Mutant Spectre Tiles! Beer Cap Display for Fridge
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The famous aperiodic Spectre / Einstein tile as you've never yet seen it. Geometry ! Art !! Printing !!! Beer !!!!
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Updated at source:
Model information
- Source
- Printables
- Category
- Wall-mounted
- License
- Creative Commons — Attribution — Noncommercial
The “Spectre” aperiodic mono-tile was devised in 2023 by David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss
Research paper : https://arxiv.org/pdf/2305.17743
Further info : https://cs.uwaterloo.ca/~csk/spectre/
The most basic form is a polygon shape, but Smith & co. described how to modify the sides in order to make it truly aperiodic:
By taking this process to a more extreme level, I now made it truly gnarly :
FreeCAD users can see in detail how it was done, using the included source model.
Surely even further improvements are possible, but those are maybe for another time and place… almost time for a beer.
I made the tile profile without any allowance for gaps, so use the offset parameter as required ("Horizontal Expansion" in Cura).
For economy they can be printed with thin walls and fairly sparse infill, weighing about 4g each.
The tiles can become fridge magnets by placing small magnets underneath the beer caps (see images & diagrams). But blu-tac is a good alternative. Not all tiles need be fixed if they are interlocking snugly.
Finally, Simon Tatham has described how to arrange 4 colours of Spectre tiles :
https://www.chiark.greenend.org.uk/~sgtatham/quasiblog/aperiodic-spectre/