Anyway, I design my blocks around these assumptions, and when I discovered one of them did not work in the way I anticipated, I started to investigate. Here is some (very preliminary) work.
For all buildings, I count the square where they appear as being square 0. I count the square where they turn around only once. I was using the Sandbox custom mission, on hard, with the enhancement pack, and with a single road block near where the settlers enter. Anyway, here's what I found:
Firewarden: My little guy had two ranges: 52 squares and 43 squares. The sequence of journeys was -43,43, 52, 43 and then repeat. Upon destroying and rebuilding the firehouse, I got -52, 43, 52, 43, repeat.
Magistrate: The magistrate had three ranges: 44 squares, 48 squares, and 54 squares. Three different trials produced different sequences: first was 48, -48, 44, 54 then -48, 54, -48, 54, -48, 54... I wasn't watching the courthouse from when it was first built, so the initial sequence is longer.
The second trial produced 48, 44,54, 44,54,44,-48, 44,48, then I missed one, then 54, 44, -48, 44, 54... this is either a really irregular sequence or I was daydreaming and missed a journey or two. Anyway, I took a third trial. This one was with the courthouse to the positive side of the housing:
The magistrate's journeys were -48, 54, -48, 44, -48, 54, -48, 54, -48, 54...
The first two trials had housing on either side of the Courthouse. The fact that the magistrate was making a special effort to go away from the center of the map made me wonder if they could "learn" where the people are. The fire warden did not learn, btw- when put on the positive side from the houses, the houses all burned down. The physician had a periodicity similar to the magistrate with range 26 and 36, as follows: 26, -26, 26, 36 and repeat. This was with houses on both sides, in case that is important. I didn't investigate the physician very long, though, so there may be something weird going on here too. I'm pretty sure that it is 26 squares and not 27. Could someone else investigate these walkers and correct/extend these results? Despite the fact that my undergraduate degree is in honors mathematics, I've been known to count things twice and get different answers. Regards, Jimhotep