I'm running a fantasy game in which the gods have mucked about with the world, upsetting the very underpinnings of reality. It's started to fray and fall apart.
To combat this, the forces of Order - notice the capitalization - have created a series of white towers that help anchor reality together. These towers kind of sew things up or pin it down so it can't move apart farther.
(And, of course, the bad guys, who are on the other side of reality, are trying to destroy them...)
As a kind of interesting touch or nice detail, I want to set the towers so many miles or leagues apart. They shouldn't just appear randomly out in the wilderness - they embody order. So I'm trying to think of a number that would be significant.
For example, I've thought about setting them 100 [blank]s apart as 100 is 10 x 10. There's some nice order and symmetry there.
Not being a big math guy, is there another number or pattern I could use? I keep thinking of the Golden Mean and it's spirals...
Seanchai
Quote from: Seanchai;447488I
Not being a big math guy, is there another number or pattern I could use? I keep thinking of the Golden Mean and it's spirals...
Seven, or the prime number sequence comes to mind.
It all depends on where the center of your world is. If you do have a center, put a tower there. Then use a Fibonacci sequence to form a spiral out from that point.
Although nothing wrong with a grid, either.
Quote from: estar;447503Seven, or the prime number sequence comes to mind.
Seven would be good. I was also thinking 21.
Seanchai
I would use the Fibonacci sequence 1 1 2 3 5 8 13 21 34 55 but then my plan would be to remove one of them and have the party work out were it would have to be but instead finding he ruins ....
Anyway the Fibonacci sequence is just complex enough that the pattern would be hidden but easy enough for the party to work out. It's also nice as it's a pattern that occurs in nature for plants and so on which suggests that there is law within Chaos
Quote from: jibbajibba;447516I would use the Fibonacci sequence 1 1 2 3 5 8 13 21 34 55 but then my plan would be to remove one of them and have the party work out were it would have to be but instead finding he ruins ....
Anyway the Fibonacci sequence is just complex enough that the pattern would be hidden but easy enough for the party to work out. It's also nice as it's a pattern that occurs in nature for plants and so on which suggests that there is law within Chaos
Excellent idea! I'm no mathematician, but the Fibonacci sequence (http://en.wikipedia.org/wiki/Fibonacci_number) and especially the golden ratio (http://en.wikipedia.org/wiki/Golden_ratio) are great math tropes (made somewhat more popular by
The Da Vinci Code).
I'd arrange the towers in a logarithmic spiral (http://en.wikipedia.org/wiki/Logarithmic_spiral). I feel it would be a perfect symbol for constancy, harmony and a well-ordered universe. I mean, check this out:
Quote from: WikipediaSpira mirabilis, Latin for "miraculous spiral", is another name for the logarithmic spiral. Although this curve had already been named by other mathematicians, the specific name ("miraculous" or "marvelous" spiral) was given to this curve by Jacob Bernoulli, because he was fascinated by one of its unique mathematical properties: the size of the spiral increases but its shape is unaltered with each successive curve, a property known as self-similarity. Possibly as a result of this unique property, the spira mirabilis has evolved in nature, appearing in certain growing forms such as nautilus shells and sunflower heads. Jakob Bernoulli wanted such a spiral engraved on his headstone along with the phrase "Eadem mutata resurgo" ("Although changed, I shall arise the same.")
To throw in the golden ratio and/or Fibonacci, you could use a golden spiral (http://en.wikipedia.org/wiki/Golden_spiral), or a Fibonacci spiral (which is nearly the same thing).
The Fermat spiral (http://en.wikipedia.org/wiki/Fermat%27s_spiral) also implies the Fibonacci sequence and the golden ratio, but it's a parabolic spiral, which is generally not considered as mathematically snazzy.
Jesus Christ, this is awesome. I should use this in a game someday. :D
Another (over-complicated of course :) ) approach would be to decide how many towers you want and work out the distance between them from that.
That also assumes you know your planet's surface area, though, so this is probably a stupid idea. You could sub in the Earth's area, though many fantasy worlds are much smaller (I've heard it said that Dark Sun's mapped area is about as big as Australia).
Assuming your world is spherical you'd presumably end up with towers in a hex grid pattern or triangular pattern, if distance between towers is consistent ? Alternatively, if they're not evenly spread, where reality 'breaks' would be the area that needs the most towers.
Another option is to arrange them in a disorderly manner and then choose one of the following explanations:
1. It was in an orderly formation but the chaos wrecked it.
2. We built the towers to stop the Chaos, not to look pretty.
3. They are in perfect order, but they look screwy because you're looking at it from a Chaos point of view.
4. They look screwy now, but they're slowly stretching everything to where it needs to be. Give it a century and it will be orderly.
Quote from: Bloody Stupid Johnson;447549Another (over-complicated of course :) ) approach would be to decide how many towers you want and work out the distance between them from that.
That also assumes you know your planet's surface area, though, so this is probably a stupid idea. You could sub in the Earth's area, though many fantasy worlds are much smaller (I've heard it said that Dark Sun's mapped area is about as big as Australia).
Assuming your world is spherical you'd presumably end up with towers in a hex grid pattern or triangular pattern, if distance between towers is consistent ? Alternatively, if they're not evenly spread, where reality 'breaks' would be the area that needs the most towers.
You could use Christaler's Central Place Theory for this and have 3 types of tower each an orger of magnitude greater than the last.
You could try to arrange the tower locations according to some natural patterns.
Constellations, east-west/north-south, moon cycles, sea tides, seasons, geography such as mountains or rivers all would do.
The last one could be especially appropriate if you want to fit towers to different thematic environments: glacial, desert, mountain, forest etch.
It looks like the Golden Mean, Golden Spiral and Golden Ratio are the same thing. As I said in the OP, I've considered the Golden Mean.
The problem I'm seeing with the spirals is large areas of no coverage and then areas where there are a lot of towers.
More info: When we created the setting, we were messing around with power sources from 4e. We've created a Divine nation and an Arcane nation. They two were fighting so much and to such devastating effect that the gods pushed the nations apart with twin mountain ranges, creating a huge open area between them and high mountain walls as a barrier just into that space. The in-between space filled with Primal energies, become a kind of paradise lost.
The in-between area is huge. It's the area where reality has been shattered and where the white towers are being built.
The towers are a combination of organic and structured forms. They're square, tall, with one "twist" in the center. I described the material they're made of as a cross between bone and stone, with there being tiny spirals in the material (these are the Golden Mean spirals).
The players haven't seen a whole tower yet - just the stub of one.
The ideas so far are great. I've got the Golden Mean already in there - it would be neat if they were mirrored on a macro scale as well, but...I'll figure out a way to work the Fibonacci Sequence in there. Perhaps in the inside of towers.
Quote from: Malleus Arianorum;4476063. They are in perfect order, but they look screwy because you're looking at it from a Chaos point of view.
That's a neat idea.
Quote from: xech;447627You could try to arrange the tower locations according to some natural patterns.
Constellations, east-west/north-south, moon cycles, sea tides, seasons, geography such as mountains or rivers all would do.
Also very interesting. It fits with the whole organic yet orderly idea.
Quote from: jibbajibba;447625You could use Christaler's Central Place Theory for this and have 3 types of tower each an orger of magnitude greater than the last.
I'm thinking about having towers and then stelae. Or baby towers - ones that are still "growing." It would make covering so much ground easier and I could use Golden Mean spirals coming out of a larger tower.
Seanchai