This is an interactive view of spectra for the almost Mathieu operator. Just click anywhere on the picture to zoom in on any point you find interesting. Each click magnifies by a factor of 2.
If your browser can deal with 3D virtual objects, try looking at 3D Mathieu Spinner.
The spectrum has many interesting mathematical properties; for instance, it is known that often the spectral lines form a Cantor set. It is also a challenging problem to compute the spectrum numerically. We can use some tridiagonalization techniques to get a good (but sketchy) picture of a vertical stack of spectra. (Here, each horizontal line represents the spectrum for the operator at theta value = y. As theta moves up and down the y axis, the spectral lines change, giving this interesting fractal-like picture.)
This is an interactive view of spectra for the almost Mathieu operator.
Just click anywhere on the picture to zoom in on any point you find interesting.
Each click magnifies by a factor of 2.
The current coordinates are
(Thanks to Bruce Bauslaugh for help with html and gif encoding.)
Click here to see a full spectral drawing.
Click here for a three dimensional rendering
of the spectra
Click here for some references
