home *** CD-ROM | disk | FTP | other *** search
- From: owner-fractint-digest@lists.xmission.com (fractint-digest)
- To: fractint-digest@lists.xmission.com
- Subject: fractint-digest V1 #532
- Reply-To: fractint-digest
- Sender: owner-fractint-digest@lists.xmission.com
- Errors-To: owner-fractint-digest@lists.xmission.com
- Precedence: bulk
-
-
- fractint-digest Thursday, January 18 2001 Volume 01 : Number 532
-
-
-
-
- ----------------------------------------------------------------------
-
- Date: Mon, 15 Jan 2001 13:51:16 -0000
- From: "Andrew Coppin" <orphi69@hotmail.com>
- Subject: (fractint) FOTDs
-
- Just got back, read all my email. Just wanted to comment on the best
- FOTDs...
-
- Impossible Fractal: Very unusual and interesting!
- Four Flying Wings: Lovely colours. Very nice!
- FMOD Midget: Good-looking image. Kinda reminds me of certain WinAmp skins...
- Subliminal Fractal: Jim, you need to get out more often.
- The Budding Midget: I really like this one!
- Challengine Midget: Ever seen crystals under a polarized light microscope?
-
- Thanks Jim, good work!
-
- Andrew.
-
- _________________________________________________________________________
- Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.
-
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- Date: Mon, 15 Jan 2001 09:05:11 EST
- From: JimMuth@aol.com
- Subject: (fractint) C-FOTD 15-01-01 (A Fractal Blast [7])
-
- Classic FOTD -- January 15, 2001 (Rating 7)
-
- Fractal visionaries and enthusiasts:
-
- Today's FOTD is late. My alibi: I got caught up in the football
- excitement as the Ravens won the championship. My restitution:
- a 7-rated above-average image, which for some vague reason I
- have named "A Fractal Blast".
-
- It's one of those all-inside images that takes advantage of the
- fmod inside fill, which appears as today's FOTD. The formula
- behind the image is number 6 in my series of 12 MandNewt
- formulae, which are variations of the ikenaga function, which
- remains kind of a mystery.
-
- At near 18 minutes, the parameter file is slow, but due to the
- lateness of this parameter posting, the GIF image file will be
- posted to:
-
- alt.binaries.pictures.fractals
-
- in only 4 hours.
-
- The image will also be available soon on the following web sites:
-
- <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
-
- <http://home.swbell.net/sdboyd56/fotd/>
-
- The fractal weather was partly sunny and 45 degrees F (7C). The
- fractal cats enjoyed the pleasant conditions.
-
- I had intended to philosophize today. Obviously, I did not.
- But there's no rush to get myself into trouble with my
- controversial opinions. I'll keep trying to make my insights
- public until I succeed. Until next time, take care, and be
- happy.
-
-
- Jim Muth
- jamth@mindspring.com
-
-
- START 20.0 PAR-FORMULA FILE================================
-
- A_Fractal_Blast { ; time=0:17:40.34 -- SF5 on a P200
- reset=2001 type=formula formulafile=mandnewt.frm
- formulaname=MandNewt06 passes=1
- center-mag=1.20469/1.63474/0.1947566/1/-2.5
- params=-0.23/-0.63/0.28/-0.59/0.48/0.76 float=y
- maxiter=500 bailout=25 inside=fmod proximity=20
- logmap=yes symmetry=none periodicity=0
- colors=0002AQmQtmQtmQtmQtmQrmPrmPrmPrkPqkPqiPrkOqkOq\
- kNo<3>kLnkLnjLnjLnjLn<2>jJmjJmjIk<2>jIkjHkhJjhIjhGjh\
- GjhFh<2>hFhhFhhDghDggDggDggCe<2>gCegCegAdgAdgAdgAdeD\
- ceCceBceBce8ceBae7ae7ae7ae5`<2>d5`d5`d4Zd4Zd4Zd4Zd2Y\
- <2>d2Ye1Zd2Yd4Yd5Yd7Wd8WdAWcCVcCVcDVcFTcGTcITaJSaLSa\
- LSaMQaOQ<2>`QP`RP`TO`SO`VOZWMZYM`ZM<2>dcIifGkgFljDml\
- Csk1tn2tk2rk2rm2rk2qk4qj4qj4oh4<2>ng5ng5ne5me5md5md5\
- kc7kc7ka7ja7ja7j`7h`8hZ8hZ8gY8gY8gW8eWAeWAeVAdVAdTAd\
- TAcSCcSCcQCaQC<2>`PD`ODZODZMDZMDYLFYLFYJFWJFWIFWIFVI\
- GVGGVGGTFGTFGTDGSDISCISCIQCIQAIQAIP8JP8JP7IO7HO5GO5F\
- M4GM4GM4GL2GL2GL1FJ1FJ0EJ0D<2>I0CI0CG0C<3>F0CF0CD0C\
- <2>C0CC0CA0CA0C80C<3>70C70C50E50E50E50E<3>45F47F4AG2\
- CH<3>2IM2JN1LO1MP1OQ1QS1SS0TSnVq<2>nVsnVsoWunVsnVsnV\
- snVsnTr<3>nTrnSqlSqkSqkSq
- }
-
- frm:MandNewt06 {; Jim Muth
- z=c=(pixel*p1):
- a=z^3+(c-p2)*z-c
- b=p3*z^2+c-1
- z=z-1*a/b
- .000000000000000000000000000001 <= |a|
- }
-
- END 20.0 PAR-FORMULA FILE==================================
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- Date: Mon, 15 Jan 2001 07:10:48 -0800
- From: "Diana L. Dubel" <dldubel@earthlink.net>
- Subject: RE: (fractint) Question on the Mandelbrot Fractal
-
- Dr. Freed,
-
- Thank you for your enthusiastic response. I appreciate it!
-
- I am currently studying "Chaos and Fractals" by Peitgen, and Mandelbrot's
- "Fractal Geometry of Nature".
-
- I am not sure that I have time to look into programming books, as I am
- starting Master's classes this month at San Jose State University in
- Mathematics. I have been reviewing Linear Algebra, and Real Analysis.
-
- It has been 25 years since I studied Math, and I am looking at fractals as
- one facet of the broad spectrum of the whole subject.
-
- Thanks again,
-
- Diana
-
- - -----Original Message-----
- From: DeBow Freed [mailto:bmc1@airmail.net]
- Sent: Sunday, January 14, 2001 8:32 AM
- To: Diana L. Dubel
- Subject: Re: (fractint) Question on the Mandelbrot Fractal
-
-
- One last comment: your questions (example attached) about the inner workings
- of
- the Fractint code, are excellent. They suggest that you would also benefit
- from
- some focussed reading about computer programming for fractals in general,
- about
- which several good books exist. Has anyone suggested them to you?
-
- My own experience was that it was almost impossible to understand the subtle
- inner workings of Fractint, UltraFract or any of the rest of them without
- first
- doing the equivalent of reading a chapter or two of a Comp Sci 100/200
- textbook.
-
- What is your educational background? I could also suggest a few such
- chapters
- which are available on-line in ComSci courses at Stanford, MIT, Duke or Rice
- University.
-
- DeBow Freed
-
- "Diana L. Dubel" wrote:
-
- > Note than in my message above, "l" is the letter L.
- >
- > So, the paragraph below---
- >
- > > Or does it do a computation of the encirclement set? In that case it
- > would
- > > determine a limit as "l" approaches infinity of the log(base2) of the
- > > modulus of z sub l, over 2^{l}, and check to see if this is less than
- 2^k,
- > z
- > > sub 0 = c.
- >
- > might be written as---
- >
- > > Or does it do a computation of the encirclement set? In that case it
- > would
- > > determine a limit as "L" approaches infinity of the log(base2) of the
- > > modulus of z sub L, over 2^{L}, and check to see if this is less than
- 2^k,
- > z
- > > sub 0 = c.
- >
- > -----Original Message-----
- > From: owner-fractint@lists.xmission.com
- > [mailto:owner-fractint@lists.xmission.com]On Behalf Of Diana L. Dubel
- > Sent: Saturday, January 13, 2001 1:58 PM
- > To: Fractint@Lists. Xmission. Com
- > Subject: (fractint) Question on the Mandelbrot Fractal
- >
- > Math and Fractal groupies,
- >
- > I am trying to understand the guts of computation of values in the
- > Mandelbrot set, and am a little confused.
- >
- > I have seen printout's of the computer computation of values for the
- > Mandelbrot set.
- >
- > For example;
- >
- > z(0) = c = pixel;
- > z(n+1) = z(n)^2 + c
- > bailout = 4
- > etc.
- >
- > Does the computer pick a pixel point on the complex plain and square it,
- add
- > c, [repeat many times], and determine if it is less than 4, for example?
- >
- > Or does it do a computation of the encirclement set? In that case it
- would
- > determine a limit as "l" approaches infinity of the log(base2) of the
- > modulus of z sub l, over 2^{l}, and check to see if this is less than 2^k,
- z
- > sub 0 = c.
- >
- > I have studied Chapter 14 in "Chaos and Fractals" in detail, but am not
- > understanding some of the applications.
- >
- > Thanks,
- >
- > Diana
- > ========================================
- > Diana L. Dubel :-)
- >
- > E-mail - - - dldubel@earthlink.net
- >
- > --------------------------------------------------------------
- > Thanks for using Fractint, The Fractals and Fractint Discussion List
- > Post Message: fractint@lists.xmission.com
- > Get Commands: majordomo@lists.xmission.com "help"
- > Administrator: twegner@fractint.org
- > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
- >
- > --------------------------------------------------------------
- > Thanks for using Fractint, The Fractals and Fractint Discussion List
- > Post Message: fractint@lists.xmission.com
- > Get Commands: majordomo@lists.xmission.com "help"
- > Administrator: twegner@fractint.org
- > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
-
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- Date: Mon, 15 Jan 2001 22:17:22 +0100
- From: "=?iso-8859-1?B?UHVza+FzIElzdHbhbiBqci4=?=" <pataki8@matavnet.hu>
- Subject: Re: (fractint) Fw: Higher resolution
-
- Have you tried UNIVBE? It fixed me a VESA problem (rubbish on screen) with
- another program. I could mail it if you want. It's about 45 kB.
-
-
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- Date: Mon, 15 Jan 2001 13:28:00 -0800
- From: Kennan C Herrick <kcha1@juno.com>
- Subject: Re: (fractint) Fw: Higher resolution
-
- Hi-
-
- No, I haven't. Could you send it via email? I'd appreciate trying it.
-
- Thanks-
-
- Ken Herrick
-
- On Mon, 15 Jan 2001 22:17:22 +0100
- "=?iso-8859-1?B?UHVza+FzIElzdHbhbiBqci4=?=" <pataki8@matavnet.hu> writes:
- > Have you tried UNIVBE? It fixed me a VESA problem (rubbish on screen)
- > with
- > another program. I could mail it if you want. It's about 45 kB.
- >
- >
- >
- > --------------------------------------------------------------
- > Thanks for using Fractint, The Fractals and Fractint Discussion List
- > Post Message: fractint@lists.xmission.com
- > Get Commands: majordomo@lists.xmission.com "help"
- > Administrator: twegner@fractint.org
- > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ________________________________________________________________
- GET INTERNET ACCESS FROM JUNO!
- Juno offers FREE or PREMIUM Internet access for less!
- Join Juno today! For your FREE software, visit:
- http://dl.www.juno.com/get/tagj.
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- Date: Mon, 15 Jan 2001 23:03:13 EST
- From: JimMuth@aol.com
- Subject: (fractint) C-FOTD 16-01-01 (Mandelbrot Specimen [7])
-
- Classic FOTD -- January 16, 2001 (Rating 7)
-
- Fractal visionaries and enthusiasts:
-
- For some strange reason, today's fractal image reminds me of a
- specimen on a microscope slide, giving me more than enough
- reason to name the picture "Mandelbrot Specimen". The rating of
- 7 may be a bit liberal, but with its striking hazy blue
- atmosphere, the image is definitely at least a little above
- average.
-
- The iterated formula adds a tiny bit of Z^(-141.42) to a far
- larger portion of Z^(-1.4142) before adding (1/C). The
- resulting teardrop-shaped parent fractal at first appears to
- have x-axis symmetry. This apparent symmetry is an illusion.
- At greater depths, the positive and negative halves are entirely
- different.
-
- The most obvious critical area of the teardrop is at the blunt
- east end. But today's scene lies not in the most obvious main
- arm, but rather deep in a tiny hole in a minor lobe just north
- of the main arm. The sharper west end of the parent fractal
- also has interesting areas, which I have not yet touched and may
- never touch. After all, I've got an infinity of other infinite
- fractals to explore and not quite an eternity in which to
- explore them.
-
- The 1-1/2 minute render time of the parameter file is reasonable
- enough for today's relatively easy image. For those with more
- patience, the GIF image file will be posted in 16 hours to
- Usenet at:
-
- alt.binaries.pictures.fractals
-
- and in an hour or so to:
-
- <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
-
- and:
-
- <http://home.swbell.net/sdboyd56/fotd/>
-
- The fractal weather today was cold, cloudy, foggy and drizzly.
- Combined with a temperature of 43F (6F), it kept the fractal
- cats indoors snug in their beds by the radiator.
-
- For now I see it's time to shutter-up the fractal shoppe and
- call it a night. Until next time, take care, and fractals make
- life wonderful.
-
-
- Jim Muth
- jamth@mindspring.com
-
-
- START 20.0 PAR-FORMULA FILE================================
-
- MandelbrotSpecimen { ; time=0:01:23.77 -- SF5 on a P200
- reset=2001 type=formula formulafile=critical.frm
- formulaname=MandelbrotMix4 function=recip passes=1
- center-mag=+2.413788574630565/+0.191409102126881/3.2\
- 20006e+011/1/-87.501/0.001 params=100/-1.4142/1/-141\
- .42/-0.98/300 float=y maxiter=272 inside=0 logmap=18
- symmetry=none periodicity=10
- colors=000Cef<3>HTaIQ`05KKKZ05KMEXWVcirorzzzuwlgt<2>\
- jHyj8zgAx<6>THjRIhOJf<2>IM`GN_FMY<6>BLPBLOALM<3>8LH8\
- LQ7WS7YUD`W<2>ULa_KceLejMgiNi<3>fSteTweUz<2>cXz<3>N`\
- zIazEbzAcz6dzXez<3>zhz<7>jhz<4>`hz<5>khzmhzohz<3>vhz\
- <3>Ghz<5>UhzXhzZhz<3>ghz<3>0hz<6>HhzKhzMhz<3>Vhz<3>J\
- hzHhzNhz<3>ghz<3>PhzLhzGhz<2>3hz<2>Khz<9>DhzChzBhz\
- <3>9hz<7>ahzehzhhz<3>vhz<4>whzwhzwhz<3>whz<8>chzahzZ\
- hz<3>Rhz<3>ehzhhzlhz<2>vhz<2>Fhz<3>`hzehzjhzFhzahzxh\
- z<3>PhzHhzIhz<3>LhzMhzMhz<2>qhz<2>ihz
- }
-
- frm:MandelbrotMix4 {; Jim Muth
- a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
- g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
- k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
- z=k*((a*(z^b))+(d*(z^f)))+c,
- |z| < l
- }
-
- END 20.0 PAR-FORMULA FILE==================================
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- Date: Tue, 16 Jan 2001 21:52:33 EST
- From: JimMuth@aol.com
- Subject: (fractint) C-FOTD 17-01-01 (Fractal of Nowhere [5])
-
- Classic FOTD -- January 17, 2001 (Rating 5)
-
- Fractal visionaries and enthusiasts:
-
- Today's image, as do so many of my recent fractal images,
- features a scene in a fractal created by a whimsical formula:
- - -0.4(Z^2)-2(Z^(-2))+(1/C). This formula draws a Mandeloid so
- grossly distorted that the period-12 buds are larger than the
- period-2 bud, which is almost lost. Today's scene lies on the
- north shore of the main bay, between the period-12 and period-13
- buds.
-
- After studying the image for a few minutes and finding no
- satisfactory name, I thought to myself that the naming process
- was going nowhere. I immediately had my name -- "Fractal of
- Nowhere". Despite, or perhaps because of all its green and
- purple, I could rate the picture no higher than a 5.
-
- With a render time of 3-3/4 minutes, running the parameter file
- is marginally the best way of enjoying, (or disparaging), the
- image. The least efficient way to view the image is to wait 15
- hours and download the GIF image file from the Usenet binary
- group:
-
- alt.binaries.pictures.fractals
-
- A far better way to view the image is to go to Paul Lee's web
- site at:
-
- <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
-
- or Scott Boyd's web site at:
-
- <http://home.swbell.net/sdboyd56/fotd/>
-
- and download the image from one of these sources.
-
- Today's partly sunny sky and mild temperature of 45F (7C) was
- ideal for fractal cats, but a brisk wind kept them skittish,
- limiting their outdoor adventure to a few minutes. They showed
- their frustration by getting into a spat, which left Thomas with
- a nicked ear and earned Tippy a claw trimming. All is now well
- however, since they made up and washed each other's faces soon
- after their spat.
-
- For now it's lights out and shut-down time in the old fractal
- shoppe. Until tomorrow, take care, and to lose weight, exercise
- with a fractal.
-
-
- Jim Muth
- jamth@mindspring.com
-
-
- START 20.0 PAR-FORMULA FILE================================
-
- Fractal_of_Nowhere { ; time=0:0X:XX.XX -- SF5 on a P200
- reset=2001 type=formula formulafile=critical.frm
- formulaname=MandelbrotMix4 function=recip passes=1
- center-mag=+11.46191326673826000/+12.729870818548550\
- 00/111.2787/1/162.499 params=0.2/2/1/-2/-3/0 float=y
- maxiter=1500 inside=0 logmap=52 periodicity=10
- colors=000K09I0BL0CM0EN0H<3>U0NW0PY0R_0T`0W<3>f2ah3c\
- j3ek3f<3>Z9XWBUSBSPCPLENKFKHHIEIFBIE8KB5L92N60P50P30\
- R20U1<4>1e01h01j02n02p02s02u00q50pR0pR0qR0qP0sP0sP0s\
- P0uP0uP0wP0wN0yN<3>0zN0zN0zL0zL0zI0zL<7>0zK0zK0zK0zK\
- 0zI<3>0zI0zI0z00z00z00u00s00s00s00s00u00u00u00u00w00\
- w00w00y0<3>0z20z20z20z30z30z30z5<3>0z60z60z60z8<3>0z\
- 90z90zB<3>0zC0zC0zE<3>0zF0zF0zH<3>0zI0zL0zU0za0uj0ps\
- 0jw0fw1fw1fw1fu1hu1hu0hu0hs0hs0js0js0jq0jq0lq<2>0lp0\
- lp0nn0nn0nn0nn0pl0pl0pl0pl0pj0qj0qj0qh0qh0sh0sh0sf0s\
- f0sf0uf0ue0ue0ue0we0wc0wc0wc0wc0ya<3>0z`0z`0z`0zZ0zZ\
- 0zZ0zZ0zX<3>0zW0zW0zW0zU0zU0zU0zU0zS<3>0zR0zR0zR0zR0\
- zP0zP0zP0zN0zN0zN0zN0zL<4>0zK0zK0zK0zI0zI0zI0zK<10>0\
- zL
- }
-
- frm:MandelbrotMix4 {; Jim Muth
- a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
- g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
- k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
- z=k*((a*(z^b))+(d*(z^f)))+c,
- |z| < l
- }
-
- END 20.0 PAR-FORMULA FILE==================================
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- Date: Thu, 18 Jan 2001 08:21:48 -0500
- From: Lee Skinner <LeeHSkinner@compuserve.com>
- Subject: (fractint) FOTD Mania
-
- While waiting for today's FOTD, I went to Google and typed in "FOTD". Su=
- re =
-
- enough, Paul's Jim Muth FOTD popular website was right at the top of the =
-
- list. But other sites returned (in this order) included:
-
- Friends of Traditional Dance
- Fruit of the Day
- Friends of the Dragon Webring
- Font of the Day
- Fact of the Day
- Flung of the Day
- Friend(s) of the Devil
- Fear of the Dark
- Foo of the Day
- Flower of the Day
- Fruit of the Doom
- Flavor of the Day
- Fairie O'the Day
- Foto of the Day
- Fish of the Day
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- Date: Thu, 18 Jan 2001 09:56:53 EST
- From: JimMuth@aol.com
- Subject: (fractint) C-FOTD 18-01-01 (Five Finger Minibrot [5])
-
- Classic FOTD -- January 18, 2001 (Rating 5)
-
- Fractal visionaries and enthusiasts:
-
- An unexpected rush job, (Why are they always unexpected?), put
- the damper on my fractal efforts today. But I did find a chance
- to dredge up a passable midget. Unfortunately, I had no chance
- to write a proper discussion. The result of all this activity
- is that the FOTD is once again late. I don't enjoy the
- lateness, preferring to be prompt in my postings, but sometimes
- it just can't be avoided.
-
- Now as to that fractal. It's an average midget, which I have
- named "Five Finger Minibrot", and rated a 5. I gave the image
- its name when I thought I spotted fingers around the edge of the
- open area. The formula that created the image is quite
- arbitrary: 26Z^(-0.98765)-52Z^(-9.8765)+C. To find the formula,
- I put my fingers on automatic. (Perhaps that's why the fingers
- appeared in the image.)
-
- The render time is slow enough to make a download of the image
- worth the effort. That download may be found in 3 hours on
- Usenet, posted to the binary newsgroup:
-
- alt.binaries.pictures.fractals
-
- And as soon as possible on the Web at:
-
- <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
-
- and at:
-
- <http://home.swbell.net/sdboyd56/fotd/>
-
- A non-eventful day in the weather aspect made the fractal cats
- far less restless than they were the day before, when they got
- into a fight. The partly sunny skies and temperature of 44F
- (6.5C) were ideal, with the light wind making conditions perfect
- for a full afternoon's outing in the yard. The dynamic duo
- carried their good mood into the evening, which helped me
- immensely in the rush.
-
- My planned philosophy fared less well however, but the rush
- design job will be out in a few hours, and I'll tackle that
- unfinished story.
-
- Until next time, take care, and when things get rushed, move
- faster.
-
-
- Jim Muth
- jamth@mindspring.com
-
-
- START 20.0 PAR-FORMULA FILE================================
-
- FiveFingerMinibrot { ; time=0:13:14.16 -- SF5 on a P200
- reset=2001 type=formula formulafile=critical.frm
- formulaname=MandelbrotMix4 function=ident passes=1
- center-mag=-0.12573544663073950/+8.93511041527769100\
- /580021.1/1/70 params=1/-0.98765/-2/-9.8765/25/300
- float=y maxiter=1200 inside=0 logmap=22 periodicity=9
- colors=000Zb0Ve0Rg0Nk0Jm0Ho0Nk0zc0Xg0<2>ib0m`0sZ0zX0\
- <4>zN0tL0z48z0Gz0LT00000000880JL6XXGgiNuuXzzdzPNzPLz\
- PLzNJzNHzNHzLGzLEzLEzJCzJCzJAzH8zH8zH6zH6zs0mR0Z00X0\
- 0V00T00R20R20P20N40L40L40J60H60G62G62CNA8dH4uP2zX0zb\
- <3>0zq0zu0zx0zz<3>0zz0zz0zz0zz2vz8qzGkzLdzTZzZTzeNzk\
- HzsCzx6zVEe0JH0P00N00N00L00L20J60J80HA4HC8GGCGHGEJJE\
- LNPLT`LXmLbxLezLizLezNdzPbzR`zRZzTXzVVzVTzXPzZNz`Lz`\
- JzbHzdGzdEzeCzg8zi6zi4zk2zm0zm0zo0zq0zq0zm0zk0ug0oe0\
- gb0b`0XX0RV0JT0EP08N02J00H<2>00AA08J06R04`82iG0qN0zV\
- 0z`0z`vzdxxezxgzvizvkzumzuozsqzqszquzovzoxzmzzmzzkzz\
- izzizzgzzgzzezz<2>dzz<2>ozzszvvzozzgzz`zzTzxLzvGzqEx\
- kCb6zRVzVRzXNz`JzbGzeCzg8zk4zo0zq0zu0zv0zz0z<4>z0z<2\
- >z0z<4>zTzzZzzdz<3>zzz<2>zzzzzzzxzxuxuqvqmumiskeqgbo\
- dZmbXkZTiVPgRLePHdLEbHA`E6ZC2X80V40T
- }
-
- frm:MandelbrotMix4 {; Jim Muth
- a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
- g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
- k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
- z=k*((a*(z^b))+(d*(z^f)))+c,
- |z| < l
- }
-
- END 20.0 PAR-FORMULA FILE==================================
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- Date: Thu, 18 Jan 2001 16:38:50 -0600
- From: Programmer Dude <cjsonnack@mmm.com>
- Subject: (fractint) Dead Horse (was: various Copyright posts)
-
- All-
-
- I hope you'll forgive this continuation after the horse is long dead (at
- least for a while), but Bob posed a couple questions I've been meaning to
- answer (but have been overwhelmed with a large project going out the door
- and had no time to address). And, because of that large project, I'm a
- bit brain-fried and don't feel like doing any useful work [grin]. And the
- list has been quiet lately, so.....
-
- Bob Margolis wrote:
-
- > I don't create fractal artwork as background designs for someone else's
- > "Wheaties box" so to speak. Would any of you enjoy seeing the Mona Lisa
- > after someone else covered it with text?
-
- Depends on how it was done. But I certainly might. I might also feel
- that it could introduce others who might not be familiar with the work
- to wonder what it was and possibly seek out the original. I don't agree
- that a great work is necessarily "cheapened" this way: I think greatness
- shines through.
-
- [SIDEBAR]
- Just a thought about Wheaties boxes... Andy Warhol opened our minds to
- the artists' work that is everywhere we look. On my desk is a box of
- Good Earth tea. It contains two drawings: one of a farm field scene with
- horse, plow and driver and another of some flowers and herbs. These small
- artworks are repeated, respectively, twice and thrice on various sides of
- the box. Someone made those drawings, someone designed the layout of the
- box.
-
- It strikes me that a Wheaties box with a fractal--even with text over it--
- would be kind of cool. (And an honor for the lucky fractal artist.) More
- to the point, we should all be aware of the artwork that lives around us
- in great proffusion and appreciate the work of all these unsung artists.
- [/SIDEBAR]
-
- > I felt that what I labored to design became quite pedestrian when it
- > the background for Mr. Miller's CD.
-
- That is *one* way to see it. Another is to see it as an honor. Someone
- found it worthy of putting on their CD. You are absolutely entitled to
- control (or try to control) your work, and I support that absolutely.
-
- But consider this scenario: you generously allow Miller to use your art
- on his CDs. As a result, a number of people discover the world of
- fractals having never seen them before. As a result, someone who does
- know fractals, but has never seen your work, really likes the image, seeks
- you out and gives you a ton of money to make him/her/it an image.
-
- Unlikely? Maybe. But who knows. Since Miller's use wasn't for profit,
- and since you seem to have no intrinsic objection to the Dead, you had a
- chance to be generous and spread the word about fractals and yourself.
-
- You had, IMO, little to lose and possibly something to gain.
-
- > I have pride as an artist, and detest seeing my accomplishments
- > cheapened in such a manner.
-
- And that obviously lies at the heart of what's going on here. You have a
- perception that your work is threatened, and that upsets you. I'd just
- like you to be aware of another way to look at it that isn't threatening.
-
- From another post:
-
- > Therefore, he's not really displaying the artwork for its loveliness;
- > he's using it as background for his text, be it a quote from the Bible,
- > contents of a CD, or Lincoln's Gettysburg Address. The texts become the
- > important item, not the pictures.
-
- Disagree on two counts. First, he almost certainly *did* choose it for
- its loveliness or he wouldn't have chosen it. Second, speaking as someone
- who does combine backgrounds and text, the important thing is the BOTH OF
- THEM.
-
- > The pictures, then, become altered from their original states because
- > of the added text. Would that alteration be considered "fair use" of
- > the fractal-art pictures?
-
- No. Fair use applies to "quoting" material for reference or illustration.
- If I were writing an essay about fractals, I *might* be legally able to
- include a small version of your fractal so long as I cited its origin,
- but fair use applies to *pieces* of a work, so I might not legally be
- able to use the full image. That's a matter for lawyers. But fair use
- in no way applies to this situation.
-
- But what might apply is that copyright laws may not apply to use when no
- profit is involved (as appears to be the case here). There is no law
- against me putting your fractals on a CD I make and use myself. I can
- even legally make two and *give* one to a friend.
-
- > Should you fault me for having pride in what I design and becoming
- > protective of it when it is used in a manner which I had not intended
- > for it?
-
- To the former, absolutely not. To the latter, well, IMO, you *might* be
- over-reacting just a little. The thing is:
-
- > What right did Mr. Miller have to make that decision for me before
- > coming to me about it? That question still has not been answered with
- > satisfaction by anyone here who is opposed to my viewpoint.
-
- But he *did* exactly that. He created a stand-alone web page exactly so
- he could show you his intended use. It appears to be an uncontested fact
- that the web page had not been made public, and when you *did* object he
- did remove it. Also uncontested is that no profit was involved
-
- Again, I completely support your position vis-a-vis your work. My only
- point was that your reaction was--IMO--a little extreme and unnecessary.
- You added a little more negativity to the world (at Christmas, no less),
- and you could have chosen a different way to make your point. I just
- felt a strong urge to speak up about that.
-
- This got long, and I haven't even answered the post directed to me.
- So, to be continued.... ;-\
-
- - --
- |_ CJSonnack <Chris@Sonnack.com> _____________| How's my programming? |
- |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL |
- |_____________________________________________|_______________________|
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- Date: Thu, 18 Jan 2001 16:47:42 -0600
- From: Programmer Dude <cjsonnack@mmm.com>
- Subject: (fractint) Dead Horse II (was: reality check)
-
- Me again,...
-
- Bob Margolis wrote:
-
- >> Are you comparing Dead Heads to neo-Nazis or White Supremicists or KKKs?
- >
- > I never made such a comparison.
-
- [shrug] You brought them up in the context of this discussion. You asked
- how I'd feel about my work being used by such, so the implication seemed
- pretty clear. Understandable you'd want to deny that implication, and
- we'll consider it retracted.
-
- >> It was an *individual* who liked your art work and thought it was
- >> worth honoring by using... He may have been well-meaning but ignorant.
- >
- > And ignorance of the law is no excuse.
-
- Agreed. Again, my only real issue here was in how you *handled* this. I
- don't want to come off like this is a huge deal; it isn't. I've supported
- your right to manage your work as you see fit from the beginning. I just
- didn't like the manner you in which you managed Mr. Miller, and I'd like
- you to see a different way of looking at the situation (and reacting).
-
- Really, it's no big deal. We're just chattin'!!
-
- >> Yes, almost certainly. My world's big enough for people with opinions
- >> 180 degrees different from mine, and I don't feel the need to attempt
- >> to control or thwart them just because I don't agree with them.
- >
- > That's most liberal of you. :-) What would go through your mind then if
- > the public associates you with those groups holding opposing viewpoints
- > because you willingly allowed those groups to use your artwork in
- > support of their cause?
-
- To be honest, I don't worry all that much about the public. Depending on
- the situation, I might view it as an opportunity to make inroads into an
- area to express a different viewpoint. I might also find it hysterically
- funny that a group might favor *my* work over others when my views were
- so different from theirs. "If they only knew...." HA!!!
-
- But we're wandering pretty far afield here. Not all situations lend to
- exaggeration and extremes as metaphors. There's no danger, I think, the
- public will associate you with the Grateful Dead because some guy used
- your work on a free CD.
-
- >> I don't think that way, nor live my life that way.
- >
- > So, because you chose to be that way, do you believe that I should model
- > my life after yours? :-)
-
- Not at all. I *would* like you to consider reacting with grace and good
- will and gentleness should such a situation happen again. (I'm big on
- The Three Gs.)
-
- >>> Would you feel then that it is okay for them to use your artwork
- >>> without seeking permission from you?
- >>
- >> But that's not what happened, is it, Bob. He *sought* your permission,
- >> and, AIUI, removed your art after your reply.
- >
- > You didn't answer my question. Put aside the discussion concerning Mr.
- > Miller. The question is a general one. What say you is your answer then?
-
- I would obviously prefer it. I don't require it. (That is, *IF* I put
- the artwork on my web page. Under such a circumstance, I consider it
- unprotectable, so I would only post work in a form I wouldn't mind being
- used without my knowledge or consent.)
-
- >>> Is all artwork posted on the Internet supposed to be *free* for the
- >>> taking, no questions asked?
- >>
- >> Regardless of the legal issues, that's pretty much the way it works
- >> out.
- >
- > You didn't answer the question again. I asked if it was supposed to be
- > "free." Answer the question yes or no, please, without the song and
- > dance. :-)
-
- [grin] How about yes or no WITH the song and dance?...
-
- Rump-a-bum-bum: *supposed* to be free: ahdonno... (cha-cha-cha)
-
- But that's pretty much how it works out. In a perfect world, I'm supposed
- to be able to leave my wallet sitting on a restaurant table and have it
- be there when I realize it half an hour later and go back. In the real
- world, not so much.
-
- People aren't *supposed* to take what isn't theirs, but if I leave a
- thing lying in public view, I'm not surprised if someone *does* take it.
-
- (Thing is, I'm not big on "supposed to be's". I'm big on "is's".)
-
- > So we should be anarchists and not live in a nation with laws?
-
- Okay. Seriously. I am something of a political anarchist, and I would
- like to see a *lot* fewer laws and a *lot* more personal responsibility.
- But that's a whole 'nother topic.
-
- > It's to be a dog-eat-dog world with every person fending for himself
- > with no law whatsoever?
-
- Well, again--as with the neo-Nazis and White Supremicists--you're taking
- this to extremes. There's a lot of ground between copyrights and a dog-
- eat-dog world with NO laws.
-
- But, honestly, I'd be happy with going in that general direction, yes.
-
- > I would have no right to call a cop if a mugger held me up
- > at gunpoint on the street? That's just the way life is, and I should
- > deal with it?
-
- Yep. Of course, in my world you'd be armed and able to shoot back. And
- there's reason to believe that would lead to a lot less muggers. At least
- a lot less *living* ones...
-
- Oops, did I just open a can of worms???? ;-\
-
- >>> Is it *toughies* for any artist who chooses to make a living by
- >>> selling artwork over the Internet, because people such as you believe
- >>> things in life should be *free* to them?
- >>
- >> Yes. ;-)
- >
- > At least your honest. :-)
- >
- >> Sorry, you deserved that reply, since you've mis-represented my
- >> position. For genuine answer, see previous paragraph.
- >
- > I was just asking a question in general without considering your
- > position. Your "yes" is what I expected to read. :-)
-
- Considering your outlook, I can see why you'd run with this ball.
-
- But, again, a *genuine* answer is this:
-
- First, as I keep saying, you have the right to (at least try to) control
- how your work is used. I want to be very clear on this, Bob. I fully
- support your desire to control your work.
-
- But. If an artist is going to use the internet to sell their work, then
- they'd better be internet-savy. If you're dumb enough to put something
- you expect to sell in plain view, then I don't have much sympathy when
- someone takes it.
-
- Post low-rez images. Put copyright text on them. Watermark them.
-
- Three simple solutions. There's plenty more.
-
- >> For all you know, there's a dozen people out there who *are* using
- >> your artwork.
- >
- > Yes, I'm sure there are. That doesn't make it any more legal.
-
- It's not clear to me Miller's use *is* illegal, since it was non-profit
- and personal.
-
- >> I *do* think people with attitudes like yours are *doomed* to go the
- >> way of .ARC files. And, perhaps, rightfully so.
- >
- > How am I *doomed*? How will I meet my demise holding the attitudes I do?
-
- Doomed .NE. Demise.
-
- By trying to retain too tight a control on your work, you may lose out to
- others who are more generous. There's a LOT of people creating fractals.
-
- This business is filled with examples. ARC/ZIP is a classic example.
- Another is the IBM-PC/Apple-Mac. IBM offered an open architecture; Apple
- offered a closed one. While the Mac is arguably better, the PC exploded
- because (at least in part) it was *accessible*. Another example that hits
- us close to home is the GIF. In attempting to control it, they lost it.
-
- There are Zen sayings about trying to control too much....
-
- >> The digital age is changing many aspects of life we previously took
- >> for granted. It calls for a new mind set.
- >
- > And everthing on the Internet should be "free for the taking" according
- > to that "new mind set?"
-
- Everything on the internet **is** free for the taking **unless** you take
- savy steps to protect it. The internet *came* from a desire to *share*
- information and data. The *web* came from a desire to make information
- accessible (and free) to all interested parties.
-
- >>> Do you find copyright laws silly and an inconvenience to you?
- >>> If any of your rights would be violated, would that be okay with you?
- >>
- >> Sheeze, talk about mis-representing. Not worth answering.
- >
- > Not misrepresentation, Dude. Just wanting to get your viewpoint
- > regarding copyright law, that's all.
-
- No, you take my position to the extreme without trying to understand
- what I'm really saying.
-
- > Would you please answer the question?
-
- Then try asking it without ascribing insulting exaggerations to me.
-
- Do I find copyright laws silly and an inconvenience? No, and no. Duh.
-
- If any of my rights are violated, would that be okay with me? Any of
- them? Gee, what do you *think* my answer to that would be? Hello.
-
- Specifically, if I put a piece of my work on my website and some person
- took it and used it in some personal way (i.e. not an organization and
- not for profit) I have no problem with that. But then I don't view that
- as a rights violation.
-
- Okay, (more than) 'nuf sed.
-
- - --
- |_ CJSonnack <Chris@Sonnack.com> _____________| How's my programming? |
- |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL |
- |_____________________________________________|_______________________|
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- Date: Thu, 18 Jan 2001 18:00:35 -0600
- From: Programmer Dude <cjsonnack@mmm.com>
- Subject: (fractint) Fractal Reality (was FOTD 13-01-01)
-
- In apology for beating a Dead Horse, I offer the following ON TOPIC thread.
- Obviously, this is all (as ever) I.M.O....
-
- Jim Muth wrote:
-
- > I often wonder, "are fractals real?" The answer can only be, "fractals
- > are the things numbers do, and numbers are pure abstractions". The
- > Mandelbrot set does not exist in the sense that a tree does.
-
- Language is sometimes not good at making distinctions we'd like to make.
- The M-set is not *concrete* like a tree, but neither is it as abstract
- as, say, "justice" or "freedom".
-
- I will, to foment discussion, argue that numbers (and hence fractals) are
- as "real" as anything you care to name. I will also pose the idea that
- maybe (just maybe) reality is only as real as numbers.
-
- Numbers. Are they invented or discovered? An interesting question.
-
- You might distantly recall (or see your young child bring home) from
- school exercises where you have a page of pictures of tall, skinny things
- and the goal is to circle the ones that are trees. What is being taught
- is the process of classification and what is sometimes called "unity".
- That is, there is a generic, abstract "unit" with the label "Tree". And
- we learn as humans to determine what matches that unit. And what does
- not.
-
- My dog has--what are to me--*three* tennis balls. To her, they are not
- at all identical. They are distinct objects in her world. Each has
- features that distinquish it totally from the others. To her, every tree
- is a separate, distinct object with its own characteristics.
-
- If humans saw the world this way, shepherds would never know how many
- sheep they had. More importantly, they'd find it difficult to know when
- the wolves got one! (If you go to a gathering of 200 hundred people you
- know, how easy is it to determine if someone didn't show up?)
-
- When we count sheep or tennis balls we say, in effect, these are all the
- same sort of thing. Early number systems often mapped symbol directly
- to object. You all know the base 1 system: 1=1, 2=11, 3=111, 4=1111 and
- 5=1111-slash (you know, how prisoners and castaways mark the days). In
- this system, each mark maps directly to the object.
-
- The next step is to create new symbols that map to a set of distinct
- collections. The symbol "1" maps to the collection containing one thing.
- The symbol "2" maps to a collection of two. And so forth. The number
- of symbols and what they map to generates a numbering system.
-
- Positional notation (our numbers) takes this process another step by
- re-using symbols to generate larger numbers. Positional notation requires
- a special invention: the symbol for zero! Since this isn't an essay on
- positional notation, I'll leave it at that.
-
- I will mention an interesting system (from Fred Pohl's Heechee series)
- where the symbols are mapped to prime numbers and you enumerate by
- listing the required symbols (primes) to sum to the desired number. In
- this system, the *order* of symbols make no difference. On the flip side
- you need a lot of them to count very high! On the other other hand, you
- sometimes only need one symbol to enumerate a large (prime) number!!
-
- The point I want to make is that each step in this path starts with real
- objects and the need to enumerate them. We just find better and better
- ways of doing it.
-
- Does that make numbers real or abstract? I claim it makes them real.
-
- Next step, math operations: add, subtract, etc.
-
- If I have an orange, and you have an apple, and we put them both on the
- table, there are two fruits. We just "invented" addition. Or did we
- merely *discover* it. Did we just make a label for a real thing? I say
- we just discovered a natural operation.
-
- An interesting point: given the definition of "1" and "2" and the
- definition of "+", "1+1=2" no matter what country, planet or galaxy you
- inhabit. Indeed math will be the initial language of communication
- should alien life be discovered *because* it is so universal. Can we
- really call mathematics "abstract" given its universality?
-
- I claim not.
-
- Now here's dessert:
-
- You may be aware of the "Many Worlds" theories of quantum physics. The
- idea is that any event with more than one outcome generates new worlds
- for each possible outcome. Resulting in an infinite number of realities.
- Mind boggling, yes? How is something like that possible? Where does
- the energy come from to generate a whole new universe?
-
- Here's a question for you. What's the answer to "x * x = 4"?
-
- Obviously 2. Also -2. And various other equations will have larger sets
- of correct answers.
-
- What if, just what if, the "real" world was nothing more than mathematics
- and the splitting of world lines for multiple-outcome events was nothing
- more than having multiple answers for the same equation!
-
- Well, that's just crazy talk.... Isn't it? ;-|
-
- Returning from deep left field, the thing is that reality is not quite
- as real as we might like to think. The more you know about quantum
- physics, the weirder the world gets....
-
- As Jim said:
- > No one will ever find a 'real' Mandelbrot set; they will find only
- > pictures of it.
-
- But no one will ever see an atom; they will find only images of it.
- Yet atoms are real. Aren't they?
-
- How about electricity? It's only *force*. But pretty real to those
- that've be struck by lightning!
-
- Perhaps it is our definition of "real" that needs work. I conclude that
- mathematics and fractals are AT LEAST as "real" as electricity and atoms.
-
- I'm just not quite sure how real *any* of them are...
-
- > The M-set exists only because human beings evolved with the sense of
- > vision, and to better understand the workings of math functions,
- > find it helpful to turn the functions into pictures. In essence, the
- > Mandelbrot set exists only because we created it with our minds and
- > sustain it with our computers.
-
- I submit that the M-set will be discovered by any intelligent race. The
- key word here is "discovered". Only real things can be discovered. The
- mathematic relationships that result in the Mandelbrot exist throughout
- the universe. We didn't *invent* them, we *stumbled* on them!
-
- > But according to quantum theory, atoms also are nothing more
- > than convenient pictures, models created in human minds from
- > mathematical functions.
-
- I would say that atoms are just our best *model* of the real thing.
- (And that model seems to be pretty accurate.)
-
- > And I have heard it said that numbers themselves are creations of the
- > human mind. So is the 'real world' the world's greatest fractal? The
- > answer to this challenging question is what I am currently seeking.
-
- I suggest the question is impossible as posed. All fractals are numbers,
- but not all numbers are fractal. Perhaps a way to ask the question ties
- back to that Many Worlds solution I mentioned. Is our reality nothing
- more than the "collapse" of an unimaginably complex wave function? Are
- we all in the box with Schroedinger's Cat?
-
- > Until tomorrow, take care, and beware of the fractal witch.
-
- Hey, not all witches are bad. I always had a crush on Samantha Tate...
-
- - --
- |_ CJSonnack <Chris@Sonnack.com> _____________| How's my programming? |
- |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL |
- |_____________________________________________|_______________________|
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- End of fractint-digest V1 #532
- ******************************
-
-