🚀 go-pugleaf

In article <1k00a5INNqrh@sumax.seattleu.edu>, khamer@sumax.seattleu.edu (Little Kenny Hamer) writes:
> From article <93024.164511WAJ@psuvm.psu.edu>, by WAJ@psuvm.psu.edu:
>> I have recently begun experimenting with modelling of chaotic systems in
>> C++. The only system I have had success with is the Lorenz water wheel
>> (as found in James Gleick's Chaos). Does anybody know of any other fairly
>> simple physical systems which exhibit chaotic behavior?
>> (btw, if anybody wants to see the wheel, i could send it)
>> thanks
>> 
>> Bill Jester
> 
> Indeed!  Try a duffing oscillator ( a nonlinear spring - mass system)
> 
> Here it is in coupled first order form (I assume you are using some
> numerical ODE integrator such as a Runge-Kutta algorithm)
> 
> dx(1)/dt = x(2)
> 
> dx(2)/dt = -k*x(2) -a*x(1) -b*[x(1)]^3 + F*cos(w*t)
> 
> k is the damping parameter, F is the forcing amplitude, w is the forcing 
> frequency, a and b are the spring parameters
> 
> A period-doubling sequence may ba observed with the parameters:
> 
> a=0
> b=1
> k=0.1
> w=1
> with initial conditions x(1) = 1, x(2) = 1
> let F range from 9.8 to 10
> 
> These parameters were studied by Ueda
> 
> Phase plots are interesting for the period doubling sequence, but 
> a first return map is far more useful for the complex regions.
> 
> Have Fun,
> 
> -Ken

I've been using chaotic systems as compositional algorithms to generate music
for several months. Some interesting systems are the Henon system, the
Henon-Heiles system, the logistic map and it's cube root cousin. I have
ANSI standard C implementations of each of the systems that I could send you.
My apologies that I can't do it now, but my code is at home and I'm not. I
could post it tomorrow though. 
BTW, these systems produce some very interesting music, and they're also 
a lot of fun on their own. The Henon-Heiles system is a simplified model
of a star's movement within a galactic gravitation field.

Hope it helps, and I'll post some code tomorrow.
-Adam
aalpern@hamp.hampshire.edu