🚀 go-pugleaf

Larry Kyrala <Larry_Kyrala@vnet.ibm.com> posted to bit.listserv.frac-l
two very fine discussions of applications of fractals.  Thanks Larry.

Recently a paper was announced for presentation at SIGCOMM '93 by
Will E. Leland <wel@bellcore.com> et al. titled "On the Self-Similar
Nature of Ethernet Traffic".  He found the traffic is self-similar
over time with time scales ranging over 10^5.  They state "our analysis
of Ethernet data shows that the generally accepted argument for the
'Poisson-like' nature of aggregate traffic, namely that aggregate
traffic becomes smoother (less bursty) as the number of traffic
sources increases, has very little to do with reality."

Now that is nice - fractal discussion on the net having a fractal
frequency.

Kerry Mitchell <mitchell@MITCH.LARC.NASA.GOV> wrote:
> I would say that only models can truly be chaotic, since chaos is a
> property of dynamicals systems, and dynamical systems are models of
> nature.  Nature is not periodic or chaotic, it simply is.

Actually, we can have a model that is either periodic or chaotic,
depending on the parameters.  The simplest, z -> z^2 + c, my favorite,
is one with the behavior depending on c.  So Nature could be likewise,
depending on the parameters.  Fine examples come to the mind of a
dynamical astronomer: planet orbits and satellite tilts.

I recall a few posts on chaos in a business.  The CEO of a small
business posted an observation of the onset of chaos he experienced.
It resulted from a feedback loop.  After a contract was over, lessons
learned resulted in bidding changes and staffing changes.  Something
like bid lower and use lower paid staff which resulted in late delivery.
Next time use higher paid staff with prompt delivery but losing money.
Then try weekly meetings to control everything tightly and you get
good staff quiting and etc etc etc.  I don't recall the details but
this is an extrapolation.  His point was the tighter the feed back
loop was the more chaotic the result.  Period doubling showing up as
alternating good and bad project performance.  Not so much in a time
sequence (yearly) but on a project by project basis.

The lesson to be learned is that any (nonlinear) system, when pushed 
too hard, will become unstable or chaotic (not the same thing).  Per-
formance will be repeatable for a vanishingly small parameter space. 

I like Larry's signature quote:

> "Once a new technology rolls over you, if you're not
> part of the steamroller, you're part of the road."

And either way you become a two dimensional object resembling the 
Mandelbrot Set...   ;-)

Warmly,
Jay 'Not tonight honey, I'm seeing everything selfsimilar' Hill
-- 
{ hilljr@jupiter.saic.com } begin writeln(3*ln(640320)/sqrt(163):17:15) end.
void main(){double sqrt(), y=1/sqrt(2.), a=.5, m=1,z; int n=0;
for(;m*=2,z=sqrt(1-y*y),y=(1-z)/(1+z),a=a*(1+y)*(1+y)-m*y,n<4;n++);
printf("%17.15lf\n",1/a);}