Gubachelier: Die Seite wurde neu angelegt: „ == Referenz == Andrienko, Y.A., Brilliantov, N.V., Kurths, J.: Complexity of two-dimensional patterns. Eur. Phys. J. B 15(3), 539–546 (2000) == DOI …“

2016-06-11T15:52:00Z

Die Seite wurde neu angelegt: „ == Referenz == Andrienko, Y.A., Brilliantov, N.V., Kurths, J.: Complexity of two-dimensional patterns. Eur. Phys. J. B 15(3), 539–546 (2000) == DOI …“

Neue Seite

== Referenz ==
Andrienko, Y.A., Brilliantov, N.V., Kurths, J.: [[Complexity of two-dimensional patterns]]. Eur. Phys. J. B 15(3), 539–546 (2000)

== DOI ==
http://dx.doi.org/10.1007/s100510051157

== Abstract ==
To describe quantitatively the complexity of two-dimensional patterns we introduce a complexity measure based on a mean information gain. Two types of patterns are studied: geometric ornaments and patterns arising in random sequential adsorption of discs on a plane (RSA). For the geometric ornaments analytical expressions for entropy and complexity measures are presented, while for the RSA patterns these are calculated numerically. We compare the information-gain complexity measure with some alternative measures and show advantages of the former one, as applied to two-dimensional structures. Namely, this does not require knowledge of the “maximal” entropy of the pattern, and at the same time sensitively accounts for the inherent correlations in the system.

== Extended Abstract ==

== Bibtex ==
@Article{Andrienko2000,
author="Andrienko, Yu.A. and Brilliantov, N.V. and Kurths, J.",
title="Complexity of two-dimensional patterns",
journal="The European Physical Journal B - Condensed Matter and Complex Systems",
year="2000",
volume="15",
number="3",
pages="539--546",
issn="1434-6036",
doi="10.1007/s100510051157",
url="http://dx.doi.org/10.1007/s100510051157 http://de.evo-art.org/index.php?title=Complexity_of_two-dimensional_patterns "
}

== Used References ==
1. A.N. Kolmogorov, Probl. Inf. Transm. 1, 3 (1965)

2. R.Wackerbauer, A. Witt, H. Atmanspacher, J. Kurths, H.
Scheingraber, Chaos, Solitons and Fractals 4, 133 (1994).

3. P. Grassberger, Int. J. Theor. Phys. 25, 907 (1986).

4. A. Neiman, B. Shulgin, V. Anishenko, W. Ebeling, L.
Shimansky-Geier, J. Freund, Phys. Rev. Lett. 76, 4299
(1996).

5. J.P. Crutchfield, K. Yong, Phys. Rev. Lett. 63, 105 (1989).

6. C.H. Bennett, in Complexity, Entropy and the Physics
of Information, edited by W.H. Zurek (Addison-Wesley,
Reading, MA, 1990).

7. D.W. McShea, Biol. Phylos. 6, 303 (1991).

8. H. Atmanspacher, C. Rath, G. Wiedenmann, Physica A
234, 819 (1997).

9. J.S. Shiner, M. Davison, P.T. Landsberg, Phys. Rev. E
59, 1459 (1999); P.T. Landsberg, J.S. Shiner, Phys. Lett.
A 245, 228 (1998).

10. P.D. Feldman, J.P. Crutchfield, Phys. Lett. A 238, 244
(1998).

11. R. Lopez-Ruiz, H.L. Mancini, X. Calbet, Phys. Lett. A
209, 321 (1995).

12. G. Chaitin, J. ACM 13, 547 (1996).

13. X.Z. Tang, E.R. Tracy, Chaos 8, 688 (1998).

14. A. Witt, A. Neiman, J. Kurths, Phys. Rev. E 55, 5050
(1996).

15. J.P. Crutchfield, D.P. Feldman, Phys. Rev. E 55, R1239
(1997); S. Lloyd, H. Pagels, Ann. Phys. (NY) 188, 186
(1988).

16. U. Schwarz, A.O. Benz, J. Kurths, A. Witt, Astron. Astrophys.
277, 215 (1993).

17. A. Witt, J. Kurths, F. Krause, K. Fischer, Geophys. Astrophys.
Fluid Dyn. 77, 77 (1995).

18. P.T. Landsberg, Phys. Lett. A 102, 171 (1984); P.T.
Landsberg, in On Self-Organization, edited by R.K. Misra,
D. Maas, E. Zwierlein (Springer-Verlag, Berlin, 1994).

19. J.S. Shiner, in Self-Organization of Complex Structures:
from Individual to Collective Dynamics, edited by F.
Schweitzer (Gordon and Breach, London, 1996).

20. J. Kurths, A. Voss, P. Saparin, A. Witt, H.J. Kleiner,
N.Wessel, Chaos 5, 88 (1995).

21. P.I. Saparin, W. Gowin, J. Kurths, D. Felsenberg, Phys.
Rev. E 58, 6449 (1998).

22. C.E. Shannon, Bell Syst. Tech. J. 27, 379 (1948). For a
recent review see M.C. Mackey, Rev. Mod. Phys. 61, 981
(1989).

23. Equation (1) is written for the case of discrete states, while
the continuum set of states implies integration over the set
instead of summation; in what follows we deal only with
the discrete states.

24. For simplicity we restrict ourselves to the case when only
the color of the upper neighbor is accounted. One can certainly
take into account the colors of the other neighbors.

25. M.C. Bartelt, V. Privman, Int. J. Mod. Phys. B 5, 2883
(1991); J.W. Evans, Rev. Mod. Phys. 65, 1281 (1993); J.J.
Ramsden, J. Stat. Phys. 79, 491 (1995).

26. G.V. Schulz, Z. Phys. Chem. Abt. B 43, 25 (1939).

27. N.V. Brilliantov, Yu.A. Andrienko, P.L. Krapivsky, J.
Kurths, Phys. Rev. Lett. 76, 4058 (1996); N.V. Brilliantov,
Yu.A. Andrienko, P.L. Krapivsky, Physica A 239, 267
(1997).

28. N.V. Brilliantov, Yu.A. Andrienko, P.L. Krapivsky, J.
Kurths, Phys. Rev. E 58, 3530 (1998).

29. P.L. Krapivsky, J. Stat. Phys. 69, 135 (1992).

30. O. Biham, O. Malcai, D.A. Lidar, D. Avnir, Phys. Rev. E
59, R4713 (1999).

31. B.B. Mandelbrot, The Fractal Geometry of Nature (San
Francisco: Freeman, 1982).

== Links ==

=== Full Text ===

[[internal file]]

=== Sonstige Links ===

Complexity of two-dimensional patterns - Versionsgeschichte

Gubachelier: Die Seite wurde neu angelegt: „ == Referenz == Andrienko, Y.A., Brilliantov, N.V., Kurths, J.: Complexity of two-dimensional patterns. Eur. Phys. J. B 15(3), 539–546 (2000) == DOI …“