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Brownian motion is random by definition

Chaos is very ordered, what appears to be random, is the system moving into another "basin of attraction (stability).

Brownian motion is random by definition..................yes.

But, is that because it hasn't been observed on a long enough time scale to see if it truly is?

it is by definition, not by observation, its described statistically.

and I think you mean small enough scale-- this is called the bifurcation interval in Chaos theory

Brownian motion produces the information harvested by Chaos into fractals, as Twitter harvests information from society into topics or snowflakes harvest water molecules from clouds to grow.

pretty poetic but not accurate. Brownian motion is the physical discription of the Bell Curve. There are to types of fractals, iterated complex numbers, Julia,Mandelbrot,and Fiboccinai- The Disney mouse ears are a familiar one to most people. as I recall if you divide the iteration by the next smaller one it approaches the Golden Spiral. Another familiar example is the Butterfly wing analogy. The other types are Hopf bifurcations of the 2nd order and high order phase plots types.

Twitter and especially Google uses fuzzy logic AI chips to redefine the definition of sets. it "fuzzies" the definition of the topic so it may fit into the set. Ex. when does a river become long. instead of a hard set, ex. a river is long at 6mi.

programmers have a special name for this but it slips my memory set currently

Used to be a roller coaster named Chaos at OpryLand USA but not to be confused with The Wabash Cannonball coaster. Of course there was also The Screamin’ Delta Demon too. Over near where them chickens played tit tack doe.

Myself I wouldn’t step foot in now so called amusement park with all of them whirly jigs. Rather be in walmarks.

Nope. Brownian motion is the random motion of particles suspended in a fluid.

Fractals are a way of describing a system of nonlinear equations which are self similar at different scales.

Chaos is the way the dice of randomness are loaded, paraphrasing Gleick's quote of Joseph Ford in Chaos.

I find this to be a book that I will probably never realy finish, like Godel,Escher, Bach by Douglas Hofstadtler.

I inquired with a friend who met his wife at a Chaos convention and just retired from an illustrious career as a math professor. Will advise if he offers further enlightenment.

This is making my hair hurt so I am going to go randomize some particals of IMR4064 and hopefully produce some self-similar groups.

Could have sworn brownian motion was a good peaceful few minutes on the throne ,and chaos was running and hurry to drop the pants cause I am not sure I am going to get there in time.

One is natural........

You are wrong again, all the gas laws PV=muxRxT---- PV/T=P'V'/T'

Julia sets, Hofstader sequences, Mandelbrot, and Fibicconci are , non-linear equations may or may not have scales of symmetry

https://en.m.wikipedia.org/wiki/Brownian_motion

Self similar is not the same as symmetry.

Gleick work is written at the layman level to introduce beginners to the concepts. If your really interested in self-organization get Herman Hakens book.

Your logic or Appeal to Authority is invalid.

While doing my post-doc work under Prof. Keener, UofU math depart. , he clearly defined the differences. Keener did the non-linear math work establishing the three dimension vectors for electrical circuits used in pace makers.
His book. Mathematical Physiology comes in 2 books and is put out by Springer.
The study material"
Ergodic Theory, Analysis and Efficient Simulation of Dynamical Sysems. Springer
Elements of Applie Bifurcation Theory. Springer
Dynamics and Bifurcations. Hale and Kocak. Springer.
Nonlinear System. Drazen. Cambridge texts in applied math.
Solitokns in Field Theory and Nonlinear Analysis. Springer

get back to me when you get caught up

Even the wikipedia reference you quote say liquid or gas

HOW DID YOU MISS IT?

go snort some more powder the nitro will dilate your blood vessels helping with your confusion

Chaos theory has broad application. Your view appears focused on chemistry rather than the broader reality of paterns appearing throughout the universe. I don't pretend to understand how it jives with the second law of thermodynamics.

You seem snooty.

Chaos is the bar, nonlinear is the drive home, and brownian is when you see the lights in the rearview mirror. Every college kid know this stuff. It always involves EtOH.

Your lack of understanding for thermodynamics extends to other patterns in the universe.

almost forgot , random noise is also in electrical systems known as "white noise"