I don't doubt your numbers, although I haven't checked them (I don't know how
). I see no reason to allow or account for the randomness when it can be virtually eliminated. Yes, it can be eliminated, or at least vastly reduced, with a few instructions and a couple extra variables. I am sure you noticed the precisity of my encircling pirrahnas around your defended cities. They do sometimes get close enough to get whacked, but that is only after I exceed the instruction cap. If you eliminate the randomness when preciseness matters, the distribution wont matter either.
As I said, I am newb enough that I can't debug, and my tests are limited to observing behavior. I can't prove my observations, they are anectodal. My guess would be square. There are 2 other distribution patterns that I am pretty sure are square, and if they are, why would this be different. The artillery splash specifically seems to reach farther when going a negative direction vs a positive, that wouldnt happen with circular distribution. Likewise, the cities seem to spawn more frequently in positive direction. It may not be square, but I know its not circular.
I have a pretty nasty artillery seigebot in hiding, it encircles a defended city much more actively than my pirahnnas do, it actually spreads out into a circle if not threatened. It doesn't ever close in the way my pirahana do, it pegs the spawns and lets the splash do the work. The positive/positive quadrant of the siegebots seem to do more work than the other 3 quadrants combined. They not only get the majority of the spawns, but when the other quadrants get spawns thier splash is much less likely to reach the city & defenders. The neg/neg quadrant is essentially worthless due to this. That is the source of my observation that the distribution seems to be not circular.