In both labs, a tiny housing block was established from which the needed worker to serve as labor recruiter for the test buildings could be drawn. Fire protection was installed in these blocks after conflagrations in the housing prematurely aborted a few early experiments. In the Sandbox, the housing was located on a different island (w/ the kingdom road) from the lab and lay approximately orthogonal to the center of the testing area. In Giza Lab the housing was close to due southeast from the experimental roads and was built on a rectangular road that was isolated from the kingdom road on which the testing was performed. This notation has the virtue of compactness for squares located on the road. For example, in Fig. 1 the plaza square that marks the walk-start point for the labor recruiter from the academy is at -4 Labor recruiters generated by the buildings all appeared on Brugle's start points for "normal" walkers, even the recruiters dispatched by police stations, tax agencies, courthouses, and dance stage drawing workers for their pavilions. Labor recruiter's from storage yards obeyed Brugle's special rules for their starting and finishing squares. All labor recruiters executed a repeating cycle of four walks (quadrambles). The locations of the squares in which labor recruiters turned around and headed back to their buildings are shown for each combination of building and quadrant in Table 1. The turn-around squares in Table 1 are listed in their order of occurrence from left to right inside each set of square brackets. The first walk by a labor recruiter from a newly placed building can be to any of the four turn-around points listed for a structure of its size and quadrant in the Table, but subsequent walks will be in the order shown, repeating the cycle once the fourth walk has been executed. Thus, if a 3x3 structure is placed in the south quadrant of a four-way intersection and it emits a recruiter that turns around 34 squares southwest of the intersection on road square -34i, the next recruiter walking from the same structure will turn around on square -34 northwest of the intersection, and the one after that will turn around 34 squares northeast of the intersection, etc. For every tested structure adjoining a four-way intersection, the turn-around points rotated in this clockwise fashion, which is why the pattern of negative signs and i's in Table 1 is so regular. The walker turn-around points for structures in the south quadrant (Table 1) all seem to be "bracketing" the intersection itself, in that they are neatly located exactly 34 squares away from it along all four possible directions. None of the turn-around points for buildings in the other three quadrants similarly bracket the intersection but each quadramble does seem to be bracketing some other point. With the sole exception of 4x4 buildings in the north quadrant, the difference between the value of SE and NW turn-around points for any quadramble in Table 1 always seems to be 68, just as it was for the south structures: 34 - (-34) = 68. In the imaginary direction the difference between the NE and SW turn-around points is always 68i. We can find the location of the target square that the turn-around points of a quadramble seem to be bracketing by taking the average of the real turn-around points and the average of the imaginary turn-around points to yield the real and imaginary components, respectively, of the bracketed or target square, as shown in the last column of Table 1. The locations of the bracketed points shown in Table 1 change with increasing building size in regular sequences. The bracketed target point for the 1x1 buildings is always the square diagonally touching the north tip of the building, i.e., in Brugle's walk-finish square #1 for most buildings. The bracketed point for the larger buildings moves generally further north from the north tip of the building as building size increases. For buildings in the east quadrant the target square is level with the square diagonally touching the building's north tip and located Fig. 1 shows the targeted square associated with the courthouse as the isolated grassy square. It is level with (i.e., on the same NW2SE line with, or horizontally level with in the figure) the north tip square but moved across the street until it is three squares away from the 3x3 courthouse. The square bracketed by the turn-around points of walkers generated by the academy is shown by the small statue in Fig. 1. This targeted point is vertically lined up with the north tip square in the figure, which means it falls on the same NE2SW line of squares. The square bracketed by walkers from the tax office is marked with a shrine in Fig. 1. It lies two squares from the north tip of the building in both the northwest and northeast directions. From the results in Table 1, we can begin to see the outlines of the algorithm used to generate the turn-around points for the labor recruiters. In 15 out of the 16 cases shown in the table, the problem simplified to one of determining the location of a single square to target with bracketing walks by the recruiters. It would go something like this: Let Target = the square diagonally touching the north tip of the building. Buildings placed in the south quadrant fail both of the tests in the algorithm. The Let statement positions their target initially in the intersection, so it The words in parentheses in the If statements probably fail to capture all the subtlety of the algorithm. A large building can extend its target a considerable distance from itself possibly crossing roads not touching the building. Does crossing such a road suppress further movement of the target parallel to the road as the target moves across the road? We are often forced to build some fairly contorted roads by the landscapes the game presents to us. Surely some of these must create geometries that trigger effects on the location of the target not captured in the simple algorithm outlined above. The granary in Table 1 and the several other 4x4 buildings I have tested in the north quadrant of four-way intersections seem peculiarly blind to the presence of roads running to the southwest and southeast from the intersection. It certainly sent its recruiters on longer walks than would have been needed to complete the bracketing of the target square. Instead of the theoretical bracketing walk to road square 26, the granary sent a recruiter to 34i. Instead of a bracketing walk to -26i, the recruiter made the longer trip to -34. The granary does not seem to be schizophrenically trying to partially bracket the intersection, since the 34i and -34 walk occurred in counterclockwise order, the reverse of the order used for bracketing walks. (Hit the size limit! Continuing in next reply.) [This message has been edited by StephAmon (edited 12-28-2001 @ 02:33 AM).]
Quadrant Structure Bracketed square North Architect -2+2i Dance stage -4+4i Ptah's temple -6+6i Granary (or senet house) -8+8i East Police station 2i Juggler school -1+3i Courthouse -2+4i Dance school -3+5i South Firehouse 0 Scribal school 0 Cattle yard 0 Senet house 0 West Apothecary -2 Bazaar -3+i Ra's temple -4+2i Academy -5+3i
If Target is "not in a road running in the real direction" {
Target = Target - (
}
/* i.e., move the target across the road but no further parallel to the road*/
If Target is "not in a road running in the imaginary direction" {
Target = Target + (
}
/* Again, the target moves across the road, but no further parallel to the road*/
The targets that were bracketed by the turn-around points of the walkers emitted by buildings adjoining the original four-way intersection appeared still to be targeted when the road to the SW was deleted. Except for the granary in the north quadrant, three out of four turn-around points in the quadramble for each building in Table 2 match the turn-around points for the same sized building in the same quadrants recorded in Table 1. Clearly the recruiters could not be sent to the target's location minus 34i since no road in the -i direction now existed, so the second turn-around point for the quadrambles in Table 2 cannot be predicted from the results in Table 1. So what happened when the -i leg of the bracketing procedure came up in the clockwise rotation through the quadrambles? The algorithm inserted placeholder walks. In the case of buildings located in the south quadrant, these placeholders were pretty simple: the recruiter got booted out the door (onto road square 1) with instructions to head SE for 26 squares (which would put him in road square 27, as shown on the table). The booth in the east quadrant and the firehouse and tax office in the west appear to have done the same thing. The apothecary in the north quadrant and (after some initial instability) the cattle farm and dance school to the west also dispatched recruiters on short 26-square runs only they were sent to the northeast (in the +i direction). Some buildings did not shoot out recruiters on 26-square placeholder walks. The temple in the north quadrant sent its recruiter to -34 as a placeholder. That was a walk-to-turn-around of length 37 squares, a distance for which I can find no significance. However, it was also a walk that took the recruiter 34 squares from the square diagonally touching the south corner of the temple, i.e., the temple's "south tip square". As we have seen, 34 is a magic number. The hunting lodge, courthouse, and senet house in the east quadrant also used placeholders for the -i leg of the full bracketing quadramble that had their recruiters turn around -34 squares from their south tip squares. The buildings in the west and south quadrants lacked roads touching their south corners, so perhaps a run-34-from-my-south-tip-square" placeholder was not an option for them, and they had to content themselves with short placeholders. Much work remains to be done to investigate the properties of labor recruiters dispatched by buildings on three-way intersections. The temptation was strong to investigate buildings like those in the south quadrant shifted one square to the northwest (so that their walker-start square) was right in the intersection. However, we allow very few three-way intersections in our housing or industrial blocks and usually none in which one of the roads is any longer than a mere stub. Accordingly, I chose to devote the next two series of observations to road geometries that we actually use a lot in our blocks: bends in the road and straight roads. (Continues in next reply.) [This message has been edited by StephAmon (edited 12-28-2001 @ 02:52 AM).]
Quadrant Structure Turn-around squares in quadramble Bracketed square North Apothecary -2+2i Physician -4+4i Ptah's temple -6+6i Granary -8+8i East Booth 2i Hunting lodge -1+3i Courthouse -2+4i Senet house -3+5i South Dentist 0 Work camp 0 Conservatory 0 Academy 0 West Firehouse -2 Tax office -3+i Cattle farm -4+2i Dance school -5+3i
Once again, the buildings in the south quadrant reward our growing faith in their predictability by dispatching labor recruiters that bracket the intersection using the only two remaining road directions with turn-around points: on the SE road at 34 and on the NE road at 34i. Both the second and third numbers in the quadrambles shown for all buildings in Table 3 (those corresponding to walks in the -i and -1 directions in Table 1) must be filled with placeholder walks, and the south quadrant buildings use the most easily recognized placeholders for this purpose: default runs of 26 squares from the walker start square to the southeast. All the buildings in the east quadrant also use default 26 square runs to the southeast as placeholder substituting for a now impossible run to the northwest (-1 direction), but their placeholders for runs in the -i direction are different: their recruiters are sent 26 squares in the i direction, but counting begins not from the walker start square (which moves southeast as building side increases) but rather from a square the buildings could be "thinking of" either as the intersection or as the square diagonally touching the west corner of the buildings. The 1x1 structure in the north quadrant substitutes default 26 runs to the northeast (turning at 27i) for both impossible negative bracketing runs. The larger buildings in the north quadrant continue to substitute default +26i runs for the walk that would have be towards the northwest, but switch to replacing runs in the SW direction with default 26 runs in the SE direction in which counting begins either from a square identified either as the intersection or as the square diagonally touching the south corners of the buildings. The blind-as-a-bat 4x4 structure in the north quadrant again fails to dispatch a bracketing recruiter in the SW direction and substitutes what should have been a walk to (positive real) 26 with the same long default walk to 34i that the north quadrant granary used on the four-way intersection (Table 1). (Continues) [This message has been edited by StephAmon (edited 12-28-2001 @ 10:25 PM).]
Quadrant Structure Bracketed square North Architect -2+2i Work camp -4+4i Ra's temple -6+6i Dance school -8+8i East Police station 2i Mortuary -1+3i Conservatory -2+4i Granary -3+5i South Fire house 0 Juggler school 0 Cattle farm 0 Senet house 0
The turn-around points in Table 4 for straight real roads all conform to patterns we have seen in the results from earlier studies with intersections. The structures below the road bracket their north tip squares (plaza in Fig. 4) with runs in the directions they have available: the first and third in their quadrambles, and substitute the most readily recognizable placeholders (default +26's) for bracketing walks in unavailable directions. The dentist above the road makes the same substitutions, and all the larger buildings above the road also use a default +26 substitution for the now impossible +i direction run (fourth number in the quadrambles). The larger buildings above the road try to confuse us by switching to default -34 runs from the south tip square as substitutes for the impossible -i direction bracketing runs that would have occupied the second position in the quadrambles, but we have seen this before as the second most common placeholder in earlier results. The turn-around points in Table 5 for straight imaginary roads (NE2SW) are just as explicable as their real-road counterparts. The labor recruiters from buildings located south of the road bracket their north tip squares with walks to -34i and 34i as the second and fourth entries in their quadrambles. Their impossible bracketing walks in the absent real directions (first and third quadramble entries) are replaced with easily recognizable default +26i runs, as are the real bracketing points in the quadramble for the police station north of the road (Table 5). The larger structures north of the road switched to long defaults of +34i from their south tip squares in a departure from the pattern of preferred default directions established by structures on the real road. On the real road, all the short default (+26) runs were dispatched to the southeast from the usual walker start square (Table 4). Buildings (2x2 through 4x4, north of the real road) that used the long default 34 walk from the south tip square dispatched recruiters on these runs in the direction (Continues) [This message has been edited by StephAmon (edited 12-28-2001 @ 10:01 PM).]
Quadrant Structure Turn-around squares in quadramble Bracketed square North Dentist -2+2i Jeweler -4+4i Ptah's temple -6+6i Granary -8+8i South Dentist 0 Work camp 0 Cattle farm 0 Granary 0 Quadrant Structure Bracketed square North Police station -2+2i Jeweler -4+4i Cattle farm -6+6i Dance school -8+8i South Firehouse 0 Potter 0 Temple 0 Dance School 0
The results reported here abundantly corroborate the hypothesis advanced by Your comments and suggests are welcomed by
The results from parallel roads give us two useful insights into the algorithm for quadramble generation: 1, a 3x3 building can "see" and the algorithm can be affected by roads that are two squares due north or northeast of its northern square; and 2, a 3x3 building north of a real road will look across the road for another road lying six squares either due south or southwest of the sourthern square of the building. If the algorithm did not look south or southwest, the quadramble for Bastet's temple in the parallel road study would not have differed even slightly from the quadramble for Ptah's temple in Table 4, but it did. If the algorithm did not "look" at least two squares north or northeast, the cattle yard on the southernmost road would not have seen any of the other roads, but it clearly did, since its recruiter's quadramble is all defaulted out. If the algorithm looked seven squares beyond a 3x3 building's north square, the middle two building's could have generated different quadrambles, but they are both so thoroughly trashed by the presence of additional roads to both the north and south that we cannot tell if they are affected by the presence of a fourth road.
To this point, I have done little more than alude to my older work at hard difficulty, scrupulously to avoid changing more than one variable at a time between experiments, but now I will play fast and loose. Some of the most thoroughly replicated data I collected at hard difficulty are for the quadrambles of labor recruiters from eight firehouses and four architects located north of four real, parallel (separated by four squares) roads. All sixteen of these quadrambles are exactly like the one shown in Table 4 for the north "quadrant" dentist: two long runs bracketing the south-tip square are separated by two short default runs to the southeast. In addition, four firehouses located (one apiece) on the south sides of each of the same parallel roads sent recruiters on quadrambles indentical to the one shown for the south quadrant dentist in Table 4. Four scribal schools located one per road on the north sides of the same parallel roads dispatched recruiters on quadrambles slightly different from the quadramble shown in Table 4 for the jeweler: instead of the deceptive, long, negative default run holding the place of the -i leg of the quadramble, all four schools switched to a short, positive default run. The quadrambles for the schools were not confirmed through a second repetition, because one school caught fire half way through the fourth leg of the first iteration of its quadramble (its recruiter disappeared at the turn-around square), and the other schools burned shortly thereafter.
The shorting-out effect of parallel roads on the recruiter quadramble-generating algorithm may help to explain the observation reported by NH_AnlaShok (02MAY00) (as the 20
There is another question to which I would like a definitive answer. Does finding housing change the quadrambles of a building's labor recruiter? JWorth (11MAR00) in
Beyond parallel-road and housing-effect research, I could envision quadramble research developing along at least two different tracks. First, and my own personal inclination, is to attack the quadramble-generating algorithm with the full force of the scientific method to see how much we can learn about it. After all, the algorithm yielded up a good many of its secrets to the casual probing reported here, and the scientific method is designed to reverse engineer natural processes with a whole lot more inexplicable variability than Pharaoh walkers seeme to exhibit. Second, research could be focused on exploiting the reproducibility of recruiter behavior to completely debug industrial blocks abutting sides of housing blocks from predetermined compass directions. We could find which locations send labor recruiters reliably toward the housing and which do not so we could avoid the latter. Once debugged, a given block could be reused in new games with confidence provided that players do not corrupt the block by bringing new roads too close.
Dissecting the algorithm has two real potential disadvantages: 1, nobody ever said that applying the scientific method was quick and anything other than labor-intensive; and 2, if the algorithm turned out to be fairly complex, nobody in his or her right mind would use it to predict the quadrambles for all the structures in a housing or industrial block to make sure that no cattle farms flickered on and off and no housing devolved for want of religion. It might be faster simply to reproduce the intended road geometry in a desert lab and plug the buildings one after the other into their proposed locations to see which spots were blessed and cursed with good and bad quadrambles. Even knowing that it may be a fool's errand, I am not sure I can resist the temptation of a good problem just waiting there when I think I have some ideas for how to solve it. Certainly, I have a pretty miserable record when it comes to resisting temptation. So, I hope the regular visitors to this site will forgive me if I return from time to time with a few more tedious reports on little things I might learn about the "wacky walkers" that have helped to make Pharaoh such a source of pleasure for so many of us.
StephAmon
ssimkins@pssci.umass.edu
That's a lot of data--perhaps it would help if you'd summarize any conclusions that appear to be universal. And I'm curious--did you repeat the experiments at several different map locations, or just in one place on each of the maps?
By the way, as far as I know, Max hold the current record for completing Rostja with 226 months.
Thank you; it's nice to finally have something worth telling the good people here about.
The Abstract is supposed to provide some kind of a summary of the major results from my study. I know my writing could be clearer, but I would not have put the claims I included in the abstract there if I did not think they were essentially universal. The only thing that keeps them from being truly universal is that they only apply to well-isolated roads, for which none of us have the slightest use in a real, working city. But, isolated roads are at least a place to start, if we really can trust that we know exactly how a given sized building on a simple pretested road geometry will instruct its labor recruiter. Isolated-road results can be extended - making just one change at a time - to see what sorts of changes affect recruiter (or other walker) quadrambles and which ones do not - expanding the set of road geometries we understand until we are talking about real-city geometries.
WHen I began the line of research that eventually led to the collection of the data for the long post above, I went on an all out hunt for the sources of variation in labor recruiter behavior. I found only road geometry. The only real mention of that hunt in my post was buried towards the end of the Results section where I mention some early results at hard difficulty. At the time, I was checking to see whether I got different results if I set up (as nearly as I could) the same well-isolated road geometry at different map locations. I was concerned that there might have been map-square-dependent variability in recruiter behavior in much the same way as we observe location-dependent variation in the tendency of housing to coallesce into 2x2 buildings; in some spots 1x1's fuse, in others they refuse to as long as they can. I was also trying to detect anything like a random number generator at work, or some kind of internal game clock (like game-time of day, or "frame of day") playing a role in determining the quadrambles.
I did most of my hunting for sources of variation using 1x1 structures in Sandbox. I never found map-square-dependent variation in the quadrambles, using (for example 8 firehouses on eight different squares). I could not find variation in the quadrambles at all unless I changed the road geometry in the vicinity of the buildings. If there are any clocks or random number generators involved in recruiter behavior, their only likely role would be in determining the starting leg of its quadramble on which a new building sends it recruiter. I also could not find any difference between the quadrambles of labor recruiters from different buildings of the same size, and I could not find any variation there, either, except for the storage yards that you (Brugle) warned us all about, and that were explicitly addressed in my post.
The fact that the behavior of recruiters from several series of 1x1, ... 4x4 buildings made such regular patterns suggests to me that, absent map-square dependency, there is simply no detectable variation between the behavior of a whole lot of buildings around two intersections located in two different maps. Right now, I am so tired of hunting in recruiter behavior for variation of the sort we see all the time in biology only to discover that I (once again) did not find any, that I'm not sure I have the heart to set up shop on a bunch of different maps. BUT, if an interested reader observes a labor recruiter on a long straight, fairly well isolated road that does not jive with the results in my Tables 4 and 5, I surely hope he or she would drop me a line about it. I'm prepared to check again!
In fact, there's a little game we play in the scientific research community that our fellow readers of the posts to this forum might want to play. One researcher advances a hypothesis about how the world works that predicts what will happen if you do a particular experiment. His colleagues/competitors all over the globe then try to prove the claim wrong with their own experiments. If they succeed, they have the pleasure of anouncing the collision of egg with the first researcher's face. But if a bunch of them try and cannot disprove the hypothesis, then they all start to believe that maybe they are looking at something real. Try it, it's fun! My ego is secure; I won't wilt like a flower if you find yourself "regretfully forced to tell me" that I'm full of it. If you prove my predictions (the quadrambles in the tables) are wrong on well-isolated, unpopulated roads meeting the descriptions in the methods section but which can be set up in any map or on any other location in Sandbox or Rostja, I WANT TO KNOW!
In the meanwhile, short of pseudonatural variability, I think my next project will be to look for housing effects on recruiter quadrambles. After that, I think we need to check out the "range of vision" or "purview" or "domains" (What should we call this area?!) around buildings that they examine for roads in determining the quadrambles on which to dispatch their recruiters. Already, I think we can be pretty sure that the a building's purview expands with building size.
StephAmon [This message has been edited by StephAmon (edited 12-27-2001 @ 04:03 AM).]
Shoot me some email at: ssimkins@pssci.umass.edu
Because I care not a hoot about reproducing the results in my earlier Tables 1 or 2, I chose to try to reproduce the numbers in Table 3, for the bends in the road that we all allow in our housing and industrial blocks. They reproduced with the same bizarre perfection that I have come to expect. I won't repeat the numbers, because they are exactly what I presented in Table 3 in my original post above. However, you folks might want to know that I chose completely different buildings for these trials. The buildings that reproduced in Cleopatra's Alexandria the earlier results in Table 3 were as follows.
North quadrant: Apothecary, Brewery, Courthouse, Granary.
East Quadrant: Booth (and dentist), Weaver, Ptah's temple, Senet house.
South Quadrant: Police station, Water supply, Conservatory, Dance School.
I also tried out a zoo in the south quadrant, and its recruiter executed the same Interested readers are cordially invited to check these results on well- isolated roads in other maps.
(soapbox) You express a true scientific attitude, which is sometimes lacking in the "scientific research community". A hypothesis that calls into question something fundamental (or at least threatens funding) may be ignored and, if that doesn't work, there may be serious pressure to prevent its investigation. The most obvious case in recent history is AIDS, where one commentator suggested (seriously, as far as I could tell) criminal charges against people who question the commonly accepted theory, even though that theory's predictions have been spectacularly wrong. (/soapbox)
I wish you (or anyone who further researches labor recruiter behavior) the best of luck. I generally design in a way that guarantees good labor access, but every now and then I don't. It would be nice to know a little more--for example, that only roads within a certain distance of a building affect the behavior of its "random" walkers.
Thank you for more kind words. I try to stay away from the big controversies in science. They can land you face down on the floor recanting your words at the feet of the pope, or get your books banned from biology classes in the great state of Tennessee.
I could not agree with you more that it would be nice to know the domains outside of which buildings ignore roads when programming their labor recruiters, since the same ranges and algorithms are likely to be reused for at least some classes of service-providing walkers (esp., "short walkers"). I fully intend to explore the domain issue as soon as I figure out if it's safe to put housing in my labs. My current working hypothesis is that the absence versus presence+distance+direction of housing are ignored when calculating walker quadrambles, but this is (as we say in the business) a "falsifiable hypothesis", which I'm currently trying to falsify. However, the buildings sure as heck notice when their recruiter passes over two squares each of which is within two squares of occupied housing. The generation of additional labor recruiters is surpressed for a long while. For industries, this means you get no more data before the building burns down. At least buildings that dispatch service-providing walkers give you something to watch, record, and compare to the tabulated quadrambles of the labor recruiters from the same buildings.
I'll be back when I learn something useful.
StephAmon
[This message has been edited by StephAmon (edited 12-27-2001 @ 02:16 PM).]
I have not had the time to study your post in detail. I just wanted you to know that I very much admire the quality, detail and methodology of your study. I anticipate having many questions and comments as soon as I have had time to absorb all of the information that you have posted here.
The behavior of so-called “random walkers” is likely Pharaoh’s last great mystery. The limited studies that I have made on this subject were enough to convince me that there was a defining algorithm to their behavior. But, I never came close to ascertaining what it might be.
Many thanks for your generous observations. After admiring so greatly the work of art into which you transformed Cleopatra's Alexandria, I have felt rather guilty about turning the same landscape into little better than a concentration camp for the cruel-hearted study of starving, hut-dwelling walkers. I hope it all proves to be worthwhile.
StephAmon
1. Adding housing to a road-plus-building problem does not change a service-providing building's quadramble; it only changes the identity of the walker who executes the quadramble.
2. If a building's labor recruiter finds abundant housing on his first search, then the building's service walker is immediately dispatched (before the recruiter's return!) on the next leg of the recruiter's quadramble. As long as the service walker continues to pass sufficient housing, further emission of the labor recruiter is suppressed. In this case, the service walker "inherits" the recruiter's quadramble.
3. If a building's labor recruiter finds insufficient access to housing on his first few searches, no service walker is dispatched until the usual access conditions are met on a single leg of the recruiter's walk. The service walker is then emitted (on the next leg of the building's quadramble) 4. A long walker (fireman, architect, police, tax puke, or magistrate) also inherits the quadramble of his building's labor recruiter. His base distance for bracketing changes from a short walker's paltry 34 squares to a magestic 51 squares. His equivalent to a short walk of 26 squares from the current geometry's walker start point ("Make klicks for 26." Or, "Hit the bricks for 26.") is 44 ("Out the door for 44.") Can you tell that I've been watching way too many walkers in my labs, if I've had to come up with mnemonics like these?. 5. Even the closest passages by a building of immigrants, other building's roaming walkers, traders by land, and destination walkers have no effect on its quadrambles. I feel extraordinarily stupid for my earlier caution, but the scientific method left me no choice but to worry about these things. 6. The proximity of other buildings, even immediately abutting ones, seems to have no effect on the quadramble of the building of interest: more absurdly misplaced concern on my part. 7. Walkers generated by buildings on linear roads (either perfectly straight or with a single, clean corner) appear to ignore (when computing their quadrambles) differential access to housing on the separate legs of their quadrambles. 8. Walkers generated by buildings within five squares of a four-way intersection follow such formal, constrained, and majestic walks that I do not see how they could squeeze in a little consideration for puny issues like where the people live. 9. Buildings within five squares of a three-way intersection may or may not consider highly differential availability of housing on the separate legs of the quadrambles they generate for their workers. One of the quadrambles footnoted as "unstable" in my Table 2 at the beginning of this thread just barely flunked a chi-squared test for indicating a preference for housing at the 95% level. However, this is such a subtle and secondary effect that I cannot believe that real Pharaoh players would ever trust in it, and I don't intend to get invaded by Roman Navies researching it further. 10. No fine-scale map-position effects appear to influence walker quadrambles in the same way that fine-scale map positions affects 1x1 vs. 2x2 housing coalescence, except (possibly) in determining which leg of a building's quadramble is the first to be walked by the labor recruiter of a newly placed building. 11. I have detected not the slightest difference between quadrambles from Rostja, Cleopatra's Aexandria, and the Sandbox, but there may be differences between maps that my limited sampling missed (although I would be rather surprised). 12. For the determination of walker quadrambles: Road geometry matters, esp. within five to seven squares of a building, where the discontinuties always seem to occur despite the best effots of the game designers to disguise them. The compass direction matters. The building's Brugle-walker-finish and -start squares matter. As far as I can tell, nothing else matters enough to worry about. 13. Anyone who tells you that Pharaoh's walker algorithm is random and unpredictable is wrong. Please forgive my tardy response to any reply that you might make to this post, but I have to submit grades on 2JAN02 for 230 students, and, even worse, I have relatives coming - for "First Night" just when I felt sure I was on the verge of cracking at least enough of Pharaoh's walker algorithm to offer results for Well Isolated(!): clean straight roads, clean corners, and clean four-way intersections. The three-way intersections still scare me. Alas, I can't do contorted roads yet or explain the shorting-out effect of parallel roads. StephAmon [This message has been edited by StephAmon (edited 01-05-2002 @ 03:39 AM).]
I finally had sufficient time last night to study your post in detail. It’s not exactly causal reading. The information is well presented and becomes clear if you make sure you understand each sentence before you proceed to the next. I printed the entire thread, and that helped a lot.
If the purpose of your venture was simply to determine that there was indeed an algorithm that defines walker behavior, and to identify the algorithm, then you are getting very close. If the hope was, that by defining the algorithm, we would have a tool to improve our city building skills, then there is a lot of work yet to be done.
Your most recent post (Reply #13) was encouraging. Your discovery that service walkers use the same algorithm as labor recruiters simplifies the problem greatly. Most encouraging was statement #12 in that reply. We know compass direction and we know the start and finish points (thanks to Brugle). If it can be determined how road geometry modifies the algorithm, we will really have a tool that we can use.
I agree that it was first necessary to run the tests in isolated locations. A benchmark for walker behavior had to be established. But, as you realize, this is not the way we layout our cities. I personally prefer to design fully connected cities, with all parts of the city interconnected by roads. Even with disconnected portions of the city (the dock and/or industrial areas), the major portion of the city is still interconnected. The impact of this interconnected road geometry can be enormous. I once ran a test to see to what extremes a walker’s start and finish points could be exploited.
For the test, I used the configuration shown in Diagram 1 (with north to the upper left). There is no road tile for the Water Supply at the most desirable start point, so the labor recruiter (and eventually the service walker) begins his walk at start point #2 and proceeds in the direction of the housing. The diagram shows the road ending near the left side, but in my first test this was actually a 101 road tile loop that ended at the most preferred finish point at the upper left-hand corner of the Water Supply.
Diagram 1
A 101 tile loop is well beyond the normal range for a labor recruiter/walker, but as Brugle described, the recruiter/walker finished the loop anyway. I next extended the loop all over a large map for thousands of rood tiles. Still, the recruiter/walker walked the entire path. I then added additional roads, creating hundreds of intersections, and a maze that had only one solution back to the preferred finish point. (At this point, I deleted and rebuilt the Water Supply just to make sure that the recruiter/walker had not somehow “learned” the correct path.) The newly generated recruiter/walker executed the entire maze with never a wrong turn. I eventually added bridges, roadblocks and gatehouses to the path with no change in behavior noted. When I did edit the road layout to create a shorter possible route back to the preferred finish point, the next walker generated “discovered” the shorter route and used it. (As a side note, even though a recruiter/walker will not cross a ferry, the addition of a ferry in the path back to the preferred finish point did generate a “long walk” that ended when the walker reached the ferry and “blinked out”.)
The reason that I mention this test is that it shows that when all roads on a map are interconnected, the recruiter/walker can “see” the entire map (at least in regards to preferred start and finish points). This could help explain observations by several players, including Brugle, that previously consistent walker behavior in an established block can be disrupted by building roads in an entirely distinct portion of the map.
(continued in next reply)
An observation: You have already determined that the algorithm is the same for hard and normal difficulties. I would like to suggest that you might run future tests at easy difficulty. This will greatly reduce the frequency of buildings catching fire or collapsing. I would be very much surprised if the difficulty level affected the algorithm. (But, as you say, this is a “falsifiable hypothesis”, and should probably be verified before proceeding.)
I was disappointed (in the results, not your methodology) that the results for three-way intersections were not consistent. A three-way intersection is the most common way that I enter a housing/industrial block. This leads me to my first real question. Does a four-way intersection with one leg roadblocked behave in the same manor as a three-way intersection? Does a three-way intersection with one leg roadblocked become a corner?
Diagram 2
Is Diagram 3 a “long straight road”, or is “road geometry” already affecting the results?
Diagram 3
Have you looked at buildings that are not located at the intersection yet? Does this only change the location of the “bracketed square”?
I apologize for only having questions. The implications of you post are just becoming clear to me, and at this point questions are all that I have. I’m looking forward to your future posts on this subject. Hopefully I will have some free time in a couple of weeks to actually assist you in further research.
Huzzah! My grades are submitted, and (like Arnold in that fine and sensitive art film "The Terminator") I'm back.
VitruviusAIA:
You are absolutely correct in asserting that many of the absurdly stringent conditions I originally imposed on my test layouts for walker study must be relaxed before any of my results have the slightest significance for actual cities we might build while playing the game. Fortunately, recent experimental results now allow us to relax almost all of them. Many of the relaxed restrictions are mentioned in the 13th reply to this thread, which I edited last night to include the observation that a building's quadramble remains unaltered when a trading caravan passes right by the front door. Certainly, other walkers and other structures even located right next door seem to have no discernable effect on a building's quadramble.
There is one condition that simply cannot be relaxed: the requirement that roads be "well isolated". This merely means that walker quadrambles are intimately a function of "local" road geometry, so if we change the "local" road geometry we have no right to expect the function to return invariant results. The word "local" in the previous sentence is so far defined in only a touchy feely way. I earnestly hope that roads located more than 20 squares from a building are ignored when the building calculates its quadramble, although the posts like like the one you mention by Bruglethat report such effects worry me. Certainly, I have always kept the roads straight for at least 26 squares from an intersection in my labs, and when I delete a road, I always remove at least the 20 squares closest to the intersection.
I am presently working on a couple of research projects intended to quantify the word "local" in the previous paragraph, at least for 1x1 and 2x2 buildings on straight roads and four-way intersections. However, I recorded over 142 quadrambles in tackling that problem, so I will defer further discussion of the "local" issue for a separate, longer posting.
In this reply, I would like to mention the results of three quick and dirty little walker experiments I did that may offer some insights into questions that you raised in your replies 13 and 14 in this thread. The first of these relates to the "vision" of a building. How far can a building "see" (when generating a quadramble) if you force it to look a long way? In my mind, a question that is strongly related to building vision is whether a roaming walker ever gets to make an independent, random choice when encountering a fork in a road. Does the building make as many of the walker's choices for him as it can during quadramble generation and then kick the walker out the door with a complete round-trip itinerary? Or, does the building only scan the roads in its own immediate vicinity during quadramble generation and then launch the walker in the desired direction with little travel advice other than "Come back when you've gone 26 squares." In the latter case, there might be some kind of "cut loose"-distance from a building, beyond which a walker gets to make its own, possibly random, decisions about which fork in a road to take. I already know that within three to six squares (the actual distance varies with building size and compass direction) of its building, a walker's road-choice decisions are rigidly preprogrammed into its travel itinerary. Your study with the multi-hundred-square walk through the maze with the water carrier already pretty much tells us the answer: Walkers have no free will. But, I had already done the study my way, so here it is.
Experiment A: Walker freedom of will
If the fireman was granted "free will" after some reasonable "cut-loose"distance, e.g., 6, 12, or even 18 squares, then he might reasonably be expected upon reaching the intersection to choose which road to take at random. Thus, about one-third of the time he should take each of the roads beginning at +i, +1, and -i. If his pattern of road choices departs significantly from a 1:1:1 ratio in the NE:SE:SW directions, then this is evidence of some kind of pre-programming of an itinerary; it might only be a bias for some preferred direction to turn more often than others, but we should be able to detect it. Only one out of each cycle of four walk in the observed sequence was a long walk. This surprised me based on the respect that the algorithm seems to accord even a one square-long road prior to a corner in the long (and, doubtless, tedious) cornering study that I will be presenting in the future. I expected one time out of four for the fireman to emerge, head NW for one square, run out of road and bounce back down the road to the south east for either 43 or 51 more squares. He didn't. Who can blame the building for saying "You call that a road?". The building generated a quadramble (albeit one in which all four entries displayed directional instability) reflecting the fact that it saw only one road direction available to it within its immediate vicinity, so only one in four walks was long. Conspicuous by their absolute and complete absence from the sequence of 30 turn-around squares listed above are any values of 8i or 15i. The road from the intersection to the northeast was never taken! If the fireman was randomly choosing his direction at the intersection, about 10 of the 30 walks should have gone up each of the three branches (assuming no "bounce back" to the northwest, which one sees occasionally). Now, 0:15:15 doesn't look like 10:10:10 to me. We can ask statistically what the odds might be that such a seemingly non-random sequence of walk directions could have occurred by chance alone even though the underlying probabilities of being chosen were equal for all three roads. Chi-squared tests are good for this purpose, but it's more fun to figure it out from scratch. Launch a "random" walker down this road and what are the odds that he does not turn NE at the intersection? About 2/3rds. What are the odds that he makes the trip twice without even once going up the NE road? (2/3)(2/3) = 4/9. So what are the odds that he does it 30 times in a row? (2^30)/(3^30), but that slightly exaggerates the unlikelihood of the observation. What we really want to know are the odds that he makes thirty trips and by chance alone never takes one of the roads, and we don't care which of the roads it is, or 3(2^30)/(3^30) = (2^30)/(3^29) = 0.000015645 or about one chance in 63,917. If you want to publish the results of your research in a reputable biological journal, you need to demonstrate that the results you observed had less than a one in 20 probability of being due to chance alone. Biological systems have oodles of variability and the amount of replication you need to reduce the likelihood of error much below 0.05 often becomes prohibitive ("Dang! We gotta get us some more rats, here.") By biological standards, we have serious overkill with our statistical results. That fireman was not choosing directions at random! But what an odd sort of non-randomness. It's like his travel itinerary said "Start towards the southeast and walk for 43 (or 50) squares turning southwest if you feel like it and have the chance, but whatever you do, avoid going northeast like taxes!". Bizarre.
This experiment actually has more relevance to a concern that Brugle in one of his posts to this thread implied about possible map-square dependency of quadrambles. He was right, in a way! Although road geometry not absolute map-square locations seem to govern the calculation of the four entries in a quadramble, the choice of the starting leg of the quadramble does indeed seem like a good candidate for map-square dependency.
But no longer! Now I use two fire houses, one located where the police station is shown on the figure and one in the architect's spot. The first few times I tried to add a second fire station, it helped very little; one fireman always seemed to follow fairly closely behind the other. Once I discovered initial-recruiter invariance it was child's play to put two fireman perfectly out of phase with one another. One fire station needs to be operating first, I used the one in the north quadrant (the police station's spot), which I will call "N". The second fire station goes in the south quadrant (in place of the architect in the figure), so I will call it "S". When fireman N is coming back to the firehouse from the southwest is the time to place firehouse S. It took me a couple of tries to get the timing really precise. Shortly after firehouse S is placed, his recruiter shoots up the road to the northeast, passes housing, walks about 10 more squares and fireman S pops out. Fireman S and his recruiter share the same quadramble, and the recruiter just used the leg to the northeast. So, in clockwise rotation, fireman S heads down the road to the SE. If timed perfectly, fireman S first appears just about exactly at the same time fireman N also reappears after having rested his feet after his run down and back along the road to the SW. Fireman N's next leg in his quadramble (one clockwise) is to the NW, and he should be heading that way at the same time fireman S is heading in exactly the opposite direction. Without roadblocks, fireman S should turn around (at square 51) about when fireman N turns around at square -53. Fireman N the proceeds to his next leg (to the NE) and fireman S next heads SW. I have a version of my cruciform hut community saved that will run like this for years and yearswith nary a whiff of smoke. Anyone who wants to reproduce my out-of-phase firemen would be well advised to load up the roads with plenty of housing: at least four pairs of huts on each of the four roads. The least dissatisfaction felt by either fireman about access to workers causes his building to emit a recruiter right before the fireman appears for his next trip, which shifts the fireman's phase 90 degrees clockwise. As you pointed out with Diagrams 2 and 3 in reply 15, we have simply got to know whether roadblocks are going to be tough to factor in to our emerging picture of how road geometries determine service-walker quadrambles, or none of these studies will be of much more use than a rubber crutch. I do not know whether I have good news or bad news to report on the subject. But, I have news! I then deleted the second firehouse, and restored the two missing road squares and put roadblocks on them, as shown in the figure in the previous reply. A new firehouse then went back in the south quadrant (at 1-i), and its walker went 1. A 1x1 building has a domain of strong road influence extending from it in the NE, SE, SW, and, NW directions for 6 squares. I do not yet know whether this domain extends out diagonally for the full six squares, however. A building that sees an intersection or corner within its domain greatly modifies its quadramble to accommodate that geometric feature. A firehouse at 1-i sees a four-way intersection (like the architect in the figure) and sends long, bracketing walks down each of the four roads. 2. If the firehouse is moved further and further away from the intersection, (viz., to 2-i, 3-i, 4-i,...) the bracketed target square moves down the road along with the firehouse (as you surmised), but it also moves one square further to the northeast, if the road is real, and one square further to the northwest if the road is imaginary (NE2SW) 3. When the firehouse is moved six squares away from the intersection, the "other road" and intersection are no longer within its domain. The effect is particularly clean and beautiful if you move a 1x1 structure - one square at a time - from the south quadrant down the road to the southeast. For example, an apothecary at 6-i can see the intersection and issues the quadramble, 4. 1x1 buildings in other quadrants moved along other roads do not always make such a nice clean break with the intersection. Along either side of the roads to the SE and SW or along the south side of the roads to the NW and NE, the break is always fairly clean. Their quadrambles at an offset of 6 are always recognizable modifications of the corresponding straight road quadramble, but may include a few runs in which the charms of the other branches seem to prove irresistible. 5. A 1x1 building moved out along the N side of either the road to the NW or NE makes a messier exit from the intersection, in which they pass through one to three squares (a zone of confusion) on which they generate quadrambles without a pair of bracketing runs. Eventually, the building can be moved far enough from the intersection to persuade it to generate a recognizable modification of the correct straight road quadramble for its size and position relative to the road, at which point I declared victory and left that road. 6. The situation for 2x2 buildings is a little trickier. I think there is east-west symmetry in the location of their domains of strong road influence, but I also think the have a little bit of north-south asymmetry in the shapes of their domains. Also, for only three of the eight possible ways you can pull a 2x2 building away from a 4x4 intersection is the break reasonably clean, six squares from the road. For two of the remaining five ways, the buildings' quadrambles do not assume modified-straight-road form until the buildings are fully 11 squares from the intersection! Even more exotically, an individual entry in at least three of the quadrambles (one in the zone of confusion, the other two in the first modified straight-road quadramble) is unstable in direction, though not in length. That's all the new stuff I've got for now. As soon as I work out the north-south asymmetry for 2x2's, I'll post the lot. My students are right. I really can be a tedious gasbag. I cannot believe I took seven and a half pages of single-spaced text to describe the results of my three quick-and-dirty little experiments, but they were certainly eye openers for me. One of them (initial recruiter invariance) even made me laugh out loud and scare my daughter when I saw the results start to come in. I hope that you, Vitruvius, and some of the other visitors to the site will enjoy them, too. StephAmon
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