

Hofstadter's butterfly - ironchief
http://en.wikipedia.org/wiki/Hofstadter%27s_butterfly

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teamonkey
I don't understand how someone can create a page like this and not find it
necessary to explain the name

[http://en.wikipedia.org/wiki/Almost_Mathieu_operator](http://en.wikipedia.org/wiki/Almost_Mathieu_operator)

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physonaught
Some very cool physics involved-- a lot of basic quantum mechanics (electrons
hopping on a lattice), but it has a lot of really broad implications about
symmetries. There is a lot of recent interest in the butterfly [1,2].

It turns out that it is a very important state to study the Quantum Hall
effect[3], and the fractional Quantum Hall effect[4], which seem to be in
vogue in Condensed Matter physics these days.

Sorry to bog you down with details, I just wanted to mention how neat it is
that Hofstadter's butterfly is still being studied today!

[1]
[http://www.nature.com/nature/journal/v497/n7451/full/nature1...](http://www.nature.com/nature/journal/v497/n7451/full/nature12186.html)
[2]
[http://physics.aps.org/articles/v6/118](http://physics.aps.org/articles/v6/118)

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VonGuard
Odd to think that physics has found so few naturally occurring fractals.

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coherentpony
Physics has found lots of naturally occurring fractals.

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gamegoblin
According to the article

    
    
        It is one of the rare fractal structures discovered in physics, along with KAM tori.
    

What are some other examples?

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esmi
[http://www.wired.com/2010/09/fractal-patterns-in-
nature/](http://www.wired.com/2010/09/fractal-patterns-in-nature/)

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gamegoblin
I think it's somewhat clear that "physics" and "nature" refer to two fairly
different concepts in this context.

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coherentpony
This is now entirely a semantic argument. I would argue "physics" and "nature"
are almost interchangeable here. KAM tori naturally occur in ocean currents.

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sphildreth
Hope I am not the only one that thought this had something to do with
Leonard...
[http://en.wikipedia.org/wiki/Leonard_Hofstadter](http://en.wikipedia.org/wiki/Leonard_Hofstadter)

