Ray-traced images and animations related to the hat and spectre monotiles

Hat (monotile) tilings with PovRay

subdivision of clusters H₇ and H₈
Wandering in a "depth-6" tiling (Land of Oz) along the infinite worm (Yellow Brick Road) and other semi-infinite worms (other roads) [animations]
Build tilings by Conway signature
Fractal limit of H₇ and H₈

Reference: An aperiodic monotile by D. Smith, J.S. Myers, C.S. Kaplan, C. Goodman-Strauss, figure 2.11 page 18.

The chiral tile(1,1): Spectre/mystic tilings with povray

[arxiv paper by David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss

Appendix: the hexagonal counterpart of the hat monotile (by Vincent Van Dongen)

This is not an a-periodic tile per se, but it exhibits, together with the same H₇-H₈ subdivision process of the of the hat monotile, the same combinatorial structure. This tiling and its subdivision process was devised by Vincent Van Dongen.

subdivision of clusters hexH₇ and hexH₈ (in progress)
Wandering in a "depth-6" tiling along the infinite worm (Yellow Brick Road) and other semi-infinite worms (other roads) [animations]
Build tilings by Conway signature

You could also be interested in my previous work in

Kites/darts Penrose tiling
Danzer ABCK 3D tiling

External references

Nice web page by Simon Tatham

[Images and animation created by M. Paolini using the PovRay raytracing software]