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

Not OS X 10.5?

[nlogax]

Damn, i thought "Spots" was some sweet new feature in OS X Leopard.

Turing test

[Anonymous Coward]

So how many questions were the leopard spots able to answer?

Ohwait...

Extracting Sunlight from Cucumbers

[Anonymous Coward]

Using Turing equations to model the growth of leopard spots reminds me of 2 other types of research. They are (1) analyzing the human navel and (2) extracting sunlight from cucumbers.

Re:Extracting Sunlight from Cucumbers

[wambaugh]

Considering that reaction-diffusion equations are thought describe (among many, many other things) the propagation of electric waves in the heart, I'd say research understanding the patterns they form is highly worthwhile even if you have no intellectual curiousity whatsoever.

Re:Extracting Sunlight from Cucumbers

[Pseudonym]

And if you're an animation TD who has been assigned the task of creating a huge school of fish, each one of which should look different and yet still look like the right kind of fish, you'll be glad that someone has studied the problem of how to model animal markings.

No, this is not hypothetical. It's real, and it's done today.

Great !

[jfclavette]

Awesome work guys ! Now on to the applications of this important discovery ! ... Lunch ?

New Adage

[DumbSwede]

... no more than a Leopard can change his Turing Equations

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.

Re:Tweaking parameters...

[QuantumFTL]

These types of nonlinear differential equations are usually very simple in form, and, most importantly, very local, as that is how most biological interaction is mediated. The parameter tweaking should not be considered too alarming when one considers that the number of biological parameters, in the sense of genetic material, involves thousands of degrees of freedom.

A short (but good) web site about this can be found here. The interpretation of these formulas is fairly trivial, as they describe a diffusion process (common in all biological systems) with a somewhat more complex reactive process, which could be mediated through all kinds of channels.

This is not akin to fitting a polynomial to the shape of a bone and calling that a "model" - there are obvious interpretations which correspond to very well known processes.

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

The point is, you never know.

[Elemenope]

Some researchers dicking around with orange molds accidentally discovered this little thing called PENICLLIN. Some Swiss mountain hiker got irritated with little seeds that kept sticking to his clothes, which upon further inspection led to the invention of VELCRO.

On the other hand, researchers trying to solve a critical rubber shortage during World War II came up with an earth-shattering invention: SILLY PUTTY.

Point is, you just never know. ;)

Re:The point is, you never know.

[Elemenope]

anyhow, i believe you ment bread mold, not orange mold.

Penicillium is a genus of what are called 'bread molds' which grow, eponymously, on most yeasted breads. However, they also have a strong affinity for orange rind, and oranges make a nearly ideal culture medium for its growth. Penicillin's antibacteriological properties were discovered in a lab when an orange was accidentally exposed to penicillium and then left in contact with a bacteria culture. Hence, for the story about serendipity and science, its affinity for oranges was more pertinent. Oddly enough, this genus provdes us with some of the molds that make some of the tastiest cheese around (esp. Gorgonzola).

i know the best place to store rubber, place it skin tight on hot girls :D

I, too, like rubber and girls. ;)

Re:Leopard spots, snail shells, and Leonardo of Pi

[Planesdragon]

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.

No, not really."

If you find something as mundane as a mathematical model of how spots deveop on leopards to be "incredible", I think the wonder is all in you and not in the thing itself. Setting aside the wonder that is life itself, leopard spots are pretty boring -- roughly the equivalent to modeling how freckles develop on redheads.

Re:Leopard spots, snail shells, and Leonardo of Pi

[ceoyoyo]

I really hope you don't think freckles on, or redheads in general are boring. They're nothing like leopards either.

This is no big deal

[crush]

Since at least 1989 (with Dictyostelium) developmental and evolutionary biologists have used Turing's mechanism to explain pattern formation. Good site here

Turing's Paper

[SirClicksalot]

For those of you that don't know what this is about:

This isn't related to Turing's work on early computer science, but concerns research he did shortly before his death.
Turing proposed that under certain conditions diffusion can destabilize a chemical system and cause spatial patterns.

His original paper on the subject can be found at the Turing Archive.

Mathematical biologists have been using these equations to model biological pattern formation for some time. If you want to read up on it, try googling for research by Gierer and Meinhardt on pattern formation