Tony,
Any Fractint code for rendering this? I don't have any. You might try searching for Fractint-compatible code an non-Fractint program web sites (UltraFractal, etc.)
I just tried a couple of searches (use the quotes to keep the two words together during the search): calculate "hofstadter's butterfly" code to calculate "hofstadter's butterfly" Since: ... "In physics, Hofstadter's butterfly is a mathematical object ... describing the theorised behaviour of electrons in a magnetic field." ... (Wikipedia) I'm not likely to be able to derive the equations myself... http://tinyurl.com/Hofstadters-butterfly-spotted or: http://physicsworld.com/cws/article/news/2013/may/15/hofstadters-butterfly-s... gives a general overview of the calculation: "Hofstadter encountered a difficulty when considering electrons exposed to a magnetic field while moving in a 2D lattice. The problem lies in the fact that electrons respond to an applied magnetic field by swimming in circles at the cyclotron frequency. However, the orbital motion of the electrons is quantized in terms of a frequency that is defined by the properties of the crystal lattice. The presence of these two, often incommensurate, frequencies means that Hofstadter's calculation of electron energy levels yielded some bizarre results. Hofstadter tried to make sense of this difficulty by plotting the *wave function* of the electron versus a parameter related to the ratio of the two frequencies. The plot produced a stunning fractal pattern that looks like a butterfly." I found what appears to be the/a calculation here: http://phelafel.technion.ac.il/~orcohen/butterfly.html Let me know if you find some code. - Hal Lane ######################## # hallane@earthlink.net ######################## -----Original Message----- From: Fractint [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of Tony Hanmer Sent: Thursday, August 13, 2015 12:58 AM To: Fractint and General Fractals Discussion <fractint@mailman.xmission.com> Subject: Re: [Fractint] I just ran across this fractal object: Hofstadter's butterfly: Beautiful, especially the 2nd version. Any Fractint code for rendering this? On 12 August 2015 at 19:19, Hal Lane <hallane@earthlink.net> wrote:
I just ran across this interesting fractal object: Hofstadter's butterfly: https://en.wikipedia.org/wiki/Hofstadter%27s_butterfly
Be sure to see the large version of the 2nd version of the fractal...
Yes, this is the Douglas Hofstadter of "Gödel, Escher, Bach" (1979).
- Hal Lane
######################## # hallane@earthlink.net ########################
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