Pattern formation by coupled oscillations: The pigmentation patterns on the shells of molluscs. (English) Zbl 0625.92002

Meinhardt, Hans; Klingler, Martin

Mathematical topics in population biology, morphogenesis and neurosciences, Proc. Int. Symp., Kyoto/Jap. 1985, Lect. Notes Biomath. 71, 184-198 (1987).

[For the entire collection see Zbl 0621.00034.]
The overwhelming richness of patterns on shells of molluscs can be explained by relatively simple reaction-diffusion mechanisms. Most of the patterns are explicable by nearest neighbor interactions, in some cases they have to be supplemented by an evenly distributed hormonlike substance. By the computer simulations, one can only uncover the logic behind the pattern formation, not how these principles are biologically realized. A paper describing a more detailed comparison between the simulations and the natural patterns as well as between naturally occurring pattern regulation after injuries and those expected from the model is in preparation.

MSC:

92B05	General biology and biomathematics
92F05	Other natural sciences (mathematical treatment)
92-04	Software, source code, etc. for problems pertaining to biology
68U99	Computing methodologies and applications

Keywords:

pigmentation patterns; shells of molluscs; reaction-diffusion mechanisms; nearest neighbor interactions; computer simulations; pattern formation

Citations:

Zbl 0621.00034