Download The Algorithmic Beauty of Sea Shells by Hans Meinhardt (auth.) PDF

By Hans Meinhardt (auth.)

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Extra resources for The Algorithmic Beauty of Sea Shells

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H. :1: Finite activator production at low inhibitor concentration: Michaelis-Menten kinetics At very low inhibitor concentrations, inhibitor production must remain finite. 1 b. Both effects limit activator production at low inhibitor concentrations. This limitation can lead to a second stable state at low activator concentrations. In an oscillating activator-inhibitor mechanism, inhibitor concentrations can become very low. So far, it has been assumed that the rate of activator production is inversely proportional to inhibitor concentration.

By saturation, the maximum activator concentration is limited and it requires more time either to accumulate sufficient inhibitor or to consume all available substrate. Therefore, it takes longer for the activation to cease. 5a,b provide simulations with and without saturation. However, the actual mechanism by which broad stripes are generated may be more complex. The natural patterns show bands of a nearly constant density of pigmentation. 3d). One possibility may be that pigmentation depends in a non-linear way on exceeding a certain threshold of activator concentration.

I . l\''-(l~). ,;. -. "".... ~ ,~ .. " . A\ • , .. ü ,,·:"" \-": :"' ( . ' .... • • 1 '- , ',,; . · ·· ,.. ~·{y.... -( (I ' i \h . 1i>o , ~. , '. I ' ... ~ ~ " . " " ,'. i'~'I;""' . :\1)). , " ", ... \ J. Position - . 5. The width of stripes. (a) without saturation, a high aetivator eoneentration is present only for a short time interval. 3), the width of the stripes beeomes broader in relation to the interstripes. (e) A rapid diffusion of the inhibitor is insufficient for the formation of a pattern in spaee.

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