Dosiero:Gee three real.jpeg

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

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[redaktu] Detailed description

This image shows the real part of the Weierstrass elliptic functions invariant g3=140 G6 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 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 intensly filigreed. In particular, notice how this image has two colored lobes running down the middle. The corresping image for G2n will show n-=1 lobes.

[redaktu] Source of Image

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

[redaktu] Copyright status

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

[redaktu] Relevant Links

  • Weierstrass elliptic functions
  • Eisenstein series
  • Q-series
date/time username edit summary
19:25, 26 February 2006 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Gee_three_real.jpeg#Detailed_description" title="Image:Gee three real.jpeg">→</a>Detailed description -</span> typo)
01:51, 23 February 2006 en:User:18.87.1.212 (spelling)
01:46, 23 February 2006 en:User:18.87.1.212 (Spelling correction)
16:03, 15 February 2005 en:User:Linas (add to description)
04:51, 15 February 2005 en:User:Linas (fix formula)
04:03, 15 February 2005 en:User:Linas (change to square of nome)
06:33, 14 February 2005 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Gee_three_real.jpeg#Detailed_description" title="Image:Gee three real.jpeg">→</a>Detailed description</span>)
06:22, 14 February 2005 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Gee_three_real.jpeg#Relevant_Links" title="Image:Gee three real.jpeg">→</a>Relevant Links</span>)
06:19, 14 February 2005 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Gee_three_real.jpeg#Detailed_description" title="Image:Gee three real.jpeg">→</a>Detailed description</span>)
06:17, 14 February 2005 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Gee_three_real.jpeg#Detailed_description" title="Image:Gee three real.jpeg">→</a>Detailed description</span>)
06:01, 14 February 2005 en:User:Linas
05:55, 14 February 2005 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Gee_three_real.jpeg#Relevant_Links" title="Image:Gee three real.jpeg">→</a>Relevant Links</span>)
05:55, 14 February 2005 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Gee_three_real.jpeg#Detailed_description" title="Image:Gee three real.jpeg">→</a>Detailed description</span>)
05:52, 14 February 2005 en:User:Linas (provide basic info)
05:43, 14 February 2005 en:User:Linas (Weierstrass invarient g three.jpeg)

[redaktu] Historio de la dosiero

Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version.

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  • (del) (cur) 04:01, 15 February 2005 . . en:User:Linas Linas ( en:User_talk:Linas Talk) . . 600x600 (52911 bytes) (image changed to show square of nome instead)
  • (del) (rev) 05:43, 14 February 2005 . . en:User:Linas Linas ( en:User_talk:Linas Talk) . . 600x600 (53758 bytes) (Weierstrass invarient g three.jpeg)

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  • (for) (nun) 19:29, 18. Mar 2006 . . Maksim-bot (Diskuto | kontribuoj) . . 600×600 (52 911 bitokoj) (La bildo estas kopiita de wikipedia:en. La originala priskribo estas: Weierstrass elliptic functions invariant g<sub>3</sub>, real part (600x600 pixels) ===Detailed description=== This image shows the real part of the [[Weierstrass elliptic function)

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