Hi, the expression “self-similar" does not mean "self-identical". For example, a dog is similar to a wolf, but they are not identical. Indeed, the entries of a so-called self-similar matrix are rather different from the original matrix (they are similar in the sense that they are matrices). For Leibniz, the red blood cells in a fish's blood are similar to the pound's fish but not identical. Of course, there are figures, like the Sierpinski triangle, that are self-identical. Concerning the multiverse's self-similarity, the conjecture was not that it is self-similar as Leibniz would think. Still, it converges to some idealized structure that is self-similar. This conjecture is based on speculations from the theory of eternal inflation, where the multiverse is represented as a Cantor set. It may be false, I do not know.