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.
If you take a look at the structures that form in the Universe, many of the things we see on large scales appears at smaller scales, too. The dark matter halos that form around the largest bound structures we know of appear identical to the ones that form around Milky Way-sized galaxies, as well as the tiny substructure clumps that exist both around smaller galaxies and in intergalactic space itself. On the largest scales in the Universe, gravitation is the only force that matters. Under many circumstances, if you wait long enough, gravitational collapse will produce identical structures, just scaled up or down in size depending on the size of your system.
The idea that, if you zoom in far enough, you’ll eventually encounter a structure that repeats the initial pattern you saw on larger scales, is mathematically realized in the concept of a fractal. When similar patterns repeatedly emerge at smaller and smaller scales, we can analyze them mathematically and see if they have the same statistical characteristics as the larger structures; if they do, it’s fractal-like in nature. So, is the Universe itself a fractal?
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