5 ms·

Lizard scale patterns described with antiferromagnetic model

56 points by shusaku 5y ago

iaw 5y ago
Always interesting when models translate to virtually unrelated problems.
civilized 5y ago
Is there anything particularly "Ising" about the lizard scales, or would any model that posits an anticorrelation between the color of a scale and the colors of its neighbors do?
- rcollyer 5y ago
  Since there's only two states, it is definitely "Ising".
- max_ 5y ago
  The thing makes the "Ising" model do what it can do i.e describing 'complexity' of what's called the renormalisation group[0]. So any model that uses some kind of renormalisation will be able to accurately describe the lizard's skin too. [0]: https://youtu.be/2jggOWsHzeg?t=188 https://youtu.be/2jggOWsHzeg?t=188
- chermi 5y ago
  Ising-like models can "model" a very, very wide range of phenomenon. It's treated in physics (of the flavor in this article, statistical physical, biophysics, "complex systems") almost like a linear model would be by statisticians.* It may be helpful to think about the Ising model purely from a structural point of view. There are variations to what I'm describing that give you more/less modeling power 1) there's interactions with nearest neighbors only. 1.a) nearest neighbors are defined by the lattice 2) interaction strength and sign depends on neighbor position. 3) external field for bias So between your choice of lattice and the rules encoded in 2) above, you can describe an awful lot of stuff, forgot about magnets! * On my phone but there was a big fad for a while (may still be going?) on in "inverse" ising models. The basic idea was, how far can we get applying MaxEnt when constrained to known pairwise correlations. Pairwise =Ising. Of course their lattice had little meaning. Remi monasson or something like that I think was the name. Edit to add link to inverse ising review in case anyone interested https://arxiv.org/abs/1702.01522#:~:text=Inverse%20statistical%20problems%3A%20from%20the%20inverse%20Ising%20problem%20to%20data%20science,-H.&text=Inverse%20problems%20in%20statistical%20physics,high%2Dthroughput%20experiments%20in%20biology.&text=A%20particularly%20strong%20method%2C%20pseudolikelihood%2C%20stems%20from%20statistics https://arxiv.org/abs/1702.01522#:~:text=Inverse%20statistic....
jmount 5y ago
And an older classic in coloration: Turing, The Chemical Basis of Morphogenesis https://www.dna.caltech.edu/courses/cs191/paperscs191/turing.pdf https://www.dna.caltech.edu/courses/cs191/paperscs191/turing...

56 points by shusaku 5y ago

iaw 5y ago

Always interesting when models translate to virtually unrelated problems.

Is there anything particularly "Ising" about the lizard scales, or would any model that posits an anticorrelation between the color of a scale and the colors of its neighbors do?

rcollyer 5y ago
Since there's only two states, it is definitely "Ising".
max_ 5y ago
The thing makes the "Ising" model do what it can do i.e describing 'complexity' of what's called the renormalisation group[0]. So any model that uses some kind of renormalisation will be able to accurately describe the lizard's skin too. [0]: https://youtu.be/2jggOWsHzeg?t=188 https://youtu.be/2jggOWsHzeg?t=188
chermi 5y ago
Ising-like models can "model" a very, very wide range of phenomenon. It's treated in physics (of the flavor in this article, statistical physical, biophysics, "complex systems") almost like a linear model would be by statisticians.* It may be helpful to think about the Ising model purely from a structural point of view. There are variations to what I'm describing that give you more/less modeling power 1) there's interactions with nearest neighbors only. 1.a) nearest neighbors are defined by the lattice 2) interaction strength and sign depends on neighbor position. 3) external field for bias So between your choice of lattice and the rules encoded in 2) above, you can describe an awful lot of stuff, forgot about magnets! * On my phone but there was a big fad for a while (may still be going?) on in "inverse" ising models. The basic idea was, how far can we get applying MaxEnt when constrained to known pairwise correlations. Pairwise =Ising. Of course their lattice had little meaning. Remi monasson or something like that I think was the name. Edit to add link to inverse ising review in case anyone interested https://arxiv.org/abs/1702.01522#:~:text=Inverse%20statistical%20problems%3A%20from%20the%20inverse%20Ising%20problem%20to%20data%20science,-H.&text=Inverse%20problems%20in%20statistical%20physics,high%2Dthroughput%20experiments%20in%20biology.&text=A%20particularly%20strong%20method%2C%20pseudolikelihood%2C%20stems%20from%20statistics https://arxiv.org/abs/1702.01522#:~:text=Inverse%20statistic....

jmount 5y ago

And an older classic in coloration: Turing, The Chemical Basis of Morphogenesis https://www.dna.caltech.edu/courses/cs191/paperscs191/turing.pdf https://www.dna.caltech.edu/courses/cs191/paperscs191/turing...