Its also of note none of these measure predictability correctly, not even my example, all we're doing is measuring distributions, since none of these examples take order ( and therefore predictability ) into account, we're only demonstrating "net discrete distribution"* ( not sure if there's a proper term )
For instance: Vlad, in sorted.png - you have actually gone through and sorted these, which is not the same as Pearson correlation. Also your axes are unlabeled which confuses me, maybe you can clarify what I am visualizing when I see the rand() producing values in a different range of
bounds and not just a different distribution. Without clarifying what it is we're measuring its just confusing to other people, pretty much. I guess that's why I was making a big deal about the OP having a "bug", I think everyone pretty much figured he was using values straight from rand for X and Y for each dot
* Just saw you called this "probability distribution" - is this in fact what your code is measuring? What I am visualizing on each axis in unsorted and sorted, what "distribution" metric are you implementing here exactly? I would have figured draw a 2d vector of randomly produced digits for each Cartesian coordinate, and then calculate the distribution as { total covered dots } / { total available Cartesian "volume" } for a "single probability" for each function ( probability of calling it Nx with 0,N as bounds giving you even distribution between 0 and N ( lower values of probability would imply empty area and therefore repeated pixels - no need to count that 2x ). Even this its still mis-leading because what does this show? Is more even distribution less predictable? In that sense if I observe the first 100/400 dots drawn in the lower left quadrant of the graph, and I had to wager money on where the next dot would be drawn, I would not pick the lower left corner - so is even distribution any "less random" or "predictable". In fact to be truly random should we not measure the values over repeated test runs - and then measure correlations between those "meta" level tests, and test those tests - ad infintum
PS - yeah you might consider this off topic, but its interesting and at least some people find it on topic, so sue us
