The obvious deduction no one wants to deduce:
People have been working to measure the fractal dimension of the Universe for more than three decades now, attempting to decipher whether it can be well described by one simple fractal parameter or whether multiple ones are required. The nearby Universe is not a good place to measure this, as dark energy has already reared its head for the past 6 billion years.
But if we look at objects that are at a redshift of ~2 or greater, we’re looking back in time to an era where dark energy was insignificant: the perfect laboratory for studying just what type of self-similar properties the Universe had. With a new generation of ground-based and space-based observatories coming online over the next few years, we’ll finally get the comparison between theory and observation that we’ve always wanted. The Universe isn’t a true fractal, but even in the realms where it’s only approximately a fractal, there are still some compelling cosmic lessons just waiting to be learned.
Ethan Siegel, “Is the universe actually a fractal?” at Big Think (December 28, 2021)