This project displays some animations of the recently discovered chiral aperiodic monotile tiling by a family of shapes called "Spectres". The picture below shows the basic tile "Tile(1, 1)", a member of the continuous family of (non-chiral) aperiodic monotile discovered previously by the same authors.

Spectres are obtained from it by replacing its edges with arbitrary paths, always oriented from the 90° corners to the 120° corners. Some examples of spectres, obtained by replacing each edge by two segments at an angle, are represented to the right of the Tile(1, 1) below.

They can of course be continuously deformed into each other.

The aperiodic tilings by spectres can be constructed from a set of 10 labeled hexagonal tiles with complicated matching rules, with each spectre being associated to a hexagon. One can color the tiling so that each of the ten types of tiles has a different color. Better, we can make these color evolve. Here is an example:

Zooming out a bit, the coloring reveals the structure of the tiling, producing interesting patterns.

One can also color the tiles in a way that reflects the hierarchy of tiles associated to the substitution rules, thereby making larger structures apparent.

Here are two other animations with random colors.

Finally, a video zooming on a 4th generation patch of the tiling.