Just like similar triangles, if there is self-similarity in latent space, you would have similar structures in which one operation on one can translate to an operation on another. Just like how mod “reduces” all operations to a base “pattern” (such as 10 % 3 going from [0,…,10] to [0, 1, 2], which is a ‘base pattern’), use an operation to reduce it all down to the base pattern equivalence class, the true abstraction that separates each different pattern. This is also like how each 2pi rotation return to the base pattern of the unit circle. Thus, solving the base pattern allows self-similar translation to many other ones, with some variations and noise.

Also, fractal self-similarity recurrence equations can model the growth dynamics, connecting ones from outwards to the base pattern of the equation being used in each iteration.