Mollusc shell pigmentation: Cellular automaton simulations and evidence for undecidability

Journal of Theoretical Biology

Volumn 178, Issue 3, 1996, Pages 333-340

  Kusch, Ingo ^a   Markus, Mario ^a  

^a MAX PLANCK INSTITUTE OF MOLECULAR PHYSIOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; MOLLUSC; PATTERN GENERATOR; PERIODICITY; PIGMENTATION; PRIORITY JOURNAL;

EID: 0029875211     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1996.0029     Document Type: Article

References (23)

1. ERMENTROUT, B., CAMPBELL, J. & OSTER, A. (1986). A model for shell patterns based on neural activity. The Veliger 28, 369-388.
2. GIERER, A. & MEINHARDT, H. (1972). A theory of biological pattern formation. Kybernetik 12, 30-39.
3. GUNJI, J. (1990). Pigment colour patterns of molluscs as an autonomous process generated by asynchronous automata. BioSystems 23, 317-334.
4. LI, W., PACKARD, N.H. & LANGTON, C.G. (1990). Transition phenomena in cellular automata rule space. Physica D45, 77-94.
5. MARKUS, M. & HESS, B. (1990a). Isotropic cellular automaton for modelling excitable media. Nature 347, 56-58.
6. MARKUS, M. (1990b). Modelling morphogenetic processes in excitable tissues using novel cellular automata. Biomed. Biochem. Acta 49, 681-696.
7. MARKUS, M. & SCHAEFER, C. (1991). Spatially periodic forcing of spatially periodic oscillators. In: Bifurcation and Chaos (Seydel, R., Schneider, F. W., Küpper, T. & Roger, H., eds) pp. 263-275. Boston: Birkhaeuser.
8. MARKUS, M., NAGY-UNGVARAI, ZS. & HESS, B. (1992). Phototaxis of spiral waves. Science 257, 225-227.
9. MARKUS, M., EMMERICH, H., SCHAEFER, C., ALMEIDA, P. & RIBEIRO, A. (1994a). A binary description of stick-slip processes. In: Fractals and Dynamic Systems in Geosciences (Kruhl, J., ed.) pp. 181-196. Winnipeg: Wuerz.
10. MARKUS, M., KLOSS, G. & KUSCH, I. (1994b). Disordered waves in a homogeneous, motionless excitable medium. Nature 371, 402-404.
11. MEINHARDT, H. (1995). The Algorithmic Beauty of Sea Shells. Heidelberg: Springer.
12. MEINHARDT, H. & KLINGER, M. (1987). A model for pattern formation on the shells of molluscs. J. theor. Biol. 126, 63-89.
13. MEINHARDT, H. & KLINGER, M. (1988). Pattern formation by coupled oscillators: the pigmentation patterns on the shells of molluscs. In: From Chemical to Biological Organisation (Markus, M., Müller, S.C. & Nicolis, G., eds) pp. 98-202. Heidelberg: Springer.
14. MEINHARDT, H. & KLINGER, M. (1991). Schnecken und Muschelschalen. Spektrum der Wissenschaft Aug., 60-69.
15. PLATH, P.J. & SCHWIETERING, J. (1992). Improbable events in deterministically growing patterns. In: Fractal Dynamics and Computer Graphics (Encarnacão, J., Peitgen, O., Sakas, A. & Englert, B., eds). Heidelberg: Springer.
16. SCHEPERS, H. & MARKUS, M. (1992). Two types of performance of an isotropic cellular automaton: stationary (Turing) patterns and spiral waves. Physica A188, 337-343.
17. TURING, A.M. (1952). The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. Lond. B237, 37-72.
18. VARELA, F. (1979). Principles of Biological Autonomy. Amsterdam: North-Holland.
19. VINCENT, J.F.V. (1986). Cellular Automata: a model for the formation of colour patterns in molluscs. J. Moll. Stud. 52, 97-105.
20. WADDINGTON, C.H. & COWE, R.J. (1969). Computer simulations of a molluscan pigmentation pattern. J. theor. Biol. 25, 219-225.
21. WILLMANN, R. (1983). Die Schnecken von Kos. Spektrum der Wissenschaft Feb., 64-76.
22. WOLFRAM, S. (1984). Universality and complexity in cellular automata. Physica 10D, 1-35.
23. WOLFRAM, S. (1986). Theory and Applications of Cellular Automata. Singapore: World Scientific.