HDTenEightyP/NetNews huggingface dataset:
From: danielg@autodesk.com (Daniel Green)
Newsgroups: sci.fractals
Subject: Re: Fractal Oscillator Circuitry
Date: 9 Oct 92 17:54:54 GMT
Reply-To: danielg@autodesk.com
Organization: Autodesk, Inc.

In article 10063@bnr.ca, kelvinp@crchh447.bnr.ca (Kelvin Porter) writes:
> I remember, way back in the early days of 'Strange Attractors', seeing an article
> (written I believe by University of Texas Non-Linear Dynamics Professors)
> which mentioned capacitors that exhibited chaotic characteristics...
> It may have been in the Springer-Verlag "Intelligeneer"?????
> 
> My question is can direct me to reference(s) regarding chaotic circuitry or better
> yet post ASCII schematics?

A recent (within the last year?) issue of Scientific American gave a schematic for
a really simple circut that can be tuned to go chaotic.  It might have been in
their Amateur Scientist column.  Sorry I can't be more specfic.

---
Daniel Green
danielg@autodesk.com
      ___________          ___________
      |         |          |         |
      |  _________         | _________
      |  |       |         | |       |
      |  |  _______        | | _______
      |  |  |     |        | | |     |
      ---|  |  _____       --| | _____
         ---|  | D |         --| | D |
            ---|  G|           --|  G|
               -----             -----
From: scavo@cie.uoregon.edu (Tom Scavo)
Newsgroups: sci.fractals
Subject: Re: Mandelbrot Set
Date: 13 Oct 92 19:52:43 GMT
Article-I.D.: nntp.1992Oct13.195243.986
Organization: University of Oregon Campus Information Exchange

In article <1992Oct13.151335.24563@sol.UVic.CA> aschoorl@engr.UVic.CA writes:
>
>Can anybody simply tell me what the equation of the Mandelbrot set is?

A point  c  is in the Mandelbrot set if the orbit of 0 with respect
to  z -> z^2 + c  does *not* escape to infinity.

-- 
Tom Scavo
scavo@cie.uoregon.edu
From: scavo@cie.uoregon.edu (Tom Scavo)
Newsgroups: sci.fractals
Subject: Re: Mandelbrot Set
Date: 15 Oct 92 16:28:38 GMT
Article-I.D.: nntp.1992Oct15.162838.24280
Organization: University of Oregon Campus Information Exchange

In article <1992Oct15.144118.27237@viewlogic.com> robl@macro.viewlogic.com (Rob Limbert) writes:
>
>In article <1992Oct14.215137.24498@nntp.uoregon.edu>, scavo@cie.uoregon.edu (Tom Scavo) writes:
>|> ...There is a Julia set
>|> for each  c  and this set lives in the complex plane.  Fix
>|> c  and iterate  z -> z^2 + c  for every  z  you can think of.
>|> For  c  in the Mandelbrot set, the Julia set is connected.
>|> For  c  not in  M , the Julia set is Cantor dust.
>|> 
>
>   In fact, isn't it possible to define the Mandelbrot set as the set of
>all c whose associated Julia set is connected? Something like:
>
>                 M = {c : J is connected}
>                           c

I suppose you could (and many authors do), but it seems more
like a theorem than a definition to me.  It's certainly not the
way  M  came about historically, nor is it calculated this way.

How would you define the bifurcation set (of which the  M  set
is a special case) for some other iteration, like say the cubic
or the complex sine?  Is it known that  J_c  is connected when
c  is in the bifurcation set of the cubic (a 4-d object), for
instance?

-- 
Tom Scavo
scavo@cie.uoregon.edu
Newsgroups: sci.fractals
From: sprott@128.104.39.173
Subject: Re: Fractal Oscillator Circuitry
Reply-To: sprott@128.104.39.173
Organization: Univ. of Wisconsin, Plasma Physics
Date: Wed, 07 Oct 1992 16:09:03 EDT

If anyone is interested in building a chaotic RLC circuit that works at
audio frequencies, I can offer some advice.  Testa, et. al. used a
varactor diode (1N953) whose reverse capacitance is small and depends on
voltage.  They operated at 100 kHz, and it is difficult to lower the
frequency into the audio range with such a device.  However, an ordinary
power diode also has a voltage variable capacitance which can be very large
(microfarads) when forward biased and which also depends on voltage.  With
a good quality inductor of around 100 mH, it's easy to get the resonance
down to around 10 kHz.  Just apply a sine wave of at least 10 V peak to the
inductor and diode in series.  Connect an audio amplifier with a high
input impedance across the diode, and you will at least four period doublings
(5, 2.5, 1.25 kHz) and then chaos as you raise the oscillator voltage.
I have such a circuit that I take around the country to illustrate chaos
presentations.  Be sure the inductor has high-Q, the oscillator can put out
in excess of ten volts, and the amplifier doesn't load the circuit.  You
can also display the attractor on an oscilloscope with the oscillator voltage
on one axis and the diode voltage on the other.  Very effective and highly
recommended!
Newsgroups: sci.fractals
From: sparapan@flash.ra.anl.gov (RA Sparapani RA/208/xxx gwing)
Subject: Question on Fractals, Chaos and Time Series
Organization: Argonne National Laboratory, Argonne IL
Date: Sun, 11 Oct 1992 00:54:26 GMT

Since this seems to be largely a Q&A group, I'm posting the question here.
My training has for the most part been in Applied Mathematics and 
Statistics and am slightly confused by the terminology.  I have found the
FAQ and Book Lists quite helpful for general information, but I think that
I may need a more specific answer.  I am looking for a reference that 
particularly deals with Fractals(possibly chaotic) in time series.  I have
found some of the dynamical systems books interesting, but since I am not
very familiar with that subject I have been unable to efficiently use that
information.  If some one would be good enough to suggest a reference, with
a short discussion of the relationship of the book to this topic, I would
greatly appreciate it.  Also, I am interested in algorithms to compute the
fractal time series parameters.  I am going to download fractint, but just
the same I would like references on such algorithms so I can understand them
and possibly code my own programs.  By the way, if someone is interested in
correspondence on this problem, I would be glad to reply(given adequate time
to research the subject of course).  If any could recommend a conference or
newsletter that would also be appreciated.  Thanks for everything and 
anything.

Rodney
From: olson@dstl86.gsfc.nasa.gov (Paul Olson)
Newsgroups: sci.fractals
Subject: Re: fractals/amiga
Date: 13 Oct 92 14:55:00 GMT
Distribution: sci.fractals
Organization: Mission Operations and Data Systems
News-Software: VAX/VMS VNEWS 1.41

In article <PARENIBA.92Oct12192808@dante.nmsu.edu>, pareniba@nmsu.edu (Patricia Arenibas) writes...
>I have heard of fractal programs for the IBM, but I was wondering
>if there are any fractal programs for the amiga and where do you
>get them?
> 
>thanks
>Patricia

Yes, there are a number of fractal programs for the Amiga.  You'll find most of
them in the Fred Fish disk collection, ftp-able from a number of sites.  Most
of those PD programs do not use HAM mode.  There is (or was within the last two
years) a commercial product out called HAMandel.

Overall, if you can find a copy of the latest AC's Guide to the Amiga (check
your local bookstore), you'll find any commercial product for the Amiga, as
well as a complete Fish disk collection listing.

If you need any more help, just let me know.

+--------+-------------------------------------------------------------+
|      __| Paul J. Olson - VAX Systems Manager & Resident Amiga Addict |
| C=  ///| Voice -     301/286-4246, 301725-5501                       |
|__  /// | DECnet-    DSTL86::OLSON                                    |
|\\\///  | Internet - olson@dstl86.gsfc.nasa.gov                       |
| \XX/   | Disclaimer: Statements in my messages are wholely my own.   |
| AMIGA  | "[the universe originated] as a quantum fluctuation         |
| RULES! |  of absolutely nothing." - Guth & Steinhardt                |    
+--------+-------------------------------------------------------------+
From: vinnie@ocf.berkeley.edu (Vince Bafetti)
Newsgroups: sci.fractals
Subject: Re: Fractal Oscillator Circuitry
Date: 13 Oct 1992 07:45:04 GMT
Organization: U. C. Berkeley Open Computing Facility
Distribution: world
NNTP-Posting-Host: monsoon.berkeley.edu


	Dr. Leon Chua, UC Berkeley Electrical Engineering, has done
a bunch of work with an oscillator that consists of a capacitor, an
inductor, and a non-linear negative resistor. The non-linear resistor
is made from two op-amps and a bunch of resistors. I'm actually
building one as part of a project, so if anyone wants the schematic
and notes as I go along, let me know. Maybe I could send it by FAX? Or
by SASE?
 	Dr. Chua has been published in many IEEE things, and the circuit
is known as, appropriately enough, "Chua's Circuit." Funny how that works.

		Vince Bafetti
		preferred email: vinnieb@ssl.berkeley.edu
		otherwise:  	 vinnie@ocf.berkeley.edu
		or call:	 510-235-0838
Newsgroups: sci.fractals
From: ajohnson@algodones.unm.edu (Alan Johnson)
Subject: Re: Fractal Heterogeneity
Date: Sat, 10 Oct 92 17:30:24 GMT
Organization: "University of New Mexico, Albuquerque"
Reply-To: ajohnson@algodones.unm.edu 
Keywords: heterogeneity

Alok Kumar writes:
>  i am presently doing research in the field of trying to understand 
>  the movement of contaminants below the surface of the earth. the 
>  inherent problem in this field is trying to characterize the
>  heterogeneous nature of the subsurface of the earth. it seems some
>  work has been done in trying to characterize such properties in other 
>  fields.
>  i would appreciate if anyone could send me informations regarding 
>  work done in this field or any related field. the key is trying to 
>  understand the variability in properties at a large scale that 
>  could be self similar in nature.

There has been some fairly concentrated effort to use fractal geometry in
the study of transport dynamics in groundwater.  Much of this work has
been done by Stephen Wheatcraft and colleagues.  A key paper is:

Wheatcraft, SW and SW Tyler. 1988. An explanation of scale-dependent
     dispersivity in heterogeneous aquifers using concepts of fractal
     geometry.  Water Resources Research 24:566-578.

You may also be interested in the work that has been done on the fractal
geometry of cave, particularly those formed in karst landscapes.
For example, see:

Laverty, M. 1987. Fractals in karst.  Earth Surface Processes and
     Landforms 12:475-480.

These papers, and the references therein, should get you started.

Alan
From: brb@qt.IPA.FhG.de (Bernd Bieberstein)
Newsgroups: sci.fractals
Subject: Re: Strange attractor questions
Date: 16 Oct 92 15:15:01
Organization: /users/brb/.organization
NNTP-Posting-Host: fanny.qt.ipa.fhg.de
In-reply-to: sprott@128.104.39.173's message of 14 Oct 92 12:31:16 GMT

In article <00962123.79FB9060@128.104.39.173> sprott@128.104.39.173 writes:

>   I'm writing a book that contains several hundred examples ...

>   2) I've heard that strange attractors arising from systems of ordinary
>   differential equations must have dimension greater than 2.0.  If this is true,
>   is there an easy way to see why?

Yes, there is an easy way to see.

In 2-D space the trajektories can NOT cross each other. This is only possible
in higher dimensions (of course they do not have common points then).

Bernd

******************************************************************************
Bernd Bieberstein
brb@qt.ipa.fhg.de
******************************************************************************
Newsgroups: sci.fractals
From: 10642749@eng2.eng.monash.edu.au (MARTIN OLBRICH)
Subject: Re: Fractal Oscillator Circuitry
Keywords: Fractal VCO Oscillator Circuit
Organization: Faculty of Engineering, Monash University 
Date: Sat, 10 Oct 1992 01:46:22 GMT

In article <1992Oct05.234429.10063@bnr.ca> kelvinp@crchh447.bnr.ca (Kelvin Porter) writes:

>My question is can direct me to reference(s) regarding chaotic circuitry or better
>yet post ASCII schematics?
>
>I'm intrigued by the possibility of making voltage controlled oscillators with
>chaotic properties for making music (a synthesizer with Voltage Controlled
>Chaos-cillators, if you will).  I would also be interested in digital implementations
>as well.

  This is going to sound very vague, but I remember seeing a circuit set up 
to do this sort of thing in Scientific American (I think), possibly in a DIY 
article.  I cannot remember if a speaker or a CRO was used for output, but 
period doubling was definitely discussed.  As for when the article was 
printed, ...welllllll....errrrrr.... ?the last few years??? (I said I was 
going to be vague) the indexes (indices??) may be useful in tracking this 
one down.
  Useful?
  Marty.
From: avr@cs.purdue.EDU (Andrew V. Royappa)
Newsgroups: sci.fractals
Subject: other iterations
Date: 16 Oct 92 18:29:27 GMT
Organization: Department of Computer Science, Purdue University

Hi, I was curious about generating fractal images with other iterations
than z = z^2 + c. Once you have the source to a fractal program it's
easy to change the computation inside the inner loop to be whatever
you want. So far I have tried
	
		z = z^3 + c
		z = exp(z)+c

(if you think the usual iteration is slow, wait till you try the
exponential one...)

The first one gives a mandelbrot-like set, while with the second the
only interesting portion seems to be a tendril-like (spiral) structure.

So my questions are: 

a) what other kinds of iterations generate particularly interesting images ?
b) is there some other "interesting" area of the exponential iteration
   other than the tendril ?

I don't have any books on fractals; but I'm maybe our library does. Do
the books discuss other iterations in much detail ?
 
Thanks for any advice/discussion.


					Andrew V. Royappa
					avr@purdue.edu
					{pur-ee,decvax,ucbvax}!purdue!avr

p.s. Incidentally, all this is originated out of sheer (idle) curiosity, not
because of some potentially useful research that I'm doing. Sorry.
Newsgroups: sci.fractals
From:  uldis@inkomi.riga.lv (Uldis Bojars)
Subject: FDESIGN question
Keywords: fractals
Reply-To: uldis@inkomi.riga.lv
Organization: inkomi
Date: Thu,  8 Oct 92 15:07:30 +0300 

Hello !

Where I can get fractal generating programm
called FDESIGN ?  I can use anonymous downloads.
I don't know other ways to get it.

I found info about it in FractInt:

FDESIGN, by Doug Nelson (CIS ID 70431,3374)
Freeware IFS fractal generator available from
Compuserve in COMART Lib 15....

Yours,
     Uldis Bojars
     ( uldis@inkomi.riga.lv )


Newsgroups: sci.fractals
From: habrams@nyx.cs.du.edu (Howard Abrams)
Subject: fractal audio?
Organization: Nyx, Public Access Unix @ U. of Denver Math/CS dept.
Date: Sun, 11 Oct 92 02:22:22 GMT

  Does anyone have/know-of any information on fractial compression
of audio?

-------------------------------------------------------------------------
-- Howard Abrams -- abramsh@erau.db.erau.edu -- (place your quote here) -
-------------------------------------------------------------------------
From: danielg@autodesk.com (Daniel Green)
Newsgroups: sci.fractals
Subject: Re: Mandelbrot Set
Date: 14 Oct 92 19:57:31 GMT
Reply-To: danielg@autodesk.com
Organization: Autodesk, Inc.

In article 24563@sol.UVic.CA, aschoorl@engr.UVic.CA (Andre  Schoorl) writes:
> 
> Can anybody simply tell me what the equation of the Mandelbrot set is?
> Ever book I've ever seen expects you to know it before cracking the cover.
> 

I'm sure most readers will know this stuff in their sleep, but I remember
going through the same head-scratching just to get started, so I've included
mandel.c which contains the relevant info embedded in simple, working C code.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

			/* * * * * * * * * *\
			 * MANDEL.C        *
			 * by Daniel Green *
			\* * * * * * * * * */

#define BIG 100.0

#define NORMSQRD(zx,zy) (zx*zx+zy*zy)

/* complex addition */
#define PLUS(resultx,resulty, ax,ay, bx,by)  \
	(resultx = ax + bx, \
	 resulty = ay + by)

/* complex multiplication */
#define TIMES(resultx,resulty, ax,ay, bx,by)  \
	(resultx = ax*bx - ay*by, \
	 resulty = ay*bx + ax*by)

/* set to most natural floating point type */
typedef double Real;

/*
 * Iterates the Mandelbrot function Z = Z^2 + C where C is a point in
 * the complex plane, and Z is initially complex zero.  Iteration ends when
 * the magnitude of Z grows too large, or if the given maximum number
 * of iterations is reached (given point is then assumed to be in the set).
 *
 * Returns 0 if in the set, otherwise number of iterations to divergence.
 * Note: zx and zy are initialized to x and y, and the counter is initialized
 * to 1 because that is what they would always be after the first iteration
 * if they were all initialized to zero as they officially should be.
 */
int mandel(x, y, max_iterations)
Real x, y;
int max_iterations;
{
	register Real zx, zy, cx, cy, tempx, tempy;
	register int iterations;

	zx = cx = x;
	zy = cy = y;
	for (iterations = 1;
	     (NORMSQRD(zx,zy) < BIG) && (iterations < max_iterations);
	     iterations++) {
		TIMES(tempx,tempy, zx,zy, zx,zy);
		PLUS(zx,zy, tempx,tempy, cx,cy);
	}
	return iterations == max_iterations ? 0 : iterations;
}

---
Daniel Green
danielg@autodesk.com
      ___________          ___________
      |         |          |         |
      |  _________         | _________
      |  |       |         | |       |
      |  |  _______        | | _______
      |  |  |     |        | | |     |
      ---|  |  _____       --| | _____
         ---|  | D |         --| | D |
            ---|  G|           --|  G|
               -----             -----

Newsgroups: sci.fractals
From: aschoorl@engr.UVic.CA (Andre  Schoorl)
Subject: Mandelbrot Set
Reply-To: aschoorl@engr.UVic.CA
Organization: University of Victoria, Victoria, BC, Canada
Date: Tue, 13 Oct 92 15:13:35 GMT


Can anybody simply tell me what the equation of the Mandelbrot set is?
Ever book I've ever seen expects you to know it before cracking the cover.

--------------------------------------------------------------------------
Andre Schoorl                            aschoorl@engr.uvic.ca
Department of Computer Engineering       e-mail preferred.
University of Victoria, Canada
Xref: sparky sci.fractals:131 alt.fractals:1501
Organization: K.U.Leuven - Academic Computing Center
Date: Monday, 12 Oct 1992 09:47:06 +01
From: <FHGAA99@cc1.kuleuven.ac.be>
Newsgroups: sci.fractals,alt.fractals
Subject: mailing list : STOP THIS MESS |||||

Please STOP REPLYING to any mail you received from that damn mailing-list.
All that crap is being forwarded to everyone who was (unwillingly) added
to that list, including me. I am fed up with my mailbox being cluttered by
mails with which I have nothing to do with.

Please post your flames, or send them directly to that 'funny' guy who started
this shit....


Henk
From: shirriff@sprite.berkeley.edu (Ken Shirriff)
Newsgroups: sci.fractals
Subject: Re: Mandelbrot Set
Date: 14 Oct 1992 18:17:43 GMT
Organization: University of California, Berkeley
NNTP-Posting-Host: hijack.berkeley.edu

In article <1992Oct13.151335.24563@sol.UVic.CA> aschoorl@engr.UVic.CA writes:
>Can anybody simply tell me what the equation of the Mandelbrot set is?

This and many other questions are answered in the sci.fractals FAQ file.
A copy of this FAQ is archived at various places such as: pit-manager.mit.edu
[18.72.1.58]: /pub/usenet/news.answers/fractal-faq and ftp.uu.net [137.39.1.9
or 192.48.96.9]: /usenet/news.answers/fractal-faq.Z .

Ken Shirriff				shirriff@sprite.Berkeley.EDU
From: scavo@cie.uoregon.edu (Tom Scavo)
Newsgroups: sci.fractals
Subject: Re: Knots and fractals
Date: 10 Oct 92 18:29:49 GMT
Organization: University of Oregon Campus Information Exchange

In article <1992Oct9.050723.6176@mnemosyne.cs.du.edu> ddixon@nyx.cs.du.edu (David Dixon) writes:
>Anybody have any references about fractals and knot theory?

Yes, look at the last chapter in Tufillaro, Abbott, and Reilly's
_An Experimental Approach to Nonlinear Dynamics and Chaos_ published
by Addison-Wesley this year.

-- 
Tom Scavo
scavo@cie.uoregon.edu
Newsgroups: sci.fractals
From: fokp@cary112.its.rpi.edu (Pingtao (Ben) Fok)
Subject: Re: Mandelbrot Set
Reply-To: fokp@rpi.edu
Organization: Rensselaer Polytechnic Institute, Troy, NY.
Date: Tue, 13 Oct 1992 22:41:21 GMT

The equation is:
Zn+1=Z^2+C   where
C is a complex number namely x+yi.
The idea is to make a grid on the computer screen with the boundary
of -2 to 2 for the x axis and -2 to 2 for the y axis.  Then you start
calculating the set by putting every coordinate in the constant C and 
Z.  You use the point as an initial value as well as a constant.
It is very similar to the Julia Set. In fact, Mandelbrot claimed that
the Mandelbrot Set have contain every Julia Set.  
I hope this can help you a little.
Ben Fok
fokp@rpi.edu
Newsgroups: sci.fractals
From: robl@macro.viewlogic.com (Rob Limbert)
Subject: Re: Mandelbrot Set
Originator: robl@macro
Organization: Viewlogic Systems, Inc.
Date: Thu, 15 Oct 1992 14:41:18 GMT


In article <1992Oct14.215137.24498@nntp.uoregon.edu>, scavo@cie.uoregon.edu (Tom Scavo) writes:
|> ...There is a Julia set
|> for each  c  and this set lives in the complex plane.  Fix
|> c  and iterate  z -> z^2 + c  for every  z  you can think of.
|> For  c  in the Mandelbrot set, the Julia set is connected.
|> For  c  not in  M , the Julia set is Cantor dust.
|> 

   In fact, isn't it possible to define the Mandelbrot set as the set of
all c whose associated Julia set is connected? Something like:

                 M = {c : J is connected}
                           c
From: fokp@bray1b.its.rpi.edu (Pingtao (Ben) Fok)
Newsgroups: sci.fractals
Subject: Chaos, fractals and society
Keywords: Chaos, fractals and society
Date: 16 Oct 92 00:12:05 GMT
Article-I.D.: rpi.#j3zr0
Reply-To: fokp@rpi.edu
Organization: Rensselaer Polytechnic Institute, Troy, NY.

I am doing a journal on Chaos, fractals and society.  I am trying
to understand the relation between those the subject above.  Please
everybody, if you have any opinion or idea, post them.  That would
be very very helpful.
Thanks
Ben 
fokp@rpi.edu   (how much you got to know before you how little you know)
                                                      by nobody.
From: bert.tyler@satalink.com (Bert Tyler) 
Newsgroups: sci.fractals
Subject: Re: Fractal Plants (LONG)
Date: 7 Oct 92 10:18:00 GMT
Distribution: world
Organization: Datamax/Satalink Connection * Ivyland, PA (215) 443-9434
Reply-To: bert.tyler@satalink.com (Bert Tyler) 


TK> 1. Name: Fractint
TK>...
TK> 6. MSDOS (There is a windows version of fractint, but I don't know if the
TK>          L-System code is included or not)

Just a quick FYI:  The Windows version does include Fractint's L-systems
code.

                   Bert Tyler   (bert.tyler@satalink.com)
---
 . DeLuxe./386 1.25 #343sa . Did you expect mere proof to sway my opinion?
From: sprott@128.104.39.173
Newsgroups: sci.fractals
Subject: Strange attractor questions
Date: 14 Oct 92 12:31:16 GMT
Reply-To: sprott@128.104.39.173
Organization: Univ. of Wisconsin, Plasma Physics

I'm writing a book that contains several hundred examples of strange attractors
with a simple description of the underlying mathematics.  Perhaps some of you
experts could answer the following questions:

1) I notice that simple attractors like the Mandelbrot set have complicated
basins of attraction, while complicated (strange) attractors like the Henon map
have simple basins.  Is this a general principle, and if so, is there a reason
for it?

2) I've heard that strange attractors arising from systems of ordinary
differential equations must have dimension greater than 2.0.  If this is true,
is there an easy way to see why?

3) Is there a mapping or system of ODE's involving only polynomials whose
solution attracts to:
     a) a 2-torus
     b) a 3-torus
     c) a Moebius strip?

I would also welcome suggestions for classes of equations that produce visually
interesting attractors other than the standard ones, such as those in FRACTINT.
(The book is "Strange Attractors," and it will be published by M&T Books in
June 1993.)