Building off of @Jon-a-tron's great Instructable on how to make a 2D Moire Slit Animation, I figured the same thing could be done but as a loop, in a circular slit pattern. With the same principles outlined in his tutorial, you can create a continuously looping four-frame animation.
Naturally, as soon as I thought of the idea, I was sure that somebody else had already done this elsewhere. After scouring the internet (i.e. Googling exactly what you'd think to Google), I was right. Damián Miroli, an artist in Argentina, has created amazing physical GIFs, and are not very well-known as far as I can tell. I hope his work provides you with inspiration, because I'm about to show you how to make these: https://traduccionestucuman.wordpress.com/damian-m...
Step 1: The Principle Is the Same, Execution Is Different
Just like the other Instructable, we'll be creating a mask that only allows 1/4 of the image to peek through and hides the other 3/4. As you rotate the mask, only 1 of the 4 frames shows through at a time.
So what's different? Well now that it's circular, there's a little more complexity. For one, alignment needs to be much more precise, because there are two degrees of freedom (up/down, left/right) as opposed to 1 degree of freedom (left/right) in the standard slit animation.
The middle becomes particularly sensitive to alignment because the slits get thinner towards the center. One way around this is to make the center solid obscuring part of the image, but also giving more structure to the fingers that make up the slits. That's totally okay because the center is nearly impossible to create with infinitely small slits anyways, whether you use a printer or a laser cutter.
Step 2: Use This Photoshop File to Print Out the Image
Again, based off of the Jon-a-tron's Instructable, I created a Photoshop file that you can use to pop in your four frames to make the layered image that will then create the animation.
Once you have the image, print it out on paper. I used a 11x17 sheet, but it works on 8.5x11.
>> SIDE BAR
If you're like me, you might want to experiment with the slit to covered ratio, or the number of slits in the circle, or how the slits are shaped. I'm attaching all the supporting files for that. Ignore the rest of this paragraph unless you want to go to this depth: In general, I created the slit pattern in Solidworks (because it's better than Illustrator at patterns and precision), then exported that as a DXF to import into Illustrator. Once in Illustrator, I Live Paint'd the parts that would be covered to get the masks, created four copies of the Artboard and rotated them by the appropriate angles. To create the slit mask, I used one of those vector files, Live Paint'd the slits (the 1/4 section as opposed to the 3/4 section), turned them into laser-cutter readable lines, and then used the Pathfinder tool to create the solid center.
Step 3: Make the Mask and Spinny Tray
At first, I tried printing the mask on acetate (aka those transparencies your middle school teacher used). Because of the alignment problem I referred to, warpage from printing on acetate, and the glossy factor, I tried other things. First I tried acrylic, because it's rigid. Black acrylic was suitable, but not great. It takes more heat to laser cut through acrylic, thus warping the thin slits near the center. Acrylic also results in some stickiness after you laser it, making it not so great for spinning.
I found that black mat board with slits in it worked best. Mat board is matte (ha ha), rigid, and thin, making a clean precise mask.
The tray wants to be slippery, so acrylic or anything thin that you have laying around makes sense.
Here's the vector file in Illustrator you can use to cut that and the tray to lay everything into.
If you don't have access to a laser cutter, you can print on acetate, and I hope you have better success than I did.
Step 4: Explore! How Can You Make This Better?
Put it all together, spin the dang mask and you got yourself an analog animation.
I tried a few different things, but it doesn't mean I got it perfectly right. I encourage you to keep playing around with the little factors you can change to make this better. What should I change about this to make it a more fluid and convincing animation? What are some awesome four-frame animations?