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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."
Or at what age do they become legal?
Damn, i thought "Spots" was some sweet new feature in OS X Leopard.
So how many questions were the leopard spots able to answer?
Ohwait...
And this one day before Apple reveals features of Mac OS X 10.5 Leopard? What are the odds?
- Henrik
- when the Shadows descend -
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.
As interesting as the link may be it does not mention any of the new findings in the header.
Awesome work guys ! Now on to the applications of this important discovery ! ...
Lunch ?
... no more than a Leopard can change his Turing Equations
Letter To Iran
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...
Error 407 - No creative sig found
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.
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
I do not respond to cowards. Especially anonymous ones.
Does it run linux?
Oh, wait...
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. ;)
All the techniques ever used to make men moral have been themselves thoroughly immoral... (Nietzsche)
[quote]
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.
Do explain.
So what was your point exactly?
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.
Yep! See DDJ Algorith Alley, December 1996
Source code can be found on:
ftp://66.77.27.238/sourcecode/ddj/1996/9612.zip
cellular automata.
Sheesh, evil *and* a jerk. -- Jade
Still no cure for cancer.
I really hope you don't think freckles on, or redheads in general are boring. They're nothing like leopards either.
There was this pale red-headed Irish fella, who once found a picture of the Holy Blessed Virgin in his freckles...
Comment removed based on user account deletion
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.
Spam: Any activity on internet to gain popularity without paying to advertising companies like Google.
Since at least 1989 (with Dictyostelium) developmental and evolutionary biologists have used Turing's mechanism to explain pattern formation. Good site here
The real Taiwan is, indeed, an independent state, but its people support most of the geopolitical objectives of Beijing. The weapons that we Americans have sold to Taiwan will find their way into the hands of Beijing.
i've read about this in keith devlin's 2001 book "The Math Gene" i think.. It is explained there how the pattern of a tiger's fur is only stored in functions in the genes... http://www.amazon.com/gp/product/0465016197/sr=8-1 /qid=1154892579/ref=pd_bbs_1/002-3922311-3366415?i e=UTF8
You read a scroll titled BOOBIE FLETCH. --More--
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!
Oh, no! You have walked into the slavering fangs of a lurking grue!
While my wife is a burnette, I do recognize the inheret wonder that is a redhead.
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.
Still no cure for leopard cancer!
Don't tease us with stories about Leopards the day before WWDC!!!
Dear Slashdot: next time you want to mess with the site, add a rich-text editor for comments.
Apparently, old Jeremiah was teaching Turing's mathematics to homeless Israelites when he told one
"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.
--
make install -not war
There's a nice account of this in Ian Stewart's The Magical Maze.
LOL...I'm posting this to Pseuds Corner in Private Eye...
You probably meany "rougue", like the classic computer game game.
"We cheerfully overfulfill our quotas for the greater good of the people and the state."
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
It is not so much that I have confidence in scientists being right, but that I have so much in nonscientists being wrong
But dissecting one part of that totality (i.e. shagging one) may reveal more interesting qualities about them as a whole.
Karnal
This is actually relatively easy to answer. Just base your calculations on the basis that the angels must be standing on at least two atoms at a time, which I think is reasonable. You then do some fancy maths and get your answer.
-TimWell if leopards are anything like lions (they're both big cats, one just seems to have put more points into strength over agility than the other), I'd rather not bother with them. I know one famous lion researcher personally: his first name is Token (but he has been called multiple last names), and he said that "lions are totally gay."
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 exactly calculate their resultant pattern. If the final morphology is some sort of hyper-religious symbol (a cross drawn over a Superman symbol with a star and sparklies all over it, a skull-and-cross-bones with burning flames and a dirty joke sealing it, the symbol for the Republic party, etc.).
The problem with this idea is if we have to skin every human baby, we will have another Moses-mom on our hands that would rather float her baby down the Nile river in a basket than give 'em over to the professionals. There's also the problem of celebrities running off to Africa to have their babies.
So our two biggest threats to this new classification system working are both with Africa. If giant dinosaurs and monsters like Kong still inhabit those lands, no wonder the people there are still primal. You never hear anybody saying "Peace in the African Congo!" as I'm sure that is even more impossible than would be for the middle-east... I'm sure Africa isn't THAT big of a country, maybe we could get Bush or some other world leader like Kim Yong Wong something, that funny Chinese man on the Team America F-Yeah show, to send in a bunch of troops. Russia is another good choice for sending in a lot of troops. India is another good choice, population-wise, but I can't imagine their people doing much more than teaching Physics 101 or doing my colonoscopies.
Wait, what were we talking about?
It took them a year to find a final solution.
Would that be the final solution to the leopard question?
What actually is this useful for again?
Now, an anonymous coward claims that the "New York Times" is lying.
Does the anonymous coward have proof that the "New York Times" is lying? Well, does he?
PUT UP OR SHUT UP!
satellite imaging reveals endless amounts of un-inhabited land that, without human interference, seems to create fractal-like patterns. google earth it. its real.
The rouge state of Taiwan is part of Peoples Republic of CHINA. Do not lend support and credibility to Taiwan seperatists backed by US thugs by refering to it as Taiwan. Taiwan is Chinese soil.
Hehe. So... how should we refer to it as? The Republic of China? I believe the PRC refers to it as the Taiwanese province...
The BBC had an article on how lead atoms could self organise into patterns
Similar patterns are found in the striate cortex in the visual part of the brain.
Interactive examples include reaction-diffusion equation applets
My favourite is quasi-crystalline patterns. They aren't periodic like squares, hexagons or triangles, but do have symmetry.
Vintage computer adverts: http://www.vintageadbrowser.com/computers-and-software-ads
The article summary refered to Taiwan as though it was a SEPERATE NATION. THIS IS INCORRECT. CAN YOU NOT READ.
anyway Yankees like you need to get out and stay out of China
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
Take a look and feel free: http://www.PieMenu.com
A Turing Space rather than a Turing machine. Turing was an excellent mathematician, and although currently most famous for his ideas on computation and the Halting Problem, this was a seperate area of research.
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 simulations of the world or parts on a computer, there is the problem of Heisenberg's Uncertainty Principle, meaning you can never form a complete 'image' of any part of the world.
ah, mod points
Go back to your commune and learn how to blog. Do not drag politics in here unless it is related to the subject. By the way, Taiwan is Chinese soil, Republic of China! You fucking commie bastard.
The purpose of writing is to inflate weak ideas, obscure poor reasoning, and inhibit clarity....Calvin
The people of Taiwan seem to regard it as a separate nation.
I am now titled "Leopard Love" by my new babe.
"(i.e. shagging one) may reveal more interesting qualities about them as a whole"
;-)
haha, you don't even know how to spell "hole"!!!
The revolution will not be televised... but it will have a page on Wikipedia
And how much LSD did we drop today?
So far, this is simply an equation that reproduces the visual appearance of spots. That's not an "explanation", it's merely a hypothesis or a model. Proving it will require actually identifying the substances and their concentrations over time that appear in the model.
Prof. Jon Jacobsen at Harvey Mudd College also studies reaction diffusion equations. He's got some cool stuff!
http://www.math.hmc.edu/~jacobsen/index3.html
Someone once said that the rate of growth of banana spots can be accurately modeled with the Avrami Equation http://gold.zvon.org/A00545.html
I actually thought about that the instant I hit "submit".
Classic.
Karnal
Oh, come on. Learn the difference between a mathematical model and reality itself. One is a human construct, a product of human intelligence. The other just is. I prefer the latter.
You should go read A New Kind of Science by Stephen Wolfram.
It's full of this kind of stuff, in florid detail. You can even read a sample chapter at the site.
You are living a sad, sad life if you can't find the beauty that lies in the mathematics of spots. Or in the organization of an ant hill. Or in the smile of the Mona Lisa. Or in a rose on a rainy day. Or in the game of Life. Or..... you get the idea. I find people who find wonder in these things are far more interesting (and coincidentally, achieve more) than those who are always chasing "real" wonder.
Those who can, do. Those who can't, sue.