6 ms·
Hofstadter's butterfly
- VonGuard 12y agoOdd to think that physics has found so few naturally occurring fractals.
- coherentpony 12y agoPhysics has found lots of naturally occurring fractals.
- gamegoblin 12y agoAccording to the article It is one of the rare fractal structures discovered in physics, along with KAM tori. What are some other examples?
- esmi 12y agohttp://www.wired.com/2010/09/fractal-patterns-in-nature/ http://www.wired.com/2010/09/fractal-patterns-in-nature/
- gamegoblin 12y agoI think it's somewhat clear that "physics" and "nature" refer to two fairly different concepts in this context.
- coherentpony 12y agoThis is now entirely a semantic argument. I would argue "physics" and "nature" are almost interchangeable here. KAM tori naturally occur in ocean currents.
- rotskoff 12y agoCritical 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 https://en.wikipedia.org/wiki/Renormalization_group
- teamonkey 12y agoI 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
- physonaught 12y agoSome 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/nature12186.html http://www.nature.com/nature/journal/v497/n7451/full/nature1... [2] http://physics.aps.org/articles/v6/118 http://physics.aps.org/articles/v6/118
- sphildreth 12y agoHope 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