Hofstadter's butterfly | Hacker News Reader

Hofstadter's butterfly

en.wikipedia.org

41 pointsironchief10 comments

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

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

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

Physics has found lots of naturally occurring fractals.

According to the article

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

What are some other examples?

http://www.wired.com/2010/09/fractal-patterns-in-nature/

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

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

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

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

Reply on news.ycombinator.com