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Comment by briteside | Hacker News Reader

Anybody manufacture actual Penrose tiles?

You can buy some here [0]. Really nifty laser-cut acrylic pieces in a variety of colors, and you can even get a vinyl mat and set of rules for a board game that uses them. (Disclaimer: I personally know the designer of the game, and helped her playtest it.)

[0] http://gamepuzzles.com/pentuniv.htm#KD

I can’t tell if you are talking about puzzle tiles or floor tiles.

Given that, these are not Penrose but check out these floor tiles.

https://officeinsight.com/officenewswire/tarkett-officially-...

All of us nerdy homeowners are looking for ceramic, marble, granite, quartzite, glass, or similar. We need a few sizes. Our square tiles are 18x18 inches (3/8 thick, 3/8 grout lines) in larger rooms and about 2x2 or 3x3 inches (1/8 thick, 1/8 grout lines) in showers. Tiles of generally similar area would be good. We also need wall tiles for kitchens (behind the sink) and for bathroom walls.

The rhombic Penrose tiling is basic and nice. The Voronoi transform of it is better I think, being less likely to chip or injure feet because there are no acute angles.

If you want a toy here is some code to generate SVGs that you can laser cut: https://github.com/jbeda/penrose-svg

This is neat, do you have any other projects on tiling, or other plane geometry designs?

No, if you mean ceramic or stone tiles for floors or walls. I spent a bunch of time digging into this when I bought my current house because I initially could not believe that these were unobtanium and that custom cutting would be the only way to install such a pattern in my bath.

In short, there are 2 reasons for this. The first is that at the physical scale required for the nifty aperiodicity of the tiling to be apparent in a typical home (<= ~100cm^2 or 16 in^2, aka the areal size of a "standard bathroom tile" in North America,) tiles are typically sold and installed not individually but in mats of many tiles adhered to a backing webbing. This is not possible with an aperiodic tile pattern where the pattern does not, by definition, repeat predictably.

So that's the first reason: practicality.

The second reason is exactly what you might expect if you have been around the sun more than 2 dozen times: Roger Penrose is notoriously litigious. He patented the aperiodic tilings he "discovered" in the late 70s, but famously sued Kimberly-Clark for making toilet tissue with one of these tilings in the 90s claiming copyright violation - and won. Even though the patent is long expired, copyright lives longer.

Ironically, given that the infringing bog rolls were almost certainly roller-embossed, Kimberly-Clark's Kompetent Counsel seems to have missed a trick - their expression was NOT strictly a Penrose tiling as they are, by definition, aperiodic. You can't emboss a continuous Penrose tiling from a roller.

You could do it with webbing. The installer would have to pop a few tiles off the edge to match things up. Those tiles could then be used to fill in gaps. Depending on webbing size and installer skill, perhaps 80% of the tiles could be left attached to the webbing.

Oh, there is another way to do this with webbing.

The tiling can be recursively generated. (called "inflation" and "deflation") That is, starting from a Penrose tiling, another one with smaller tiles can be generated. This means that the patches of webbing can be tiled as Penrose tiles, yet be subdivided such that the result is a valid Penrose tiling with smaller tiles.

In case you are trying to imagine this... good luck. The recursive generation does not retain the large tile divisions as small tile divisions. The large tile divisions become jagged edges. This is fine; the tile industry already tolerates this issue with hex tiles on webbing.

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