Limiting Space of an Edge Replacement System

This is me practicing obtaining limiting spaces of an expanding edge replacement system. While not rigorous (for example, I don’t prove that the limiting space I obtain is homeomorphic to the Vicsek fractral, but it is “obvious”, and I don’t show that the list of equivalent sequences is exhaustive), it is still good for me to understand the concepts for another project I am working on. I drew the elements of the full expansion sequence by hand since my handle on tikz isn’t good enough to draw graphs of those complexity yet.