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litigilicious

Re:Impossible Cookware and Other Triumphs of the Penrose Tile on Friday February 08, 2019 @04:09PM (#19118693)
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.