HDTenEightyP/NetNews huggingface dataset:
Newsgroups: bit.listserv.frac-l
Date:         Thu, 5 Nov 1992 09:03:17 EST
From:         McClelland_R%PSB%BLS@NIH3PLUS.BITNET
Subject:      RE: DOCUMENTS

|Date: 11-5-92  8:58am
|From: McClelland_R:PSB:BLS
|  To: FRAC-L@GITVM1:BITNET:NIH
|Subj: RE: DOCUMENTS
|In-Reply-To: Message from FRAC-L@GITVM1:BITNET of 11-4-92
------------------------------------------------------------------

>Rather than keeping on asking for papers and documents (thing that can be
>done personally), why don't we start some useful new discussion????

>For example, speaking about the search for determinism and chaos in
time
>series, what do you think of the different methods to choose the two
parameters: 1) LAG TIME (tau)
>2) EMBEDDING DIMENSION (m)

>used in the time-delayed phase reconstruction (Takens method)

>I'm aware of the methods by Liebert, Pawelzik and Schuster, 1991,
>the one of Matt Kennel et al. (false nearest neighbours), and the one
>by Fraser and Swinney (mutual information and similar things).

>Have some of you used and perhaps compared them?

>Hoping to have given new life to FRAC-L, I wait for your comments.

>Roby.
-----------------------------------------------------------------
Could you supply the full references to the above?

Thanks in advance...

  |\/\/\/|  Rob McClelland
  |      |  Bureau of Labor Statistics      Voice (202)606-6573 ext. 607
  |      |  2 Massachusetts Ave, NE         Fax (202) 606-7080
  | (o)(o)  Room 3105                       BITNET XUM@NIHCU
  C      _) Washington, DC 20212
  | ,___|
  |   /
 /____\
/      \
Newsgroups: bit.listserv.frac-l
From: jjcarett@daisy.uwaterloo.ca (Jacques Carette)
Subject: Re: A Conjecture regarding the Mandelbrot Set
Organization: University of Waterloo
Date: Thu, 12 Nov 1992 18:54:27 GMT

In article <9211120301.AA07178@grits.valdosta.peachnet.edu> msouth@GRITS.VALDOSTA.PEACHNET.EDU ((Michael South)) writes:
>It is interesting to note that it is not known at this point whether all of the
>points of the Mandelbrot set are periodic (or preperiodic).  In other words, it
>is unknown whether all orbits eventually settle down to a repeating cycle or if
>there might be points that never converge to any cycle.  Your question might
>touch this larger question.  Keep thinking.

Not true.  The Fibonnacci polynomial (as studied by Milnor & Lyubich) is
a counter-example.  What is not not known (and is also one of the main
remaining conjectures in the theory) is if there are open sets of such
beasts in the M set.  It is known that the Fibonnacci polynomial is 
not in such an open set (it is what is called "rigid").

Jacques Carette
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Newsgroups: bit.listserv.frac-l
Date:         Mon, 9 Nov 1992 16:50:10 EST
From:         "(Stina Bridgeman)" <95ssb@CS.WILLIAMS.EDU>
Subject:      lyapunov exponents, universality, and delta

Guillermo (in particular) and everyone (in general):

What is the Wolf method for Lyapunov exponents?

I have been doing some experimenting with Lyapunov exponents and
bifurcation trees and it how all relates to delta (one of Feigenbaum's
constants of universality).  If anyone has any ideas about such things
might be related, I'd be interested in hearing about it.
Also, does anyone have an algorithm for calculating delta?  (Granted,
this has more to do with universality and chaos than fractals, but chaos
and fractals are often related.)
      Delta = lim_n->infinity (r_n-r_(n-1))/(r_(n+1)-r_n)
I have been experimenting with an algorithm, but have run into problems
with rounding - the closer the computation gets to a value of r_n (and
the higher the value of n), the more rounding affects the result.
My algorithm is something along the lines of: (using the equation
f(x_(n+1)) = r*x_n*(x_n-1))
      Looking for next bifurcation after r:
        Pick a value for r and iterate f(x) until it settles down.
        Iterate f(x) with r+dr (dr is some arbitrary increment) until
          this settles down.
        Continue incrementing r until the period for r+(n*dr) is greater
          than the period for r.
        Then use a converging algorithm similar to the bisection method
          of finding roots of algorithms until the distance between the
          current r and the previous value is arbitrarily small.
Any suggestions?

Thanks.

Stina Bridgeman
95ssb@cs.williams.edu
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Date:         Wed, 11 Nov 1992 20:34:53 -0500
From:         MITCHELL@ACODVAX.LARC.NASA.GOV
Subject:      RE: A Conjecture regarding the Mandelbrot Set

Michael Freeman writes:

<After many hours of staring at displays of the Mandelbrot set, I have a
<conjecture:

<          Any point in the Mandelbrot set is part of either
<          a disc or a cardioid.

A minor nit to pick.  Strictly speaking, your hypothesis is false.  Consider
counterexamples c = (-2,0) and c = (0,1) or (0,-1).  They all lie on the
boundary of the set, but not in any of the filled-in regions.  It may be
more appropriate to restrict your conjecture to the *interior* of the set.

Kerry Mitchell
mitchell@acodvax.larc.nasa.gov
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Newsgroups: bit.listserv.frac-l
Date:         Fri, 6 Nov 1992 10:20:12 EST
From:         McClelland_R%PSB%BLS@NIH3PLUS.BITNET
Subject:      RE: DOCUMENTS

|Date: 11-6-92  10:17am
|From: McClelland_R:PSB:BLS
|  To: FRAC-L@GITVM1:BITNET:NIH
|Subj: RE: DOCUMENTS
|In-Reply-To: Message from FRAC-L@GITVM1:BITNET of 11-5-92
------------------------------------------------------------------
>Yes, of course, Rob (by the way, I've just received your paper,
thanks!).

>Send comments!

>Roby.
------------------------------------------------------------------
You *JUST* got the paper? Man, I sent out papers weeks ago. Some post
office we have...


Rob McClelland
Bureau of Labor Statistics      Voice (202)606-6573 ext. 607
2 Massachusetts Ave, NE         Fax (202) 606-7080
Room 3105                       BITNET XUM@NIHCU
Washington, DC 20212
From: dfowler@UNLINFO.UNL.EDU ((david fowler))
Newsgroups: bit.listserv.frac-l
Subject: Re: natural scene decomposition++
Date: 5 Nov 92 18:56:08 GMT
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X-Mailer: ELM [version 2.3 PL8]
              "JBB%WATSON.ACC.VIRGINIA.EDU@KSUVM.KSU.EDU" at Nov 5, 92 12:47 pm

J Burch writes:>
> Some time ago, if memory serves correctly, there appeared a brief notice
> in a popular trade journal about a propriatary procedure that could break
> down a picture of a natural scene into a set of arguments for a comple-
> mentary, fractal-based algorighm able to generate a close approximation
> to the original picture.
>
> This seems too good to be true! Does anyone have any information on this?
>
> Thanks in advance,
>
> Joseph B. Burch                        jbb@virginia.edu
> Computer Systems Engineer
> ITC-ACS
> University of Virginia
>
This is the system developed by Michael Barnsley at Georgia Tech. One
of the articles was in a Scientific American news release. Barnsley
has his own company, I don't know addresses, however.
dfowler@unlinfo.unl.edu
Newsgroups: bit.listserv.frac-l
From: jjcarett@daisy.uwaterloo.ca (Jacques Carette)
Subject: Re: A Conjecture regarding the Mandelbrot Set
Organization: University of Waterloo
Date: Thu, 12 Nov 1992 18:51:06 GMT

In article <9211111654.AA22536@unixg.ubc.ca> mfreeman@UNIXG.UBC.CA (Michael Freeman) writes:
>After many hours of staring at displays of the Mandelbrot set, I have a
>conjecture:
>
>          Any point in the Mandelbrot set is part of either
>          a disc or a cardioid.
>   2.  This is wrong, because----
>        (please provide co-ordinates of a counterexample)

This is false.  z^2-2 is a counter-example.  Not only is it not in a 
disc or cardiod, it is not even on the boundary of a disc or cardiod.

Another counter-example is the Feigenbaum polynomial.
In fact, any polynomial that is "infinitely renormalizable" is a counter
example, along with all Misiurewiz points (of which -2 is one).

Jacques
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Newsgroups: bit.listserv.frac-l
Date:         Thu, 5 Nov 1992 12:47:01 EST
From:         JBB@WATSON.ACC.VIRGINIA.EDU
Subject:      natural scene decomposition

Some time ago, if memory serves correctly, there appeared a brief notice
in a popular trade journal about a propriatary procedure that could break
down a picture of a natural scene into a set of arguments for a comple-
mentary, fractal-based algorighm able to generate a close approximation
to the original picture.

This seems too good to be true! Does anyone have any information on this?

Thanks in advance,

Joseph B. Burch                        jbb@virginia.edu
Computer Systems Engineer
ITC-ACS
University of Virginia
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Date:         Thu, 12 Nov 1992 00:11:00 EST
From:         MDAST6@PITTVMS.BITNET
Subject:      Re: lyapunov exponents, universality, and delta

Dear All:

        Does anyone out ther know of an algorithm for the Gabor
Spectrum??  I know this is not EXACTLY fractal realted, but thelist has
been weak lately...

                                                Michael D. Aesoph
From: CSFLYTHE@ECUVM1.BITNET (Mac Flythe)
Newsgroups: bit.listserv.frac-l
Subject: Re: Fractals Computer Programs
Date: 6 Nov 92 19:39:41 GMT
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
              6 Nov 1992 14:33:04 -0500 from <C2MXALL@FRE.TOWSON.EDU>


    Jon, thanks for the reply.  FRACINT sounds great.  I have one problem
though, I have a 286 with just 640k.  I really appreciate it anyway.

    About CHAOS THEORY,  I think its wild.  Did you see The Nature of Things
episode about it last night on the Discovery Channel?
It was really interesting.  They talked about the Lorezo Attractor, and
how the minutest details like a butterfly's breathing can dramatically change
the outcome of the weather within a few days.  I just got this book the other
day about it.  I think it's called COMPLEXITY.  If you want I'll check who
the author is and send it to you tomorrow.

                                    Mac Flythe
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Newsgroups: bit.listserv.frac-l
Date:         Wed, 11 Nov 1992 16:30:31 -0500
From:         "(Cogito->Ergo Sum!?)" <cordones@LIHAI.CS.NYU.EDU>
Subject:      Re: A Conjecture regarding the Mandelbrot Set

	Michael Freeman says...:
> After many hours of staring at displays of the Mandelbrot set, I have a
> conjecture:
>
>           Any point in the Mandelbrot set is part of either
>           a disc or a cardioid.
>
> I'd like to learn that
>    1.  This is obvious, because----
>    2.  This is wrong, because----
>         (please provide co-ordinates of a counterexample)
>    3.  This is interesting.
>
>                         - Mike Freeman -
>

I hesitantly dare (since I am just a Fractal 'buff') to point out something
 closely related to your conjecture...I have heard of a proof done by two
 scientists...One in Cornell University and the other in Paris (not sure of the
 place).  I tried to lookup the information so I could give you names, dates and
 places but I happen to have returned the book where I think I read it from.
 Anyway, the proof states (I haven't seen it myself...I think just read
 reference to it in the book _The Beauty of Fractals_ by Peitgen) that ALL
 points in the M set are conected. Perhaps someone familiar with it or with the
 book close to his computer can pick it up from here...

Jose'
My two cents..
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Date:         Wed, 11 Nov 1992 08:54:41 PST
From:         Michael Freeman <mfreeman@UNIXG.UBC.CA>
Subject:      A Conjecture regarding the Mandelbrot Set

After many hours of staring at displays of the Mandelbrot set, I have a
conjecture:

          Any point in the Mandelbrot set is part of either
          a disc or a cardioid.

I'd like to learn that
   1.  This is obvious, because----
   2.  This is wrong, because----
        (please provide co-ordinates of a counterexample)
   3.  This is interesting.

                        - Mike Freeman -
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Newsgroups: bit.listserv.frac-l
Date:         Thu, 12 Nov 1992 15:11:30 ITA
From:         MSANDRI@IVRUNIV.BITNET
Subject:      Mackey Glass Equation

I'm looking for a program to integrate the Mackey-Glass equation.
I know the initial condition and the value of the parameters, but I don't
know how to calculate the trajectory starting from such initial state.
I know Runge-Kutta method for numerical integration of dynamical systems.
Can one apply this method to the difference-differential Mackey-Glass
equation case? If yes, how?
Thank You in advance.
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Date:         Wed, 11 Nov 1992 22:01:37 EST
From:         "(Michael South)" <msouth@GRITS.VALDOSTA.PEACHNET.EDU>
Subject: Re: A Conjecture regarding the Mandelbrot Set

>After many hours of staring at displays of the Mandelbrot set, I have a
>conjecture:
>
>          Any point in the Mandelbrot set is part of either
>          a disc or a cardioid.

There is actually, beleive it or not, only one true disc (if by that you
mean "circle") and only one true cardioid in the Mandelbrot set.  All others
are approximate circles and approximate cardioids.  (This tripped me out
when I first heard it).  However, it may still be true that each point is
within either a quasi-circle or quasi-cardiod, although I think there are
special points that could be shown to not fit these quasi-restrictions, either.

It is interesting to note that it is not known at this point whether all of the
points of the Mandelbrot set are periodic (or preperiodic).  In other words, it
is unknown whether all orbits eventually settle down to a repeating cycle or if
there might be points that never converge to any cycle.  Your question might
touch this larger question.  Keep thinking.

Mike
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Date:         Thu, 12 Nov 1992 21:18:07 UTC+0100
From:         Guillermo Heredia <guiller@CICA.ES>
Subject:      Mackey-Glass Equation

>I'm looking for the algorithm to integrate the Mackey-Glass diff
>differential equation, which shows, for certain values of the pa
>a chaotic behavior.
>Any idea, source code and/or references are welcome!


        Here is a program that I was posted some time ago. I
have not tried it, and is in Fortran, but I think it can be
easily translated to other language.

-------------------------------------------------------------

From azwar@duke.cs.duke.edu Thu Oct 18 11:32:35 1990
Return-Path: <azwar@duke.cs.duke.edu>
Date: Thu, 18 Oct 90 11:31:05 -0400
From: azwar@duke.cs.duke.edu (Ubit Azwar)
To: hsg@duke.cs.duke.edu
Subject: Mackey-Glass Generator

This program was given to me by Prof. David Hsieh from Fuqua School of Business.
He took it from the Grassberger-Procaccia paper titled Measuring The
Strangeness of Strange Attractors, Physica 9D (1983) 189-208.

Output is written to mg.dat.
The starting function is x=2.
Tau (timestep) is = 100.

----------------------CUT HERE----------------------------------------

C     This program generates the mackey-glass equation
c     according to the algorithm described in Grassberger-Procaccia
      DIMENSION x(1200)
      INTEGER n,i,j,k,total,start
      DOUBLE PRECISION a,b,dt,tau,k1,k2
      DOUBLE PRECISION x
      a = 0.2
      b = 0.1
      n = 600
      tau = 100
      dt = tau/n
      k1 = (2.-b*dt)/(2.+b*dt)
      k2 = dt/(2.+b*dt)

      write(6,'(a)') ' enter number of observations'
      read(5,*) total
      open(unit=12,file='mg.dat',status='unknown')
c-----supply 600 starting values
c     here, we set arbitrarily to two
      DO 10 i = 1, 600, 1
      x(i) = 2
10    CONTINUE
      DO 50 j = 1, total, 1
      DO 30 i = 601, 1200, 1
          x(i) = k1*x(i-1)+k2*(a*x(i-n)/(1+(x(i-n))**10)+a*x(i-n+1)/
     +               (1+(x(i-n+1))**10))
30    CONTINUE
      DO 40 k = 1, 600, 1
          x(k) = x(k+n)
40    CONTINUE
      WRITE (12,48) x(n)
48    FORMAT(E25.15)
50    CONTINUE
      STOP
      END



----------------------------------------------------

        Guillermo Heredia
        guiller@cica.es
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Organization: North Dakota Higher Education Computer Network
Newsgroups: bit.listserv.frac-l
Date:         Mon, 9 Nov 1992 17:06:03 CST
From:         Dave Uherka <UHERKA@NDSUVM1.BITNET>
Subject:      Re: lyapunov exponents, universality, and delta
              9 Nov 1992 16:50:10 EST from <95ssb@CS.WILLIAMS.EDU>

On Mon, 9 Nov 1992 16:50:10 EST Stina Bridgeman said:
> ...
>      Delta = lim_n->infinity (r_n-r_(n-1))/(r_(n+1)-r_n)
>I have been experimenting with an algorithm, but have run into problems
>with rounding - the closer the computation gets to a value of r_n (and
>the higher the value of n), the more rounding affects the result.
>My algorithm is something along the lines of: (using the equation
>f(x_(n+1)) = r*x_n*(x_n-1))
  ...
>Stina Bridgeman

   In Devaney's new book, _A First Course in Chaotic Dynamical
Systems_, pp. 128-130, he suggests that, instead
of using the method you described to find the Feigenbaum
constant, delta, do the following (He said this is essentially
what Feigenbaum did with his hand-held calculator):

   For n = 0,1,2,... compute the root r_n to f^(2^n)(1/2) = 1/2.
This gives the sequence of "centers" of the stability intervals
for the logistics map, rather than the sequence of endpoints.
The "centers" do not actually fall at the real centers of
the stability intervals but at the places where the 2^n-cycles
contain the critical point x=1/2.  One does not have as much
roundoff problem in determining these r_n as with the ones
you described above.  One uses the same limit as you have above
to obtain delta.

   Using this method with double precision and using Aitken's
delta-squared acceleration method, my students quite "easily"
(after a few false starts) obtained the Feigenbaum constant
to about 4 significant figures, and I am sure they could
have obtained more accuracy if I had asked them to.

Dave Uherka
Math Dept, Univ. of ND, USA
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Date:         Thu, 5 Nov 1992 10:09:00 GMT
Comments:     Warning -- original Sender: tag was
              LANDINIG@IBM3090.COMPUTER-CENTRE.BIRMINGHAM.AC.UK
From:         Gabriel Landini <g.landini@BHAM.AC.UK>
Subject:      R/S vs. RMSF

Hi there,
I would like to know what are the differences between the results
obtained by the R/S (rescaled range analysis) compared to the
Root Mean Square Fluctuation (RMSF) of a time series.
Both are supposed to give the Hurst exponent of a time series of
data, but... do they give the same H ?

Gabriel
G.Landini@bham.ac.uk
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Date:         Fri, 6 Nov 1992 01:53:02 WST
From:         "(Keith H. K. Chow)" <keith@UXMAIL.UST.HK>
Subject:      UNSUBSCRIBE
              "McClelland_R%PSB%BLS@NIH3PLUS.BITNET" at Nov 5, 92 9:03 am

UNSUBSCRIBE Keith Chow
From: CSFLYTHE@ECUVM1.BITNET (Mac Flythe)
Newsgroups: bit.listserv.frac-l
Subject: Re: 'behind'
Date: 6 Nov 92 18:55:21 GMT
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU


    I'm interested in fractal programs written in TURBO PASCAL or even
 GW-BASIC.  If there is anyone who can send me some source code files,
 I would be very grateful.
                                           Thanks,
                                             Mac Flythe
From: U32796@UICVM.BITNET
Newsgroups: bit.listserv.frac-l
Subject: Lacunarity
Date: 12 Nov 92 18:23:32 GMT
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU

Thanks for all the inquiries concerning my lacunarity paper.  Please
send request for preprints, including paper mail addresses, to me (not
the list).  In addition, interested parties should note that our paper
uses the algorithm recently published by Allain and Cloitre (1991;
Physical Review A, 44:3552-3558).  - Roy E. Plotnick
(U32796@uicvm.uic.edu)
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Date:         Wed, 4 Nov 1992 12:48:01 -0500
From:         "The Mad Hatter" <C2MXALL@FRE.TOWSON.EDU>
Subject:      Hello all!

Greetings from Frostburg State University!
        My name is Jonathan Alloy, and I am a new subscriber to FRAC-L.  So here
    is a brief introduction of who I am, and perhaps, why.
        I currently am a freshman at Frostburg State University in Frostburg Mar
   yland, where I am a double major in Physics and Political Science.
        I intend to pursue Physics through the doctorate level, and work in basi
   c research in (hopefully!) quantum mechanics and elementry particles.
        My interest in Fractals springs from a Fractal textbook I read on them a
    few years ago (I believe it was "Understanding Fractals").  They have fasten
   ated me ever since.  I currently have a program called "Fractint", which runs
    on my 486-25.
        I am VERY glad to have found this list, and would *LOVE* to recieve any
   information, both virtually and in reality, that is free and out there.  Any
   leads on other software programs or reccommended textbooks would also be GREA
   TLY appreciated.
        Till next time, yours virtually,        Jon Alloy

BITNET:         C2MXALL@FRE.TOWSON.EDU
INTERNET:       C2MXALL@FRE.FSU.UMD.EDU
REAL LIFE:      211B Annapolis Hall
                Frostburg State University
                Frostburg, MD  21532
From: C2MXALL@FRE.TOWSON.EDU (NAME JON ALLOY)
Newsgroups: bit.listserv.frac-l
Subject: Fractals Computer Programs
Date: 6 Nov 92 19:33:04 GMT
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Folk:

        The only programs I know of currently are Fractint and Fractal Magic.  F
   ractint is Freeware, and is GREAT!  The manual (it is one of the files on dis
   k) is ~70 pages, but you can do anything with this program.
        Some things I have experimented are zooming in to an immense degree (i.e
   . 150-fold), and playing with the equations.  You can also (I believe - I hav
   e not tried it) get into the code and modify it to create new fractals that w
   ill run.
        Currently I use it on my 486-25, using DOS 5.0.  I have heard there is s
    Windows version out, but have not seen it.  It runs very smoothly, supportin
   g both keyborad and mouse.  Space requirements are 1 meg, including the manua
   l.
        I have Version 13, which is from 1990.  Based on the # of revisions from
    v. 1-13, I suspect that they are up to a higher Version now.

        I have less info on Fractal Magic.  It runs on both Apple and PC, and co
   sts around $60.  I could be wrong.  It, too, lets you modify the code to crea
   te and fiddle with fractals.

        If you would like the address for Fractint, EMail me and I'll zoom it of
   f to you.

        In a related field, what do all of you out there know of, and think of,
   Chaos Theory?

        Peace.
Jon Alloy               Internet: C2MXALL@FRE.FSU.UMD.EDU
College:                Bitnet:   C@MXALL@FRE.TOWSON.EDU
211B Annapolis Hall
Frostburg State University
Frostburg, MD  21532
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