Here a cat is made from 9 paintings of cats in the style of popular painters:
https://twitter.com/marekgibney/status/1521500594577584141
You might have to squint your eyes to see it.
I made a few of them and then somehow lost interest.
The problem would be this: In the picture at hand, the big cat is rather simple. Just a portrait of a smiling cat. While the 9 smaller cats are doing all kinds of poses to adjust to the form of the big cat portrait. So the subcats are more complex than the main cat.
When doing the recursive cat, it would be hard to make a subcat from 9 subsubcats because the subcat is already a complex image that is not as easy to recognise as the main cat.
Now what would be interesting is a "demixer" which allows you to locate the source image(s) from multiple interations of a given image. Like a reverse image search but for generative images. I suppose it would rely on artefact matching or some other kind of granular pattern matching, along with other more general methods (assuming the source material is actually available online in the first place).