HDTenEightyP/NetNews huggingface dataset:
X-Mailer: ELM [version 2.3 PL6]
Newsgroups: bit.listserv.frac-l
Date:         Sun, 24 Jan 1993 20:47:13 PST
From:         Michael Freeman <mfreeman@UNIXG.UBC.CA>
Subject:      Chaotic Modelling

The description of a simple physical system exhibiting chaotic behaviour
can be found in the new edition of Physics, by Tipler (volume 1) - he calls
it the "Bender bouncer" - a driven, damped harmonic oscillator with a reflector
at x = 0 (the velocity is reversed when x reaches 0).  It's a nice one to
model.
                               - Mike Freeman -
Organization: Penn State University
Date: Sun, 24 Jan 1993 16:39:48 EST
From: <WAJ@psuvm.psu.edu>
Newsgroups: bit.listserv.frac-l
Subject: chaotic modelling

I have recently experimented in modelling chaotic systems in C++. The only
system I have had success on is the Lorenz water wheel (as displayed in
James Gleick's Chaos). Are there any other fairly simple physical systems
which exibit chaotic behavior?
(btw, if anybody is interested in seeing the wheel I could send it to you)
Thanks

Bill Jester
Xref: sparky bit.listserv.frac-l:1366 sci.fractals:638
Organization: Penn State University
Date: Tue, 26 Jan 1993 02:05:09 EST
From: <WAJ@psuvm.psu.edu>
Newsgroups: bit.listserv.frac-l,sci.fractals
Subject: water wheel II

Pardon me, but I neglected to mention that I put the Lorenz water wheel
in wuarchive.wustl.edu  /pub/MSDOS_UPLOADS/graphics (water.zip)...
Sorry about the mild oversight...

Bill Jester
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.frac-l
Date:         Wed, 27 Jan 1993 21:06:16 EST
From:         "dan goldwater" <ST202013@BROWNVM.BITNET>
Subject:      FracXtra v2 Fractint Extras released!

I have released v2 of my FracXtra huge collection of Fractint Extras
(.map, .par, .l, .ifs, .frm, etc files).  the collection is available
on wuarchive.wustl.edu in /pub/MSDOS_UPLOADS/graphics/ as 'fracxtr2.zip'
and 'fracxtr2.txt'

-dan goldwater-  daniel_goldwater@brown.edu    dgold@math.umass.edu
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Subject: (no subject given)
Newsgroups: bit.listserv.frac-l
Date:         Thu, 28 Jan 1993 12:57:49 EST
From:         muddy@ATHENA.MIT.EDU

Please un-subscribe me
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
X-Mailer: ELM [version 2.3 PL8]
Newsgroups: bit.listserv.frac-l
Date:         Fri, 22 Jan 1993 17:33:19 CST
From:         david fowler <dfowler@UNLINFO.UNL.EDU>
Subject:      Re: Mathematica discussion list?
              "MSANDRI%IVRUNIV.bitnet@KSUVM.KSU.EDU" at Jan 22, 93 12:50 pm

Try sci.math.symbolic
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
X-Charset: US
X-Char-Esc: 0
Newsgroups: bit.listserv.frac-l
Date:         Thu, 28 Jan 1993 16:31:16 EST
From:         chris@SCHKOL.SCH.BME.HU
Subject:      Matematica discussion

Hello Marco and other Matematica users,

I'm interested in discussion of Matematica, also. I haven't any book given
with the software, so I made a help file, what is the full built-in help of
Matematica. I'll send it, if anyone would like.
What is "sci.math.symbolic"?

Thanks.
                                        Chris (chris@schkol.sch.bme.hu)
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Return-Path: <dok@fwi.uva.nl>
X-Organisation: Faculty of Mathematics & Computer Science University of
                Amsterdam Plantage Muidergracht 24 NL-1018 TV Amsterdam The
                Netherlands
X-Phone:        +31 20 525 5200
X-Telex:        16460 facwn nl
X-Fax:          +31 20 525 5101
Newsgroups: bit.listserv.frac-l
Date:         Fri, 22 Jan 1993 12:16:55 +0100
From:         "P.J.van Dok W92" <dok@FWI.UVA.NL>
Subject: Re: Speeding up Calculation of Mandelbrot Set

Picjover????? Nou ja, in de literatuur is het toch echt van Pickover, en als jij
 je idee gecredit had willen hebben, had je dat toen maar moeten publiceren.
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
X-Envelope-to: FRAC-L@GITVM1.BITNET
X-VMS-To: IN%"FRAC-L@GITVM1.BITNET"
X-VMS-Cc: C1754
MIME-version: 1.0
Content-transfer-encoding: 7BIT
Newsgroups: bit.listserv.frac-l
Date:         Thu, 28 Jan 1993 08:47:33 -0600
From:         Hal Harris <C1754@UMSLVAXA.BITNET>
Subject:      Re: Need info on "Phaser"

The book that Richard Bowman was looking for is probably:
Dynamics and Bifurcations
by Jack K. Hale and Huseyin Kocak
New York:Springer-Verlag, c1991
OCLC NO.: OC25084679
I hope this helps.  I haven't actually seen the book but it is in two of
the University of Missouri Math Department Libraries (Columbia and Rolla).
Hal Harris
Department of Chemistry
University of Missouri-St. Louis
c1754@slvaxa.umsl.edu
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
X-Mailer: ELM [version 2.3 PL6]
Newsgroups: bit.listserv.frac-l
Date:         Thu, 21 Jan 1993 22:10:32 PST
From:         Michael Freeman <mfreeman@UNIXG.UBC.CA>
Subject:      Speeding up Calculation of Mandelbrot Set

Assuming programming information is sought, two types of thing should be done:
1. Try to optimize the routine that calculates the dwell of a given point.
   This means writing it in assembler.  For MSDOS machines, 80x87 floating
   point machine instructions, or, if no coprocessor (or 486DX) but having
   a 386, using extended integer arithmetic.  A time comparison:
         386 extended integer -  28 units
         C floating point        35 units (with coprocessor)
         C floating point      2797 units (no coprocessor)   (ughh)
         80x87 assembler         24 units
   Fractint does all this very well.

2. Try to avoid calculating some of the points.
   a) block subdivision (used by Fractint)
   b) boundary tracing  (used by Fractint, slower, nicer to watch)
   c) Mariani recursive algorithm:  calculate the dwells around the perimeter
      of a rectangle; if they're all the same, fill in the rectangle with that
      value - otherwise divide it in half and recurse on each half (when you
      reach a certain minimum size, just calculate them all)
     - NOT used by Fractint, but it's very effective

Looking for periodicity inside the set is expensive, and most good pictures
don't contain that many interior points (value judgment!).  There are rumoured
methods that are even better, but I've yet to see or understand them.

                               - Mike Freeman -
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.frac-l
Date:         Wed, 27 Jan 1993 15:42:43 GMT
From:         Gerry Callaghan <eeigcn@EEIUC.ERICSSON.SE>
Subject:      Re: Chaotic modeling

P.J van Dok was asking about modelling chaotic systems.

An interesting chaotic system to model is a double pendulum set.
There was an article and construction details in the U.S. magazine
'Amateur Scientist' last Summer (I'm at work and don't have the reference )

Let's see if I can draw it

                                A
                ...............[  ].............
                               |0 |     Fixed beam
                ...............|  |.............
                               |  |
                               |  |
                               |  |
                               |  |
                               ...|
                              \  \|
                               \0 \  B
                                \  \
                                 \  \
                                  \  \
                                   \  \
                                    \  \  Weight
                                    <<< >>>
                                    <<< >>>

The system can rotate at both points A and B. A LED and battery can be
mounted on the lower arm for interesting time delay photographs.
It exhibits an astonishing range of chaotic behaviour.
This  might be easier to model than a pendulum that moves in 360 degrees
as it stays in one plane.

I'd love to see the wheel too!
Gerry

Gerry Callaghan                 Email:  eeigcn@eeiuc.ericsson.se
Ericsson System Expertise       Phone:  +353 902 74601 ( work )
Cornamaddy, Athlone                              85054 ( home )
Co. Westmeath, Irish Republic
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.frac-l
Date:         Fri, 22 Jan 1993 12:50:05 ITA
From:         MSANDRI@IVRUNIV.BITNET
Subject:      Mathematica discussion list?

I'm looking for discussion list related to the software Mathematica.
Any information is welcome. Thanks. Marco.
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
X-Delivery-Notice:  SMTP MAIL FROM does not correspond to sender.
X-Mailer: ELM [version 2.4 PL17]
Content-Type: text
Content-Length: 1093
Newsgroups: bit.listserv.frac-l
Date:         Thu, 28 Jan 1993 20:48:11 +0100
From:         Karol Grudzinski <kagru@MAT.TORUN.EDU.PL>
Subject:      Re: Matematica discussion
              28, 93 04:31:16 pm

>
>
> Hello Marco and other Matematica users,
>
> I'm interested in discussion of Matematica, also. I haven't any book given
> with the software, so I made a help file, what is the full built-in help of
> Matematica. I'll send it, if anyone would like.
> What is "sci.math.symbolic"?
>
> Thanks.
>                                         Chris (chris@schkol.sch.bme.hu)
   Please do send me the help file !!!.
   sci.math.symbolic is a usenet group. If Usenet means nothin' to you -
   I'm sorry but I can't explain what it is right now cause I got no time
   You can read about it in ZEN and  the art of the internet or ask someone
   in your computer center - they certainly know what usenet is.Or if you
   prefer , just let me know and I'll tell you when I have time.



///////////////////////////////////////////////////////////
//KAROL GRUDZINSKI//E-MAIL:KAGRU@MAT.TORUN.EDU.PL        //
//                //       KAGRU@VM.CC.TORUN.EDU.PL      //
//                //       KAGRU@PLTUMK11.BITNET         //
///////////////////////////////////////////////////////////
Xref: sparky bit.listserv.frac-l:1375 comp.music:6403 sci.fractals:644
From: aalpern@hamp.hampshire.edu
Newsgroups: bit.listserv.frac-l,comp.music,sci.fractals
Subject: Chaos C code(Was:Re:chaotic modelling)
Date: 27 Jan 93 14:17:24 GMT
Distribution: inet
Organization: Hampshire College
NNTP-Posting-Host: hamp.hampshire.edu


Here's those code snippets I promised. Apologies for the delay, but all the
computing facilities here at Hampshire were closed yesterday.
The algorithms presented here were taken from Rick Bidlack's 
paper entitled "Chaotic Systems as Simple (But Complex)
Compositional Algorithms. Computer Music Journal Vol. 16
No. 3, Fall 1992, MIT Press

Here's a C code snippet for iterating the Henon system.
ITERATIONS is the number of iterations you desire. After about
80 iterations or so the transients filter out and the system
assumes a chaotic behavior.

float 	new_iota, new_theta,
		A = 1.43, B = 0.3;		
/* A and B are parameters which determine the orbit */
			
for(counter = 0; counter < ITERATIONS; counter++)	{
	output(iota,theta) /* produce sound, graphics, or whatever */

	new_iota = theta + 1.0 - (A*(iota*iota));
	new_theta = B * iota * P;
		
	iota = new_iota;	
	theta = new_theta;
}

This is a loop for iterating the Standard Map.

float 	new_iota, new_theta, K = 1.1;
/* K is the controlling parameter in this system */
for(counter = 0; counter < length; counter++)	{
	output(iota,theta);
	new_iota = iota + (K * sin(theta));
	new_theta = theta + new_iota;

	iota = new_iota;
	theta = new_theta;
}

Here are some parameter values that will produce a Chaotic 
orbit. For Henon:
	with B = 0.3, use A = 1.076, 1.4, 1.43
For the Standard Map:
	K = 1,1.02,1.1,2.6. Values for K above 1 will usually produce
a chaotic orbit, but there are "windows" of periodicity to
be found too. 

In order to produce music from these, one has to figure out a way to 
interpret the results. You could map the results directly to frequency and
delta-time, or mess with them to get something like a scale index.

-Adam
aalpern@hamp.hamsphire.edu
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
X-Mailer: ELM [version 2.3 PL6]
Newsgroups: bit.listserv.frac-l
Date:         Wed, 27 Jan 1993 11:00:24 PST
From:         Michael Freeman <mfreeman@UNIXG.UBC.CA>
Subject:      Chaotic Modelling - the Water Wheel

I recently downloaded the waterwheel program and tried it on a
couple of computers.  On a 486DX, it's beautiful - the motion looks
physically realistic.  On a 16 MHz 386 without 387 - forget it, it's
way too slow.  It won't work properly on EGA - requires VGA

An opinion regarding programming: there was no real advantage in using
C++ rather than C for this program, aside from using different I/O
routines.  Not everyone has C++.
                         - Mike Freeman -
Newsgroups: bit.listserv.frac-l
From: dboese@spartan.ac.BrockU.CA (Darcy Boese)
Subject: Scientific American
Organization: Brock University, St. Catharines Ontario
X-Newsreader: Tin 1.1 PL4
Date: Thu, 28 Jan 1993 16:05:09 GMT

After a lot of messing around, I discovered that using |x| is not the same
as abs(x) in Fractint formula files.  In any case, I finally managed to get
a Fractint formula for the fuzzy logic image from the February 1993 issue
of Scientific American:

-----CUT HERE-----
fuzzy {
a=real(pixel), b=imag(pixel):
x=1-abs(a-b), y=1-abs(b-1+a), a=x, b=y, sqr(abs(a*a)+abs(b*b))<=p1
}
-----CUT HERE-----

To center this on your screen use the command corners=-2/3/2.5/-1.5

Enjoy!
From: lsonko@pearl.tufts.edu (ARISIA WAS AMAZING... LET'S DO LUNICON)
Newsgroups: bit.listserv.frac-l
Subject: Re: chaotic modelling
Date: 27 Jan 93 11:38:00 GMT
Organization: Tufts University - Medford, MA
News-Software: VAX/VMS VNEWS 1.41

In article <199301260835.AA08665@ollie.fwi.uva.nl>, dok@FWI.UVA.NL (P.J.van Dok W92) writes...
>>I have recently experimented in modelling chaotic systems in C++. The only
>>system I have had success on is the Lorenz water wheel (as displayed in
>>James Gleick's Chaos). Are there any other fairly simple physical systems
>>which exibit chaotic behavior?
> 
>I think you might try simulating some magnets on a plane, each having it's own
>positive or negative charge, after which a metal ball is hung above it (also si-
>mulated of course, hanging it above your screen wouldn't do much) which ithen is
>attracted and repelled etc. by the magnets. I saw it in the program called
> afterthe book 'Chaos'.
> 

try a pendulum with a pendulum hanging where the weight should be.  Allowing
both pendulums to swing in 360 degree arcs  (for the graphical approach)
try timing the difference between water droplets dripping from a sink
                  (experimental)

have you modeled extreme cases of Predator-Prey models?  (plug 'n' chug!)

enjoy
lee
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
X-Mailer: ELM [version 2.3 PL8]
Newsgroups: bit.listserv.frac-l
Date:         Tue, 26 Jan 1993 20:01:12 CST
From:         david fowler <dfowler@UNLINFO.UNL.EDU>
Subject:      Re: THE DIVINE MASTERS OF THE UNIVERSE-buzz off
              "MCELWRE%UWEC.bitnet@KSUVM.KSU.EDU" at Jan 26, 93 7:19 pm

I've wondered what that noise was...or is it your brains frying?
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Organization: Universidad de Costa Rica
X-Acknowledge-To: <RMAG@UCRVM2>
Newsgroups: bit.listserv.frac-l
Date:         Thu, 28 Jan 1993 10:41:15 UCR
From:         Roberto Magana <RMAG@UCRVM2.BITNET>
Subject:      Unable to get wheel.zip

I have tried to obtain water.zip twice, and the results are strange.
When I use bitftp@pucc everything appears    normal, except that after
the message that the transference has been completed, instead of saying
"file has been sent to you as .......", which is normal, the server just
 quits. Needles  to say i never got the file. Is this a bug in the server ?
 (more important) Would some kind soul send me the file directly ?
 The transcript of the transaction follows:




> ftp wuarchive.wustl.edu
> user anonymous guest
>> OPEN WUARCHIVE.WUSTL.EDU
>>> Connecting to WUARCHIVE.WUSTL.EDU 128.252.135.4, port 21
<<< 220 wuarchive.wustl.edu FTP server (Version 1.1(48) Fri Nov 20 10:29:
    15 CST 1992
>>> ) ready.
>> USER anonymous
>>> USER anonymous
<<< 331 Guest login ok, send your complete e-mail address as password.
>>> Password:
>> RMAG@pucc.Princeton.EDU
          (stuff deleted ....)

<<< 230 Guest login ok, access restrictions apply.
> binary
>> BINARY VARIABLE
>>> TYPE i
<<< 200 Type set to I.
> cd pub/MSDOS_UPLOADS/graphics
>> cd pub/MSDOS_UPLOADS/graphics
>>> CWD pub/MSDOS_UPLOADS/graphics
<<< 250 CWD command successful.
> get water.zip
>> GET water.zip WATER.ZIP.D ( REPLACE
>>> PORT 128,112,129,99,242,203
<<< 200 PORT command successful.
>>> RETR water.zip
<<< 150 Opening BINARY mode data connection for water.zip (48131 bytes).
<<< 226 Transfer complete.
<<< 48131 bytes transferred. Transfer rate 21.81 Kbytes/sec.
> quit
>> CLOSE
>>> QUIT
<<< 221 Goodbye.

 oops, i just realized that the subject is wrong.... too late to make
 changes now....

   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %                                                                  %
   %  J. R. Magaa.      <rmag@ucrvm2>  Escuela de Fisica. UCR.       %
   %                                    Costa Rica.                   %
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
X-Mailer: Mail (1.7 20feb92)
Newsgroups: bit.listserv.frac-l
Date:         Wed, 20 Jan 1993 20:14:52 EST
From:         David Ross <snakey@PRO-CYNOSURE.CTS.COM>
Subject: Re: Stuff

        What exactly do you mean by a geography?  It's z = z^2 + c, where c
is the coordinates on the real plane.  When iterated, if it passes a
certain test that shows that z is still not going off to infinity after a
set amount of iterations, that point is said to be in the mandelbrot set.
It is normal for all of those points to be colored black and the points
that eventually have 'z's that go off to infinity get colored according to
how fast they go off to infinity.  It is a very pretty set indeed.  There
are a couple of tricks that make it really fast though, and I was wondering
if anyone knows them.  Thanx.

                                              Dave
----
ProLine:  snakey@pro-cynosure
Internet: snakey@pro-cynosure.cts.com
UUCP:     crash!pro-cynosure!snakey
ARPA:     crash!pro-cynosure!snakey@nosc.mil
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
X-Envelope-to: FRAC-L@GITVM1.BITNET
X-VMS-To: IN%"FRAC-L@GITVM1.BITNET"
Newsgroups: bit.listserv.frac-l
Date:         Thu, 28 Jan 1993 12:05:00 MET
Comments:     Sent using PMDF-822 V3.0, routing is done by KUNRC1
From:         Marc <MARC@MPI.NL>
Subject:      RE: IP Address for wuarchive.wust1.edu

> Hi all,
>
> Please could someone make known the IP address for WUARCHIVE.WUST1.EDU?
> I think this would make it easier for all those who want to get the Water
> Wheel and others via FTP.
>
> Andy.

Andy, I think you misspelled the name of the machine you want---it's

    WUARCHIVE.WUSTL.EDU
                  ^- the letter 'el'

I believe someone already sent the IP-number, and
with the number you are undoubtedly able to connect, but
you might give it a shot like this.

Marc
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
X-Mailer: ELM [version 2.3 PL11]
Newsgroups: bit.listserv.frac-l
Date:         Wed, 27 Jan 1993 22:49:37 EST
From:         Regis C Phelan <phelanre@STUDENT.MSU.EDU>
Subject:      Re: FracXtra v2 Fractint Extras released!

>
> I have released v2 of my FracXtra huge collection of Fractint Extras
> (.map, .par, .l, .ifs, .frm, etc files).  the collection is available
> on wuarchive.wustl.edu in /pub/MSDOS_UPLOADS/graphics/ as 'fracxtr2.zip'
> and 'fracxtr2.txt'

How do you connect to get these files?
phelanre@student.msu.edu
Xref: sparky bit.listserv.frac-l:1365 sci.fractals:637
Organization: Penn State University
Date: Tue, 26 Jan 1993 01:22:27 EST
From: <WAJ@psuvm.psu.edu>
Newsgroups: bit.listserv.frac-l,sci.fractals
Subject: Water Wheel

Since many people have requested my Lorenz water wheel, I'm posting it on
wuarchive.wustl.edu .  If anybody has any other sites you want me to post it
to, I can do that, but wuarchive is the best choice I know of.

Bill Jester
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
X-Mailer: ELM [version 2.3 PL11]
Newsgroups: bit.listserv.frac-l
Date:         Thu, 28 Jan 1993 09:02:16 EST
From:         husch@MATH.UTK.EDU
Subject:      Re: Need info on "Phaser"
              Jan 28, 93 8:42 am

>
> Recently a student requested info on fractals and chaos of systems such as
> dripping faucets and waterfalls.  Another professor suggested I find a book
> authored by H. Kocak.  That book will deal with the software "Phaser" written
> by Kocak.
>
> "Books In Print" did not come up with the book and software package.  Can
> anyone help out with more info?
>
> Thanks.
>
> --Richard L. Bowman
>   Dept. of Physics
>   Bridgewater College
>   Bridgewater, VA  22812
>   <r.l.bowman@cescc.bridgewater.edu>
>
   Hu"seyin Kocak, Differential and Difference Equations through
   Computer Experiments, Springer-Verlag
   ISBN 0-387-96918-7
   ISBN 3-540-96918-7
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Newsgroups: bit.listserv.frac-l
Date:         Tue, 26 Jan 1993 09:17:21 EDT
From:         Manoel Cesar Valente Lopes claus <mcvs@LSI.USP.BR>
Subject:      Re: chaotic modelling

        Dear Bill!

        I am interested in seeing the wheel. Could you send to me?!
        Thanks in advance.

        Manoel Cezar

        mcvs@lsi.usp.br
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
X-Mailer: Pegasus Mail v2.2 (R4).
Newsgroups: bit.listserv.frac-l
Date:         Thu, 21 Jan 1993 12:51:28 MET
From:         "The great Jesper -'Jesper'" <NORJJ@STUD.HUM.AAU.DK>
Subject:      Re: Looking for ... found it ... Lyapunov

There's been a bit of talk 'bout Lyapunov Space:

> > The article that generated a lot of interest was:  "Leaping
> >into Lyapunov Space," A.K. Dewdney, Scientific American, Sept.,
> >1991.
>
> I saw that article, and it was very interesting. Does anyone out there
> know what values to plug into Fractint to make Lyapunovs like those?

For those of you with access to an Amiga, I can recommend the program
"Lyapunovia" (to which I am the author) on Fish Disk #784. It
includes some sample pictures and coordinates which you could then
copy into Fracint.... Or, alternatively, you could also buy an Amiga
and become a registered user of my program, well....

The article in itself does say what sequence was used for each of the
pictures. The sequence determines a basic structure of the picture;
but zooming and changing the number of iterations will always lead to
new results....

Of the pictures in the article, the only one I can spot is the first
one:
X: from 2.0 to 4.0
Y: from 2.0 to 4.0
Iterations 500 or above, probably more.

Hope that helps a bit.....

-Jesper Juul
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Return-Path: <dok@fwi.uva.nl>
X-Organisation: Faculty of Mathematics & Computer Science University of
                Amsterdam Plantage Muidergracht 24 NL-1018 TV Amsterdam The
                Netherlands
X-Phone:        +31 20 525 5200
X-Telex:        16460 facwn nl
X-Fax:          +31 20 525 5101
Newsgroups: bit.listserv.frac-l
Date:         Fri, 22 Jan 1993 09:53:19 +0100
From:         "P.J.van Dok W92" <dok@FWI.UVA.NL>
Subject: Re: Speeding up Calculation of Mandelbrot Set

Hi there!

On the topic of speeding up calculation:

As mike points out, there are two aspects to the speeding up.

>1. Try to optimize the routine that calculates the dwell of a given point.

If you have no knowledge of assembler, there are still ways of speeding things
 up a bit. When you check wether the point has escaped to infinity, do not
 calcu-
late x*x and y*y seperate, but put those values in two variables, so that you
 can re-use them for the calculation of the next x-value. a
Also, instead of :     y := 2*x*y;
do this:
                       q := x*y;
                       y := q+q+b;

An addition is much faster than a multiplication.
Also, if you dont test for escape from a circlelike border, but against a square
area, an idea from mr. Pickover, I believe, which means:

in stead of :      if x*x+y*y > 4 then ....
you get            if abs(x) >2 or abs(y) >2 then ...
you can reduce the multiplication by using:
                        x := (x+y)*(x-y) + a;

instead of the usual two squares.

I will send sth about point two as well if anybody's interested.

See Ya!

Hans van Dok.
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU