Dosiero:Gee three imag.jpeg

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

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[redaktu] Detailed description

This image shows the imaginary 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 imaginary 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_real.jpeg for the real part; both images use the same color scale.

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.

[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.

Permeso estas donita kopii, distribui kaj/aŭ modifi tiun ĉi verkon sub la kondiĉoj de la GNU Free Documentation License, Versio 1.2 aŭ ia ajn alia versio eldonita de la Free Software Foundation; kun neniaj Senvariaj Sekcioj, neniaj Antaŭ-Kovrilaj Tekstoj, kaj neniaj Malantaŭ-Kovrilaj Tekstoj.
Kondiĉe de malgarantioj.

[redaktu] Relevant Links

  • Weierstrass elliptic functions
  • Eisenstein series
  • Q-series
date/time username edit summary
19:27, 26 February 2006 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Gee_three_imag.jpeg#Detailed_description" title="Image:Gee three imag.jpeg">→</a>Detailed description -</span> typo)
01:49, 23 February 2006 en:User:18.87.1.212 (yet more spelling)
01:48, 23 February 2006 en:User:18.87.1.212 (more spelling)
01:47, 23 February 2006 en:User:18.87.1.212 (Spelling correction)
16:00, 15 February 2005 en:User:Linas (add to description)
04:52, 15 February 2005 en:User:Linas (fix formula)
03:59, 15 February 2005 en:User:Linas (change image to be square of nome)
06:34, 14 February 2005 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Gee_three_imag.jpeg#Detailed_description" title="Image:Gee three imag.jpeg">→</a>Detailed description</span>)
06:23, 14 February 2005 en:User:Linas
06:02, 14 February 2005 en:User:Linas
05:57, 14 February 2005 en:User:Linas (Weierstrass invarient g three imaginary part.jpeg)

[redaktu] Historio de la dosiero

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(nun)19:29, 18. Mar 2006Maksim-bot (Diskuto | kontribuoj)600×60050 KBLa bildo estas kopiita de wikipedia:en. La originala priskribo estas: Weierstrass elliptic functions invariant g<sub>3</sub>, imaginary part (600x600 pixels) ===Detailed description=== This image shows the imaginary part of the [[Weierstrass ellipti

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