A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3- [Un pavage périodique du plan utilisant 3 flocons de neige de type von Koch -itération 3-].




  • Some few fractal shapes (like the von Koch snowflake) can be used to tile the plane using scaling and rotations:



    • 2 snowflakes
    3 iterations.
    3 snowflakes
    3 iterations.
    4 snowflakes
    3 iterations.

    2 snowflakes
    3 iterations.
    3 snowflakes
    3 iterations.
    4 snowflakes
    3 iterations.

    2 snowflakes
    3 iterations.
    3 snowflakes
    3 iterations.
    4 snowflakes
    3 iterations.



  • Some few fractal shapes (like the von Koch snowflake) can be used to tile the plane using scaling and rotations:



    • 2 snowflakes
    2 iterations.
    2 snowflakes
    3 iterations.
    2 snowflakes
    4 iterations.
    2 snowflakes
    5 iterations.

    2 snowflakes
    2 iterations.
    2 snowflakes
    3 iterations.
    2 snowflakes
    4 iterations.
    2 snowflakes
    5 iterations.




    2 snowflakes
    5 iterations.



  • Some few fractal shapes (like the von Koch snowflake) can be used to tile the plane using scaling and rotations:



    • 3 snowflakes
    2 iterations.
    3 snowflakes
    3 iterations.
    3 snowflakes
    4 iterations.
    3 snowflakes
    5 iterations.

    3 snowflakes
    2 iterations.
    3 snowflakes
    3 iterations.
    3 snowflakes
    4 iterations.
    3 snowflakes
    5 iterations.




    3 snowflakes
    5 iterations.



  • Some few fractal shapes (like the von Koch snowflake) can be used to tile the plane using scaling and rotations:



    • 2 snowflakes
    3 iterations.
    3 snowflakes
    3 iterations.
    4 snowflakes
    3 iterations.

    2 snowflakes
    3 iterations.
    3 snowflakes
    3 iterations.
    4 snowflakes
    3 iterations.


    Mapping of a finite subset on a cylinder:


    2 snowflakes
    3 iterations.
    3 snowflakes
    3 iterations.
    4 snowflakes
    3 iterations.


    Mapping of a finite subset on a sphere:


    2 snowflakes
    3 iterations.
    3 snowflakes
    3 iterations.
    4 snowflakes
    3 iterations.


    Mapping of a finite subset on a torus:


    2 snowflakes
    3 iterations.
    3 snowflakes
    3 iterations.
    4 snowflakes
    3 iterations.


    Mapping of a finite subset on the Möbius strip:


    2 snowflakes
    3 iterations.
    3 snowflakes
    3 iterations.
    4 snowflakes
    3 iterations.


    Mapping of a finite subset on the Klein bottle:


    2 snowflakes
    3 iterations.
    3 snowflakes
    3 iterations.
    4 snowflakes
    3 iterations.


    Mapping of a finite subset on the Bonan-Jeener double bottle:


    2 snowflakes
    3 iterations.
    3 snowflakes
    3 iterations.
    4 snowflakes
    3 iterations.


    Mapping of a finite subset on a quadridimensional Calabi-Yau manifold:


    2 snowflakes
    3 iterations.
    3 snowflakes
    3 iterations.
    4 snowflakes
    3 iterations.



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