Chaos thread

What was actually the significance of chaos theory? Is research being done today on chaos, or was it just a fad?

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en.wikipedia.org/wiki/Feigenbaum_constants
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It's how nonlinear functions work.
In real life, almost everything is nonlinear.

soo can we 'solve' non-linear functions with chaos? or are they too complex?

If you could then you'd be able to predict the weather

Minus by minus.

To add on OP's questions:

What are Chaos Theory applications in real life like? How have we benefited from researching chaos theory? was there a point or it's just "you can't really know nothing"?

The terrifying thing about chaos is that you can draw anything from it.

The beautiful thing about chaos is that you can draw anything from it.

Applications usually rely on approximation algorithms. In short everything relies on this thing but no-one has been able to grasp it fully except now. No. Now. No. Now. No. Now. No. Now. No. Now. No...

Chaos has nothing to do with the solvability of systems. It has to do with how sensitive your solution are to initial conditions. This even in the same configuration a slight change in some initial value, makes the syatem go wild, which makes it impossible to analyze case by case. For example, a double pendulum will make really different paths if you change anything before you start it, but a pendulum will move back an forth periodically.

Bifurcation diagram and Mandelbrot are related

en.wikipedia.org/wiki/Feigenbaum_constants

>how sensitive
it's more subtle than that
y=x^(graham's number) is insanely sensitive but not chaotic at all

...

>function
>system
Not the same thing

missing the point

...

What part of sensitive to initial conditions you don't understand?

>trolling

its a retarded field, don't bother with it
t. published papers related to dynamical systems

>published papers
>dynamical systems
lmao are you from the 1800s retard

You're both idiots.
Idiot 1: Idiot 2 means the initial input doesn't just produce a very different initial outpt, it produces a very different series of data points which aren't even described by whatever function might have approximated the same system with a different initial input.
Idiot 2: Idiot 1 is trying to make the point that there's a difference between sensitivity and predictability by suggesting you could have situations that are both very sensitive and very predictable.

wut?

I'm sorry, I don't speak brainlet. Try asking an adult to help you make a new post.

I dont actually study math, I just read Gleicks book on chaos but felt that I didnt really understand the significance...also the word 'chaos' is a bit confusing since chaos theory has nothing to do with randomness, right?

pseudorandomness
just cuz it's mathematical doesn't mean it's profound

But idiot 1 is right.

huh?

well he says in the book its one of the three biggest scientific achievments in the 20th century lol

And Lorenz attractor is related to logistic map

Hmmmmmmmmm really makes you think

Some linear functions are remarkably complex especially when you start from random conditions.

The unpredictable nature of things and inability to control more than simple events/systems