Year 12s: what will be the first way you research your future options? >>

Chaos

How could I link non-linear dynamic systems (ie - deterministic chaos) to the study of dimension and its 'quirk's... i wrote about fractals, which leads to non-linear dynamic systems which is all fine and dandy.... but what's chaos' link to dimension??

thanks for any help!! much appreciated!

Reply 1

WhiteAndNerdy1729

Hi there - when it comes to this level of maths I'm just an interested amateur, but have you talked about fractal dimension? By this I mean the fact that fractals have 'dimensions' other than what we might expect from looking at them: for example the Sierpinski Gasket has dimension

log_2 3

. This is also referred to as 'Hausdorff Dimension' or 'Hausdorff Measure'. This link: http://math.bu.edu/DYSYS/chaos-game/node6.html might be handy. Sorry if you know this all already!

Reply 2

Adalia

WhiteAndNerdy1729

when it comes to this level of maths I'm just an interested amateur

, it's a research paper :biggrin:

i've already done that but thanks for the link!! i think it might be able to help! :biggrin:

have you got any more that explicitly relate chaos and dimension to one other?

cuz i've gone dimension--> fractals--> fractal geometry & fractal dimension --> chaos in the essay

so whats the arrow in chaos --> dimension?

Reply 3

WhiteAndNerdy1729

A bit of googling found this link: http://www.somlev.net/chaos/index.html which has the promising title of 'Chaos, fractals and dimension' and includes several pages on 'Measuring Chaos', but a few pages in I stopped being able to follow the maths! Good luck with your paper and I hope you find the answer - sorry I wasn't much help!

Reply 4

Adalia

no, i think you just found me my answer!! :yep:

THANK YOU!!!!!!

and props to your googling skills, mine must be failing me :p:

THANK YOU!!!! :biggrin:

Reply 5

WhiteAndNerdy1729

NP - Have fun writing it! How many words?

Reply 6

Adalia

up to 4000, have 1474
but no limit in maths really, as a maths essay of 3500-4000words has way more content than an english essay of that word count, b/c thats discounting calculations, formulae, pictures, tables, diagrammes, etc

Thanks!! :smile:

ps - i was reading the stuff, and the first link alone gives me answers to 3 questions :biggrin:

so cheers!

EDIT: if you're really interested in this stuff, i could send it to you when i'm done, maybe you'll learn something new :smile:

Reply 7

WhiteAndNerdy1729

Ooh yes please! I'll PM you my email address. Glad to help out - when I'm in my fresher year and all confuzzled you'll help me out, right? :-D

And essays? In maths? I thought I'd escaped from all that after dropping English!

Reply 8

Adalia

yes, essays in maths (who woulda thought, honestly... its not like im doing my PhD right now :eek:

)

but yeah, in the IB the satndard and higher level students get portfolios, and my first one last year got up to 32 pages i think it was, that was a fun 3 days...

and in the IB we have to do this thing called extended essay, and i chose to do it in maths cuz the portfolios were fun, it was a challenge, interesting, and i might wanna study maths :smile: