An infinity mirror is part of an upcoming build of mine. There are lots of great descriptions of how to make these on the site already, and I checked a lot of them out - especially Ben Finio's excellent and encouraging Arduino-powered version. However, I was keen to leverage my novice skills with Fusion360 (the first solid 3D modeling program I've used) and 3D printed the enclosure for a flexible string (rather than a strip) of LEDs. I was very happy with the look of the final product - the diffusers made it easy on the eye, it had an interesting exposed look to the wiring, and I liked how the back of each LED case glowed. The first one I made was 6" in diameter and had 25 LEDs: this one is 9" in diameter and has 50 LEDs (the entirety of one string). If you've never made an infinity mirror because it looks too complex, but would like to and you have access to a 3D printer, try this one. It doesn't use much resin (and needs no support material) and no significant making/computing/programming/wiring skills are required. It also has an interactive twist: a handle on the front allows you to warp the mirror, creating interesting wormhole effects.
You can also tune the position of the rear mirror, but because it is made of glass, you can only tilt it, not warp it.
I've tried to make this build as kit-like as possible, but you will still need access to some modern making facilities: a laser cutter and a 3D printer. However, the laser cutting job is just a simple circle and the 3D print has been designed to be printed in 3 low-volume parts with no supports required, so the actual procedures are not difficult. Very doable at any makerspace. You will need:
The 3D printed parts were designed in three pieces, for two purposes: I wanted the infinity mirror to be easy to assemble AND easy to print. Printing without supports is always desirable because it saves resin and cleanup. Print the three pieces flat side down. They're all under 10" in diameter, so any 3D printer with a build area of at least 10x10" will be able to print them just fine. Print in black if possible. I used a Stratasys Fortus, and the base, middle and top used 3.1, 0.7 and 1.5 cubic inches of model material respectively.
If your build volume is not big enough to print the part in one piece, chop it up (e.g. using Meshmixer), print separately, and glue back together. The final product will be plenty strong enough because the glue joints can be offset.
Note there are two "top" parts, one warping, one not. The warping one is just taller, to allow the mirror to move.