Lizard scale patterns described with antiferromagnetic model(physics.aps.org)
physics.aps.org
Lizard scale patterns described with antiferromagnetic model
https://physics.aps.org/articles/v15/s12
6 comments
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?
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%20statistic....
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%20statistic....
Since there's only two states, it is definitely "Ising".
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
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
Always interesting when models translate to virtually unrelated problems.
And an older classic in coloration: Turing, The Chemical Basis of Morphogenesis https://www.dna.caltech.edu/courses/cs191/paperscs191/turing...