Image:Q-euler.jpeg
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Euler's Q-series on the complex plane (600x600 pixels)
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[edit] Detailed description
This picture shows the modulus | φ(q) | on the complex plane, inside the unit circle 
, where
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.
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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. Subject to disclaimers. |
[edit] Relevant Links
- See also Q-series
- See also Pentagonal number theorem
- See also Partition of an integer
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Dimensions | User | Comment | |
|---|---|---|---|---|
| current | 17:47, 2 January 2005 | 600×600 (26 KB) | Linas (Talk | contribs) | (Euler's q-series on the complex plane) |
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