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Re: VMs: Follow-up

> > [....]  Are there any other laws that
> > Cardans grille doesn't explain?
> There are many detailed features of the MS
> that, to my taste, cannot be explained by the use
> of a Cardan grille, but these can all be fixed
> by making more different grilles, or very specific
> rules about how they should be used.
> And that's all reverse-engineering.

usually there are two main properties of (symbol) series:

1) distribution of occuring symbols. I can imagine that this Cardan Grille
(I don't know how it works) can reproduce the Zipf law.

2) correlations depend on the order of the symbols. If you shuffle the
symbols, the distribution remains, but the correlation structure vanishes.
Correlations mean, that there is a dependence between the elements of the
series. In numbers, a big is more probably follwed by another big, and a
small by another small one. The often mentioned long-range correlations
are a special kind of correlation. Unfortunately I have not yet found
the references related to this topic. The correlation function decays like
a power-law, thus the mean correlation length diverges. It is simple to
create long-range correlated sequences with gaussian distribution, but
even today it is a rather difficult task to create long-range correlated
power-low distributed sequences. I know that it is possible for
exponential distributed.

Diego :^v
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