Liu Yao 刘杳
@liuyao12.bsky.social
AI ⋉ Math. Blogs at Observable on interactive math.
I love that it's not just "turtles all the way down", but turtles all the way up, down, left and right, filling up the entire plane.
It was also soon discovered that you can decorate the tiles with stripes that line up. (The reflected turtles get three stripes, as they are where three lines meet.)
It was also soon discovered that you can decorate the tiles with stripes that line up. (The reflected turtles get three stripes, as they are where three lines meet.)
December 4, 2024 at 9:50 AM
I love that it's not just "turtles all the way down", but turtles all the way up, down, left and right, filling up the entire plane.
It was also soon discovered that you can decorate the tiles with stripes that line up. (The reflected turtles get three stripes, as they are where three lines meet.)
It was also soon discovered that you can decorate the tiles with stripes that line up. (The reflected turtles get three stripes, as they are where three lines meet.)
They noticed early on that they needed to use reflected hats, and they'd see a long stack of hats that go through those reflected ones.
If they had used turtles, the stacks would be more straight. With such clues, they found that the tiles do follow some pattern, not translational but hierarchical.
If they had used turtles, the stacks would be more straight. With such clues, they found that the tiles do follow some pattern, not translational but hierarchical.
December 4, 2024 at 9:50 AM
They noticed early on that they needed to use reflected hats, and they'd see a long stack of hats that go through those reflected ones.
If they had used turtles, the stacks would be more straight. With such clues, they found that the tiles do follow some pattern, not translational but hierarchical.
If they had used turtles, the stacks would be more straight. With such clues, they found that the tiles do follow some pattern, not translational but hierarchical.
For background, aperiodic tilings are tilings of the plane (no gaps, no overlaps) that do NOT follow a translational (i.e. periodic) pattern. The most famous are the Penrose tilings with a five-fold rotational symmetry, made up of two base tiles (either two "rhombs", or a kite and a dart).
December 4, 2024 at 9:50 AM
For background, aperiodic tilings are tilings of the plane (no gaps, no overlaps) that do NOT follow a translational (i.e. periodic) pattern. The most famous are the Penrose tilings with a five-fold rotational symmetry, made up of two base tiles (either two "rhombs", or a kite and a dart).
In 2023, David Smith, Joseph Myers, Craig Kaplan, and Chaim Goodman-Strauss shocked the world with the discovery of the first aperiodic monotiles, the so-named hat, the turtle, and (a bit later) the spectre.
In fact there is a continuum of 13-sided polygons, with all the angles multiples of 30°.
In fact there is a continuum of 13-sided polygons, with all the angles multiples of 30°.
December 4, 2024 at 9:50 AM
In 2023, David Smith, Joseph Myers, Craig Kaplan, and Chaim Goodman-Strauss shocked the world with the discovery of the first aperiodic monotiles, the so-named hat, the turtle, and (a bit later) the spectre.
In fact there is a continuum of 13-sided polygons, with all the angles multiples of 30°.
In fact there is a continuum of 13-sided polygons, with all the angles multiples of 30°.