Hofstadter's butterfly

http://en.wikipedia.org/wiki/Hofstadter%27s_butterfly

by ironchief • 12 years ago

41 10 12 years ago

en.wikipedia.org

VonGuard• 12 years ago

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

coherentpony2• 12 years ago

Physics has found lots of naturally occurring fractals.

gamegoblin2• 12 years ago

According to the article

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

What are some other examples?

rotskoff• 12 years ago

Critical phenomena, like phase transitions, are essentially defined by fractal like properties. Scale invariance in systems near a phase transition inspired the technique now called renormalization group. It remains a central tool in statistical physics, but isn't really in vogue at the moment. Kenneth Wilson won a Nobel prize in 1982 for his work on RG.

[1] https://en.wikipedia.org/wiki/Renormalization_group

teamonkey• 12 years ago

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

physonaught• 12 years ago

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... [2] http://physics.aps.org/articles/v6/118

sphildreth• 12 years ago

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

Hofstadter's butterfly

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