I bought a consumer die-cutting machine late last year, after thinking a lot about the possibilities of using machine-driven cutting to do elaborate fractal pieces that’d be difficult to execute with an x-acto knife.
The machine’s a Cricut Explore Air 2, and I’m very happy with it and will write a bit more about how it operates and what I’ve been doing with it at some point.
But what I was doing with it yesterday evening was cutting out an approximately one foot square Sierpinski carpet. (Slightly less than, because the cutting material itself was a 12×12 sheet and leaving a small margin at the edges is a safe bet.)
At this scale, the design is 27 small squares wide and tall, and took about a half an hour for the machine to get through, most of it spent on those tiny squares.
But of course it doesn’t have 27 x 27 = 729 small squares in it; the larger squares that make up the lower level iterations of the pattern occupy a lot of space that the smallest squares would need to be cut out of in a regular grid. Instead it’s only 512 of the smallest squares, plus 64 of the next size up, and 8 of the next, and 1 of the largest, that monster in the center. All of which are powers of 8! 8^0 = 1; 8^1 = 8; 8^2 = 64; 8^3 = 512.
If I’d taken the design a step further, I’d have been asking the machine to cut an additional 8^4 = 4,096 squares out. Which, at this scale, would not have cut out cleanly, and would have taken the machine on the order of four hours to accomplish. But it’s a polite machine and would have given it a go anyway.
The resulting design is pretty striking; it’s at just about this level of recursion that the Sierpinski carpet starts to become for me a little visually overwhelming, with the four different sizes of squares nestled together creating a visual contrast that feels almost unstable.
It’s also about this level where doing something like this by hand begins to seem nightmarish if I’m not really specifically in a zone-out-into-the-tedium headspace. Contrast the post-it note version of the same pattern, which I wrote about the other day, and how clean the one is vs. the other:
It’s nice to be able to let the machine do the work sometimes.
Though one real-world aspect of cutting a lot of holes out of something to create a piece of art is that, at the end, you’ve still got all the holes to clean up:
The cutting mat is adhesive, to keep the material in place while the machine wheels it back and forth and takes a knife to it, and peeling a finished piece off leaves some (hopefully most or all) of the cut-out bits behind on the mat. Here you see the 75%-ish outcome I had with this one, with the rest of those gaps being bits I needed still to detach from the piece itself.
But: the mat’s adhesive. Which means that you need to use a knife or spatula or whatever to scrape the left-behind bits up off the surface of the mat, and need to get them clear of the mat after you scrape ’em up or they’ll just adhere again. For a few bits and pieces, it’s easiest to scrape each up and grab it with your spare hand and set it aside; for something like this, that’d be a huge fiddly effort. And this is the most cruft I’ve left of any of my cutting projects so far, so I was despairing a little last night.
Fortunately, I remembered gravity exists, and reasoned that I could hold the cutting mat up on edge and just scrape bits down off it to fall to the desk below. A couple minutes work to get a nice pile of confetti and a clean mat.