[HN Gopher] Combinatorial coordinates for the aperiodic Spectre ...
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       Combinatorial coordinates for the aperiodic Spectre tiling
        
       Author : colinprince
       Score  : 35 points
       Date   : 2023-07-04 04:04 UTC (1 days ago)
        
 (HTM) web link (www.chiark.greenend.org.uk)
 (TXT) w3m dump (www.chiark.greenend.org.uk)
        
       | btilly wrote:
       | The 4-coloring is interesting.
       | 
       | Here is an example of what you can do. You could have 4 designs,
       | say sheep in field, lost shepherd, barn, and lost sheep dog. The
       | even and odd edges could have paths lined up to go a bit to the
       | side of the edge, with fences. And now you get a pastoral scene
       | that your eye gets to wander over and never _quite_ see the
       | pattern to.
       | 
       | I wonder how hard it would be to actually tile a wall or floor
       | with a design like this?
        
         | isoprophlex wrote:
         | I've been inspired by the linked article and your comment to
         | draw a vector file of the chiral monotile and get that lasered
         | out of plywood.
         | 
         | There's a shop down the road here that cuts out your vector
         | drawings with a laser, it's pretty nifty. I want to get at
         | least 50-100 of these tiles, paint them in 4 distinct colors...
         | sounds like a wonderful cool thing to do together with the
         | kids.
        
       | OscarCunningham wrote:
       | > Distorting the shapes of the tile edges a tiny bit is enough to
       | prevent the unwanted extra tilings, and produce a tile which
       | rules out all but single-handedness non-periodic tilings of the
       | plane by its shape alone.
       | 
       | > The distortion can be anything you like: the precise shapes
       | don't matter, as long as they match.
       | 
       | My favourite way to do this is to make each of the original edges
       | the hypotenuse of a 1-by-2 right-angled triangle. This results in
       | a 27-sided shape with only two different edge lengths and lots of
       | rectangular 'tabs' and 'slots' to help fit the tiles together.
       | Image: https://mathstodon.xyz/@OscarCunningham/110488184680656303
        
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