Rubber Flooring
Hmmm… more Escher than Penrose but that’s nothing a quick trip to my local laser cutting place can’t solve… 
I wonder if they could be talked out of some bulk material
Laser cutters are awesome and I want one for the workshop. (…along with a high-power gyrotron for melting stuff… 
but that’s another thread…)
I know very little about math. Could you consider a tiling non-repeating if the bathroom contains only one single bathroom-shaped tile?
Also (after all the other links I added above) and lastly, this claims the pavement outside Oxford University’s Maths Dept has a Penrosey design. Off to see if I can find that.
Yes, you are right, but sadly that solution receives the rather derogatory mathematical label “trivial”. 
Nonetheless, the good stuff often flows from a surprisingly simple starting point…
Went online shopping for penrose tiles and found that Penrose is rather vehement and litigious about enforcing his IP licensing. So no go.
Part of the problem is that Roger Penrose patented the shapes.
He also sued someone that put the patterns on toilet paper. The patent has since expired, but copyright lives a bit longer.
From the second link I posted in the set of 4 above
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.
Seems like their lawyer should have been a bit more of a mathematician 
What a square 
Colors and shapes should not be possible to patent.
America’s great, isn’t it? I seem to remember basic words could be patented too.
Patent system is broken.
When a copyright suit comes down to facts rather than being thrown out on procedural grounds, it becomes ruinously expensive. It’s much cheaper to settle the case.
Otherwise, Kimberley-Clark could have argued that they were copying the pattern of the Khatryka meteorite, which Penrose surely did not create.
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