GtT:
I'm sorry it took me a couple of days to realize that your post was about roamers (labor recruiters) rather than about military matters. There are a couple of the questions (numbers 2 and 3) that you raised that have, I believe, definite numerical answers. As an enthusiastic, but not always terribly clever, student of walker behavior, I can at least provide those two numbers. First some ground rules: Labor recruiters behave for walk-start, walk-finish, and quadrambling purposes as common, short walkers. Even labor recruiters from a courthouse behave like common short walkers, despite the fact that the magistrate who will eventually inherit his labor recruiter's quadramble is a bureaucratic, long walker (in Brugle's terminology, introduced in the article to which he provided a link above). Therefore, all the tables of roamer quadrambles that I have posted (some of which contain errors) or made available in debugged *.pdf versions (which are as error-free as I can make them to date) via links from my quadramble-related posts are immediately applicable to labor recruiters. Now for your questions.
Minimum distance that a labor recruiter will travel = 26. I assume you mean in "out-the-door form", i.e., you count the (Brugle's walk-start) square on which the walker appears as square 0 and the first square to which he moves as square 1, and so on. Counted in this way the minimum distance that a common, short walker will travel appears to be 26, i.e., the length of a default walk. My best evidence for this assertion comes from examining the breaks in series of quadrambles that if extrapolated to larger buildings would force the game to generate a walk shorter than 26. At exactly that point in the series, the algorithm creates a discontinuity within the series to avoid generating a walk with length shorter than 26. Here's an example of a series of quadrambles for buildings of increasing size on the northeast side of a long, well-isolated, perfectly straight road running from NW to SE. All the "quadrambles" listed are in out-the-door form; the negative signs indicate walks heading towards the NW.Building size: "Quadramble" (o-t-d form)
1x1: 33, 26, -35, 26
2x2: 31, -33, -37, 26
3x3: 29, -33, -39, 26
4x4: 27, -33, -41, 26
5x5: -27, -33, -43, 26
6x6: -29, -33, -45, 26The algorithm's designer loved these nice, regular series of numbers that we see, for example, formed by the third entries in the six quadrambles above. But, look at the series formed by the first entries in those quadrambles. The first four numbers form a nice series but the next entry in that series after 27 would logically be 25, and the algorithm won't permit a walk that short. Instead, it starts a new series. If there were a 7x7 building in the game, I think we could predict how it's entry in the above table would look, don't you?
Maximum travel distance = 51 (or 52) Be assured, it is very seldom that you see walks that long from common, short walkers. After all, travel distances to turn-around of 51 squares are the hallmark of long walkers like firemen, architects, cops, and magistrates, any of whom will quadramble as (51, -51i, -51, 51i) if their building of origin is tucked up tight under the south quadrant of a four-way (viz., great big "X") intersection. Here is one way to see such a walk. We will be looking at a series of quadrambles (in intersection-relative, IR, complex notation) of zoo recruiters from zoos located east of a well-isolated, four-way intersection of long straight roads. The zoo is always positioned on the northeast side of the road leading from the intersection towards the southeast, but we will place the zoo at increasing distances from the intersection (i.e., at increasing "offsets", where the offset is the width of the gap between the NW side of the zoo and the road to the NE from the intersection.Offset: Quadramble (IR form)
0: (-23i, -27i, -39, 41i)
1: (-22i, -26i, 38i, 42i)
2: (-21, -25i, 37i, 43i)
3: (-20i, -24, 36i, 17i)
4: (-19, -23i, 35i, 16i)
5: (-18i, -22, 34i, 15i)
6: (-17i, 0 :> 21, 33i, 38)
We are interested in the series formed by the last numbers in these quadrambles. There are two discontinuities in this series. There is a massive discontinuity that occurs when the building is moved from offset 5 to offset 6. At offset 5, three squares of the road leading away toward the northeast (the "+i" direction) fall within the zoo's "domain". (I know you read my little article on domain shape, since you replied to it.) This means the algorithm will be strongly influenced and will respond to the presence of the road to the northeast. Since the formal direction associated with the fourth leg of a building's quadramble is northeast, it only makes sense for the walker to head that way on the fourth leg of the quadrambles in the above series.
When the building is moved to offset 6, the road to the northeast no longer lies within its domain. Believe it or not, the last quadramble in the series in intersection-relative form is the same as the last quadramble in the series shown in out-the-door form above. To get to any of the turn around squares that the walker has to reach by passing through the intersection when his zoo is at an offset of 6, he must first travel 12 squares to reach the intersection. Add 12 to the absolute values of -17i, 21, and 33i, and you get 29, 33, 45 as the distances to the left that the walker traveled. Subtract 12 from 38, and you see that when the building could no longer see the road leading to the northeast, it filled the fourth (NE) entry in its quadramble with a default walk.
Incidentally, the funny-looking entry forthe second leg of the quadramble for the zoo at an offset of 6 means that (for the walk I actually observed) the recruiter hiked 12 squares northwest to the intersection (to square 0) and "bounced off it" by reversing course and heading back towards the southeast, right past his stop and start squares to a turn-around point on the 21st square of the SE road before heading back to the zoo. Although I don't think I have seen service walkers exhibit this "bounce back" behavior more than once or twice, labor recruiters seem to do this more often.
The other discontinuity in the series formed by the fourth legs of the quadrambles in intersection-relative form occurs between offsets 2 and 3. At an offset of 2 from the intersection, the zoo's recruiter must first travel 8 squares from his walk start square towards the northwest to reach the intersection before turning towards the northeast and walking 43 more squares in that direction to reach his turn-around square. The algorithm generated this walk of 43 + 8 = 51 squares, but refused to issue the walk length of 53 that would have allowed it to stretch the series to offset 3. I found discontinuities in other series at the same point: always the walk of 51 is allowed, but a walk of 53 is not. Granary recruiters obey this rule, and so do town-palace recruiters. Temples (and smaller buildings) cannot be used to explore this limit because they lose sight (within their domains) of the road to the northeast right at the critical moment (or earlier for 2x2's) when we expected the nothing-longer-than-51 discontinuity so they are already giving us a domain-edge discontinuity. I have not been clever enough to find a series that allows me to see whether a walk of length = 52 is allowed or not.Disclaimer. My assertion that maximum recruiter travel distance to turn-around is a mere 51 or 52 squares applies only to recruiters from buildings whose quadrambles can be explicitly measured on one of the nine fundamental intersections (four corners, four T's and the X). I have recently begun to explore genuinely "implicit" quadrambles that can only be detected with road geometries formed from combinations of intersections. We may be able to break the 52-square limit with some of these geometries. If so, I'll be back.Although it's fun to know what numbers like this are, I think the shorting-out effect (especially the stuff that begins in reply 14) and how it can be used to make labor recruiters and other roamers head the "right way" (for a change!) would be far more useful for your industrial-block design purposes. You can use that information, for example, to create a fireman that marches towards the northwest on all four legs of his quadramble on a long straight NW-to-SE road, despite the fact that on a pure, well-isolated road the fellow goes SE on three walks out of four. If you really are as much of a control freak about walker behavior as I am, I would be positively delighted to show you how to calculate the quadramble of any or all of the buildings in your papyrus-producing, industrial block.I hope the walkers treat you well!
StephAmon
[This message has been edited by StephAmon (edited 06-29-2002 @ 02:20 AM).]