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Comment by imurray | Hacker News Reader

Those counts look fairly typical from a uniform distribution to me. There are fancy tests you could do, but to get a feel for it, I suggest simulation and eyeballing. Add up the counts after drawing 135 characters from a uniform character distribution 20 times, and compare the sorted lists of counts to this set of numbers after sorting.

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Somehow the really random distributions look less random than ones biased towards flattening-out. Within 500 truly random points in a square you'll see suspiciously looking clusters of points, choose 5 in each of the 10x10 subsquares and suddenly it looks much more "random".

Edit: A bookmarklet to display some random points in a square, tested in Firefox 10 only:

javascript:"<html><body><canvas id=\"tutorial\" width=\"150\" height=\"150\">foo</canvas><script>var canvas = document.getElementById('tutorial');var ctx = canvas.getContext('2d');ctx.fillStyle = \"rgb(000,0,0)\";for (var i=0;i<150;i++) {ctx.fillRect (Math.random() * 150,Math.random() * 150, 2, 2); };</script></body></html>"

...and one showing true random and flattened random side by side:

javascript:"<html><body><canvas id=\"tutorial\" width=\"200\" height=\"200\">foo</canvas><-><canvas id=\"tutorial2\" width=\"200\" height=\"200\">foo</canvas><script>var canvas = document.getElementById('tutorial');var ctx = canvas.getContext('2d');ctx.fillStyle = \"rgb(000,0,0)\";for (var i=0;i<400;i++) {ctx.fillRect (Math.random() * 200,Math.random() * 200, 2, 2); };</script><script>var canvas = document.getElementById('tutorial2');var ctx = canvas.getContext('2d');ctx.fillStyle = \"rgb(000,0,0)\";for (var i=0;i<20;i++) for(var j=0;j<20;j++) for(k=0;k<1;k++) {ctx.fillRect (i * 10 + Math.random() * 10, j * 10 + Math.random() * 10, 2, 2); };</script></body></html>"

Wow, you're right. The random distribution looks far more "meaningful".

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