamatzky A., De Lacy Costello B., Asai T. Reaction Diffusion Computers (Elsevier, 2005).
3. Adamatzky A. and Tcuscher C. From Utopian to Genuine Unconventional Computers (Luniver Press, 2006).
4. Adamatzky A. Growing spanning trees in Plasmodium machines, Kybernetes: The International Journal of Systems & Cybernetics 37 (2008) 258-264.
5. Adamatzky A., Bull L., De Lacy Costello B., Stepney S., Teuscher C. Unconventional Computing 2007 (Luniver Press, 2007).
6. Adamatzky A. Physarum machine: implementation of a Kolmogorov-Uspensky machine on a biological substrate. Parallel Processing Letters 17 (2007) 455-467.
7. Adamatzky A., De Lacy Costello B., Shirakawa T. Universal computation with limited resources: Belousov-Zhabotinsky and Physarum computers. Int. J. Bifurcation and Chaos (2008), in press.
8. Akl S.G., Inherently parallel geometric computations, Parallel Processing Letters 16 (2006) 19-37.
9. Aono, M., and Gunji, Y.-P., Resolution of infinite-loop in hyperincursive and nonlocal cellular automata: Introduction to slime mold computing. Computing Anticiaptory Systems, AIP Conference Proceedings, 718 (2001) 177-187.
10. Aono, M., and Gunji, Y.-P., Material implementation of hyper-incursive field on slime mold computer. Computing Anticipatory Systems, AIP Conference Proceedings, 718 (2004) 188-203.
11. Burgin M., Inductive Turing Machines, Notices of the Academy of Sciences of the USSR, 270 (1983) 1289-1293.
12. Burgin M., Arithmetic hierarchy and inductive Turing machines, Notices of the Academy of Sciences of the USSR, 1988, 299, No. 3, pp. 530-533.
13. Delaunay B. Sur la sphere vide, Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskikh i Estestvennykh Nauk, 7 (1934) 793-800.
14. 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 (2003) 4714-4722.
15. Gabriel K. R. and R. R. Sokal. A new statistical approach to geographic variation analysis. Systematic Zoology, 18 (1969) 259-278.
16. Jaromczyk J. W. and G. T. Toussaint, Relative neighborhood graphs and their relatives. Proc. IEEE 80 (1992) 1502-1517.
17. Kirkpatrick D. G. and Radke J. D. A framework for computational morphology. In G. Toussaint, editor, Computational Geometry (1985) 217-248.
18. Matula D. W. and Sokal R. R. Properties of Gabriel graphs relevant to geographical variation research and the clustering of points in the same plane. Geographical Analysis 12 (1984) 205-222.
19. Mills J. The nature of the Extended Analog Computer. In: Teuscher C, Nemenman I.M ., and Alexander F. J. (Eds). Physica D. Special Issue: Novel Computing Paradigms: Quo Vadis? (2008), in press.
20. Nakagakia T., Yamada H., Ueda T. Interaction between cell shape and contraction pattern in the Physarum Plasmodium, Biophysical Chemistry 84 (2000) 195-204.
21. Nakagaki T., Yamada H., and Toth A., Maze-solving by an amoeboid organism. Nature 407 (2000) 470-470.
22. Nakagaki T., Smart behavior of true slime mold in a labyrinth. Research in Microbi ology 152 (2001) 767-770.
23. Nakagaki T., Yamada H., and Toth A., Path finding by tube morphogenesis in an amoeboid organism. Biophysical Chemistry 92 (2001) 47-52.
24. Nesetril J., Milkova E., Nesetrilova H., Otakar Boruvka on minimum spanning tree problem, Discrete Mathematics 233 (2001) 3-36.
25. Paterson M. S. and Yao F. F. On nearest-neighbour graphs. Automatica, Languages and Programming (623) 416-426.
26. Preparata F. P. and Shamos M. I. Computational Geometry (Springer-Verlag, 1985).
27. http://www.processing.org/
28. Shirakawa T. And Gunji Y. -P. Computation of Voronoi diagram and collision-free path using the Plasmodium of Physarum polycephalum. Int. J. Unconventional Computing (2008), in press.
29. Shirakawa T., Adamatzky A., Gunji Y.-P., Miyake Y. On simultaneous construction of Voronoi diagram and Delaunay triangulation by Physarum polycephalum (2008), submitted.
30. Takamatsu A. Mobiligence in an amoeboid cell, Plasmodium of Physarum polycephalum 2nd International Symposium on Mobilgence, Awaji, Japan, 2007, 48-51.
31. Toussaint G. T., The relative neighborhood graph of a finite planar set, Pattern Recognition 12 (1980) 261-268.
32. Toussaint G. T., Some unsolved problems on proximity graphs, 1st Workshop on Proximity Graphs, Las Cruces, New Mexico, December, 1989. http://cgm.cs.mcgill.ca/-godfried/publications/openprox.pdf
33. Tsuda, S., Aono, M., and Gunji, Y.-P., Robust and emergent Physarum-computing. BioSystems 73 (2004) 45-55.
34. Tsuda, S., Zauner, K. P. and Gunji, Y. P., Robot control: From silicon circuitry to cells, In: Ijspeert, A. J., Masuzawa, T. and Kusumoto, S., Eds. Biologically Inspired Approaches to Advanced Information Technology, Springer, 2006, 20-32.
35. Urquhart R. B. Algortihms for computation of relative neighborhood graph. Electronics Letters 16 (1980) 556-557.