File:Discriminant real part.jpeg
Summary
Modular discriminant, real part, as function of nome. (600x600 pixels)
Detailed description
This image shows the real part of the modular discriminant 
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 or negative; 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.
In the above, g2=60 G4 and g3=140 G6 are Weierstrass elliptic functions invarients, whereas 
is the Dedekind eta function.
See also Image:Gee_three_real.jpeg and Image:Gee_three_imag.jpeg for the real and imaginary parts of g3.
The imaginary part is quite similar. It, and other related images, can be seen at http://www.linas.org/art-gallery/numberetic/numberetic.html
Copyright status:
GNU Free Documentation License, Version 1.2
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 02:41, 24 April 2021 | | 600 × 600 (66 KB) | Thales (talk | contribs) | Modular discriminant, real part, as function of nome. (600x600 pixels) ===Detailed description=== This image shows the real part of the modular discriminant <math>\Delta=g_2^3-27g_3^2=(2\pi)^{12}\eta^{24}</math> as a... |
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