en:Information entropy of a en:Bernoulli trial X. If X can assume values 0 and 1, entropy of X is defined as H(X) = -Pr(X=0) log₂ Pr(X=0) - Pr(X=1) log₂ Pr(X=1). It has value if Pr(X=0)=1 or Pr(X=1)=1. The entropy reaches maximum when Pr(X=0)=Pr(X=1)=1/2 (the value of entropy is then 1). The image was created in the following steps. First I have created a DVI version starting from a LaTeX/Pstricks source. Here is the code:

 %Plot of information entropy of bernoulli variable % %latex binary_entropy_plot; dvips binary_entropy_plot %open .ps file in gimp, choose strong antialias in both text and graphics, %resulution 500, color mode, crop, scale to 45%, save as .png documentclass[12pt]{article} usepackage{pst-plot} begin{document} psset{unit=4cm} begin{pspicture}(0,0)(1.01,1) psgrid[gridlabels=0pt,gridcolor=lightgray,subgriddiv=10,subgridcolor=lightgray](0,0)(0,0)(1,1) newrgbcolor{myblue}{0 0 0.7} psaxes[arrows=->,arrowsize=2pt 4,Dx=0.5,Dy=0.5](0,0)(0,0)(1.1,1.1) psplot[plotstyle=curve,plotpoints=100,linewidth=1.8pt,linecolor=myblue]{0.0001}{0.9999}{-1 x x log 2 log div mul 1 x sub 1 x sub log 2 log div mul add mul} rput(0.5,-0.22){$Pr(X=1)$} rput{90}(-0.28,0.5){$H(X)$} end{pspicture} end{document} 

compile it with latex to get the DVI. Then it was converted to PS with dvips. Finally it was converted to SVG using ps2svg.sh; it needed some post-processing with Inkscape

original work by Brona, published on Commons at Image:Binary entropy plot.png. Converted to SVG by Alessio Damato

April 2007

Brona and Alessio Damato

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