Image:Discriminant real part.jpeg
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[edit] Summary
originally uploaded to en:wiki, with this history:
- 04:11, 15 February 2005 . . Linas (Talk | contribs) . . 600×600 (67,813 bytes) (Modular discrimnant, real part, as function of nome.)
Comments made by the author follow.
Modular discriminant, real part, as function of nome. (600x600 pixels)
[edit] Detailed description
This image shows the real part of the modular discriminant 
as a function of the square of the nome q = exp(iπτ) on the unit disk |q| < 1. That is, πτ runs from 0 to 2π along the edge of the disk. Black areas indicate regions where the real part is zero or negative; blue/green areas where the value is small and positive, yellow/red where it is large and positive. The fractal self-similarity of this function is that of the modular group; note that this function is a modular form. Every modular function will have this general kind of self-similarity.
In the above, g2=60 G4 and g3=140 G6 are Weierstrass elliptic functions invarients, whereas η is the Dedekind eta function.
See also Image:Gee_three_real.jpeg and Image:Gee_three_imag.jpeg for the real and imaginary parts of g3.
The imaginary part is quite similar. It, and other related images, can be seen at http://www.linas.org/art-gallery/numberetic/numberetic.html
[edit] Source of Image
Created by Linas Vepstas User:Linas <linas@linas.org> on 14 February 2005 using custom software written entirely by Linas Vepstas.
[edit] Copyright status
Released under the Gnu Free Documentation License (GFDL) by Linas Vepstas.
[edit] Licensing
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. Subject to disclaimers. Asturianu | Български | Català | Deutsch | English | Español | Français | Gaeilge | Italiano | 한국어 | 日本語 | Polski | Português | Română | Türkçe | +/- |
File history
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| Date/Time | Dimensions | User | Comment | |
|---|---|---|---|---|
| current | 20:54, 21 September 2006 | 600×600 (66 KB) | Ylebru | (originally uploaded to en:wiki, with this history: * 04:11, 15 February 2005 . . Linas (Talk | contribs) . . 600×600 (67,813 bytes) (Modular discrimnant, real part, as function of nome.) Comments made by the author follow. [[Weierstrass elliptic funct) |
