I've been using these differential equations, taken from Alan Turing's "The Chemical Basis of Morphogenesis," for sound synthesis over the past couple of months; today I decided to build a Jitter implementation. Endless fun.
(These are a straight-ahead port of Christopher Jennings' Java code. Images will tile.)
Can you explain a little the mechanism behind the formation of those patterns? I have read an article about these morphogenesis based in the mixture of two substances discovered by Alan Turing. The article explained that the generation of those patterns depends of the changes of concentrations of these two substances overtime. It seems that these elements are in your simulation, right? Exciting.
Could you explain your sonoric approaches too?
Have you go further in Turing´s researches? In the article also talks about ´geometrical phyllotaxis´. It says that when a system is growing, is formed locally rather than globally. It is directly connected with your differential equations.
The above mentioned article is ´Morphogenesis and the mathematics of emergence´ by Michael Weinstock in the ´Architectural design´ magazine.
I´m trying to implement the Ztutz amazing patch, with some of the explanations of that article.
The approach that Ztutz has done, is with a 2d matrix and displayed in a window object.
What I want to achieve now, is to recreate these Ztutz Turing patterns in a 3d world.
In the article says that the patterns appear because of a ´collection of diferential equations (already exist at the Ztutz patch) arranged in a structural network´.
I´m beginning to construct this structural network with nurbs, attached you can find the patches. I would like to recreate the Turing patterns in this nurb, but still I´m very far. I have reduce the number of noise elements (in order to make it handable in the 3d world). This noise tool in the Ztutz version, works in one plane (only black and white). Because I need this noise matrix to reproduce 3d coordinates inputs, it has 3 planes now, the patterns are in colour now and there are more difficult to see.
Attached my closest approach to the issue.
I will try to introduce other aspects described in the article, so if someone is interested in the subject and wants to collaborate in the game, please. I´m a Max begginer, hehe.