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It's also possible to prove that certain CA rules sets mimic natural
proceses, such as fluid/gas hydrodyamics, etc. These are typically called
lattice-gas CAs, and lots of work was done on these in the 80's and 90's,
much of it based on original work by Steven Wolfram (of Mathematica fame).
There are lots of books on this modeling aspect of CAs [do a search for
'cellular automata' at Amazon, for example ] -- most of them insufferably
confusing ;-)
Of course Wolfram now claims, in his book "A new Kind of Science" [1],
that the entire universe is really a giant CA, and that the fundamental
laws of physics are just an approxmation of of this 'universal' CA.
So I suppose if you could get XSLT to function like a CA, then you could
say that XSLT (and hence XML) models all the physical laws of the entire
universe.
... clearly XML is _far_ more important than I thought ;-)
Ian
[1] http://www.wolframscience.com/
On Mon, 13 Oct 2003, Thomas B. Passin wrote:
>
>
> Roger L. Costello wrote:
>
> > Hi Tom,
> >
> > I recall you mentioning this before. I am interested! Another confession - I
> > am not familiar with The Game of Life. Can you provide me with the info to get
> > me smart on this? /Roger
> >
>
> See e.g., http://www.math.com/students/wonders/life/life.html
>
> Here is an applet -
>
> http://javaboutique.internet.com/LifeApp
>
> Here is a page of related links, although some of them seem to be broken -
>
> http://www.aridolan.com/ad/CA.html
>
>
> Life is one example of a "cellular autonomon". It comprises a grid of
> cells. The game proceeds in steps. The color of a cell is determined
> by the color (or aliveness) of its surrounding cells according to a
> small set of rules. The grid is salted with an initial pattern, then
> the system proceeds tock by tick, recalculating the grid each time.
>
> Some initial patterns die out rapidly. Some create interesting patterns
> that traverse the grid or expand and contract. And a few develop stable
> patterns - sometimes the patterns cycle between two or more states as
> they traverse across the grid. That is the emergent behavior.
>
> The system has feedback in the sense that the output from one tick
> becomes the entire input for the next tick. The key is the set of
> rules, as it turns out. The rules of Life occasionally lead to
> interesting behavior, but apparently most sets of rules do not.
>
> The stable patterns can act as primitive logic gates, like NAND and NOR
> gates - I think this was discussed in Scientific American years ago,
> IIRC. Thus in principle a sufficiently large grid could act as a
> general purpose computer, since a clock and a set of NAND gates can be
> used to perform any logic function.
>
> Cheers,
>
> Tom P
>
>
>
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