File:Gee three real.jpeg
Summary
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 
on the unit disk |q| < 1. That is, 
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 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.
Copyright status:
GNU Free Documentation License, Version 1.2
Source:
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 02:36, 24 April 2021 | | 600 × 600 (52 KB) | Thales (talk | contribs) | Weierstrass elliptic functions invariant g<sub>3</sub>, real part (600x600 pixels) ===Detailed description=== This image shows the real part of the Weierstrass elliptic functions (wp) invariant ''g''<sub>3</sub>=140 ''G''<sub>6</sub> as a func... |
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