[Haskell-cafe] Re: (Chaos) [An interesting toy]

[Andrew Coppin]

jerzy.karczmarczuk at info.unicaen.fr wrote:
> I appreciated the elegance of
> overloading, the usage of Num classes, etc, which makes it more readable,
> although somewhat slower.

The source code has explicit monomorphic types all over it; I would 
expect GHC to be able to optimise out any method calls. (OTOH, I'm not a 
GHC expert... Simon? Don?)

> For those who don't have patience to execute the program, I converted the
> ppms to a XVID coded AVI file. Thanks, Andrew
> http://users.info.unicaen.fr/~karczma/Work/Chaos0.avi

Thanks for that. I did try encoding the video as MPEG 1, but it was 
still far too large. (20 MB.) Would have taken me several months to 
upload...

> What I didn't appreciate was the use of simple extrapolating Euler's
> method which for oscillating systems is known to be unstable, so the 
> results
> of the simulation may be far from the reality. Well, one chaos is worth
> another one, and the sin is not as mortal as in the case of truly 
> periodic
> systems, but it may be the cause that it is difficult to see the 
> classical
> fractal structure of the attraction domains on the generated images.

Fact #1: I don't *know* of any other numerical integration algorithm. 
(I've heard of RK4, but it's too complicated for me to understand.)
Fact #2: I have tried running the simulation with several different, 
non-comensurate time step values, and it always seems to produce the 
same output, so I'm reasonably confident there are no integration errors.