Self replicating art: you replicate it yourself. In this case, Penrose Tiles, a type of tile that makes patterns based on fivefold symmetry, and can be scaled up to make huge beautiful mosaics.
You need something to color with, scissors, pen and straight edge.
Step 1: Trace Tiles
You can find the so-called P2 or kite and dart type of tile here: https://en.wikipedia.org/wiki/Penrose_tiling#/med...
zoom in on that on your screen and trace the corners onto paper, using your screen like a light table.
Step 2: Add Sides
Use the straightedge to draw lines connecting the points to make the kite shape and the dart shape
Step 3: Cut Out Around Both Tiles
leave a bit of paper on all sides for the next step
Step 4: Laminate With Tape(OPTIONAL!) and Cut Out
Cover both sides with packing tape as shown and cut right along lines to make a pair of laminated tiles.
Step 5: Trace More Tiles, Add Self Documentation
Trace many tiles out on paper and add links to instructions on how to make more, color it all in decoratively, add whatever other information or designs you might want to replicate.
Step 6: Release, Spread
To release this into the wild you want to find a place where it will blend in with the environment like an arts and crafts room of some kind, a break room in a workplace, a maker space, a school, a math department at a university, or an art museum. Leave it with scissors, pens and something to color with as well as a stack of paper. If it blends in effectively enough to the environment people will think it belongs there and replicate it.