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   Re: [xml-dev] Creating a Complex System using XSLT. Step 1: CreateFeedba

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Roger L. Costello wrote:

> I would like to see if collectively we can create a complex system
> using XSLT.  Several people have been hinting at doing this.
> Now let's do it!
> ...
> This feedback loop is "amplifying" (increasing):
>    - the number of members
>    - the total revenue of the Fitness Center
>    - the amount of equipment.
> This is called "positive feedback".  Positive feedback means that big
> things have a tendency to get even bigger, e.g., big Fitness Centers
> get bigger, big newspapers get bigger, etc.
> The amplification will reach a steady state once the Fitness Center has
> as much equipment and members as it can hold, given the size of the
> building they are in.  Thus, the size of the building imposes a
> "negative feedback" on the system, keeping it from expanding
> indefinitely.

Well, just because you have negative feedback is no guarantee that you 
will ever reach a steady state.  Stability depends on the phase (or 
frequency response) of the feedback as well. What you really want is to 
have oscillations damp out, which generally requires some dissipative 
element, as well as controlling the phase of the feedback.  So you want 
to be looking for an analog to friction or electrical resistance.

> The initial stimulus which resulted in the system entering into the
> feedback loop was that some new people joined the Fitness Center.
> A small change in the system resulted in a big overall change;
> aka The Butterly Effect.

A small input resulting in a big output is not really the Butterfly 
Effect.  It is more like an arbitrily small input resulting in an 
arbitrarily large change in the output.  Otherwise, "big" and "small" 
are only relative to some scale factor, which is generally not that 

 > ... Perhaps instead the focus should be on the
> stylesheet itself.  Perhaps some aspect of the stylesheet should get
> amplified, e.g., perhaps the output of the stylesheet is another
> sylesheet which is "amplified" with more template rules.  I don't know.
> I have run into a wall.  I am hoping that someone can help me to be
> break through the wall and see the light. 

Well, if you cannot articulate what you are after, it is no wonder you 
find a wall in front of you.  I am quite puzzled because you have just 
shifted from creating new source documents to having it create a new 
stylesheet.  That is quite a difference.

So try out some of the standard approaches - come up with a use case, 
write a scenario, personalize the system and write a story for it, 
invent some users and walk through their using the thing.

It is easy to have a stylesheet exhibit exponential growth, possibly up 
to some limit.  Just write a recursive template - like one of those 
templates that escapes a character - and pass it a string parameter that 
equals the previous paramter concatenated with itself.  It will run away 
until the stack grows too large, which you could control with some kind 
of a limit on the parameter length.

Exhibiting complex dynamical behavior almost by definition calls for 
modeling or solving or simulating some mathematical system of equations.

Simpler chaotic systems exhibit their dynamical behavior in a 
two-dimnensional phase space, e.g., plotting x(t+1) vs x(t) on the 
horizontal and vertical axes.  A "normal" system will be repesented by a 
point that traversed some smooth path in the phase space plot, a chaotic 
system will have each point be found on (or near) the attractor, but the 
location of one point is apparently unrelated to the location of the 
next point in time, except for being near the attractor.  I wonder if 
this could be simulated by describing an attractor with a polar 
equation, then setting calues of delta(angle), delta(radius) randomly 
for each step.

If so (and it seems plausible to me but I have never looked into it), 
this might suggest some way to proceed with a stylesheet.

If you are just after some behavior that metaphorically you can call 
"complex", rather than actually enhibiting complex dynamics, well, 
again, it needs more articulation.


Tom P


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