Self-tiling tile set

https://en.wikipedia.org/wiki/Self-tiling_tile_set

by vinchuco • 11 years ago

139 21 11 years ago

en.wikipedia.org

reilly3000• 11 years ago

many thanks for sharing. This is rather amazing to me.

tunnuz2• 11 years ago

Very interesting. Is there a real-world application for this?

teraflop• 11 years ago

It reminds me of a technique for using recursive self-similar tiles to generate pseudorandomly distributed points: http://johanneskopf.de/publications/blue_noise/

The idea is that you can model an infinite set of points generated by an infinitely-deeply-nested tiling, and then efficiently sample from it at arbitrary levels of detail. This lets you do things like zoom in and out while retaining frame-to-frame coherence, and without having to explicitly store the entire point set. (It's worth watching the full 5-minute video, which explains it better than I can.)

The implementation in that paper used squares with labeled edges to tile the plane non-periodically. This seems like it could be used to do something similar, except with a periodic but irregular tiling. No idea if that would have any practical benefits, but it's interesting, at least.

anon4• 11 years ago

Oh wow, I was looking for ways to do exactly this the other day.

vinchuco• 11 years ago

There need not be. 1+1=2 is true whether we are adding dollars or lines of code. Another answer is that I'm trying to make a puzzle with different solutions, all of which can't be solved simultaneously.

tunnuz2• 11 years ago

I never said that there must be an application, I was wondering whether there was one.

kleer001• 11 years ago

I think that depends on the world you're trying to apply it to.

chavesn• 11 years ago

https://en.wikipedia.org/wiki/Digital_camouflage ?

paublyrne• 11 years ago

Bathrooms?

shawabawa3• 11 years ago

My first thought was for tiled textures, to make repetition less obvious

scott_karana• 11 years ago

Wouldn't it be difficult to make a texture whose edges were contiguous with every possible permutation?

brento• 11 years ago

That feels a little like Inception (https://en.wikipedia.org/wiki/Inception) or the Infinity mirror (https://en.wikipedia.org/wiki/Infinity_mirror).

vishnuharidas• 11 years ago

I'd rather get these tiles for paving in my house floor.

amelius2• 11 years ago

These tiles have nice properties, but it seems the property that you can cover an arbitrary shape with them is missing (even if allowing cropping of the result).

gjm112• 11 years ago

If you allow cropping, you can always do this.

Suppose the tiles are T1, ..., Tn. The "self-tiling" property means you can tile each Tk with smaller copies of T1, ..., Tn. Or, equivalently, you can tile a larger copy of each Tk with copies of T1, ..., Tn.

So: pick one of the tiles. Tile it with smaller copies of the tiles. Tile each of those with still-smaller copies. Tile each of those with still-smaller copies. Etc.

Now pick a region in the original tile that's the same shape as the thing you're trying to cover. This process covers (the whole original tile, and hence in particular) that region with finer and finer copies of the tiles.

madcaptenor• 11 years ago

I was thinking the same. I've got a couple bathrooms that need updating.

maweki• 11 years ago

The article is an interesting read. I wonder why it took so long to realize there are longer loops.

I'd think, but this may well be hindsight speaking, about everything that holds for tearm rewriting should hold for tiling.

reedlaw• 11 years ago

I wonder if any of these tile sets could work in a Tetris-like game.

BillTheCat• 11 years ago

When you complete a tile shape using smaller tiles the game zooms out and the shape you just completed is falling into a new self-tiling shape. Inception Noise

Self-tiling tile set

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