Map of Regulus?

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Jem
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Map of Regulus?

Pity about the search function being down; I know there was a topic on this a while back but I can't find it. Sorry if this idea has been done before. Anyway, the question was "how are the 64 cogs of Regulus arranged?" We know that one of them is in the center, so the other 63 cogs must have some kind of symmetry about that one. It's also a requirement that the cogs be physically able to rotate against each other (no locked groups of odd numbers of gears in loops). I thought about this for a bit and came up with:

http://earl.of.sandwich.net/Mechanus.pdf .

(My art skills will not be showing up in Artist's Alley any time soon. ;^) )

Each circle represents a gear; regions (4 gears), and quarters (16 gears) are also color-coded, with regions being hue variants on the main color of the quarter and the central gear being singled out.

This is one of the most geometrically degenerate possible arrangements, actually -- while its simplicity might appeal to the modron mind, I'm trying to come up with something more complex and hopefully aesthetically pleasing. Three dimensions would rock; I'm fiddling around with gears on the faces of octahedrons and cubes but it's slower going.

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Map of Regulus?

Your configuration fits the basic requirements pretty well.

I'll note that Planes of Law describes Regulus this way:

"The 64 cogs of Regulus seem to be stacked in a pyramid, if viewed from the side. A huge rod, nearly as thick around as the spire in the Outlands, runs through the center of these gears and is apparently the agent by which they turn (if they don't turn it instead)."

The earlier thread (with my take) is here. Strictly speaking, my version has more than 64 gears, though the lowest tier encompasses precisely 64.

Jem
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Map of Regulus?

A pyramid, eh? Hmm... hm. *fiddles*

Okay, here we go. http://earl.of.sandwich.net/RegulusPyramid2.jpg .

Still exactly 64 cogs, still has a central cog, still color-coded by region and quarter, still not going to win an art contest any time soon. ;^) They are, however, at least roughly in a pyramidal shape; the part on the top left is an attempt at a perspective view of one side of the structure when assembled in 3D, while the hexagonal display on the bottom right is a more precise rendering of all the interconnections. There are 16 cogs on each of the three "sides," four cogs in each of the three "edges", and the central cog sits atop three more at the top. Foreshortened cogs are flat, and connect at right angles to vertically-stretched cogs. (This will require some worming and beveling of the gear teeth, but it's still physically workable and nothing the Plane of Perfect Order can't handle.)

All the cogs are, regardless of perspective, the same size, but this doesn't have to be the case. The central cog can be one of the largest if the other cogs of the red/brown 1st Quarter are similarly increased in size, to no more than twice the radius of the other cogs.

I think it's a rather pretty arrangement, if I may say so myself. ;^) Perhaps someone with greater artistic talent could render it visually, rather than abstractly drafted.

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Map of Regulus?

'Jem' wrote:
I think it's a rather pretty arrangement, if I may say so myself. ;^) Perhaps someone with greater artistic talent could render it visually, rather than abstractly drafted.
I believe the Mordrons would like that visual presentation more than an artistic drawing... Don't know why. Just a hunch.

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Map of Regulus?

From the dark, distant, and possibly dank past (aka almost a year ago), I dredge up this topic with a deplorable diversity of alliteration. Why? Well, to bring you the short animation of a 3D flyaround of a rather spherical and not at all successful attempt at Jem's Regulus. Needless to say, although it looks pretty, the cogs just do not fit together. I'll try for a pyramidal structure next.

If it doesn't load, that means Angelfire took away my bandwidth, so first come first serve.

Jem
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Map of Regulus?

I tried to take a look, but Angelfire seems to object more to the remote linking than to the bandwidth at the moment. Can you link it directly from quendibar? I'd love to see what happened!

When you say that the cogs don't fit together, do you mean that they don't turn against each other? I've fiddled with the draft since, and I think it works rotationally but might require impossible beveling; I've gotten another arrangement that I think works better I'll try to upload soon.

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Map of Regulus?

Well, the link should be a direct link to the *.mov file, so try doing right-click and save-as. If that doesn't work, it probably is angelfire's restrictions. Unfortunately, I don't know anywhere else where I can easily host it. If you want, I would be happy to email it to you. Just PM me the address. It is about 3mb, if I'm not mistaken.

As for what I mean by the gears not fitting - I made them all the same size and because of the spherical arrangement, not all of them touch each other.

Jem
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Map of Regulus?

Ahah.

What I meant was that Angelfire refuses to load links that come to it from others' pages, like planewalker. If you could change your front page -- quendibar's index.html -- and link to the file from there, people should be able to see it by clinking on the link there.

However, yeah, emailing it should be fine. Try william.keith @ gmail.com ; that mailbox should have the space required.

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Map of Regulus?

Okay. The [url="www.angelfire.com/wizard/quendibar/index.html"]above link[/url] (as well as that one) now lead to a practically blank page with a text link. Hope that works.

Jem
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Map of Regulus?

Got it. And wow, the pyramid arrangement looks great!

Yeah, the gears definitely don't fit in that arrangement on a sphere, but since they're said to be in a pyramid arrangement I like that one better anyway. And hey, I don't even think the beveling's anywhere near the problem I thought it was, either. Awesome.

I see what you mean about the first-quarter gears. I suppose they'd have to be larger than the others... a bit of a break in the perfect order, but not necessarily from a modron's point of view (after all, they're also serving a qualitatively different function in the structure). Perhaps we might even expand them enough to make Regulus larger still, though the first-quarter "stair steps" can't touch (they wouldn't rotate against each other).

But there's no need for that now. I'm filing this away -- fantastic work!

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Re: Map of Regulus?

This a necro post of several years, but this subject has been haunting me for as long, haha.

The pyramid diagram is really great.

My only issue with it is that the cogs are stated to be of differing size and sector 64, the location of Primus' tower which is neither a quarter or region hub, is stated to the largest and located at the top.

This makes me think that sector 64 should be located at the very top, and quarters 1, 2 and 3 should descend on three sides from that, while the central spoke should descend straight down from Sector 64 with all regions and sectors of Quarter 4 somehow arranged either inside the pyramid and/or as the bottom face of it.

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Re: Map of Regulus?

Whatever I was trying to link to above is gone, but these were my original diagrams.

Top view (not to scale):

Side view (not to scale):

Basically, I thought the best way to do it was to make a grid of 64 interlocking gears (constituting the "main" gears of Regulus), and add additional gears for the hierarch supervisors to occupy, with Primus on top. Primus's gear, as Jeffrey said, would be the largest one, with the primary rod running through it.

That's 64 gears on the bottom level (ruled by octons), 16 gears on the level above that (ruled by quartons), 4 gears on the level above that (ruled by secundi), and 1 gear, Primus's, on the top level. That seems to best reflect the modron hierarchy and the original intent of the plane of lawful neutrality as something like a chessboard.

The color coding is supposed to indicate which hierarch gear is responsible for which gears around it. It's not supposed to represent the actual colors of the gears of Regulus.

My take isn't quite canonical, in which there seem to be only 64 gears total instead of 64 gears on the bottom level, but I like it better than the canonical take.

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Re: Map of Regulus?

Rip, your solution as a non-canonical one is most serviceable.

The reason I (and probably many others) have been so obsessed with sorting out the canonical version is that there are some almost obvious patterns with the numbers involved which indicate there is some form of method to the madness and a reason to try and work with the canon unmodified.

For instance, the numbers of heirarch modrons of each caste are square numbers. The breakdown of military units are patterened on the numbers 12 and 64 (evident at various tiers so it's difficult to see if this is intentional or haphazard). The whole population number ratios display factors which happen to be the same numbers used in computer memory sizes, coincidence? Also, the placement of Primus in sector 64 is so obviously counter to the whole scheme that it seems very much a riddle... which implies that there is an actual reason which fits the grand pattern. Or maybe its just a red herring?

The original AD&D Monster Manual II entry for modrons described Nirvana as one unbroken plane with Primus located at the hub and the Quarters, Regions and Sectors radiated outward but, these numeric patterns were still evident. The AD&D 1st Edition Monster Manual II authors then apparently had some idea of pattern in mind. One of the more poignant mysteries is the range of telepathic communication for each of the heirarch modrons... I gather that this could be an indicator of heirarch domain size in the original Nirvana (and extrapolated to cog/sector sizes in Regulus). I feel that the 2nd Edition designers wouldn't (or shouldn't) have ignored this since they propogated the telepathic ranges to the new material.

When 2nd Edition material was published in the boxed sets, it seems like the formation of a 64 cog realm for Regulus carried the patterns into the new design... I am hoping against hope that Colin McComb and friends actually knew what they were doing and that this is a riddle... with a solution. If they just randomly threw together an attempted logical and purposeful design which was supposed to illustrate order and law in it's very being but didn't actually put some thought into it, I would be rather disappointed, lol. Then, after getting over the dissappointment, I would probably just fake it and pretend there was some grand purpose in the design after all, lol.

If I were of greater means, I'd offer a significant reward to whoever could display a visual working model of Regulus which answered all of the canonical points in its design. Sticking out tongue

1) Cogs must somehow at least vaguely form a pyramid in their arrangement

2) Quarter cogs are larger than region cogs are larger than sector cogs which are all dwarfed by sector 64 (Primus' cog) though it is merely a sector cog. (I'd try to somehow factor in telepathy ranges of heirarchs to help me determine cog sizes while also considering that since each cog has at least several million monodrones and lesser amounts of other types such that each cog most probably at least takes up the space of Los Angeles if not a much larger area). At the very least, an Octon more than likely has telepathy range from the center of his sector cog to reach the edge of his own cog, if not the center of his local regional hub's cog to communicate with the staff of the Quarton there.

3) A central shaft descends from sector 64 cog located at the top.

There's quite a bit of room for play given all of these ambiguous specs

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Re: Map of Regulus?

Every modron can only, according to the Planescape Campaign Setting's Monster Supplement, communicate with castes immediately above and below it. If this is assumed to hold true for the hierarch castes, that means every quarton needs a quinton to pass its orders to, and every quinton needs a hexton, and every hexton needs a septon, and every septon needs an octon available to pass orders down to the nonatons, and so on. A nonaton can't communicate directly with its pentadrone lieutenants, so it needs a decaton with it at all times to pass its orders along.

However, perhaps we should assume that the rule that modrons can only communicate with those castes immediately adjacent to them only applies to the base types, and modron hierarchs can communicate directly with their own staffs, which was obviously the designers' intent. It seems like the hierarchy of the hierarchs is less linear than that of the base types.

So my 85-cog version of Regulus works like this:

There are 64 sectors in Regulus, representing the bottom tier of its gears. Each sector is a wheel with an 84-mile radius (the limit of an octon's telepathic power). Each sector meets with three others together in a regional hub, where the tower of the quarton rises precisely 84 miles from the towers of its four subordinate octons. The four sectors rotate around their regional hub as the gears of Regulus turn. Each quarton dwells in a gear above the four gears of the sectors above its jurisdiction in a wheel exactly 384 miles in radius.

Each region is grouped together with three adjacent regions to spin around the central hub of each quarter, where (the next tier up) the tower of that quarter's secundus rises. Each secundus dwells in a gear above the gears of the quartons, exactly 420 miles in radius. Primus's cog is above those, and it has no limit to its telepathic range.

BUT, what if instead it was arranged in a way to help consolidate the various positions and make sure that, for example, Primus also had an octon and a secundus on his personal gear?

So there are 64 sectors in Regulus. Primus's cog is one of them, and his tower is also the home of one of the secundi, one of the quartons, and one of the octons.

Below Primus's gear orbit three other gears, evenly spaced around the central axis. These are the homes of the other three secundi, and each of their towers also contains a quarton and an octon.

Now we've accounted for Primus, all four secundi, and four of the quartons and octons. Beneath each of the secundus gears are three quarton gears, evenly spaced just as the secundus gears are spaced around Primus's gear, and there needs to be an additional three quarton gears beneath Primus's gear. That makes twelve quartons in the quarton tier, three quartons in the secondus tier, and a final quarton in Primus's tier. Every quarton gear also has an octon in it, so we've accounted for sixteen of the sixty-four octons.

Beneath the quarton tier is the tier of gears ruled by octons only, of which there are 48, so each of the twelve quarton gears must interlock with exactly four octon gears, which isn't too far from the way I had it above.

So that's Regulus. One gear on top, three gears beneath that, twelve gears beneath that (three of them interlocking the central shaft and nine of them interlocking with the three Secundus gears), and 48 gears on the bottom tier, four each orbiting around each of the shafts from the tier above it.

That makes sense to me, and seems to fit with canon and allow the hierarchy to more closely interact. I think I like that better than the scheme I illustrated above.

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Re: Map of Regulus?

Rip, your second solution which holds with 64 cogs is a nice one, but again is not entirely canonical, though close. The problem is that the canon doesn't allow for a Secundus residing on cog 64 with Primus. At best, a tertian is rumored to hang out there and serve Primus directly (though he gets his orders from a Secundus residing on one of the Quarter cogs and doesn't truly comprehend the being he's attending). Several quintons and hextons do hang out on cog 64, but it's also missing a quarton (64 isn't a region hub or a quarter hub). Primus obviously has to deal with his Secundis always at range, thankfully his stretches far enough.

As to the role of octons, because they not only govern cogs, but are probably constantly acting as telepathic switchboard operators in their role of conveying orders up and down the line, I believe telepathic ranges will probably be key here. I would hate to be an octon... I am horrible at multitasking. It would seem worse when orders stem from where bottlenecks would seem to occur like where Hextons are sharing Septons... at first glance, the modron heirarchy looks like it was invented in the Abyss, but after careful study it does seem like it could begin to work.

I'm guessing the most critical relationship is between decatons and pentadrones since this is where the administration bottleneck occurs. My feeling is that groups of pentadrones acting together can do just about anything with little actual need for direction. Thus octons down to decatons can convey some idea of what's good for the sector to pentadrone adminstrative ganglias and the pentas figure it out from there, extrapolating the stepped down will of Primus to the millions of other base modrons residing in a sector. Octons do have the title of governor, however, I believe that's got to be mostly just title... their primary job would seem to me as expediting the ball rolling and I think by the time it gets to Pentadrones, the details actually start to get hashed out.

If the modrons had just used a corporate management consulting firm rather than gamers to sort out the workings of the heirarchy of Regulus, we wouldn't be in this mess, lol.

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Jeffrey Boyd Garrison
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Jem
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Re: Map of Regulus?

Obviously there will never be a "perfect" solution, so we can use what looks cool to us. Whether Colin had something specific in mind is iffy, I'd think -- one way to write cool mysteries about transcendent stuff is to write something that sounds deep and doesn't immediately contradict itself, and has room for your audience to fill in their preferred particulars.

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Re: Map of Regulus?

Jeffrey Boyd Garrison wrote:
The problem is that the canon doesn't allow for a Secundus residing on cog 64 with Primus.

I'm not so certain it doesn't. The secundus isn't considered part of Primus's "staff," but that doesn't mean it can't live on the same gear.

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Re: Map of Regulus?

@Jem: Agreed, there is no perfect solution and it's definitely useful to use what looks good. Smiling

@Rip: Agreed, there is no reason a Secundus couldn't reside with Primus in gear 64. That being said, the canon does establish residence of all the Secundi's on their respective quarter hub cogs. Since Primus has such great telepathy, this doesn't present a problem as he can order them about wherever they may be. Additionally, there is no reason they cannot travel or attend him personally. I'm really just talking placement of the quarter towers which they are said to rule from.

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Jeffrey Boyd Garrison
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