HDTenEightyP/NetNews huggingface dataset:
From: noel@reg.triumf.ca (NOEL)
Newsgroups: sci.fractals
Subject: Re: Syntax for the L-Systems part of FractInt?
Date: 9 Nov 1992 01:02 PST
Organization: TRIUMF: Tri-University Meson Facility
Distribution: world
NNTP-Posting-Host: reg.triumf.ca
News-Software: VAX/VMS VNEWS 1.41    

In article <92312.221051SRK106@psuvm.psu.edu>, Senthil Ramas Kumar <SRK106@psuvm.psu.edu> writes...
>Can somebody let me know where to find the Syntax for the L-Systems
>part of Fractint properly documented and explained? Thanks in advance.

	Well I don't know about fractint's explicit documentation for the 
L-system fractals, but I do know that L-systems in general were well explored
and developed with the LOGO language.  It was an interpeter designed to
explore such fractal geometry as hilbert and peano curves.  A good book on
this type of mathematics is "Turtle Geometry" by Harald Abelson & Andrea
DiSessa.  It develops from simple examples and leads to very complicated
explorations in this novel area of geometry.  Fractint's l-systems are
faster and their descriptive syntax is more concise but the fundamentals
are the same.
						Noel Giffin 
Newsgroups: sci.fractals
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: Interpolation & Chaotic TS
Organization: Department of Chemistry, University of Toronto
Date: Thu, 5 Nov 1992 16:48:38 GMT

In article <!7h13=#@rpi.edu> sassoj@rs6416.ecs.rpi.edu (John J. Sasso Jr.)
writes:
>    Given a chaotic time series with a fractal dimension, does anyone know of
>    any theory or whatever which relates splines to the interpolation of the
>    chaotic time series corresponding to the given fractal dimension?

     I'm not an expert, but if I understand your question, you should go
to the library and look up papers or books on nonlinear forecasting.  It
has gotten quite sophisticated in recent years so I would be surprised
if your question hasn't been answered by someone.  Most of the
literature on nonlinear forecasting includes interpolation methods as a
way of checking the validity of the forecast.

                                Good luck.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
From: jgostin@mal-s1.gatech.edu (Jill Gostin)
Newsgroups: sci.fractals
Subject: Conferences on Fractals?
Date: 11 Nov 92 20:37:39 GMT
Organization: Georgia Tech Res. Inst., Modeling & Analysis Lab


Anyone know of any upcoming conferences on fractals, or conferences
that will have some sessions devoted to fractals? I'm especially
interested in applications of fractals, of any sort.

Thanks,
jibg

-- 
Jill Butterfield Gostin                EMAIL: jgostin@mal-s1.gatech.edu
Georgia Institute of Technology, GTRI Modeling and Analysis Lab
"Happiness is excitement that has found a settling down place..."
-E.L. Konigsburg, _From the Mixed-up Files of Mrs. Basil E. Frankweiler_
Newsgroups: sci.fractals
From: noring@netcom.com (Jon Noring)
Subject: Looking for 3-D "Lake Mandelbrot" Parameters
Organization: Netcom - Online Communication Services  (408 241-9760 guest) 
Date: Thu, 12 Nov 1992 17:10:40 GMT

I have seen several 3-D renderings of the Mandelbrot set (or a mini-
mandelbrot) which can best be termed "Lake Mandelbrot".  I'd like to
get a Fractint v17.2 parameter file or files to help me generate them
on my machine.

Much thanks.

Jon Noring

-- 
=============================================================================
| Jon Noring          | noring@netcom.com        | "The dogs bark, but the  |
| JKN International   | IP    : 192.100.81.100   |  caravan moves on."      |
| 1312 Carlton Place  | Phone : (510) 294-8153   | "Pack your lunch, sit in |
| Livermore, CA 94550 | V-Mail: (510) 862-1101   |  the bushes, and watch." |
=============================================================================
"If your annual income today is $50,000, you have the same buying power as
the average coal miner did in 1949, adjusted for taxes and inflation," John
Sestina, nationally recognized Certified Financial Planner;  quoted in 1987.

------->   I VOTED FOR PEROT IN '92
------->   support UNITED WE STAND!
Organization: Penn State University
Date: Fri, 13 Nov 1992 12:51:23 EST
From: Mark J. Laufersweiler <L89@psuvm.psu.edu>
Newsgroups: sci.fractals
Subject: Re: Lorenz' Weather
 <gordon.721582896@tramp.Colorado.EDU>
 <1992Nov12.201358.3135@alchemy.chem.utoronto.ca>

In article <1992Nov12.201358.3135@alchemy.chem.utoronto.ca>,
mroussel@alchemy.chem.utoronto.ca (Marc Roussel) says:
>
>     These are indeed the Lorenz equations (as they are now known) but
>these aren't the original weather simulation equations where Lorenz
>noticed sensitive dependence on initial conditions.  Lorenz actually
>started out with some specialized version of the Navier-Stokes equation
>(a PDE) and noticed sensitive dependence in these equations under the         s
>condition
>of his weather simulation.  The Lorenz ODEs shown above are a truncation
>of the Navier-Stokes equation for the special case of (I think)
>Rayleigh-Benard convection under certain fairly restrictive conditions.
>Lorenz cooked up these equations as a simple example of what he was
>seeing in his more sophisticated weather models.
>
Barry Saltzman (a Lorenz grad student I believe) ran the experiment which is
discussed in his paper 1962 J. Atmos. Sci vol 19. Lorenz saw that there
were primarily only three active modes for R-B convection and thus started
to help generate this great field.
--
  =======================================================================
        Mark J. Laufersweiler      |  I consider the day to be a TOTAL
        l89@psuvm.psu.edu          |     loss unless I receive HELL
        laufers@psumeteo.psu.edu   |            from someone!
                                   |
From: haydenw@elp.aero.org (bill hayden)
Newsgroups: sci.fractals
Subject: Winfr173 and GIF
Date: 12 Nov 1992 21:55:21 GMT
Organization: The Aerospace Corporation
NNTP-Posting-Host: hayden.aero.org
Summary: help

Why would a normal GIF (ex NASA mars1 photo) display ok with Fractint 17.2
but not come out right (loses color?) when attempt to display it using 
Winfr173 ?
From: groot@jupiter.idca.tds.philips.nl (H. de Groot)
Newsgroups: sci.fractals
Subject: Re: Colour printing with fractint
Date: 6 Nov 92 16:02:08 GMT
Reply-To: groot@idca.tds.philips.nl (Henk de Groot)
Disclaimer: This opinion is mine alone

In <1csgr8INN9t9@agate.berkeley.edu> shirriff@sprite.berkeley.edu (Ken Shirriff) writes:

>Color printing in xfractint and fractint is broken.  If you use the
>compresseed format (with rleps=yes), it should work.  The following patch
                          ^^^^^^^^^

   I'm so sorry. Both fractint 17.1 AND 17.2 respond on the argument
   rleps=yes or 'rleps=yes' or "rleps=yes" with a humming sound and the
   message:
   Quote:	

   *** Error during startup:

   Oops. I couldn't understand the argument:
     rleps=yes

   (see the Startup Help screens or documentation for a complete
    argument list with descriptions)

   Unquote.

   What am I doing wrong. Is there a newer version that works with this
   option?

   There is no word about 'rleps' in the documentation either.

Kind Regards,

Henk.

--
  /   /            Henk de Groot      | Dep.: IISS-SE (System Management)
 /---/ __  __  /   Loc: V2/A14        | Mail: groot@idca.tds.philips.nl
/   / (-_ / / /(   Tel: +31 55 432104 | Digital Equipment Enterprise bv
Disclaimer: I only speak for myself, not for my employer.
Newsgroups: sci.fractals
From: mccasal@nyx.cs.du.edu (Massimo Casal)
Subject: julia sets of c*e^z
Organization: Nyx, Public Access Unix (sponsored by U. of Denver Math/CS dept.)
Disclaimer1: Nyx is a public access Unix system run by the University of
Disclaimer2: Denver for the Denver community.  The University has neither
Disclaimer3: control over nor responsibility for the opinions of users.
Date: Wed, 11 Nov 92 18:23:09 GMT

Hello!!  
when must i stop the iteration when i calculate the julia set of c*e^z?
when the real part is > value?or when the modulus is >value?

Thanx
Massimo Casal



Massimo Casal
Viale Volontari della Liberta` 36/2
33100 Udine
Italy

email:casal@udmi5400.cineca.it
From: alain@elevia.uniforum.qc.ca (W.A.Simon)
Newsgroups: sci.fractals
Subject: something for the stone soup
Date: 05 Nov 92 16:23:49 EST

Here is a proposal for another way of picking colours in
escape orbit type fractals:

For every pixel
    If NOT coloured
        Do Until ( maxiter OR escaped )
            [Begin Proposal]
            calculate distance of calculated point z(n+1) from z(n)
            set colour of z(n+1) according to calculated distance
            [End Proposal]
        Done
    EndIf
EndFor

This is essentially an escape velocity representation of
the orbits.  Yet another variation would consist in giving
all pixels in the orbit the same colour as the last pixel
of the orbit.

There is also an interesting way of generating the image
in slow motion:

Do Until ( maxiter )
    For every pixel
        If ( ( NOT escaped ) AND ( NOT coloured ) )
            perform just one iteration
            [escape velocity colouring would fit here]
        EndIf
    EndFor
Done

Enjoy...



--
 Alain
 [ ... usual disclaimer... ]
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.fractals
Subject: Re: Boundary of Mandelbrot set
Date: 6 Nov 1992 14:39:26 -0500
Organization: The Ohio State University, Dept. of Math.
Distribution: na
NNTP-Posting-Host: function.mps.ohio-state.edu
Keywords: circle, characterization, separation properties


The boundary of the M-set is not a simple closed curve.  For example,
the neck at c=-3/4 disconnects the boundary (in fact the whole set).
The open question asks whether this boundary is locally connected.
-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
From: scavo@cie.uoregon.edu (Tom Scavo)
Newsgroups: sci.fractals
Subject: Re: julia sets of c*e^z
Date: 13 Nov 92 04:42:11 GMT
Article-I.D.: nntp.1992Nov13.044211.8466
Organization: University of Oregon Campus Information Exchange

In article <1dro9cINN8rb@agate.berkeley.edu> shirriff@sprite.berkeley.edu (Ken Shirriff) writes:
>In article <1992Nov11.182309.8811@mnemosyne.cs.du.edu> mccasal@nyx.cs.du.edu (Massimo Casal) writes:
>>when must i stop the iteration when i calculate the julia set of c*e^z?
>>when the real part is > value?or when the modulus is >value?
>
>The stopping limit for c*e^z is problematic, since an extremely large value
>of z can get mapped back to something small.  The second problem is that
>your floating point can overflow very quickly.  The usual stopping point is
>real part > large value (note: not abs(real part)), since this implies the next
>iteration will be extremely large.  The disadvantage is that you will stop
>for some large values where you shouldn't.  The visual appearance is that
>the many thin petals will suddenly clump together into one thick petal, when
>they should remain as thin petals.

But apparently there is justification for this algorithm.  See

   Marilyn B. Durkin.  The accuracy of computer algorithms in
   dynamical systems.  _International J. of Bifurcation and Chaos_
   1(3), 1991.

for details.  Or you might want to contact Lynne directly at
lynne@math.bu.edu.

-- 
Tom Scavo
scavo@cie.uoregon.edu
From: henebry@matt.ksu.ksu.edu (Geoffrey M Henebry)
Newsgroups: sci.fractals
Subject: books detailing quaternions?
Date: 10 Nov 1992 16:47:05 -0600
Organization: Kansas State University
NNTP-Posting-Host: matt.ksu.ksu.edu
Keywords: quaternions

greetings! i'm trying to find readable detailed information on quaternions and
their uses.  suggestions?  thanks much! -- geoff         
+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ 
 Geoffrey M. Henebry                voice: (913) 532-7997   fax: (913) 532-6653 
 Division of Biology/Ackert Hall    internet:   gmh@andro.konza.ksu.edu         
 Kansas State University                        henebry@matt.ksu.ksu.edu        
 Manhattan, KS 66506 USA            Heraclitus: PANTA HREI                      
Newsgroups: sci.fractals
From: ara@wam.umd.edu (Ford Prefect)
Subject: Request for Info on software.
Organization: University of Maryland, College Park
Date: Tue, 10 Nov 1992 19:24:53 GMT

I just got a book called image lab, written by the same people
who did fractint and Fractal Creations,
on one of the back pages it mentions some software called
C Render
Worm
Lissajous
and something else,
a disk of these for some price $20 or something

I have no money left since I purchased the book, I want to know
if these things are available for ftp from somewhere
I have an old version of lissajous as far as I know, so the most
current versions would be appreciated.

-ara
ara@wam.umd.edu

Newsgroups: sci.fractals
From: scavo@cie.uoregon.edu (Tom Scavo)
Subject: Re: Is this thing a fractal?
Keywords: dimension.
Organization: University of Oregon Campus Information Exchange
Date: Thu, 5 Nov 92 18:10:57 GMT

In article <1816@spam.ua.oz> ahanysz@spam.ua.oz (Alexander Hanysz) writes:
>
>Now I'm going to ask that eternally difficult question: WHY?  The
>Mandelbrot set is such a complicated object, how do we know that its
>boundary has topological dimension 1?

A proof was given earlier in this thread by Gerald Edgar.

>More fundamentally, does anyone know a nice _definition_ of topological
>dimension?  It's hard to argue when you don't know what the terms mean.
>All I've been told about topological dimension is "a line has dimension
>1, a surface has dimension 2, a volume..."  I have yet to see a formal
>definition.

I suspect that others have the same question so here goes:

   A set has topological dimension  0  if every point has arbitrarily
   small neighborhoods whose boundaries do not intersect the set.

   A set  S  has topological dimension  k  if each point in  S  has
   arbitrarily small neighborhoods whose boundaries meet  S  in a
   set of dimension  k-1 , and  k  is the least nonnegative integer
   for which this holds.

See, for example, Section 14.5 in Devaney's _A First Course in Chaotic
Dynamical Systems_.  (Does anyone know of a better reference?)

For instance, the rationals have topological dimension  0  since the
boundary of a disk with irrational radius fails to intersect the
rationals (that is, the sum of a rational and an irrational is
irrational).  The irrationals also have topological dimension  0 ,
I believe.  Suppose it were true that (1) if  A  is a subset of  X ,
then the  t-dim A <= t-dim X ; and (2) for any  A  in  R^n , t-dim A
= n  if and only if  A  contains a nonempty open subset of  R^n .
Then by (1) the irrationals have topological dimension no bigger than
1.  But by (2) they can not have topological dimension equal to  1
since they contain no open subset.  Hence, they have topological
dimension  0 .  (Can anyone think of a simpler proof?)

Here's another example.  Consider the fractal generated by the 
following geometric transformation:

                                  _____
                                 |     |
                                 |     |
     ---------------   -->   -----     -----

Each leg of this "hat" is one-third the length of the original line
segment.  Now the fractal dimension of the resulting image is
log 5 / log 3 , but the topological dimension is  1  since any disk
intersects the curve at a set of discrete points having topological
dimension  0 .  (There's a related exercise in Devaney that I can't
solve:  Can a fractal that is totally disconnected, with topological
dimension  0 , have a fractal dimension larger than  1 ?)

-- 
Tom Scavo
scavo@cie.uoregon.edu
From: schultrj@NeXTwork.Rose-Hulman.Edu (Richard J Schultz)
Newsgroups: sci.fractals
Subject: NeXT Fractint
Date: 11 Nov 1992 06:29:47 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: schultrj@NeXTwork.Rose-Hulman.Edu (Richard J Schultz)
NNTP-Posting-Host: o233-16.nextwork.rose-hulman.edu

Is there any version of FractInt for the NeXT either available or planned?   
All I have been able to find is the XWindows version, which I have not yet  
been able to compile properly on the NeXT.  Any help is appreciated...

Rick Schultz
Newsgroups: sci.fractals
From: ddixon@nyx.cs.du.edu (David Dixon)
Subject: Mappings with singular points
Organization: Nyx, Public Access Unix @ U. of Denver Math/CS dept.
Date: Sun, 8 Nov 92 23:41:55 GMT

Is anybody aware of any differences between mappings with and without
singular points?  For example, say I have a map x[n+1] = f(x[n]), where
df/dx is singular at some point.  Does this show any behavior not seen
in maps involving analytic functions?  References would be greatly
appreciated.

				Dave
From: aalpern@hamp.hampshire.edu
Newsgroups: sci.fractals
Subject: Fractal and Chaotic music, et al...
Date: 9 Nov 92 21:02:53 GMT
Organization: Hampshire College

Does anyone know of where one can obtain information, or find discussions,
concerning musical applications of fractals, the 1/f nature of music, source
code(preferably C, but anything will do), random number generation using
fractal principles, chaos theory, and musical applications of chaotic systems?
I would particularly like to know if there are any source code examples of
anything related to any of these topics. Also, does anyone have info they
would like to share?

Thanks for your help!
	- Adam Alpern




-- 
Adam Alpern			* "All that is gold does not glitter, not all  *AAlpern@hamp.hampshire.edu	* those who wander are lost." - JRR Tolkien    *				* "When I look in the mirror I see the days to *				* come, and my face is just a trace of where   *				* I'm coming from." - Ani DiFranco	       *
From: shirriff@sprite.berkeley.edu (Ken Shirriff)
Newsgroups: sci.fractals
Subject: Re: julia sets of c*e^z
Date: 11 Nov 1992 19:52:12 GMT
Organization: University of California, Berkeley
NNTP-Posting-Host: hijack.berkeley.edu

In article <1992Nov11.182309.8811@mnemosyne.cs.du.edu> mccasal@nyx.cs.du.edu (Massimo Casal) writes:
>when must i stop the iteration when i calculate the julia set of c*e^z?
>when the real part is > value?or when the modulus is >value?

The stopping limit for c*e^z is problematic, since an extremely large value
of z can get mapped back to something small.  The second problem is that
your floating point can overflow very quickly.  The usual stopping point is
real part > large value (note: not abs(real part)), since this implies the next
iteration will be extremely large.  The disadvantage is that you will stop
for some large values where you shouldn't.  The visual appearance is that
the many thin petals will suddenly clump together into one thick petal, when
they should remain as thin petals.

Ken Shirriff				shirriff@sprite.Berkeley.EDU
Newsgroups: sci.fractals
From: ddixon@nyx.cs.du.edu (David Dixon)
Subject: New routes to chaos
Organization: Nyx, Public Access Unix @ U. of Denver Math/CS dept.
Date: Sun, 8 Nov 92 23:46:55 GMT

Are there any recently discovered routes to chaos?  My list is
	1) Period doubling (or n-tupling)
	2) Intermittency
	3) Hopf bifurcations

I'm aware that there are variations on each of the above (i.e., Type I
and Type II intermittency).  I'm looking for anything radically different.
Thanks for any info.

				Dave
Newsgroups: sci.fractals
From: twegner@mwunix.mitre.org (Timothy Wegner)
Subject: Re: Can Resolution in Fractin
Organization: The MITRE Corporation
Date: Tue, 10 Nov 1992 14:31:38 GMT

bert.tyler@satalink.com (Bert Tyler)  writes:

>JN>I'm in the process of producing high quality fractal prints/posters using
>JN>Fractint v17.2.  To maintain resolution for large posters, I'd like to exceed
>JN>the maximum resolution of 2048x2048 in Disk/RAM Mode.
>JN>Can this be done by a simple tweaking of the source code, or is it a much more
>JN>involved programming job to do this?

I'll bet it's not too hard to make software that
--
Tim Wegner     Fractint co-author
Internet: twegner@mwunix.mitre.org  Compuserve: 71320.675@compuserve.com
From: bert.tyler@satalink.com (Bert Tyler)
Newsgroups: sci.fractals
Subject: Gif to postscript
Date: 13 Nov 92 10:02:00 GMT
Reply-To: bert.tyler@satalink.com (Bert Tyler)
Organization: Datamax/Satalink Connection * Ivyland, PA (215) 443-9434

GE>I recently got FRACTINT and have been trying out some of its wonderful
GE>features. I have managed to generate .gif files of the images, but when I
GE>use my giftops coverter, it complains about the GIF version being 89A
GE>(rather than 87A?). Do earlier versions of FRACTINT have a different
GE>gif type, or does someone know where I can get an appropriate giftops
GE>converter for FRACTINT output. Please e-mail me at gathe@ul.ie

Eugene, you can force Fractint to use the older-style 87a version
of GIF files with the "gif87a=yes" command-line option.  Note, though,
that GIF files saved this way cannot be restored as fractal images,
because the old GIF87a standard did not include the application-specific
extension block that Fractint uses to squirrel away its fractal-specific
information.

                   Bert Tyler   (bert.tyler@satalink.com)
---
 . DeLuxe./386 1.25 #343sa . Did you expect mere proof to sway my opinion?
From: shirriff@sprite.berkeley.edu (Ken Shirriff)
Newsgroups: sci.fractals
Subject: Re: xfractint
Date: 7 Nov 1992 01:12:09 GMT
Organization: University of California, Berkeley
NNTP-Posting-Host: hijack.berkeley.edu

In article <OBRY.92Nov6171532@cheesesteak.flash.bellcore.com> obry@flash.bellcore.com (Pascal Obry) writes:
>I'am unable to use the batch mode with xfractint-1.07.

I tried it and it looks like the batch mode is indeed broken in xfractint.
I'll try to fix it when I get the time, but if anyone else fixes it first,
please let me know.

Ken Shirriff				shirriff@sprite.Berkeley.EDU
From: shirriff@sprite.berkeley.edu (Ken Shirriff)
Newsgroups: sci.fractals
Subject: Re: Mappings with singular points
Date: 9 Nov 1992 00:31:04 GMT
Organization: University of California, Berkeley
NNTP-Posting-Host: sabotage.berkeley.edu

In article <1992Nov8.234155.14813@mnemosyne.cs.du.edu> ddixon@nyx.cs.du.edu (David Dixon) writes:
>Is anybody aware of any differences between mappings with and without
>singular points?  For example, say I have a map x[n+1] = f(x[n]), where
>df/dx is singular at some point.  Does this show any behavior not seen
>in maps involving analytic functions?

I've done some experimenting with maps x[n+1] = x^(-n)+C.  The main
difference I noted with this map is that the map doesn't diverge to
infinity.  (I.e. infinity gets mapped back C, as opposed to the mandelbrot
set, where infinity is mapped to infinity.)

I guess rational polynomial functions (i.e. P(x)/Q(x)) have singular points.
Their behavior isn't very different from polynomial functions, although
there are a few differences (I can't remember the details).

A good reference for rational polynomial fractals is:
%T Complex Analytic Dynamics on the Riemann Sphere
%A P. Blanchard
%J Bull. of the Amer. Math. Soc
%V 11
%N 1
%D July 1984
%P 85-141

(I highly recommend that paper for anyone interested in the mathematical
side of fractals.)

Ken Shirriff				shirriff@sprite.Berkeley.EDU
Newsgroups: sci.fractals
Subject: Syntax for the L-Systems part of FractInt?
From: Senthil Ramas Kumar <SRK106@psuvm.psu.edu>
Date: Sat, 7 Nov 1992 22:10:51 EST
Organization: Penn State University

Can somebody let me know where to find the Syntax for the L-Systems
part of Fractint properly documented and explained? Thanks in advance.

SRK
PSUVM
========
From: shirriff@sprite.berkeley.edu (Ken Shirriff)
Newsgroups: sci.fractals
Subject: Re: Colour printing with fractint
Date: 6 Nov 1992 22:58:55 GMT
Organization: University of California, Berkeley
NNTP-Posting-Host: hijack.berkeley.edu

In article <groot.721065728@jupiter.idca.tds.philips.nl> groot@idca.tds.philips.nl (Henk de Groot) writes:
>   Both fractint 17.1 AND 17.2 respond on the argument
>   rleps=yes or 'rleps=yes' or "rleps=yes" with a humming sound and the
>   message:
>   *** Error during startup:

I guess the rleps option didn't get into fractint yet, so ignore my previous
suggestion of using rleps to fix the color printing problem.

Ken Shirriff			
Newsgroups: sci.fractals