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File:Box Muller.svg

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Original file (SVG file, nominally 292 × 687 pixels, file size: 19 KB)

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]];

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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e568b72e84339da5c6a4c63dc001549ef42b87a5

19,487 byte

687 pixel

292 pixel

File history

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Date/TimeThumbnailDimensionsUserComment
current18:54, 26 May 2006Thumbnail for version as of 18:54, 26 May 2006292 × 687 (19 KB)DcoetzeeWhite background
16:47, 26 May 2006Thumbnail for version as of 16:47, 26 May 2006290 × 674 (19 KB)DcoetzeeVertical alignment
16:40, 26 May 2006Thumbnail for version as of 16:40, 26 May 2006690 × 288 (18 KB)DcoetzeeDiagram 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 spa
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