Turing Equation Explains how Leopard Spots Develop

BilZ0r writes "A slight modification of an equation developed by Alan Turing in 1952 has been used to show how the patterns of big cats change from kitten to adult markings. Sy-Sang Liaw of National Chung-Hsing University in Taichung, Taiwan, and colleagues set out to replicate these patterns using Turing's equations. But they found they had to do more than just tweak the parameters of the reaction-diffusion equation. Instead they had to assume two stages of spot growth with different rules: the first to get the baby cats their spots, and the second to create the final configurations. It took them a year to find a final solution."

Comments

This is really getting old

[agent dero]

Sheesh, I'm really sick and tired of this WWDC, Mac OS X speculation... ;)

But seriously, where in this silly blog posting does it ever talk about the Leopard spots? Is it just me, or is TFA missing here...

Tweaking parameters...

[posterlogo]

This work is pretty interesting. My concern with complex mathematical models has always been that nearly any phenomena can be perfectly described given enough variables -- pretty much any curve, any pattern, any shape. In biology, when we try to fit models to data, we have to be very careful not to just keep trying to curve fit with more and more complex equations, because in the end we will be left with something that is not biologically very descriptive -- it leaves us with little understanding of the underlying biology. So when I hear these guys had to tweak parameters to make the reaction-diffusion equation fit the data, I am left wondering what biological factors those extra parameters are supposed to define? The original set of equations was meant to model a system with multiple morphogens that diffuse in two dimensions. When they act upon (or are acted upon) appropriate receptors, a particular "phenotype" emerges at that location. I did RTFA, but it doesn't actually say much about these things -- just makes up a dumb analogy with missionaries and cannibals in competition.

Leopard spots, snail shells, and Leonardo of Pisa

[The Living Fractal]

I find this kind of research amazing. It's like nature has given us a hint at something, something on the tip a vastly larger and more profound realization. The ability to recognize these natural patterns, such as the Fibonacci sequence, is IMHO one of the fundamental qualities of intelligence and sentience. It seems to be something tied to the very basis of existence, upon which our human minds are a layer with a depth that may indeed have no bounds or may merely be a small slice. The potential infinity of it all is staggering, and yet beautiful, and is the primary reason I chose this handle which I use here.

Here we witness the micro through the macro, through all scales of physical dimension, in an interplay of force, energy and motion, with the final result happening both all at once and forever spread over time. Incredible.

TLF

It's really great !!

[himanshuarora]

I remember my professor telling us in the class that anything which can be expressed/solved by any turing machine is an algorithm. Those equations seems different than the description of a turing machine[ To Me :( ]. I would say that it's a great finding. He was able to describe some natural phenomenon from a set of turing equations. It implies that we can simulate the whole world[or a part] on a computer.

Re:The point is, you never know.

[blackest_k]

silly putty, does have interesting properties.
it can flow like a liquid and act like a solid when pushed rapidly.
whats that good for polishing internal holes if you mix an abrasive in with it. Which might help get the best out of high performance engines.

it's an interesting material wonder how it would cope with a leak in a pressurised container could it contain or slow that leak for a period of time.

it also bounces and lifts ink off paper.