Image:Voronin-3.png
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[edit] Summary
| Description |
The Riemann zeta-function on the strip 1/2<Re(s)<1, 103<Im(s)<109, to illustrate Voronin's universality theorem. |
|---|---|
| Source |
self-made, with Mathematica 6.0 |
| Date |
December 2007 |
| Author | |
| Permission (Reusing this image) |
see below |
The image uses the following color function: 
. This means that the color of a point s encodes the value ζ(s) in the following manner: the hue of the color encodes the argument of the value, and the strength of the color encodes its absolute value. Strong colors represent values close to zero (black=0), weak colors represent values far away (while=infinity).
The following Mathematica 6.0 code was used to generate the image:
ComplexGraph[f_, xmin_, xmax_, ymin_, ymax_, points_: 100] :=
(* f is the complex function to be graphed in the region
[xmin,xmax] * [ymin,ymax].
The parameter points controls how many points will be
sampled in each direction; good values are 100-500. *)
RegionPlot[True, {x, xmin, xmax}, {y, ymin, ymax},
ColorFunction -> Function[{x, y},
Hue[Mod[Arg[f[x + I*y]], 2 Pi]/(2 Pi),
1/(1 + 0.3 Log[Abs[f[x + I*y]] + 1]),
1 - 1/(1.1 + 5 Log[Abs[f[x + I*y]] + 1])]],
ColorFunctionScaling -> False,
AspectRatio -> Automatic,
PlotPoints -> points]
Show[ComplexGraph[Zeta, 1/2, 1, 103, 109, 200], AspectRatio -> 5]
[edit] Licensing
 |
I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide. In case this is not legally possible: Afrikaans | Alemannisch | Aragonés | العربية | Asturianu | Български | Català | Česky | Cymraeg | Dansk | Deutsch | Eʋegbe | Ελληνικά | English | Español | Esperanto | Euskara | Estremeñu | فارسی | Français | Galego | 한국어 | हिन्दी | Hrvatski | Ido | Bahasa Indonesia | Íslenska | Italiano | עברית | Kurdî / كوردی | Latina | Lietuvių | Latviešu | Magyar | Македонски | Bahasa Melayu | Nederlands | Norsk (bokmål) | Norsk (nynorsk) | 日本語 | Polski | Português | Ripoarisch | Română | Русский | Shqip | Slovenčina | Slovenščina | Српски / Srpski | Svenska | ไทย | Tagalog | Türkçe | Українська | Tiếng Việt | Walon | 中文(简体) | 中文(繁體) | zh-yue-hant | +/- |
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Dimensions | User | Comment | |
|---|---|---|---|---|
| current | 22:48, 25 December 2007 | 418×2,011 (147 KB) | AxelBoldt | ({{Information |Description=The Riemann zeta-function on the strip 1/2<Re(s)<1, to illustrate Voronin's universality theorem. |Source=self-made, with Mathematica 6.0 |Date=December 2007 |Author= AxelBoldt |Permission= |other_versions= }}) |
