Fibbonacci's Dungeon Crawl

[ExtravagantEvil]

Myconids.
Who doesn't like Myconids?

I recently came up with an interesting place for them I'n a setting some friends/players of mine and I are slowly building, and during one portion of the campaign, I'm introducing the Myconids into a swamp environment with their farms surrounded by Yellow Musk Creepers.

Regardless, I'm trying to think of how their underground lair would look, given sentient fungi presumably not operating on any humanoid measure of thinking, and I remembered how the Fibbonaci sequence is one of those ubiquitous patterns.

I decided to make this the basis of the dungeon design.

Problem is, I don't know how to implement it. If anyone could provide advice
On how to realistically design a lair for them with a Fibbonacci pattern involved I'd greatly appreciate it.

Also, any other fun Mathy patterns like this that I could use would be interesting, and this is coming from someone who is not the most mathematically inclined, thank you very much

[Kurald Galain]

Try this one, it fits fungi very well.

[Rorrik]

Here's an approach that doesn't make for a very interesting dungeon crawl, and severely limits the possible growth of the colony, but follow the Fibbonacci Sequence (1 1 2 3 5 8 13 ...).

The 1s at the beginning are the "throne room" and "antechamber"(or the equivalents for a Myconid society). From the ante chamber two rooms branch off with important people dwelling therein. These branch to 3 rooms (each or between them, either way) with less important fungi in them, and so on through 5, 8, 13 until the dungeon is as large as desired and/or supports the entire Myconid population in the colony.

The problem with this dungeon in that it essentially funnels the party to the "throne room", which is likely their main goal. A way to make this play differently is for them to enter the colony from a tunnel connecting to a chamber somewhere in the middle. The crawl could also be an attempt to escape from the colony starting at the throne room, but that is anticlimactic and just about any path would lead to an exit.

Alternately, there could be one entrance, going through one hall, to two rooms, then three, and so on to a decided point before converging back to one: 1 1 2 3 5 8 5 3 2 1 1. Again, this will result in mapping a large amount of dungeon that will never be explored. Sacrifices must be made.

[Urpriest]

Well for one, you can size rooms based on the golden ratio, so one side about 1.6 times the other. All the stereotypical nautilus diagrams will help as well (for example, use a set of rooms designed like this).

I'd come up with a reason why certain elements follow the Fibonacci sequence, though. Perhaps myconids share authority, with two levels having command over an equal number of servants in the next level. Then the king and queen would command two princes, who along with the queen would command three dukes, who along with the princes would command five counts, etc.

[mint]

Sometimes I doodle fib spirals on graph paper during math class. You draw a quarter circle through squares equal to the element in the series.
Like, 1 and 1 through single squares making a semi-circle. 2 is a quarter-circle through 2x2 squares and so on.
It strikes me that you could partition the rooms after this model but you would end just end up with a bunch of squares that don't seem super interesting.
Maybe make multiple fib spirals and see if the squares or spiral lines intersect in some pleasing way and base the dungeon on whatever you find.
Could be cool if the dungeon was organic and the first squares in each spiral represents a spore from which the rooms sprout.

[ExtravagantEvil]

Hey, here's a thought.
I've been pondering over what you've said so far, and I've got a clever way of making the crawl more interestingly patterned. Further makes it cleverly 3D.

Mix I'n Pascals triangle.

It would be a cone shaped underground series of rooms, each level being a curve on the Sequence from Fibbonacci. The # of rooms based on the middle of the Pascal triangle.

Ex. Fibbonacci sequence: 1,1,2,3,5

Pascals Triangle
1
1 2 1
1 3 3 1
1 4. 6 4. 1

The bolder #'s are the ones that would be focused on I'n the dungeon level design.

At the 4th portion of the curve, there's be 6 rooms. rooms, and as you go down the # of rooms shrink, with the top layer being the one with the most/largest rooms, while we would see at the end that there'd be one room at the 'center' of the spiral with the leader at that center room.

Viewed from a birds eye it would be the spiral, but with less and less rooms going done,

[navar100]

Try a tesseract.

It's a pain to map out but possible. It helps to use 8 six-sided dice of the same orientation. Stack them in the three-dimensional representation of the tesseract. Physics may demand you leave one off to the side and just imagine it in its place. Then you can map where each room leads to another. Always remember that the direction of "down" is towards your feet. The fun part is the cross-over where two dice aren't physically touching but are otherwise adjacent in the tesseract.

How you enter and exit is up to you.

[averagejoe]

A good place to start is looking up where the sequence shows up in nature. Though keep in mind that when people say that you find the Fibbonacci sequence in nature, they often mean that you find a logarithmic spiral, which can be approximated using a series of squares with side length equal to the Fibbonacci numbers. At any rate, both of these may give some ideas as far as the spacial organization of such a place.

[Rorrik]

snip

At the 4th portion of the curve, there's be 6 rooms. rooms, and as you go down the # of rooms shrink, with the top layer being the one with the most/largest rooms, while we would see at the end that there'd be one room at the 'center' of the spiral with the leader at that center room.

Viewed from a birds eye it would be the spiral, but with less and less rooms going done,

Assuming I've understood you correctly (no gaurentees there) this still leads to the problem of it being a really straight shot down to the leader, avoiding most of the caverns with ease. Aside from making you do a ton of work they will never see, it's just not a good defensive tactic. Usually you'd want to bottleneck the enemy near the beginning of your caverns.

However, reading your description reminded me of an effective dungeon crawl in Raymond E Fiest's series The Serpent War Saga. It's porbably in the second book, but the gist of it is that their are spiraling caverns like you've described going up into a mountain, and they've come from below and know there are others below. These have lots of branches that they could spend a long while exploring. For the sake of applying it to our Fibbonacci/Pascal spirally dungeon, we have the party enter at ground level and encounter spirals going both up and down.

There are probably several ways to handle this, but two come to mind:

......................13
.......................8
.......................5
.......................3
.......................2
.......................1
.......................1
13 8 5 3 2 1 1 Entrance
.......................1
.......................1
.......................2
.......................3
.......................5
.......................8
......................13
or

1
1
2
3
5
8
13 Entrance
8
5
3
2
1
1

Of course, I've simplified out the pascal aspect of it, but believe it would make a lovely addition to the concept.

[Gravitron5000]

These three videos might provide some inspiration:

Doodling in Math Class: Spirals, Fibonacci, and Being a Plant (1 of 3)

Doodling in Math Class: Spirals, Fibonacci, and Being a Plant (2 of 3)

Doodling in Math Class: Spirals, Fibonacci, and Being a Plant (3 of 3)