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J-inv-modulus.jpeg (600 × 600 pixels, file size: 36 KB, MIME type: image/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)
en user Linas, the copyright holder of this work, hereby publishes it under the following license:
GNU head 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.

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.

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.

Released under the Gnu Free Documentation License (GFDL) by Linas Vepstas.

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This licensing tag was added to this file as part of the GFDL licensing update.
GNU head 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.

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21 May 2005

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Date/TimeThumbnailDimensionsUserComment
current09:02, 11 December 2008Thumbnail for version as of 09:02, 11 December 2008600 × 600 (36 KB)Keyi{{Information |Description= Klein's J-invariant, modulus portrait (600x600 pixels) |Source= en.wikipedia.org |Date= 21:21, 21 May 2005 |Author={{user:Linas}} |Permission={{GFDL-user-w|en|projectname|Linas}} |other_versions= }} ===Detailed description===

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