You are viewing a single comment's thread from:
RE: Gardening with Alan Turing, and sketching evolution of plants with Da Vinci - Phyllotaxis
I don't have a full enough grasp of the mathematics to make a sound hypothesis, but this seems very similar in spirit, if not in form, to the advection-diffusion equation we use for modeling chemical transport.
In that case, certain common mathematical constructs pop out not because they are the most efficient, but simply because they tend to always appear when you're working with systems of differential equations. Could that be the case here?
Yeah it's pretty close to it because they are both built up on system of diffusion PDE. And that was mostly the point that of Turing that using these mathematical constructs you can explain the patterns in nature. But as far as efficiency is concerned you are partially right. The patterns are the way they are because the underlying math of PDE is same. However there is another parameter we need to consider when we think of biological systems. They need to maximize their copies - by long survival or high reproduction rate. So all possible patterns that can be made by tweaking components of the equations can compete.