# File:Gee three real.jpeg

Gee_three_real.jpeg(600 × 600 pixels, file size: 52 KB, MIME type: image/jpeg)

## Summary

originally uploaded to en:wiki, with this history:

• 04:01, 15 February 2005 . . Linas (Talk | contribs) . . 600×600 (52,911 bytes) (image changed to show square of nome instead)
• 05:43, 14 February 2005 . . Linas (Talk | contribs) . . 600×600 (53,758 bytes) (Weierstrass invarient g three.jpeg)

Weierstrass elliptic functions invariant g3, real part (600x600 pixels)

### Detailed description

This image shows the real part of the Weierstrass elliptic functions (wp) invariant g3=140 G6 as a function of the square of the nome ${\displaystyle q=\exp(i\pi \tau )}$ on the unit disk |q| < 1. That is, ${\displaystyle \pi \tau }$ runs from 0 to ${\displaystyle 2\pi }$ along the edge of the disk. Black areas indicate regions where the real part is zero; 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.

See also Image:Gee_three_imag.jpeg for the imaginary part; both images use the same color scale, and thus give a hint of the relative magnitudes.

The corresponding image for g2 is quite similar. It, and other related images, can be seen at http://www.linas.org/art-gallery/numberetic/numberetic.html

The images for general Eisenstein series G2n will appear to be similar, but more intensely filigreed. In particular, notice how this image has two colored lobes running down the middle. The corresponding image for G2n will show n-=1 lobes.

### Source of Image

Created by Linas Vepstas User:Linas <linas@linas.org> on 13 February 2005 using custom software written entirely by Linas Vepstas.

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

## Licensing

 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.

### Captions

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## File history

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Date/TimeThumbnailDimensionsUserComment
current20:53, 21 September 2006600 × 600 (52 KB)Ylebruoriginally uploaded to en:wiki, with this history: * 04:01, 15 February 2005 . . Linas (Talk | contribs) . . 600×600 (52,911 bytes) (image changed to show square of nome instead) * 05:43, 14 February 2005 . . Linas (Talk | contribs) . . 600×600 (53,758
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