Keywords: Brownian hierarchical.svg 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 <pre> g last 0 0 Dog Appendg last last + Sqrt-LogRandom Cosθ Sinθ / θ -> RandomReal 2Ï 2048 g2 Partitiong 8All 1; g3 Partitiong2 8All 1; plot Show ListPlotg PlotJoined -> True PlotStyle -> RGBColor0 78 1 DisplayFunction -> Identity ListPlotg2 PlotJoined -> True PlotStyle -> Blue DisplayFunction -> Identity ListPlotg3 PlotJoined -> True DisplayFunction -> Identity DisplayFunction -> DisplayFunction AspectRatio -> Automatic ImageSize -> 1000 </pre> Brownian motion Images with Mathematica source code |