Summary

This graph image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}. It is recommended to name the SVG file “BenfordBroad.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.

Licensing

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.

(* Source code written in Mathematica 6.0, by Steve Byrnes, 2008. I release this code into the public domain. *)

LabelsList = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 70, 100, 200, 300, 500, 1000, 2000, 5000, 10000};
LineList = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600,
   700, 800, 900, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000};

ff[x_] := 
  x Exp[-.1 x] .1 + x Exp[-.03 x] .03 +  x Exp[-.01 x] .01 + 
   x Exp[-.003 x] .003 + x Exp[-.001 x] .001 + x Exp[-.0003 x] .0003;

firstdig1[xx_] :=
  (1 < xx && xx < 2) || (10 < xx && xx < 20) || (100 < xx && xx < 200) || (1000 < xx && xx < 2000);
firstdig8[xx_] :=
  (8 < xx && xx < 9) || (80 < xx && xx < 90) || (800 < xx && xx < 900) || (8000 < xx && xx < 9000);

plotA = LogLinearPlot[{ff[x], If[firstdig1[x], ff[x], 0], If[firstdig8[x], ff[x], 0]}, {x, .99, 10100}, 
  Ticks -> {LabelsList, {}}, PlotRange -> {0, 1}, TicksStyle -> Directive[Black, 10],
  GridLines -> {LineList, {}}, ImageSize -> 401, AspectRatio -> .3,
  Filling -> {2 -> Bottom, 3 -> Bottom}, PlotPoints -> 1000, PlotStyle -> {Black, Red, Blue}, 
  FillingStyle -> {2 -> Red, 3 -> Blue}]

Export["plotA.gif", plotA, ImageSize -> 500]

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