7 ms·

Alan Turing's 1950s tiger stripe theory proved

132 points by acangiano 15y ago

gradstudent 15y ago
Wouldn't "Turing's Tiger Stripe Conjecture" be a better name for this? Considering there was no prior evidence for it until now?
- pvarangot 15y ago
  Hmm, I beleive conjecture is used when you are speaking about a potential theorem (i.e. something than can be mathematically proven to be right given certain axioms). This is a biological/chemical/natural theory, and is believed to be true given certain findings in some observed phenomena (i.e. statistics are involved in a certain way).
  - gradstudent 15y ago
    A conjecture is an assertion made on the basis of incomplete evidence. I'm not familiar with Turing's work in this area but if (as others have commented) he studied PDEs and that appear to mimic biological processes, yet did not find a definitive link, then the conclusion that a connection between the two may exist can only be described as conjecture.
- impendia 15y ago
  Turing worked on a family of partial differential equations called "reaction-diffusion equations", and determined that for particular choices of the parameters, they produce phenomena similar to tiger stripes, leopard spots, and the like. One doesn't have to describe this in terms of biology; mathematically it is already interesting on its own. But how much cooler is it that this can be observed by a visit to a zoo! He (or perhaps biologists who studied his work?) conjectured that some biological process behaved according to his equations, and therefore produced the behavior they model. However, until now, no one had ever found such a process.
- bo1024 15y ago
  My understanding was that Turing's theory of morphogenesis had already been shown to be correct in some cases in biology; they just didn't know it to be true in the case of tiger stripes. In fact, they had shown it not to be true for some other striped animal (can't recall which one), which I think makes this discovery even more interesting.
mvanveen 15y ago
Here is the wikipedia article on Turing's paper: http://en.wikipedia.org/wiki/The_Chemical_Basis_of_Morphogenesis http://en.wikipedia.org/wiki/The_Chemical_Basis_of_Morphogen...
impendia 15y ago
The first time I ever took a graduate math course, I did my term project on precisely this theory. Analyzed the PDE's, did some numerical experiments on it, gave a lecture on it. I had to tell my audience "Well, we think this produces tiger stripes and giraffe spots, but honestly we're just blindly guessing." What a treat to read this! Shows that us mathematicians are often fifty years ahead of the times ;)
tokenadult 15y ago
I read about this in 2011 in Ian Stewart's book The Mathematics of Life. I see the relevant passage can be viewed in Google Books. http://books.google.com/books?id=u4X4cRaZlJUC&pg=PA199&dq=Turing+tiger+stripes&hl=en&sa=X&ei=Sp5BT6PRLMGM0QHU-O3cBw&ved=0CE4Q6AEwBQ#v=onepage&q=Turing%20tiger%20stripes&f=false http://books.google.com/books?id=u4X4cRaZlJUC&pg=PA199&#... Any book by Ian Stewart on mathematics is a good read.
bootload 15y ago
Interesting find & I wondered in this post, "Why Startup Hubs Work" ~ http://news.ycombinator.com/item?id=3077165 http://news.ycombinator.com/item?id=3077165 could the randomness of Startup described by "pg" really be Morphogenesis? ~ http://www.flickr.com/photos/bootload/6215220131/ http://www.flickr.com/photos/bootload/6215220131/ The original paper, Turings last can be read here ~ http://www.dna.caltech.edu/courses/cs191/paperscs191/turing.pdf http://www.dna.caltech.edu/courses/cs191/paperscs191/turing....
yread 15y ago
I am quite surprised that such a simple question of why does a tiger have stripes (which kids are asking all the time) went so long unanswered. I wonder how many questions like this are there?
- pja 15y ago
  This doesn't explain why a tiger has stripes. It explains how a tiger has stripes.
  - Shorel 15y ago
    True. The why seems simpler: camouflage.
    - yread 15y ago
      why 1. for what? for what reason, cause, or purpose? [1] I am talking about cause and you're talking about purpose. I think we can both ask why [1] http://dictionary.reference.com/browse/why http://dictionary.reference.com/browse/why
tim_hutton 15y ago
The physorg article summary is wrong, I think. The first morphogens were found in 2006, for hair-follicle placement in mice: http://phylogenous.wordpress.com/2010/12/01/alan-turings-reaction-diffusion-model-simplification-of-the-complex/ http://phylogenous.wordpress.com/2010/12/01/alan-turings-rea...
SimHacker 15y ago
The late Andy Witkin's classic SIGGRAPH paper on reaction diffusion textures: http://www.cs.cmu.edu/~aw/pdf/texture.pdf http://www.cs.cmu.edu/~aw/pdf/texture.pdf We present a method for texture synthesis based on the simulation of a process of local nonlinear interaction, called reaction-diffusion, which has been proposed as a model of biological pattern formation. We extend traditional reaction-diffusion systems by allowing anisotropic and spatially non-uniform diffusion, as well as multiple competing directions of diffusion. We adapt reaction-diffusion systems to the needs of computer graphics by presenting a method to synthesize patterns which compensate for the effects of non-uniform surface parameterization. Finally, we develop efﬁcient algorithms for simulating reactiondiffusion systems and display a collection of resulting textures using standard texture- and displacement-mapping techniques.

132 points by acangiano 15y ago

Wouldn't "Turing's Tiger Stripe Conjecture" be a better name for this? Considering there was no prior evidence for it until now?

pvarangot 15y ago
Hmm, I beleive conjecture is used when you are speaking about a potential theorem (i.e. something than can be mathematically proven to be right given certain axioms). This is a biological/chemical/natural theory, and is believed to be true given certain findings in some observed phenomena (i.e. statistics are involved in a certain way).
- gradstudent 15y ago
  A conjecture is an assertion made on the basis of incomplete evidence. I'm not familiar with Turing's work in this area but if (as others have commented) he studied PDEs and that appear to mimic biological processes, yet did not find a definitive link, then the conclusion that a connection between the two may exist can only be described as conjecture.
impendia 15y ago
Turing worked on a family of partial differential equations called "reaction-diffusion equations", and determined that for particular choices of the parameters, they produce phenomena similar to tiger stripes, leopard spots, and the like. One doesn't have to describe this in terms of biology; mathematically it is already interesting on its own. But how much cooler is it that this can be observed by a visit to a zoo! He (or perhaps biologists who studied his work?) conjectured that some biological process behaved according to his equations, and therefore produced the behavior they model. However, until now, no one had ever found such a process.
bo1024 15y ago
My understanding was that Turing's theory of morphogenesis had already been shown to be correct in some cases in biology; they just didn't know it to be true in the case of tiger stripes. In fact, they had shown it not to be true for some other striped animal (can't recall which one), which I think makes this discovery even more interesting.

mvanveen 15y ago

Here is the wikipedia article on Turing's paper: http://en.wikipedia.org/wiki/The_Chemical_Basis_of_Morphogenesis http://en.wikipedia.org/wiki/The_Chemical_Basis_of_Morphogen...

impendia 15y ago

The first time I ever took a graduate math course, I did my term project on precisely this theory. Analyzed the PDE's, did some numerical experiments on it, gave a lecture on it. I had to tell my audience "Well, we think this produces tiger stripes and giraffe spots, but honestly we're just blindly guessing." What a treat to read this! Shows that us mathematicians are often fifty years ahead of the times ;)

tokenadult 15y ago

I read about this in 2011 in Ian Stewart's book The Mathematics of Life. I see the relevant passage can be viewed in Google Books. http://books.google.com/books?id=u4X4cRaZlJUC&pg=PA199&dq=Turing+tiger+stripes&hl=en&sa=X&ei=Sp5BT6PRLMGM0QHU-O3cBw&ved=0CE4Q6AEwBQ#v=onepage&q=Turing%20tiger%20stripes&f=false http://books.google.com/books?id=u4X4cRaZlJUC&pg=PA199&#... Any book by Ian Stewart on mathematics is a good read.

bootload 15y ago

Interesting find & I wondered in this post, "Why Startup Hubs Work" ~ http://news.ycombinator.com/item?id=3077165 http://news.ycombinator.com/item?id=3077165 could the randomness of Startup described by "pg" really be Morphogenesis? ~ http://www.flickr.com/photos/bootload/6215220131/ http://www.flickr.com/photos/bootload/6215220131/ The original paper, Turings last can be read here ~ http://www.dna.caltech.edu/courses/cs191/paperscs191/turing.pdf http://www.dna.caltech.edu/courses/cs191/paperscs191/turing....

yread 15y ago

I am quite surprised that such a simple question of why does a tiger have stripes (which kids are asking all the time) went so long unanswered. I wonder how many questions like this are there?

pja 15y ago
This doesn't explain why a tiger has stripes. It explains how a tiger has stripes.
- Shorel 15y ago
  True. The why seems simpler: camouflage.
  - yread 15y ago
    why 1. for what? for what reason, cause, or purpose? [1] I am talking about cause and you're talking about purpose. I think we can both ask why [1] http://dictionary.reference.com/browse/why http://dictionary.reference.com/browse/why

tim_hutton 15y ago

The physorg article summary is wrong, I think. The first morphogens were found in 2006, for hair-follicle placement in mice: http://phylogenous.wordpress.com/2010/12/01/alan-turings-reaction-diffusion-model-simplification-of-the-complex/ http://phylogenous.wordpress.com/2010/12/01/alan-turings-rea...

SimHacker 15y ago

The late Andy Witkin's classic SIGGRAPH paper on reaction diffusion textures: http://www.cs.cmu.edu/~aw/pdf/texture.pdf http://www.cs.cmu.edu/~aw/pdf/texture.pdf We present a method for texture synthesis based on the simulation of a process of local nonlinear interaction, called reaction-diffusion, which has been proposed as a model of biological pattern formation. We extend traditional reaction-diffusion systems by allowing anisotropic and spatially non-uniform diffusion, as well as multiple competing directions of diffusion. We adapt reaction-diffusion systems to the needs of computer graphics by presenting a method to synthesize patterns which compensate for the effects of non-uniform surface parameterization. Finally, we develop efﬁcient algorithms for simulating reactiondiffusion systems and display a collection of resulting textures using standard texture- and displacement-mapping techniques.