What Brownian motion practically describes through observation is that any medium experiences extreme variation.
Where this becomes important in cosmology is in Hawking effect describing the virtual particle field, which states that absolute entropy intrinsically evolves a black hole universe.
Doesn't really relate to chaos theory directly, which is most correctly stated as complex evolutionary diversity. It does, but it doesn't, it's about latent fields and the fact there is truly no such thing as an empty space even in an empty space. For the potential for something to exist there must be an existence potential latent in the environment. It's like extrapolating quantum physics from classical rules like conservation of energy.
That is interesting.
I don't really study or read about Chaos Theory specifically. When I think of chaos I think of the unpredictable events from random interactions.
With gravitation waves being recently confirmed I find the black hole Universe more likely. Random interactions less likely because there is a pattern to gravitational effects. I wonder if gravitational waves persist at quantum?
I also see the allure of vacuum energy (zero point energy) in chaos but as chaotic as they may seem, I suspect there is a pattern governing the effect. I even sense that entropy has a pattern.
Negentropy is reverse entropy. It means things becoming more in order. By 'order' is meant organization, structure and function: the opposite of randomness or chaos. ~ simple wiki
During the formation of a star system like our solar system it appears chaotic as negentropy initiates. The material that coalesces into planets, moons, asteroids and comets is moving every which way. As time passes, the chaotic events slowly become orderly. Gravitational waves cause stabilization to occur in that system.
I imagine that even during the period of high orbital bombardment a pattern exists in the chaos. We just can't see (measure) it because we don't live long enough to study multiple systems during their entire negentrophic period. We only see snapshots and it appears chaotic.
Like I said earlier, chaos exists because we don't know everything about everything, everywhere. If we did, we might see patterns in everything, everywhere, everywhen and chaos would not exist.
This idea is driven home by the Mandelbrot set, the Julia set and all the fractal calculations inspired by the Hausdorff dimension.
Until 1920, nature was thought to have no pattern, was chaotic. Now, fractals describe a pattern to nature. While we don't understand it completely yet, there is less chaos and more pattern to natural order in mathematics.
Is the Universe governed by Brownian motion?
Do fractals predict a patterned Universe?
We don't know because we can't calculate it yet.
Far too many variables, far too many levels of interaction.
However, if we could calculate the exact pattern of everything in the Universe, chaos would cease to exist.