Chaos

[Dirac]

Any system is chaotic if it is governed by a non-linear differential equation. Difficulties arise because the solutions lose uniqueness and do not obey the superposition principle (linear combinations of solutions are also solutions). These are heavily relied upon in solving linear differential equations.

Characteristics of chaotic systems involve the obvious: non-periodic behavior, unpredictability, as well as extreme sensitivity to initial conditions (the butterfly effect).

Because of this, non-linear systems were historically ignored, or linearized to produce approximate solutions under certain limiting cases. However, new approaches to non-linear systems (what you might call The Chaos Theory) have produced an enormous amount of insight despite the inherent difficulties. Patterns (or semi-periodic behavior) can be identified as well as some universal characteristics across many chaotic systems.

Due to these advances, non-linear systems (a more appropriate title than Chaos Theory) has become a research field of its own over the last 20 years.

Whew, I just needed to get that off my chest. Thanks for listening. -Dirac

[Pfamily]

Mares eat oats,
and does eat oats,
and little lambs eat ivy.


Whew...done for the day!

[Ringos]

I guess the last thread must have been reported. Go figure...

[Ministry]

I guess the last thread must have been reported. Go figure...

Yup, reported, locked and more warnings given... as usual.

[Jundak]

Meh...

It was time for some of the old server-merge drama, anyway. I've not posted here in so long because...well...it was friggin' boring!

[Uamhas]

um... Chaotic ninja butterflies did what to who's theory of wavy lines for how many dollars??

Any system is chaotic if it is governed by a non-linear differential equation. Difficulties arise because the solutions lose uniqueness and do not obey the superposition principle (linear combinations of solutions are also solutions). These are heavily relied upon in solving linear differential equations.

Characteristics of chaotic systems involve the obvious: non-periodic behavior, unpredictability, as well as extreme sensitivity to initial conditions (the butterfly effect).

Because of this, non-linear systems were historically ignored, or linearized to produce approximate solutions under certain limiting cases. However, new approaches to non-linear systems (what you might call The Chaos Theory) have produced an enormous amount of insight despite the inherent difficulties. Patterns (or semi-periodic behavior) can be identified as well as some universal characteristics across many chaotic systems.

Do to these advances, non-linear systems (a more appropriate title than Chaos Theory) has become a research field of its own over the last 20 years.

Whew, I just needed to get that off my chest. Thanks for listening. -Dirac

[Chaari]

Yeah.. chaos theory and all that... whoop te-do. I'm not buyin into that whole line of dreg unless I can kick my neighbors (dog) and have that cause Muck to drop me a muckbane or two.

Hmm.. interesting idea that. Gonna go test it, thanks for the idea!!


Chaari, Paladin of ?

PS : I hate that mutt. Anything that yips instead of barks is not a dog no matter what the experts tell you. Its a rodent.

[MrWizard]

today is tomorrow.
tomorrow is today.
today is tomorrow's yesterday.

it's not 'open seasame' it's "open says-a-me"

[dungeonrat07]

today is tomorrow.
tomorrow is today.
today is tomorrow's yesterday.

it's not 'open seasame' it's "open says-a-me"

Thats why my knock spells were not work! Gee and all this time I was just saying it wrong! Thanks!!

[MrWizard]

think i just derailed the thread, sorry, chaos and all you know