Image:Box Muller.svg

[edit] Summary

Diagram of the Box Muller transform, which transforms uniformly distributed value pairs to normally distributed value pairs. The initial circles, uniformly spaced about the origin, are mapped to another set of circles about the origin that are closely spaced near the origin but quickly spread out. The largest circles in the domain map to the smallest circles in the range and the smallest to the largest.

Created by Derrick Coetzee in Mathematica and Adobe Illustrator using the following Mathematica code:

Export["box_muller_1.eps",
Show[Table[{Graphics[Hue[r/1.1 + 0.1]], Graphics[Circle[{0, 0}, r]]}, {r, 0.1,
       1, 0.1}], Axes -> Automatic, AspectRatio -> 1]];

Export["box_muller_2.eps",
Show[Table[{Graphics[Hue[r/1.1 + 0.1]], 
      Graphics[Circle[{0, 0}, Sqrt[-2.0 Log[r]/r]]]}, {r, 0.1, 1, 0.1}], 
  Axes -> Automatic, AspectRatio -> 1]];

[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: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. 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 | +/-

• Box-Muller transform