On Thu, 2011-06-01 at 15:56 +0100, Daniel Carrera wrote:
> Is it possible to explain briefly wht the Rulle-Takens algorithm is?
> That web page seems to mainly explain how some fractals like the

I can't remember exactly.  I found the abstract for a conference paper,
published in 2000, by the person for whom the work was done (not the
perl programmer).  The abstract describes the algorithm as "proprietary"
but saying "proprietary algorithm" was very popular marketing ploy in
bioinformatics around that time.  It may still be.

What was done was examining the GC-content of DNA sequences to look for
any kind of patterns.  So, I think the DNA data was converted to GC -> 1
and AT -> 0 and then the sequence was fed into the algorithm.  

I think the idea was to treat each subset of lenth M as a point in space
and iterate over small M from 2 until the points were no longer
space-filling.  Call that K.  At this point you either have a K-1
dimensional manifold or a strange attractor with some fractal dimension
between K-1 and K.  If I find the code I could verify this part.  The
algorithm works out whether or not there's an attractor and what the
fractal dimension is, if so.

So your sequence becomes: S = 1 0 0 1 1 1 0 0 0 1 0 ...
so S1 = 1, S2 = 0, S3 = 0, ...
and your points for N=3 are then:

 1 0 0 (Si, i=1..3)
 0 0 1 (Si, i=2..4)
 0 1 1 (Si, i=3..5)

That's as much as I remember.  I think the original application was
probably only interested in dimensions 2/3 because turbulence is most
interesting in boundary-layers.

The biologists understood none of this as far as I know (I took courses
in plasma turbulence in grad school, which covered this in more detail
but the biologists found the paper).  I've forgotten most of grad school
by now.  The results were fractal dimensions in the range 5-7, iirc.  No
idea what that means and I doubt the biologists did either.  GIGO.

I may have asked them why they did not map (A,C,G,T) -> (0,1,2,3) but
since then, I've learned more about what GC-content implies in terms of
chemistry -- it also seems to have evolutionary implications, about
which I know nothing.  So I don't think they even bothered trying that
(since no-one else was doing it) ... old-age makes me more cynical ...
and forgetful ;-).

> Mandelbrot set and the Julia set are generated. Is there a specific,
> simple algorithm that we can try to implement in PDL, Perl 5 and Perl
> 6?
> On Thu, Jan 6, 2011 at 3:36 PM, Guy Hulbert <gwhulb...@eol.ca> wrote:
> > Changed the subject so people don't complain ;-)
> >
> > On Thu, 2011-06-01 at 09:32 -0500, Guy Hulbert wrote:
> >> The algorithm was the ruelle-takens algorithm (ca 1979, iirc) to compute
> >> the fractal dimension of a series.
> >
> > Google ( http://www.google.com/search?q=ruelle+takens+algorithm ) found:
> >
> > http://www.emayzine.com/infoage/math/math2.htm
> >
> > Looks like 1979 is about right.
> >
> > --
> > --gh
> >
> >
> >


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