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I was browsing through the local University's library, and came upon some books by the Santa Fe Institute on complex Systems. Unfortunately, I don't go to that library, and stuck out like a sore thumb; so I was forced to leave.
My college doesn't really have too much on chaos theory, or complex systems. This is particularly fascinating to me, does anyone know about it?
http://en.wikipedia.org/wiki/Chaos_theory try that link... I have drank a 6 pack of coors so im not at full searching potential but i tried :)
Complex systems and chaos theory cover a LOT of different areas so it might be a good idea to narrow down your search. What are your interests? What courses are you taking? These might help you choose a specific area to start with.
Some ideas to get you started....
chaos theory:
I have just one word. FRACTALS :D
If you have not come across fractals before then this is definatly where I would reccommend starting (though chaos theory does cover a LOT more than just fractals). The truest form of computer artwork around, these images are created from a simple mathematical formula but are infinite in complexity. I have been exploring fractals and their variations for many years now and am still fascinated by them.
xaos is a good program to try...
http://xaos.sourceforge.net/english.php
you could also try this link for some nice examples of various types of fractals...
http://sprott.physics.wisc.edu/fractals.htm
complex systems:
This tends to deal with understanding systems that are so complex that prediction of the systems becomes very difficult. ie turbulance in water and clouds, human population interaction and information flow over the internet.
Try a google search for 'john conway' and 'game of life' for some nice descriptions of complex systems - this deals with complex systems emerging from some very simple rules and can be quite astonishing to see in action.
This link offers a nice intro to the game of life...
http://www.math.com/students/wonders/life/life.html
As I said, both these subjects cover WAY more than I have just mentioned. To describe all related subjects would take a LONG time and many, many pages. This is why I reccommend finding areas that you are particularly interested in and staring there.
Remember, Google is your friend. There is a plethora of information about these subjects on the internet already so search, explore, read and play.
If you are prepared to do A LOT of reading into these fascinating subjects then you will be highly rewarded. But be warned. This can become addictive. :cool:
omin
http://www.google.co.uk/search?hs=OF...G=Search&meta=
Try to ignore the film references.
Hi,
My first move would be to go to my local librarian and see if you cannot borrow the books through him/her.Quote:
My college doesn't really have too much on chaos theory, or complex systems. This is particularly fascinating to me, does anyone know about it?
They also might be able to arrange "guest reader" rights for you at the other library?
Over here in the UK, this would not be a problem...........a bit like guest membership at a golf/tennis/squash/shooting club?..............except that libraries are free :D
Tex~ drink the other six, and I am sure that you will come online? :DQuote:
I have drank a 6 pack of coors so im not at full searching potential but i tried
Spot on!............/off topic................they make great Christmas presents, for people you do not know what to buy for? \Quote:
The truest form of computer artwork around these images are created from a simple mathematical formula but are infinite in complexity.
:)
Hi
As omin has pointed out, the applicability of such theories[1] is
enormous. Myself, I tried to use multi-agent systems[2] to beat
stochastic volatility models of the stock market like Heston-Nandi
or GARCH for option pricing - unfortunately, so far I always was
"over par" (if you want to say so), but who knows... :D
Anyways, when I stare at the Heston-Nandy (or GARCH) process, I
recognise a similarity to chaotic systems: finite difference equations
or differential equations. If the degrees of freedom are coupled
non-linearly, you have a chaotic system - in other words, the
similarity of the above processes indeed is given, but "boring" from a
chaos theoretical point of view.
Hence, my suggestion: Read a paper[3], which theoretically deals
with chaotic behaviour. The reference I have given introduces the
concepts with the Drosophila melanogaster of chaos theory, the
one dimensional logistic map and extends from there.
If you understand the underlying concepts, you will be able to
understand the interdiscplinary applications. Check scholar.google.com
for additional readers.
Cheers
[1] http://www.andymeneely.com/Prog/Frac...%20-%20mjd.pdf
[2] http://www.kuenstliche-intelligenz.d...carley-web.pdf
[3] http://ma-yue.net/study/bib/chaos/pr...ntrolchaos.pdf
Very interesting papers sec_ware (got myself a new sig). :)
Just as a side note, xaos does not display 'true' fractals as it only goes through a finite number of iterations (after you have zoomed in for a while it 'runs out') but because of the real-time zooming it is still one of my favourite fractal gererators.
You can even find it in the default download of Knoppix! (at least it was in the most recent Knoppix that I downloaded)
Here are some more links to other fractal generators...
http://www.ultrafractal.com/
http://www.eclectasy.com/Fractal-Explorer/
http://spanky.triumf.ca/www/fractint/fractint.html
...and one of my favourite sites. This has LOTS of resources for anyone interested in exploring fractals further...
http://www.fractalus.com/
Arkimedes: inter college loan. they may be willing to lend you the book through your university. this is esecialy true if the schools aer geographicly close.
My favorite fractal generator has always been, and may always be, fractal forge. To my knowledge it will never run out by zooming in too much.You can get it here.
http://sourceforge.net/projects/fractalforge/
Well the problem with interlibrary loan is that my family lives in L.A. (where I am at the moment), and it was at Caltech. I go to Reed in Portland, Oregon.
That too may be a problem with the "guest card" to the library. The requirements are:and I qualify for none of these!Quote:
Users with a legitimate need to use the specialized collections at Caltech may apply for this card. Graduate level status and the recommendation of two members of the Caltech Faculty or administration is required. Application is initiated at the Millikan Library circulation desk between the hours of 8am & 5pm, Monday through Friday. Applicants will be notified by mail following review of their application (approximately two weeks from date of application).
If anyone here can get me a lifetime permenant card to the Caltech Library System, I'll give you one hundred dollars cash.
Anyways, I think sec_ware explained it best.
Are complex systems nothing more than a system of chaotic equations? Similiar to the system of equations used in linear algebra and matrices, et al. ?
Hi
I will try to relate those terms. The following is nothing you can readQuote:
Are complex systems nothing more than a system of chaotic equations?
Similiar to the system of equations used in linear algebra and matrices
in a book or article. It is so to say my interpretation of things I have
read. I also checked the Wikipedia-articles, which are okay. I first try
to be mathematical, then I give some "intuitive" interpretation or examples.
the math
complex systems are given by a number of entities (variables x_1(t),x_2(t), ...),
which are connected non-linearly, e.g. d x_1(t) / d_t = -x_1(t)^2 * x_2(t)... plus
similar equations for x_2(t) etc, where "t" can be interpreted as the time.
Note that if you set x_2(t)=x_3(t)=...=1 you will recover something like a marginal
version of the logistic map (just discretise time).
The study of those complex systems is called system theory.
Mathematically, one is interested in two different things: fixed points and dynamics.
- A fixed point is a set of specific values of x_1(t), x_2(t), such that they do not
change while further evolving the system in time.
- Then, the dynamics could be such that certain values of x_1(t), x_2(t) etc. are
repeated periodically (or in another similarity pattern).
- Further, the dynamics could be that no such similiarity pattern can be found. Then,
the complex system is called "chaotic".
interpretation etc.
Since the dynamics of complex systems is difficult to control, one may
perform simulations. Typically, so-called multi-agent systems/cellular automata
are used. Why?
A complex system can be understood as a set of individuals, who interact
with each other. Thus, the reference to the "Game of Life" above. They may
adapt their strategy (called complex adaptive systems) or not.
For example, Psychologists have invented a "multi-agent system" called the
"Cybernetic model": since one cannot "calculate" why certain animals form
certain "societies", one invented a model, which controls the movements of
an animal based on some interactions with the environment. Thus, the way
how animals herd, allows to extract information about the "character" of
the animals. The same, in some limits, is also possible for human beings.
For example, Blackjack players (me :) ) have tried to model interaction to
extract the optimal game strategy. In the end, several millions of games have
been played using computer simulations.
For example, the stock market: shared/derivatives etc. show a certain time history,
which can be analysed. Typical properties of complex (adaptive) systems, like memory
and "fat tails" in the distribution can be seen. All this can be interpreted in
the context of a "multi-agent system".
etc.etc. :D
It even can be a way to analyse "network traffic", and hence, security: you have
entities, which interact with each other. Having a "baseline", you may detect deviations.
In some context of interpretation, we here even may talk of a reference monitor.
Cheers