Exquisite TESSELLATION Prints

While working on making collaborative prints -- like an Exquisite Corpse -- the model suggested we make collaborative TESSELLATION prints, like M.C. Escher.

The beginnings of a linocut

UPDATE (May 14, 2024): We made our first Tessellation print proof:

Ellie, Cassandra and Krrrl's "hat" linocuts

printed together

 

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:

GitHub -- aperiodic-monotile

The "hat" --

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.

 

How a Hobbyist Created An Infinite Pattern That Never Repeats

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:

I bumped the passed to 7 times -- at 100% power, and 25 speed -- which cut cleanly through the linoleum, most of the time:

The LightBurn settings

• Online laser cutter helper for cutting several tiles

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,

and even in a few other variations in the same family

OTHER RESOURCES

INTERACTIVE WEBSITES

These interactive websites are all linked from this main website -- An Aperiodic Monotile:

• Tile "hat" shapes
• Tile variations in the family of "hat" shapes
• Move the tiles around online

• (GitHub by Christian Lawson-Perfect) Aperiodic Monotile files to download 
• somethingorotherwhatever.com/aperiodic-monotile/interactive.html

Note that there are other "aperiodic monotile" shapes in the same family:

3D PRINTING

3D Printed aperiodic monotiles:

• 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.