Quasicrystals forming fractal patterns

[nomadreid]

I have read (sorry, I no longer have access to the source, which is the reason for the question (1) below) that one can find a fractal pattern if one
(a) shoots an electron through a two-dimensional plane perpendicular to a homogeneous magnetic field traversing a quasicrystal so that the magnetic field is one of certain irrational numbers with respect to the electric energies
(b) graphs the magnetic field versus the allowed energy levels of the electron.

I have several questions concerning this description:
(1) Do I have this description right?
(2) If so, how can one insure that a magnetic field/electric energy ratio is an irrational number if measurements are all rational?
(3) Since the fractal pattern requires a huge number of data points, wouldn't this also mean an impractical number of trials? [I am presuming a large number of trials rather than a single trial because of the twin requirements that the field be homogeneous and that one vary it in order to graph it. Is this an incorrect assumption?]

 

[eljose79]

Thank you for your question and interest in fractal patterns. I would like to address your questions and provide some clarification on the described experiment.

Firstly, your understanding of the experiment seems correct. The idea is to shoot an electron through a two-dimensional plane perpendicular to a homogeneous magnetic field that traverses a quasicrystal. This magnetic field should have a specific ratio with respect to the electric energies of the electron, which will result in a fractal pattern when graphed against the allowed energy levels of the electron.

To answer your second question, it is indeed a challenge to ensure that the magnetic field/electric energy ratio is an irrational number. This is because, as you mentioned, measurements are typically rational. One way to overcome this is by using theoretical calculations to determine the desired ratio and then adjusting the experimental setup accordingly. Another approach could be to use a superconductor, which can produce highly precise magnetic fields.

Regarding your third question, it is true that obtaining a fractal pattern would require a large number of data points. However, the exact number of trials needed would depend on various factors such as the sensitivity of the equipment and the precision of the measurements. It is difficult to determine an exact number without knowing the specifics of the experiment.

In terms of varying the magnetic field, it is possible to do so without compromising its homogeneity. This can be achieved by using multiple magnets or by adjusting the distance between the magnet and the experimental setup.

I hope this helps to clarify your doubts. If you have any further questions or concerns, please do not hesitate to ask.