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>"