Turing Equation Explains how Leopard Spots Develop 109
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."
Not OS X 10.5? (Score:5, Funny)
Re: (Score:1)
Re:Not OS X 10.5? (Score:2)
Turing test (Score:5, Funny)
Ohwait...
Re:Turing test (Score:2)
"How sexy is that female leopard's spots?"
and
"Would you like to be my new coat?"
OSX Leopard? (Score:3, Funny)
OSX Leopard - not a coincidence (Score:1)
Extracting Sunlight from Cucumbers (Score:3, Funny)
Re:Extracting Sunlight from Cucumbers (Score:1, Funny)
The point is, you never know. (Score:5, Insightful)
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. (Score:5, Informative)
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:The point is, you never know. (Score:1)
Re:The point is, you never know. (Score:3, Informative)
Everyone knows that Velcro was a Vulcan invention [wikipedia.org].
Re:The point is, you never know. (Score:2, Funny)
Re:The point is, you never know. (Score:3, Interesting)
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.
Re:Obligatory Farkism (Score:2)
Re:Extracting Sunlight from Cucumbers (Score:3, Informative)
Re:Extracting Sunlight from Cucumbers (Score:5, Insightful)
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.
Re:Extracting Sunlight from Cucumbers (Score:2)
What's an animation "TD?"
Re:Extracting Sunlight from Cucumbers (Score:2)
Re:Extracting Sunlight from Cucumbers (Score:2)
Ah, now there's a long story.
Back in the day when the movie business was being unionised, everyone tried to grab an impressive job title. The coolest title was "director", so everyone tried to get that in their title. This is why the cinematographer is called the "director of photography" and the production designer was called the "art director" (that was changed recently, I believe).
The director's guild successfully complained about the dilution of the term "director", so no more titles were made with
Re:Extracting Sunlight from Cucumbers (Score:2)
Link to article? (Score:3, Informative)
Great ! (Score:3, Funny)
Re:Great ! (Score:2)
Step 2: ???
Step 3: Profit!
New Adage (Score:5, Funny)
This is really getting old (Score:4, Interesting)
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...
Re:This is really getting old (Score:2)
Tweaking parameters... (Score:5, Interesting)
Re:Tweaking parameters... (Score:5, Informative)
A short (but good) web site about this can be found here [sjsu.edu]. 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.
Re:Tweaking parameters... (Score:3, Insightful)
In machine learning (really statistical modelization), people are interested in developing methods of representing relations. Express
Re:Tweaking parameters... (Score:3, Insightful)
The objective of
Leopard spots, snail shells, and Leonardo of Pisa (Score:4, Interesting)
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
Re:Leopard spots, snail shells, and Leonardo of Pi (Score:4, Insightful)
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 (Score:5, Funny)
Re:Leopard spots, snail shells, and Leonardo of Pi (Score:2)
However, I think that redheads, like automobiles, are far more interesting as a whole than with a disscection of one small part of their totality.
Re:Leopard spots, snail shells, and Leonardo of Pi (Score:2)
Re:Leopard spots, snail shells, and Leonardo of Pi (Score:2)
haha, you don't even know how to spell "hole"!!!
Re:Leopard spots, snail shells, and Leonardo of Pi (Score:2)
Classic.
Re:Leopard spots, snail shells, and Leonardo of Pi (Score:2, Funny)
But now with this research, we can perhaps someday take a baby human child and determine if they will grow up to be the Messiah or Antichrist. We map all their freckles and
Re:Leopard spots, snail shells, and Leonardo of Pi (Score:2)
Re:Leopard spots, snail shells, and Leonardo of Pi (Score:1)
Re:Leopard spots, snail shells, and Leonardo of Pi (Score:2)
Similar patterns are found in the striate cortex [benbest.com] in the visual part of the brain.
Interactive examples include reaction-diffusion equation [texturegarden.com] applets
My favourite is quasi-crystalline patterns [caltech.edu]. They aren't periodic like squares, hexagons or triangles, but do have symmetry.
Re:Leopard spots, snail shells, and Leonardo of Pi (Score:1)
Re:Leopard spots, snail shells, and Leonardo of Pi (Score:2)
It's full of this kind of stuff, in florid detail. You can even read a sample chapter at the site.
Re:Yes, but... (Score:2)
Sounds like (Score:3, Informative)
Re:Sounds like (Score:3, Informative)
Actually, it's the precursor to cellular autonoma. There's a period of Alan Turrings life, that most people don't study and know about, which involves him studying a number of biological models. His 1952 paper 'On the Chemical Basis of Biological Morphogenesis' contains the foundations of what Wolfram would later go on and call 'cellular autonoma'. Go check it out, and form your own opinion. Having read both Wolfram and Turing, I have to give clear credit to Turing for coming up with t
Re:Sounds like (Score:2)
Von Neumann was the first. Conway popularized the idea with the Game of Life. Wolfram just did an intensive study of 1-d CAs. The applicability of CAs to biological patterns has been known since the early days though.
Re: Sounds like (Score:2)
Actually the term predates Wolfram by a long time. Wikipedia gives some references [wikipedia.org] from 1968.
Re: Sounds like (Score:2)
And strangely, people really dislike him for it. I don't think he ever says -he- invented them (he just fails to provide a ton of references---like most scientific wr0ks... but then maybe his book is more of a pop-science type of book, rather than a serious research thing).
(in any case, I found it interesting that the `random' number generator in Mathematica uses one of the automatas presented in the book
Re:Sounds like (Score:1)
Re:Sounds like (Score:1)
CA pigmentation models [wolframscience.com]
First page shows sample animal patterns, next 3 show CA emulations of them.
There is also this history note about Turing's work o
It's really great !! (Score:2, Interesting)
Re:It's really great !! (Score:2)
Re:It's really great !! (Score:2)
Re:It's really great !! (Score:1)
They have only suggested, they haven't proved it. It's a big deal to prove or disprove these kind of things.
Re:It's really great !! (Score:2)
Turing was a very talented mathematician, and worked in several areas besides the theory of computation and cryptograhpy. The equations discussed in the article (reaction-diffusion equations) are partial differential equations that model chemical reactions. They don't have anything to do with Turing machines, other then the fact that you could use a Turing machine to solve them numerically.
Re:It's really great !! (Score:2)
In this case, it is a Turing Space (Score:3, Informative)
This area of study (colourations on animals) is based on Reaction Diffusion Equations, of which a canonical example is the Belousov-Zhabotinskii equation derived from a chemical experiment, and a simpler one is the Heat Equation. These take the form of partial differential equations.
As to simulation
Re:It's really great !! (Score:1)
This is no big deal (Score:4, Informative)
This should be added to nethack (Score:1, Funny)
This is a scroll of pr0n. Read? [y/n] y
You think impure thoughts, and start fapping. --More--
Suddenly, a bolt of lightning hits the kitten! The kitten is killed!
Re:This should be added to nethack (Score:3, Informative)
This _should_ be seriously added to NH.
--
BMO
And yet... (Score:1)
Ack! (Score:2)
Bible Science (Score:3, Funny)
"Can the Ethiopian change his skin, or the leopard his spots? then may ye also do good, that are accustomed to do evil."
If one of the grad students working on this paper is an Ethiopian who's spent the year in a Taiwanese office rather than in the equatorial sun, we might have all the proof we need to test this ancient riddle.
The basic idea is old news (Score:2)
Turing's Paper (Score:3, Informative)
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 [turingarchive.org].
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
so.. (Score:1)
Morphogenesis (Score:3)
Collected Works of A.M. Turing
Morphogenesis
P.T. Saunders, Editor
Introduction
Turing's work in biology illustrated just as clearly as his other work his ability to identify a fundamental problem and to approach it in a highly original way, drawing remarkably little from what others had done. He chose to work on the problem of form at a time when the majority of biologists were primarily interested in other questions. There are very few references in these papers, and most of them are for confirmation of details rather than for ideas which he was following up. In biology, as in almost everything else he did within science -- or out of it -- Turing was not content to accept a framework set up by others.
Even the fact that the mathematics in these papers is different from what he used in his other work is significant. For while it is not uncommon for a newcomer to make an important contribution to a subject, this is usually because he brings to it techniques and ideas which he has been using in his previous field but which are not known in the new one. Now much of Turing's career up to this point had been concerned with computers, from the hypothetical Turing machine to the real life Colossus, and this might have been expected to have led him to see the development of an organism from egg to adult as being programmed in the genes and to set out to study the structure of the programs. This would also have been in the spirit of the times, because the combining of Darwinian natural selection and Mendelian genetics into the synthetic theory of evolution had only been completed about ten years earlier, and it was in the very next year that Crick and Watson discovered the structure of DNA. Alternatively, Turing's experience in computing might have suggested to him something like what are now called cellular automata, models in which the fate of a cell is determined by the states of its neighbours through some simple algorithm, in a way that is very reminiscent of the Turing machine.
For Turing, however, the fundamental problem of biology had always been to account for pattern and form, and the dramatic progress that was being made at that time in genetics did not alter his view. And because he believed that the solution was to be found in physics and chemistry it was to these subjects and the sort of mathematics that could be applied to them that he turned. In my view, he was right, but even someone who disagrees must be impressed by the way in which he went directly to what he saw as the most important problem and set out to attack it with the tools that he judged appropriate to the task, rather than those which were easiest to hand or which others were already using. What is more, he understood the full significance of the problem in a way that many biologists did not and still do not. We can see this in the joint manuscript with Wardlaw which is included in this volume, but it is clear just from the comment he made to Robin Gandy (Hodges 1983, p. 431) that his new ideas were "intended to defeat the argument from design".
This single remark sums up one of the most crucial issues in contemporary biology. The argument from design was originally put forward as a scientific proof of the existence of God. The best known statement of it is William Paley's (1802) famous metaphor of a watchmaker. If we see a stone on some waste ground we do not wonder about it. If, on the other hand, we were to find a watch, with all its many parts combining so beautifully to achieve its purpose of keeping accurate time, we would be bound to infer that it had been designed and constructed by an intelligent being. Similarly, so the argument runs, when we look at an organism, and above all at a human being, how can we not believe that there must be an intelligent Creator?
Turing was not, of course, trying to refute Paley; that has been done almost a century earlier by Charles Darwin. But the argument from design had survived, and was, and indeed remains, still a potent force in biolog
far from proven (Score:2)
Re:There is no TAIWAN (Score:2, Funny)
The rouge state of Taiwan is part of Peoples Republic of CHINA.
[/quote]
Yes, Taiwan is a nice shade of pink, unlike the red commie bastards in China.
Re:The Real Taiwan (Score:1)
Since when do they speak French in Taiwan? (Score:1)
"We cheerfully overfulfill our quotas for the greater good of the people and the state."
Re:Since when do they speak French in Taiwan? (Score:2)
Re:There is no TAIWAN (Score:1)
Hehe. So... how should we refer to it as? The Republic of China? I believe the PRC refers to it as the Taiwanese province...