File:Box Muller.svg
Original file (SVG file, nominally 292 × 687 pixels, file size: 19 KB)
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Summary
[edit]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
[edit]Public domainPublic domainfalsefalse |
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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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 18:54, 26 May 2006 | 292 × 687 (19 KB) | Dcoetzee (talk | contribs) | White background | |
16:47, 26 May 2006 | 290 × 674 (19 KB) | Dcoetzee (talk | contribs) | Vertical alignment | ||
16:40, 26 May 2006 | 690 × 288 (18 KB) | Dcoetzee (talk | contribs) | 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 spa |
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