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[NW_Kohaku]

I've been making fractal bedrooms for a while, and I've always been interested in ideas like making my whole fortress a hexagonal pod structure with my fortress descending from there, however, I'm becoming more and more obsessed with trying to find a way to make a serious three-dimensional fractal fortress.

That means the entire fortress would have to be a continuation of the same single pattern, including stockpiles, workshops, residences, dining hall, and trading area.  (Outer defenses need not necessarily be part of the fractal, especially if I just dig a giant moat around the whole thing.)

Now, I know I can easily make a repeating tetrahedral structure, which would probably be impressive in its own right, but I'm wondering if there is something more challenging that is still possible to fit into a floorplan that could service a workshop.

One of the things I was thinking of doing at first, thanks to the lamia/naga mod I was working on, was making my fortress a giant Caduceus, with two hallways as "spines" of the snakes, and all of the actual rooms patterned as "scales" that come off that central helix of ramped hallways, with the smaller "tail" ends being more residential, and the larger scale sections being the workshops and stockpiles.  However, I'm not sure how well I can actually manage to cram something into a broad enough fort to be useful, without making those snakes look ridiculously chubby and short for the space I have to work with.  (Plus side of this, however, would be that it would come up out of the earth and be very photogenic in a way that a regular tetrahedral figure that remained completely underground would not be.)

The most complex ideas I have, however, are the "geode" or "spiral ball" formations, where I have a single "core" of my fortress, from which "crystaline" shaped rooms (parallelograms or hexagons repeating in outward concentric rings) that could spike outwards in ever-larger rings for the geodes.  Spiral balls would be something like the helix pattern, but with four or more arms wrapping around the core in an ever-expanding spiral as the arms get "fatter" as they expand.

The major problem with the geodes and spiral balls, as wonderful as they would be in concept to see (although visualizers would probably have great difficulty actually making sense of them) would be that building long vertical shafts in regular shapes tends not to leave much living space since DF is unfortunately so fixated upon its silly fetish with horizontally-built rooms.

So, I'm basically asking for help coming up with ways to implement some sort of workable (non-square/cube based!) fractal three-dimensional structure that I can actually implement into a fortress, be that by helping iron out some of the kinks of some of these, or proposing other forms of fractal to try.  (And this thread may as well act as a repository of those ideas, as well, for those looking for a more artistic fortress layout.)

[Loud Whispers]

BUMPING FOR GLORIOUS VICTORY

[Andrakon]

Something kind of like this?

Spoiler (click to show/hide)

☼OceanPalace☼

Yes those are adamantine wafer outer walls. The purple inner walls are rose gold that I changed the color for. The floor pattern is microcline and cobaltite, with a little rose gold. So far I got 8 floors built like this and 2 floors made with gold outer walls, one has gold inner walls, and floors of steel and silver.

Spoiler (click to show/hide)

Here is a hive design but the floor plan is not very usable unless the inner set of rooms have the walls torn down and the pattern is used for a decorative floor.

Spoiler (click to show/hide)

Neat that we were thinking of doing the same sort of thing around the same time! ^,^

[NW_Kohaku]

Well, I've done things somewhat similar to that before (not hexagons, I wanted to have something that was more brain-hurty to look at), but I'm now trying to evolve to having fully 3d repeating fractals.

An example of what a repeating three-dimensional geometric fortress would look like, with repeating tetrahedrons (a giant series of pyramids) as the case:

Spoiler: Lotta images (click to show/hide)

Floor +1:

These are the bases of "upright" pyramids that grow narrower as they reach upwards.

Floor 0:

This shows the repeating "base" of an inverted tetrahedral pyramid repeating.

The following are the inverted pyramids as they continue downward to a point, at which point they become the tops of the next set of upright pyramids:
Floor -1:


Floor -2:


Floor -3:


Floor -4:


Floor -5:


Floor -6:


Floor -7:

The intersection of the inverted and upright pyramids

Floor -8:

This is the top of the next set of upright pyramids right here.

Note that the pyramids should technically be roughly 7.34 z-levels in height, as the proper height is square root of 6 over 3 times the length of one edge (which is 9 in this image).  Making the pyramids larger is possible, but requires commensurate expansion of the pyramids on every level, unless a "conglomeration" of multiple levels of pyramids (combining 4 regular pyramids and the "negative space" between them into a single giant pyramid) were performed, which may be acceptable in some circumstances, such as dining hall and king's court.

However, again, while this is a very possible fractal, I think it's also a little too simple.  I kind of want to try something a little more complex than this, like the tetrahedral spiral ball.

[Girlinhat]

This looks like it needs to be visualized in Minecraft to fully understand what's happening.

[NW_Kohaku]

This looks like it needs to be visualized in Minecraft to fully understand what's happening.

Those are still floors inside the pyramids, so it would be impossible to really get a sense of it from a first-person perspective.

It's really only meant to be visualized mentally, anyway.

It's done mostly to satisfy the ability to have a three-dimensional fractal in the first place.

[Andrakon]

Actually a 3d fractal would probably look quite nice in a visualizer if you built it on the surface. 

[NW_Kohaku]

Some of the DF visualizers won't actually block view if you put the "camera" inside of the ground except on an "inside wall", so it's actually quite possible to see the sort of fractal built.

I could also easily have a fractal made of tetrahedral pyramids that use that "conglomerate multiple pyramids together" trick to have a fractal decrease in size, where a single massive pyramid is in the center, followed by four slightly smaller but still huge pyramids at its corners, followed by smaller pyramids at their corners, etc. 

[expwnent]

I've been planning on doing something similar. Do you just want something that has a fractal surface pattern, or do the "guts" have to be fractal also?

Here's some 2D ones I found on Wikipedia that might extend to 3D nicely:

http://en.wikipedia.org/wiki/Sierpinski_carpet is a pretty obvious one to extend to 3D, but it's a little too rectangley.

It would be neat if you could do something with http://en.wikipedia.org/wiki/Dragon_curve . The nice thing about that one is that it's very approximable with axis-aligned squares.

Googling 3D fractal just gives a bunch of sites people who only like fractals for the pretty pictures and not for the mathematical properties. /mathrant

This one might look nice: http://en.wikipedia.org/wiki/T-Square_%28fractal%29

Personal favorite: http://en.wikipedia.org/wiki/File:Cicle_inversion.svg

The complement of this one would look cool in 3D: http://en.wikipedia.org/wiki/Sierpinski_gasket

You said you use 2D fractal layouts. What do they look like?

[slink]

This was one that I built in response to a challenge posted in this forum, back in 40d.  There was one level underground for growing subterranean crops, otherwise all of the living and working areas were inside the pyramids.  It's not as complex as your triangle-based plan, but it is similar.

Spoiler (click to show/hide)

Edit:  Here it is from above, showing the moat made from the stream, the leveled terrain, and the pyramid entrance facing west.  The depot was inside the gate, which led to a tunnel under the moat and into the subterranean level.  Retracting bridges originally connected to the mainland, but were left permanently retracted once the pyramids were completed.  Similarly, the ground level doors in the central staircase were sealed at that time.

Spoiler (click to show/hide)

[NW_Kohaku]

Yes, the Sierpinsky model is basically what the tetrahedron plan I was thinking about having the repeating size decline would look like.  (Or rather, the inverse version.)

I'm honestly thinking of just trying the "Geode" for now, however.  Concentric rings of polyhedrons around a core that would serve as the dining hall (although the dining hall would require an unfortunate floor in the middle of it to be useful, darn that silly inability to designate rooms across z-levels!) and then work outwards.  It will be difficult to make the system work on the very heavily sloped areas, however.  I'll need to make the "crystal" sizes very thick in order to have room for at least a workshop in every floor.

[kenpoaj]

I think I'm going to do a Green Glass Menger Sponge. Made from all green glass. Maybe I can fit a volcano in the middle? Anyone have an embark with a perfectly Square volcano? If not, I'll just have to pump it from the magma sea 

[Girlinhat]

Very interesting idea, but I'd worry a bit about how to craft the innermost cubes, since you can't exactly see them easily to visualize.

[kenpoaj]

They are hollow all the way through!
Might use gem/glass windows on them though. Not sure yet.

[Girlinhat]

What size units would you be using?