The Algorithmic Beauty of Sea Shells
As mentioned repetitively in the book, the models describing shell patterning are only special applications of a mechanism developed to account for biological pattern formation in general. To illustrate the dose connection) a new chapter originally written for the first German edition - has been added that provides a survey of these general models. Discussed is, for instance, how an embryo can obtain its primary axes, how gene activation can proceed under the influence of such signals in a position-dependent manner, how complex netlike structures such as the vein of leaves can be generated and how legs and wings are initiated during development at precise positions. Other sections of this chapter deal with phenomena at which the intimate connection to the mechanisms worked out for shell patterning are especially obvious. The utilization of travelling waves in blood coagulation, in the conduction of nerve pulses and in the chemotactic orientation of cells are examples. Closeparallels between a shell pattern and phyllotaxis suggest an alternative view of how the helical arrangement of leaves is achieved. Using the shell patterns as a natural exercise book, the computer program supplied with the first edition has been used in the meantime at several universities to teach students in basic properties of dynamic systems. I have been frequently asked to make the programs for general pattern formation available. The programs for the above mentioned models have been added to the accompanying diskette.
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Shell patterns as dynamic systems
Oscillations and travelling waves
Superposition of stable and periodic patterns
Meshwork of oblique lines and staggered dots
Branch initiation by global control
two or more timedependent patterns
Other editions - View all
activated cells activated region activator concentration activator production activator-inhibitor system activator-substrate arrow assumed autocatalysis background pattern background pigmentation background system become bistable border branch formation breakdown causes chapter Clithon Clithon oualaniensis collision constant Conus textile curve Cymbiola diffusible inhibitor direction of growth enhancing reaction Equation 2.1 example extinguishing reaction formed Frenet frame gene growing edge helico-spiral Hydra increase indicates influence inhibition initiation interaction lateral inhibition leads maxima maximum mechanism molecules molluscs morphogen natural pattern neighbouring cells non-activated oblique lines occur organizing region oscillating system oscillation frequency parallel lines parameters patches pattern elements pattern formation phase pigment production pigmentation lines pigmentation reaction pigmentation system porphyria Position Figure possible pulse refractory period saturation self-enhancing shell patterns shown in Figure signal simulation Sonic hedgehog source density space spontaneous spread stable pattern stripes structure substance substrate production survive takes place tongues transition travelling waves triangles trigger white drops
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Page 230 - Krinks M. 1995. Anti-dorsalizing morphogenetic protein is a novel TGF-/3 homolog expressed in the Spemann organizer. Development 121:4293 Niehrs C, Steinbeisser H, De Robertis EM.
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