I'm with you not being an expert and being unable to understand most of the lingo and the article. The conformal invariance example in the pictures spoke to me about the fractal nature in the universe. Fractality just keeps popping up in my readings and that may have colored my read of the article.
Yes, these when these models become critical (eg. where the distinction between liquid & gas goes away [1]) they form clouds of condensation at all scale sizes, so it is like a fractal.
