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  • "ovoid tile"

    From Stewart Robert Hinsley@21:1/5 to All on Tue Sep 13 14:29:28 2016
    The latest addition at ifstile.com is a striking figure which is called
    an ovoid tile.

    On visual inspection I can identify it as an octapletal - that is a
    rep-8-tile built on a square grid, and with a base rotation of the
    elements of 45 degrees (to which can be added rotations by multiples of
    90 degrees and reflections)

    https://ifstile.com/view/File:OvoidTile.png

    I'd hardly know how to start to find this from scratch (the
    combinatorial explosion would get in the way of a systematic search),
    and unlike some other tiles (e.g. the Cross of Lorraine rep-9-tiles) it
    doesn't look to be easy to reverse to engineer either.

    --
    SRH

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  • From Roger Bagula@21:1/5 to All on Sat Sep 17 07:14:44 2016
    Дмитрий Мехонцев
    Thanks for giving us a place to start.
    I'm with Steward Robert Hinsley: this is great work.
    And appears to be a new approach.
    Can you gives the reasoning that made you come to this sort of
    fractal tiling. You just published one with a border dimension 5/3
    that is also very wonderful.
    Roger Bagula

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  • From =?UTF-8?B?0JTQvNC40YLRgNC40Lkg0JzQt@21:1/5 to All on Fri Sep 16 22:32:09 2016
    Hi!

    Here Fractint ifs representation:

    OvoidTile {
    0.25 0.25 0.25 -0.25 0 0.5 0.125
    -0.25 0.25 -0.25 -0.25 -0.25 0.25 0.125
    -0.25 -0.25 -0.25 0.25 -0.25 0.25 0.125
    -0.25 0.25 0.25 0.25 -0.25 0.25 0.125
    -0.25 0.25 -0.25 -0.25 0 0.5 0.125
    0.25 0.25 -0.25 0.25 -0.25 0.25 0.125
    -0.25 0.25 0.25 0.25 -0.5 0.5 0.125
    -0.25 -0.25 -0.25 0.25 0 0 0.125
    }

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  • From Stewart Robert Hinsley@21:1/5 to All on Mon Sep 19 11:43:36 2016
    On 17/09/2016 06:32, Дмитрий Мехонцев wrote:
    Hi!

    Here Fractint ifs representation:

    OvoidTile {
    0.25 0.25 0.25 -0.25 0 0.5 0.125
    -0.25 0.25 -0.25 -0.25 -0.25 0.25 0.125
    -0.25 -0.25 -0.25 0.25 -0.25 0.25 0.125
    -0.25 0.25 0.25 0.25 -0.25 0.25 0.125
    -0.25 0.25 -0.25 -0.25 0 0.5 0.125
    0.25 0.25 -0.25 0.25 -0.25 0.25 0.125
    -0.25 0.25 0.25 0.25 -0.5 0.5 0.125
    -0.25 -0.25 -0.25 0.25 0 0 0.125
    }


    Thanks.

    It turns out that there are more easily accessible octapletals than I
    thought. Each c2-symmetric octapletal seems to have 3 c2-symmetric
    demitiles (plus 117 other demitiles), which leads to quite a few tiles
    in total.

    Some of the symmetric demitiles are broken into 2 or 4 parts, but from
    these you can get to a connected tile after another 1 or 2 iterations.

    The questions that arise are is the set of c2-symmetric octapletals
    finite or infinite, and if finite how many members does it have. (I
    haven't demonstrated the existence of cycles in the iteration yet, but I suspect that they exist.)

    The other approaches I have for generating octapletals are dissecting
    the dipletals, and producing dipletal-tetrapletal product fractals. With
    5 reflected elements the ovoid tile isn't going to fall out directly
    from either of the latter.

    --
    SRH

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