Chaos Theory

[Saberdude]

Let me get this straight: Chaos Theory is deterministic as well as random?

I'm lost. T.T

Ur not the only one buddy
xP

[nitrofreez]

You have inspired me to do some research of my own on the topic. I have always found the concept intriguing though I am ashamed to say I was too lazy to look up detailed information about it.

[Saberdude]

You have inspired me to do some research of my own on the topic. I have always found the concept intriguing though I am ashamed to say I was too lazy to look up detailed information about it.

What sup with the all the italics?

[nitrofreez]

What sup with the all the italics?

Heh, I just like the way it looks is all.

[Saberdude]

What sup with the all the italics?

Heh, I just like the way it looks is all.

we should imitate The Joker! :o

[t0rch]

They say imitation is the sincerest form of flattery, you wouldn't want to flatter a forum gimmick would you?

[Priam]

Let me get this straight: Chaos Theory is deterministic as well as random?

I'm lost. T.T

not really.

As far as i get it.

The chaos theory in mathematics is only deterministic. They try to logically explain chaos, which seems random, in a way where everything does come together logically. E.g. Chaos not being random, but explainable.




Oh, and all those scrubs whom can't keep there mouth shut about the joker who's actually contributing nicely in this topic, get out please, before you potheads get this locked as well.

[t0rch]

Oh, and all those scrubs whom can't keep there mouth shut about the joker who's actually contributing nicely in this topic, get out please, before you potheads get this locked as well.

http://www.youtube.com/watch?v=Xz7_3n7xyDg

Made me think of that

[Priam]

Oh, and all those scrubs whom can't keep there mouth shut about the joker who's actually contributing nicely in this topic, get out please, before you potheads get this locked as well.

http://www.youtube.com/watch?v=Xz7_3n7xyDg

Made me think of that

Excellent, though i kindly asked you to contribute to the subject.

[Doron]

trying to explain chaos can only run out to be a bigger chaos, right?

[The Joker]

trying to explain chaos can only run out to be a bigger chaos, right?

explain....

If we try to explain chaos, how can it be more chaotic?

True, it will be hard to explain, since we don't have anything to begin with and anything to end with.

But that is the fun part. That's the thing that makes it so interesting for me.

[Grandpa]

Pardon my quoting, I'm very new to this.
I liked the idea when it was first presented (to me and millions of others) in the Jurassic Park movie - but never looked into it except briefly.
When I'm attempting to learn a new subject I find it useful to define elementary terms but in this case there seems that nothing is 'elementary', hence the quotes.

____________________________
CHAOS THEORY AND DATA ANALYSIS
Introduction to Chaos
Essentially, chaos is a nonlinear behavior that exists between the realms of periodic and
random. At first glance, some chaotic systems may appear to regular and periodic, whereas
others will appear strictly random; in both cases closer examination topples these assumptions.
Strictly speaking, chaotic systems are deterministic and, the exact system state can be written:
X(t) =(x(t),x(t −τ ),x(t − 2τ ),...,x(t − (k −1)τ)

1. where t is a scalar index for the data series and τ is the interval of observations.
   Let F: ℜk →ℜk be the nonlinear function governing the system; then, the future state of the system at any time t+τ can be ascertained.
   However, as no real-world system is likely to be completely deterministic, a (relatively small) probabilistic component, p(t), with mean zero is added to account for random effects (Lu and Smith, 1991): x(t+τ) = F(X(t)) + p(t).
   
2. The state of the system, X(t), is critical to knowing the progression of a system, and even
   a small change in it will radically alter the manner in which the system evolves. Thus, after a
   short interval, the system effectively becomes unpredictable. This effect is known as sensitivity to initial conditions and is a hallmark of chaotic systems.

I've added emphasis by way of bolding and italics to what I consider the essential parts.

While attempting to further define this I've found it useful to look at what Chaotic Systems are NOT.
Wiki comes in handy here and provides many examples, one of which is called a "Random Walk".
It's easy enough to skim through and get the idea if you're not familiar with the term.
Since I like probability it was familiar: Wiki Random Walk.

We need to examine 'change states' in order to determine if each process is stochastic (random) the counterpart to deterministic processes.
I was already familiar with Brownian Motion so that helped me a bit.
The Intro to Chaos (quoted above) goes on to show how "dissipative¹, nonrandom system eventually will settle onto a path called an attractor."
Understanding of 'attractors' is also essential to basic understanding of the theory.

My next 'step' is to try to find a good visualization of an analysis of a chaotic system and post it here. It actually helps me quite a bit to try to 'teach' when I'm learning because it forces me to fix my thoughts in such a way that they can be communicated. For those of you who don't appreciate my method I'd suggest that you follow your own path and add to the discussion here as others have done I'm stretching quite a bit here so (it was much easier to learn new things when I was younger) and again, pardon if it doesn't make complete sense yet.

~Granps

____________________
EndNotes, Annotations & Credits
Quote 1: CHAOS THEORY AND DATA ANALYSIS

Footnote¹ A dissipative system is essential one that requires a constant supply of energy to keep running. Thus, such a
system will, over time, attempt to move towards an equilibrium in terms of energy (i.e. an attractor).

[Stephanus]

There is a way to search Google.com and limit the search to .edu sites (and .pdf files) for specific subjects.
*****

Oh, from Google.com you can enter these search parameters to duplicate my result:

I prefer klingon.
http://www.google.hu/search?q=chaos+theory&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:hu:official&client=firefox-a

[Grandpa]

Introduction [1/12]
Welcome to the online course "What is Chaos?"
We hope you find it a useful and entertaining way to learn about one of the most exciting topics in physical science.


[ Continue ]

The above is from Univ of Texas at Austin.
Click [ Continue ] for an interactive introduction for everyone to Chaos Physics and Chaotic Motion in Classical and Quantum Mechanics.

Let me get this straight: Chaos Theory is deterministic as well as random?

I'm lost. T.T

Ur not the only one buddy
xP

Best 'Intro' that I've found so far: [Continue] Yes / No

~Granps

[The Joker]

Thank you so much Grandpa.

You have given us much interesting information, especially that online course.

You are truly a kind and intelligent person.

[PuppetOfGaea]

Thank you so much Grandpa.

You have given us much interesting information, especially that online course.

You are truly a kind and intelligent person.

Xemnas... you just went way too far out of character there.

[Priam]

Xemanas? new members?

[crazyskwrls]

does that mean...

i go outside and fart... cause enough heat to create a thunderstorm, the thunderstorm makes lightening... cause massive forest fire, a specie is destroyed, cause ecosystem imbalance, the whole planet is destroyed.....

[Saberdude]

does that mean...

i go outside and fart... cause enough heat to create a thunderstorm, the thunderstorm makes lightening... cause massive forest fire, a specie is destroyed, cause ecosystem imbalance, the whole planet is destroyed.....

Thats a scary though
o_o

[Grandpa]

does that mean...

The main difference is found within our "Cause and Effect" thinking. The systems that are termed "chaotic" are very sensitive to initial conditions. That sensitivity would be the 'cause' not your fart, not the flapping of butterfly wings, but the systems themselves.

If it were the flatulence the country, nay - the world(!) would be destroyed already, oh my!