Vision: Size vs Distraction

First thing you probably notice is that all of these are more difficult. However, the increase in difficulty for the fourth box is a lot larger than the increase in difficulty for the first. That's because it's filtering problem. In the first set of examples, it is trivial to filter out the dots, so you only need to look at 9 letters (the values 0-8) to find the one you're looking for. By comparison, the second set of examples is using a random fill of letters that don't easily get distinguished from the value you're looking for. In leftmost example, there are only 18 cells in my table, so we've only doubled the set we're examining, which is not a big deal. The rightmost example has 162 cells, so we've multiplied the size of the set of possible values by 18.

GURPS gives a fairly modest penalty for distance: a doubling of distance is only a -2. In reality detection odds are likely to fall off much faster than that; the situations in which you can see a person at 1,000 yards are very different from the situations in which you can miss someone at two yards. That's because there's really two issues going on: how easy is it to recognize what you're looking for, and how many possible false positives are there. If the number of objects we need to filter is unchanged, difficulty is really not that subject to size. Consider these three examples. The game is 'find the 2'.

Each of these cases is in fact about one step on the range/speed chart, and in fact, there really isn't a terribly large difference in difficulty. Now, let's do the same thing, only we fill the grid with noise: