This is a bit of a dumb question, but I can't seem to find a clear answer online:
Does self-similarity with respect to F mean that every part of a whole that is F, is F? Or does it mean that at least one part of a whole that is F, is F?
It's neither of these. The first condition is not necessary for self-similarity, and the second is not sufficient.
Consider an archetypical example of a self-similar structure, the Sierpinski triangle. Looking at that picture, you can see that not every part of the triangle looks like the triangle. There are parts of the triangle that look like two triangles side by side, for instance. So it's not necessary that every part of the whole be identical to the whole.
On the other hand, it is also not sufficient that at least one part of the whole be identical to ...
Previous open thread
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one.
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.