While working on making collaborative prints -- like an Exquisite Corpse -- the model suggested we make collaborative TESSELLATION prints, like M.C. Escher.
UPDATE (May 14, 2024): We made our first Tessellation print proof:
CONCEPT
We then decided to make collaborative prints from linocuts in the "hat" shape below -- the "Ein Stein" -- because this shape will tile infinitely without repeating a pattern -- as it is an APERIODIC MONOTILE:
David Smith discovered this single shape in 2022, which would tile infinitely without repeating a pattern. Previously Nobel laureate Roger Penrose had reduced the aperiodic tiles down to just TWO tile shapes.
LASER CUTTING
We laser cut a bunch of "hat" shapes out of linoleum at Quelab in Albuquerque -- the widest part of the linocut being 7 inches:
Laser cut linoleum in "hat" shape,
7 inches at the widest
The LIGHTBURN file that we used -- 7inch_hat_square.LBRN2 (10.51 KB)
- We first laser cut the middle "hat" shape 3 times -- at 100% power, 25 speed.
- Then we laser cut the outside square 3 times -- at 100% power, 25 speed.
Laser cutting at slow speeds
brought out a big flame
UPDATE (May 6, 2024): I laser cut more "hat" tiles at Quelab, but this time there was no flame. That is probably because the "air assist" was not working correctly when cutting the first batch above:
The LightBurn settings
PRINT COLLABORATIONS
Next we will hand out the "hat" linocuts and ask people to carve them.
Stack of linocuts
to hand out
Then we will print them -- both INDIVIDUALLY and TILED COLLECTIVELY.
INDIVIDUALLY
The 7 inch wide linocut will print on an 8x8 inch piece of paper, which can frame and carry around in bucket, for pop-up BUCKET EXHIBITIONS.
We can also carve the remainder linoleum -- ie the outside pieces -- and make a 7 inch print. We can even make a framed multi-colored print, by inking the separate puzzle pieces in different colors:
I saved the outside remainder pieces,
to make multi-colored 7 inch prints
on 8x8 inch paper
TILING COLLABORATIONS
The individual linocuts will tile infinitely, in many ways, without making a repeating pattern. So we can piece linocuts from two people together, or linocuts from 200 people together, and make a print:
Three "hat" linocuts
piecing together
Six "hat" linocuts
making a row
Arbitrary piecing together
Robert discovered that we can make a pentagon
while still tiling the "hat" linocuts infinitely
Robert used Adobe Illustrator to expand on the tiling
The tiling goes on and on and on infinitely,
OTHER RESOURCES
INTERACTIVE WEBSITES
These interactive websites are all linked from this main website -- An Aperiodic Monotile:
- (GitHub by Christian Lawson-Perfect) Aperiodic Monotile files to download
Note that there are other "aperiodic monotile" shapes in the same family:
3D PRINTING
- Einstein Hat
- einstein spectre - world's first chiral aperiodic monotile
- Aperiodic Monotile PipesAperiodic Monotile with a twist
- Einstein Aperiodic Monotile Lego
Other thoughts:
- Perhaps we could write a program in ChatGPT3 that would divide any image into "hat" shaped aperiodic monotiles, which we could then separate -- say for laser engraving on linoleum, to print different variations.
- I Googles "aperiodic monotile prints" and did not find any prints, but I did find this drawing by Joseph Reyes.
