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#tilingTuesday a walkway in Tokyo

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#tilingTuesday a walkway in Tokyo

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  • birdperhour@mas.toundefined

    #birdbot

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    birdperhour@mas.toundefined
    #birdbot
  • clever_reports@mastodon.artundefined

    We report: we chance a last look at the sky before going to sleep, out of habit.

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    clever_reports@mastodon.artundefined
    We report: we chance a last look at the sky before going to sleep, out of habit. We think we know it will be too cloudy to see anything, but we can never go to bed without a last look. We remember why that it is upon seeing the stars. A bit of fog moves between constellations.
  • lasolitalaura_@sociale.networkundefined

    Meglio a tarda sera #parle Par🇮🇹le n°1476 3/6

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    luiginapoli@sociale.networkundefined
    @lasolitaLaura_ Par🇮🇹le n°1476 5/6⬛⬛⬛🟨🟩⬛⬛🟩⬛🟩⬛⬛🟩⬛🟩⬛🟩🟩⬛🟩🟩🟩🟩🟩🟩
  • simontatham@hachyderm.ioundefined

    I wonder how many times it's possible to be wrong in sequence about the same thing.

    Uncategorized tilingtuesday oops
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    simontatham@hachyderm.ioundefined
    I wonder how many times it's possible to be wrong in sequence about the same thing.In my last blog post about tilings and finite-state transducers, I mentioned making a mistake about the Ammann-Beenker tiling. I had a description of it in my software, and I had believed it didn't admit a deterministic transducer, because my code reported failure when trying to construct one. But I later found out that it did: my construction algorithm had an overzealous failure detector, and had given up too soon.But it turns out I was right the first time, if for the wrong reasons. It _doesn't_ admit a transducer after all, because I _also_ got the tiling description slightly wrong!The Ammann-Beenker rhombus tile is 180° symmetric, but its orientation matters nonetheless (it forms part of the proof of aperiodicity). My description of the tiling had the rhombuses wrongly oriented, in a way that – as it turns out – made the system accidentally simpler.The first picture here is the Ammann-Beenker analogue of the Penrose 'cartwheel pattern': a singular instance of the tiling, having the symmetry group of a regular octagon _except_ for the dark-coloured tiles, of which the blue ones vary their shape under rotation by some multiple of 45°, and the red ones keep the same shape but change orientation.The second picture is the same pattern, but generated using my earlier wrong description of the tiling. Because I got some of the rhombus orientations wrong, the red tiles are in much weirder places. _That_ diagram has been puzzling me for a week, until I figured out last night what mistake had caused it!Oh well, at least I got some pretty pictures out of it.#TilingTuesday #oops