File:J-inv-modulus.jpeg
Description | Klein's J-invariant, modulus portrait (600x600 pixels) | ||
Date | 21 May 2005, 21:21 (original upload date) | ||
Source | Transferred from en.wikipedia to Commons by Keyi. | ||
Author | en:user:Linas | ||
Permission (Reusing this file) |
|
Original upload log
All following user names refer to en.wikipedia.
Detailed description
This image shows the modulus |j| of the J-invariant as a function of the square of the nome on the unit disk |q| < 1. That is, runs from 0 to along the edge of the disk. Black indicates regions where the modulus is near zero, green where the modulus is about one, and red where the modulus is greater than ten. The color scale is logarithmic. Inside of every black region is a zero; note the zeros are cubic.
The small black dot on the far right, in the large red cardioid, is a numerical artifact.
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 this sense, this particular image clearly illustrates the tesselation of the q-disk by the modular group.
- See also Image:J-inv-poincare.jpeg for this J-invariant on the Poincaré disk.
- See also Image:J-inv-real.jpeg for the real part.
- See also Image:J-inv-phase.jpeg for the phase.
It, and other related images, can be seen at http://www.linas.org/art-gallery/numberetic/numberetic.html
Source of Image
Created by Linas Vepstas User:Linas <linas@linas.org> on 21 May 2005 using custom software written entirely by Linas Vepstas.
Copyright status
Released under the Gnu Free Documentation License (GFDL) by Linas Vepstas.
![]() ![]() ![]() |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Subject to disclaimers. | |
| ||
This licensing tag was added to this file as part of the GFDL licensing update. |
![]() |
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. A copy of the license is included in the section entitled GNU Free Documentation License. Subject to disclaimers. |