Penrose tiles are geometric shapes that are non-periodic or they lack translational symmetry. They are named after Roger Penrose, an English mathematical physicist, who explored the mathematical properties of these shapes. These tile shapes also make for some intriguing stamp action. First off you’ll need a nice sharp x-acto knife.
Then an eraser, although I guess a potato would also work.
Then you will need a template to cut the shapes. In this case I will use the P2 or kite and dart tiling. There are also the P1 and P3 tilings as well.
Print out the template to the desired size and then use the x-acto knife to cut two Penrose stamps. My kite and dart stamps are shown below after some use. They aren’t completely perfect since I cut them out by hand, but it’s good enough to get started.
Lastly is an optional step. If you have a couple push pins you can use them as handles for your stamps. If you do this you should probably leave the paper templates with the color coded circles to match up the stamps as you go.
Then it’s time to stamp. You’ll also need a stamp pad.
The rules for how the edges connect are a little tricky but you can read up on Penrose tiles (1, 2, 3) or just experiment. The top of the post has one of my first examples with a nice bit of fivefold symmetry. In this case I am stamping with gaps between each one but this is optional. Below is an example of a Penrose stencil.
The result is, I think, a nice irregular geometry that is visually distinct and eye catching. Finally you can scan the Penrose stamped patterns and then have even more fun digitally editing the patterns into additional patterns and shapes. The challenge of a sudoku and the simplicity of stamping. Funky geometric forms liberated from dry mathematical journals and spray painted on the side of my bright red toolbox. If you’ve had more fun with a stamp pad and an eraser, it probably wasn’t legal, or least the mathematicians weren’t interested.
Bold Lentil 
