There’s been an exciting new development in tiling the plane. Aperiodic tiling with a single tile.
And, hey, I hate my kitchen floor (mostly because the ceramic tiles are too hard, and always look dirty) so maybe this is a good time to do something really exciting.
I think I’d have to find someone with a laser cutter to cut the tiles out of something like vinyl, and I’d have to lay them myself.
So, um, how hard would this be? If vinyl flooring material can be cut with a laser cutter, I am confident I could find someone who could do it for me. But can it be? Where would I buy the pieces to be cut? How hard would it be to remove the existing ceramic tile? To glue down vinyl tiles? Will they stay down, or peel at all the seems?
I probably won’t do this, but it’s a serious question, and I might do it, and any information you have would be appreciated.
I seem to recall that at one point Penrose’s two-polygon tilings were patented: no commercial venture could use that pattern without permission. Have the latest monotilings been similarly controlled?
That’s an interesting question. The paper doesn’t say anything about it, but i suppose it wouldn’t. I don’t think “tiling my own kitchen floor” is likely to count as a commercial venture, and there are a lot of ways to vary the basic shapes, so i think patenting the thing would be challenging.
Removing old ceramic tile is a noisy nasty job needing power tools. All (as in 100.00%, not 99.5%) of the grout / mortar / cement under the old tiles also needs to be removed if you’re planning on installing vinyl or other thin flexible sheet material.
After all the grout / mortar is gone you need to level (flatten really) the surface. Often the underfloor underneath a tile floor isn’t flat because it doesn’t need to be; the variable thickness of the heavy undercoat of grout/mortar addresses all the unevenness. That solution isn’t available with sheet material flooring. It takes some skill and specialized floor-leveling cements to get everything ready for the finish layer of thin goods.
I suggest you might consider contacting a flooring contractor about doing a removal and prep for a vinyl re-installation. This is not a nice job, not at all.
Then do the re-install yourself, especially if the Penrose tiling aspect of your proposed parts is weird and counter-intuitive. Tile workers are real good at the standard patterns but few of them are geometrical creative genius thinkers.
If this is a kitchen, and especially an older kitchen, you have the potential “fun” that the current base cabinets are installed on top of one or more old layers of tile. Which leads to either needing to saw along all the cabinet bases and leave the cabinets and old tile underneath, or pull up all the cabinets to take out the tile layer(s) under them. If you pull up old cabinets, pretty surely one will break or be water-logged. Pretty quickly you can ratchet a kitchen tile job into a whole new kitchen.
A local pro can quickly evaluate all your personal kitchen’s pitfalls. We can’t 'cus we can’t come visit.
As an aside, the Numberphile video on this was really subpar. They spent 20 minutes basically asking the discoverer “How excited were you when you saw this?”, but never actually got around to saying what an aperiodic monotile is.
I guess the good thing, kinda, is that the cabinets are older than the floor. The floor won’t be under the cabinets. But while i hate the floor, i love the original built-in cabinets, and it would be a disaster if taking out the tile messed up the cabinets.
You’re best off hiring someone to do that demolition work for you. We had the tile in our kitchen removed before getting new floors- it took the guys who did it about a week to finish it and get it prepped appropriately. And dust got everywhere, etc… despite their attempts to mask off the rest of the house.
I’ve often thought that if I ever build my dream house I’d do Escher and/or Penrose tiles on the bathroom floors. I don’t know how difficult it would be to do, either practically or legally.
Just remember that if you hire someone to do the job, watch over them carefully. A friend had contractors tile a bathroom wall using black and white squares. But the black squares were to go in particular places marking the coordinates of the Gaussian primes* and he laid out carefully where they should go. They basically ignored his diagram, apparently figuring he wouldn’t know the difference. He did.
*A gaussian integer is a complex number of the form a+bi where a and b are ordinary integers and it is prime if it cannot be factored unless one of the factors is a unit: \pm 1 or \pm i. As examples 2=(1+i)(1-i) is not a gaussian prime, but 3 is, as are 1+i and 1-i.
I had contractors tile my bathroom walls, and apparently the instructions I gave weren’t explicit enough, because the general contractor called me at work and asked me to draw a picture. So I made some graph paper, and quickly marked out where I wanted the colors to go – meaning it to be “something along these lines”. I was shocked but pleased to come home and find every tile was exactly where I had drawn it.
.