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A chiral aperiodic monotile

arxiv.org

81–83 of 83 posts

Re: A chiral aperiodic monotile

#81
post #63

Earlier quoted context omitted.

Oh that's an interesting point actually. I hadn't considered the tiles needing to be designed around the grout width. Still, I don't think you'd need to be particularly exact with the tiles or grout. In fact it would probably be best to eyeball it and make sure you work outward from a single spot. Trying to tile by e.g. starting around the outside edges and working inwards is bound to get you in trouble with compound…

On reflection I've realised my point was nonsense. Sorry.

It's not nonsense. The fact that aperiodic tiles like these need to be designed for a specific grout width is non-obvious and quite interesting.

Re: A chiral aperiodic monotile

#82

Random thought/nerd snipe hazard: would a Wolfram-style classification of cellular automata running on this tiling kick up anything interesting?

There have been some experiments along these lines for "hat" tilings:

  https://conwaylife.com/forums/viewtopic.php?p=161571#p161571
As far as I know, HatLife hasn't been adjusted to make SpectreLife yet, but it's probably only a matter of time!

Re: A chiral aperiodic monotile

#83
post #34

There was a rumour that if they found a chiral aperiodic monotile then they might call it a Vampire Tile, because it doesn't have a reflection. Seems like they didn't go with that. I also see that the old discussion has come up: "But what can it be used for?" These sorts of things are pursued because they are fun, and there's a community of people who find it interesting. Is Rachmaninoff's second piano concerto usefu…

You've reminded me of an older Quora post about: What do grad students in math do all day? Do they just sit at their desk and think? [1] Here are excerpts: """ The main issue is that, by the time you get to the frontiers of math, the words to describe the concepts don't really exist yet. Communicating these ideas is a bit like trying to explain a vacuum cleaner to someone who has never seen one, except you're only al…

A vacuum cleaner described in 'words that are four letters long or shorter':

a tool to suck dirt and dust into a bag

;)

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