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#mengersponge — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #mengersponge, aggregated by home.social.

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  1. Finally completed this absolutely huge 81x81x81 Menger sponge in a survival Luanti world! This is a total of 160,000 sandstone blocks placed!

    #luanti #mathart #fractal #MengerSponge

  2. Finally completed this absolutely huge 81x81x81 Menger sponge in a survival Luanti world! This is a total of 160,000 sandstone blocks placed!

    #luanti #mathart #fractal #MengerSponge

  3. Finally completed this absolutely huge 81x81x81 Menger sponge in a survival Luanti world! This is a total of 160,000 sandstone blocks placed!

    #luanti #mathart #fractal #MengerSponge

  4. Finally completed this absolutely huge 81x81x81 Menger sponge in a survival Luanti world! This is a total of 160,000 sandstone blocks placed!

    #luanti #mathart #fractal #MengerSponge

  5. Finally completed this absolutely huge 81x81x81 Menger sponge in a survival Luanti world! This is a total of 160,000 sandstone blocks placed!

    #luanti #mathart #fractal #MengerSponge

  6. Is there enough paint on earth to paint a #MengerSponge level 100?

  7. Is there enough paint on earth to paint a level 100?

  8. Here's a \(\textit{void-sponge}\) using sphere inversion, unlike for instance the #MengerSponge which is built using only linear transformations.

    Unlike the previous inversion sets, this one is built in 4D and then stereographically projected into 3D. That's because the most symmetric structure of spheres is at the vertices of a regular polychoron, and the projection to 3D is conformal, so retains the uniform sphere intersection angles.

    To render, the sample point is stereographically projected into 4D, then sphere inversion iteratively applied around the polychoron vertices.
    The sphere radii are identical and set such that they meet at angles of \(\pi/j\) for integer j. This value affects how thick the limbs of the sponge are.

  9. Here's a \(\textit{void-sponge}\) using sphere inversion, unlike for instance the #MengerSponge which is built using only linear transformations.

    Unlike the previous inversion sets, this one is built in 4D and then stereographically projected into 3D. That's because the most symmetric structure of spheres is at the vertices of a regular polychoron, and the projection to 3D is conformal, so retains the uniform sphere intersection angles.

    To render, the sample point is stereographically projected into 4D, then sphere inversion iteratively applied around the polychoron vertices.
    The sphere radii are identical and set such that they meet at angles of \(\pi/j\) for integer j. This value affects how thick the limbs of the sponge are.

  10. Here's a \(\textit{void-sponge}\) using sphere inversion, unlike for instance the #MengerSponge which is built using only linear transformations.

    Unlike the previous inversion sets, this one is built in 4D and then stereographically projected into 3D. That's because the most symmetric structure of spheres is at the vertices of a regular polychoron, and the projection to 3D is conformal, so retains the uniform sphere intersection angles.

    To render, the sample point is stereographically projected into 4D, then sphere inversion iteratively applied around the polychoron vertices.
    The sphere radii are identical and set such that they meet at angles of \(\pi/j\) for integer j. This value affects how thick the limbs of the sponge are.

  11. Here's a \(\textit{void-sponge}\) using sphere inversion, unlike for instance the #MengerSponge which is built using only linear transformations.

    Unlike the previous inversion sets, this one is built in 4D and then stereographically projected into 3D. That's because the most symmetric structure of spheres is at the vertices of a regular polychoron, and the projection to 3D is conformal, so retains the uniform sphere intersection angles.

    To render, the sample point is stereographically projected into 4D, then sphere inversion iteratively applied around the polychoron vertices.
    The sphere radii are identical and set such that they meet at angles of \(\pi/j\) for integer j. This value affects how thick the limbs of the sponge are.

  12. As with the other inversion sets, they change class when the scaling factor becomes large enough. In this case it becomes a \(\textit{void-sponge}\), the same class as the #MengerSponge and #SierpinskiPyramid.

  13. As with the other inversion sets, they change class when the scaling factor becomes large enough. In this case it becomes a \(\textit{void-sponge}\), the same class as the #MengerSponge and #SierpinskiPyramid.

  14. As with the other inversion sets, they change class when the scaling factor becomes large enough. In this case it becomes a \(\textit{void-sponge}\), the same class as the #MengerSponge and #SierpinskiPyramid.

  15. As with the other inversion sets, they change class when the scaling factor becomes large enough. In this case it becomes a \(\textit{void-sponge}\), the same class as the #MengerSponge and #SierpinskiPyramid.

  16. As with the other inversion sets, they change class when the scaling factor becomes large enough. In this case it becomes a \(\textit{void-sponge}\), the same class as the #MengerSponge and #SierpinskiPyramid.

  17. Hatching plans for a large modular #origami #MengerSponge. Please, someone stop me!