Image:Q-euler.jpeg

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Q-euler.jpeg‎ (26KB, MIME type: image/jpeg)

Euler's Q-series on the complex plane (600x600 pixels)

1 Detailed description
2 Source of Image
3 Copyright status
4 Relevant Links

[edit] Detailed description

This picture shows the modulus $| φ(q) |$ on the complex plane, inside the unit circle $|q| \le 1$ , where

$\phi(q)=\prod_{k=1}^\infty (1-q^k)$

is Euler's q-series for the Partition of an integer. The fractal self-similarity of this function is that of the modular group; note that this function is closely related to a modular form, the modular discriminant. Every modular function will have this general kind of self-similarity.

It is colored with a rainbow of colors, with black representing values near zero, and red values near four. Note the Modular group symmetry, and the general resemblance to colorings of the interior of the Mandelbrot set.

[edit] Source of Image

Created by Linas Vepstas User:Linas <linas@linas.org> on 2 January 2005 using custom software written entirely by Linas Vepstas.

[edit] Copyright status

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

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.
Subject to disclaimers.

[edit] Relevant Links

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