Ditto Kevbo and Francis Vaughan. I don’t think much about the universe is fractal in nature. There is a range over which the clumping of galaxies is somewhat scale symmetric, and likewise for the distribution of stars of varying brightness. A test of these is whether you could sketch a typical view and somebody else could deduce from the view what its scale is. Offhand I think galaxy distribution on the scale of 10^7 to 10^9 ly looks pretty similar, and star distribution on the scale of 10^2 to maybe 10^4 ly does also (if you except globular clusters). But that’s it, I think.
I think we need a word for “thing that is like a fractal but only for a few factors of magnification rather than infinitely in both directions.”
A fractal, to a first order approximation.
Or maybe a word for “thing that is fractal infinitely in both directions”. The things that are discussed as fractals are, I think, usually only scale symmetric over a limited range. Certainly the geometry of physical objects must be so, because space and matter have scale limitations. The famous Mandelbrot (sp?) set has a limit at large scale. I only know of conjectural objects like Serpinski (sp?) gaskets that could be infinitely scale symmetric.