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The "Einstein Tile" A geometric shape that does not repeat itself when tiled

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Comments

  • ColinFrenchColinFrench Posts: 647

    Escher would have had fun with this tile.

  • LinwellyLinwelly Posts: 5,955

    ColinFrench said:

    Escher would have had fun with this tile.

    That for sure surprise

  • LeatherGryphonLeatherGryphon Posts: 11,562
    edited April 2023

    Are we sure that its apparent repetition isn't really just momentary stuttering?indecision   And would a momentary stutter be sufficiently exact to establish a proper repeating tile? 

    Post edited by LeatherGryphon on
  • PerttiAPerttiA Posts: 10,024

    LeatherGryphon said:

    Are we sure that its apparent repetition isn't really just momentary stuttering?indecision   And would a momentary stutter be sufficiently exact to establish a proper repeating tile? 

    And, so far there has only been pictures of untextured tiles, the surface would look quite different if there was real textures rotating with the tile. 

  • LeatherGryphonLeatherGryphon Posts: 11,562
    edited April 2023

    PerttiA said:

    LeatherGryphon said:

    Are we sure that its apparent repetition isn't really just momentary stuttering?indecision   And would a momentary stutter be sufficiently exact to establish a proper repeating tile? 

    And, so far there has only been pictures of untextured tiles, the surface would look quite different if there was real textures rotating with the tile. 

    But would be perfect if one was trying to tile a large plane with T-shirts(or stylized teapots).yes

    Post edited by LeatherGryphon on
  • parrotdolphinparrotdolphin Posts: 110

    Here's one I made in Illustrator and Photoshop Elements, just messing around with putting a pattern on the tiles.

    Einstein Tiles 03.jpg
    2748 x 1924 - 1M
  • stem_athomestem_athome Posts: 518

    Chumly said:

    The cool thing, for our purposes though, is that if each of those tiles was a Patch of Grass, or a section of cobblestone, it would look a lot better and natural than the normal tiling Daz uses now and which the eye can find the pattern pretty quickly.

    You can make tiling look more random by creating a procedural mix.

    Simple example.

    Pic1: Stone texture repeated 3 times.

    Pic2: Same texture repeated 3 times, but with a rotated layer, mixed using perlin procedural texture.

     

    It is a case of rotating/translating the top layer and scaling the weight (perlin noise) size to get a good result.

     

     

    Tile.jpg
    800 x 800 - 726K
    TileMix.jpg
    800 x 800 - 731K
  • ArtiniArtini Posts: 9,500

    parrotdolphin said:

    Here's one I made in Illustrator and Photoshop Elements, just messing around with putting a pattern on the tiles.

    Sorry, but I still see the pattern repetition on that.

  • ArtiniArtini Posts: 9,500
    edited April 2023

    stem_athome said:

    Chumly said:

    The cool thing, for our purposes though, is that if each of those tiles was a Patch of Grass, or a section of cobblestone, it would look a lot better and natural than the normal tiling Daz uses now and which the eye can find the pattern pretty quickly.

    You can make tiling look more random by creating a procedural mix.

    Simple example.

    Pic1: Stone texture repeated 3 times.

    Pic2: Same texture repeated 3 times, but with a rotated layer, mixed using perlin procedural texture.

     

    It is a case of rotating/translating the top layer and scaling the weight (perlin noise) size to get a good result.

     

     

    That second image (with perlin noise applied) is a good example and gives illusion of non repetitive patterns.

     

    Post edited by Artini on
  • LinwellyLinwelly Posts: 5,955

    parrotdolphin said:

    Here's one I made in Illustrator and Photoshop Elements, just messing around with putting a pattern on the tiles.

    I like that laugh

  • FirePro9FirePro9 Posts: 456

    Another article about potential use of the Einstein Tile in material science.

    https://www.thebrighterside.news/post/einstein-shape-tiles-will-revolutionize-material-science

    Also, cool alternate image provided.

    Einstein tiles alt colors zoomed out.jpg
    1108 x 698 - 286K
  • FirePro9FirePro9 Posts: 456

    Here is a link to a Jan. 2024 article in Scientific American bringing us up to date on the latest discoveries in non-repeating tiles, and a summary of how the "Hat", the first "Einstein Tile", was found.  In short, there are more ein-stein tiles such as the "Turtle", and a family of tile shapes that do not require a tile to occassionally be flipped (reflection), they call "Spectres".

    https://www.scientificamerican.com/article/inside-mathematicians-search-for-the-mysterious-einstein-tile/

  • kyoto kidkyoto kid Posts: 41,094

    ...years ago (back in the 3DL days) I found an Einstein Tile texture. May still have it on backup media.

     

  • NotAnArtistNotAnArtist Posts: 388

    If you use apps which create seamless repeating patterns and do it from an image of Einstein Tiles, the Universe will explode (again).

  • Matt_CastleMatt_Castle Posts: 2,593

    kyoto kid said:

    ...years ago (back in the 3DL days) I found an Einstein Tile texture. May still have it on backup media.

    Given that the Einstein tile wasn't even known to exist until last year (and some theorised it might not even be possible), I'm not sure how you could have a texture of it from many years ago.

    There's even relatively recent Youtube videos on the entire subject of these non-repeating tiles that eventually conclude "The smallest known sets are two, and we're still not sure if a single tile set can exist".

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