Walking Randomly

I learned about entropy as part of my undergraduate Physics education but it turns out that the concept of entropy turns up in many fields including linguistics, themodynamics, information theory, chemistry and artificial intelligence.

As part of Sheffield’s Open Data Science Initiative, computer scientist, Neil Lawrence, has teamed up with linguist, Dagmar Divjak, to organise a cross-faculty discussion meeting on the subject of entropy.

For more details on the day’s events, and to register, see http://opendsi.cc/ed2016/program

I wasted a little time producing the above logo for the event using Mathematica.

Here’s the source code:-

(*consider column one pixel at a time. Invert the pixel if a random number is below some threshold*)
flipbit[col_, prob_] := Module[{result, temp, x},
  result = col;
  Do[
   If[RandomReal[] <=  prob,
    If[result[[x]] == 1, result[[x]] = 0, result[[x]] = 1];
    ]
   , {x, 1, Length[col]}
   ];
  
  Return[result]
  ]

text = "Entropy";
image = Rasterize[Text[Style[text, White, Italic, 190]], 
   Background -> Black];
imageData = ImageData[Binarize[image]];
const = 1/Dimensions[imageData][[2]]*0.42;
(*Apply flipbit to all columns. Increase probability of flipping as you move along the x-axis*)
logo = 
  Transpose[
   MapIndexed[flipbit[#1, const*#2[[1]]] &, Transpose[imageData]]];
Image[logo]

Finally, I found this quote about entropy that I quite like:

You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.

John von Neumann to Claude Shannon a name for his new uncertainty function. Source: Wikiquotes