File:Brownian hierarchical.svg

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Brownian_hierarchical.svg‎ (SVG file, nominally 1,195 × 1,250 pixels, file size: 56 KB)

An image of Brownian motion, done with three different step sizes. The hierarchical structure is clearly visible. Vector version of Image:Brownian_hierarchical.png made using Mathematica.

Mathematica code:

g = {last = {0, 0}}
Do[g = Append[g, last = last + Sqrt[-Log[Random[]]]{Cos[θ], Sin[θ]} /. θ -> Random[Real, 2π]], {2048}]
g2 = Partition[g, 8][[All, 1]];
g3 = Partition[g2, 8][[All, 1]];
plot = Show[
   ListPlot[g, PlotJoined -> True, PlotStyle -> RGBColor[0,.78,1], DisplayFunction -> Identity],
   ListPlot[g2,PlotJoined -> True, PlotStyle -> Blue, DisplayFunction -> Identity],
   ListPlot[g3,PlotJoined -> True, DisplayFunction -> Identity],
   DisplayFunction -> $DisplayFunction, AspectRatio -> Automatic, ImageSize -> 1000]
Public domain 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.

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Usage:

File history

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Date/TimeThumbnailDimensionsUserComment
current21:10, 21 March 2008Thumbnail for version as of 21:10, 21 March 20081,195×1,250 (56 KB)Di Gama (Talk | contribs) (An image of Brownian motion, done with three different step sizes. The hierarchical structure is clearly visible. Vector version of Image:Brownian_hierarchical.png made using Mathematica.)

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