File:J-inv-real.jpeg
J-inv-real.jpeg (600 × 600 pixels, file size: 70 KB, MIME type: image/jpeg)
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Contents
Summary
DescriptionJ-inv-real.jpeg |
English: Klein's J-invariant, real part (600x600 pixels)
Detailed descriptionThis image shows the real part 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. The imaginary part Zeros are visible where-ever the three-pointed triangle tips come together. The j-invariant has a pole at every rational multiple of π on the circumference of the disk. The correct way to understand this image is to note that j takes on every possible value on the fundamental region. Each fundamental region takes the form of a hyperbolic triangle in this image, with one vertex of the triangle on the edge of the disk. Thus, the red regions deceivingly hint that they are centered on a pole; this is not the case, as the poles lie on the disk boundary. There is exactly one exception to this: there is one very tiny triangle (about two pixels in size), taking the shape of an oval, that is wrapped around the dead-center of the disk. One corner of that triangle is exactly at the center See also Image:J-inv-phase.jpeg for the phase part. It, and other related images, can be seen at http://www.linas.org/art-gallery/numberetic/numberetic.html Relevant Links |
Date | 15 February 2005 (original upload date) |
Source | Created by Linas Vepstas User:Linas <[email protected]> on 15 February 2005 using custom software written entirely by Linas Vepstas. |
Author | The original uploader was Linas at English Wikipedia. |
Permission (Reusing this file) |
Released under the Gnu Free Documentation License (GFDL) by Linas Vepstas. |
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Licensing
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This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Subject to disclaimers. | |
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This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue |
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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. A copy of the license is included in the section entitled GNU Free Documentation License. Subject to disclaimers.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
Captioned As
Page | Caption |
---|---|
J-invariant | Real part of the -invariant as a function of the nome on the unit disk |
Original upload log
Date/Time | Dimensions | User | Comment |
---|---|---|---|
2005-02-15 15:31 | 600×600× (71763 bytes) | Linas | Klein's J-invariant, real part (600x600 pixels) |
Captions
Items portrayed in this file
depicts
15 February 2005
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 12:36, 15 December 2014 | ![]() | 600 × 600 (70 KB) | Mx. Granger | Transferred from en.wikipedia |
File usage
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