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fractint-digest          Sunday, May 28 2000          Volume 01 : Number 477




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

Date: Mon, 22 May 2000 19:55:00 +1200
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Re: The Wonder Returns

At 10:49 16/05/2000 -0400, Collin Merenoff wrote:
>
>As far as I know, a critical line or curve would be impossible.
>
The function f(z)=Re(z)^2 is critical at every point on the imaginary axis,
while f(z)=cos(|z|) is critical on concentric circles centred on the
origin, with radii npi for n=0,1,2,...

Morgan L. Owens.



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

Date: Mon, 22 May 2000 17:40:02 +0200
From: "Jean-Pierre Louvet" <[e-mail]>
Subject: (fractint) New version of the draft of the Fractal Art FAQ

Hi all,

Version 0.4 of the FAQ draft is on line. It is a pre-release version, i.e. I
wish to have version 1 on line in one or two weeks, after the latest
additions and corrections that you may send me as soon as possible.
You remember I have been incautious to a slight extent in the first versions
about the descriptions of the main fractal programs.
In this version I have freely used or modified parts of the texts sent by
the authors and I have added some personal information. Therefore the texts
are under my own responsibility and I will not change them, except to
correct obvious errors.
As always I hope that [e-mail] is the best place to
discuss about this FAQ. For private replies about the FAQ the best is
[e-mail]

http://www-hs.iuta.u-bordeaux.fr/F-art-FAQ/

Remember that I wish that no link points to this address before version 1 is
ready.
- -------------------------------------------------------------------------
J.P. Louvet                | Phone :  [phone]
IUT Universite Bordeaux 1  |
33405 Talence CEDEX France | email : [e-mail]
- -------------------------------------------------------------------------
Fractales sur serveur Web Universite Bordeaux I :
http://www.cribx1.u-bordeaux.fr/fractals/
- -------------------------------------------------------------------------


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

Date: Tue, 23 May 2000 01:44:26 +0200
From: Guy Marson <[e-mail]>
Subject: Re: (fractint) New version of the draft of the Fractal Art FAQ

At 17:40 22/05/00 +0200, you wrote:
>Hi all,
>
>Version 0.4 of the FAQ draft is on line.=20
>
>http://www-hs.iuta.u-bordeaux.fr/F-art-FAQ/
>
>J.P. Louvet                | Phone :  [phone]
>IUT Universite Bordeaux 1  |
>33405 Talence CEDEX France | email : [e-mail]
>-------------------------------------------------------------------------
>Fractales sur serveur Web Universite Bordeaux I :
>http://www.cribx1.u-bordeaux.fr/fractals/
>-------------------------------------------------------------------------

tr=E8s bien, gratulations pour ce boulot!


Guy


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

Date: Mon, 22 May 2000 22:26:48 -0400
From: "Barry N. Merenoff" <[e-mail]>
Subject: Re: (fractint) Re: The Wonder Returns

But those functions don't have a complex derivative. They only have
separate partial derivatives that don't agree.
This is because they use the functions Re and Abs, which are non-analytic=
.

Sincerely,
        Collin Merenoff

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

Date: Mon, 22 May 2000 22:42:43 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 23-05-00  (Bubbling Misfit [6])

FOTD -- May 23, 2000  (Rating 6)

Fractal visionaries and enthusiasts:

Today's FOTD has a midget in it.  There's nothing unusual with
that, since most FOTD's have at least one midget in them.
Today's midget however is a misfit.

While studying the scene for a name, I got a funny feeling about
the midget.  Something was not quite right with it.  Then I saw
it.  The normal 2-4-8... series of features converging on the
midget has gone awry.  Instead there is a 6-12-24... series.
The series doubles as it should, but apparently begins beyond
the borders of the picture with 3 elements instead of 2.

Not being a math expert, I will not venture a guess why this
particular midget should be so different, but it is different,
and I appreciate things that deviate, (in an unobjectionable
manner of course), from what would normally be expected.

The six bubbly elements instead of the expected eight make this
image stand out from the ordinary.  I named the picture
"Bubbling Misfit" because that name accurately describes the
scene and also because the name is unusual enough to make one
stop and take notice.

As usual, the formula is once again the MandelbrotMix4.  I'm
using this formula so often that it is becoming a notable event
when I use a different formula.  Today's parameters define the
expression Z^(-sqrt(2))+Z^(-10(sqrt(2)))+(1/C), which is another
parameter set I chose at random.

I doubt that the negative square root of 2 in the formula has
anything to do with the odd number of elements around the
midget, since I have seen this type of irregularity appear in
fractals created by other formulae.

The area of the parent fractal where I found today's scene
almost resembles the extra valley that splits buds of the cubic
Mandelbrot set, and this could be the cause of the irregular
number of elements surrounding the midget.  As I said earlier
however, I'm not a math expert, so I'm not too concerned with
the reason why the odd number of elements appear.  I simply make
the most of them when they do appear.

The attached parameter file takes 10 minutes to render on a
Pentium 200mhz.  The JPEG'd image file has been posted to:

          <alt.binaries.pictures.fractals>

and to:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

from where it may be downloaded virtually instantly.

The fractal weather today started with serious rain and even
some thunder, but the rain became mere drizzle by afternoon,
with a max temperature of 59F (15C).  Unable to go outdoors due
to the rain, the fractal cats are developing cabin fever.  I
can't blame them -- this is the fourth consecutive day they have
been housebound.

There is no philosophy today, but it is simmering along just
beneath the surface, and could erupt at any time.  The time of
eruption may even be as close as tomorrow.  So keep checking
back.  One of these days you'll be rewarded with the wisdom of
the ancients.

Until tomorrow, take care, and whatever happened to the wise
old ancients?


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Bubbling_Misfit    { ; time=0:10:01.76 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+2.09541430829565900/+0.00001537142778094\
  /117561.4/1/-90 params=1/-1.4142/1/-14.142/0/0
  float=y maxiter=1500 bailout=25 inside=0 logmap=121
  symmetry=none periodicity=10
  colors=000JDHJDI<3>VHKYIL`JL<2>iMNlNNoOQrPSuQU<7>xJj\
  xImxHo<3>yEw<3>ZFcSGZLGUEGP8GL<6>BKUBLVBLW<3>CO`DOXD\
  KTDFQEGREEKEESEKUFNXFPXFTX<3>FWWGWWGXVGXVGYV<3>H_QH`\
  PHaO<2>HbKrcJmcImdJrQKrWLmWMkfNjaOcfPIgQ<10>Il`IlaIl\
  b<3>InfIwgKrdMea<3>UOSWKPXGN<10>QcAPe9Pg8Oi7Ok6Nm5Mq\
  4wz3Lw2Lz1Kw2Jt3Jq4<3>Gj7Fi8Fg9EfADdB<10>6cK5cL5cL<3\
  >2cQ2cR1cS1cT0cU0cV<3>8cPAcNCcM<2>IcHccGmcEwcDwcBzcA\
  zc8zh9zcAwcBwcC<3>LcG<3>FcJEcKCcL<3>7kP6mPAoXDqdFsq<\
  4>KnTLmOMlJHi6<3>dpciqkjpi<24>tVEtUDuTC<2>vQ8vQ7wR8<\
  2>zS8zTGzTGzTH
  }

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==================================


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

Date: Tue, 23 May 2000 19:22:54 +1200
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Re: The Wonder Returns

At 22:26 22/05/2000 -0400, Collin Merenoff wrote:
>But those functions don't have a complex derivative. They only have
>separate partial derivatives that don't agree.
>This is because they use the functions Re and Abs, which are non-analytic.
>
Mea culpa! Mea maxima culpa! How do I expect them to be analytic when they
have so much trouble just being differentiable?!

I can only offer in excuse the fact that over the last week I've lost a
cumulative total of eighteen hours sack time. This didn't stop me
successfully completing the project I was losing sleep over though, so it's
kind of a weak excuse.

Morgan L. Owens
"I have to keep shifting mental gears, but the clutch keeps sticking."



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

Date: Tue, 23 May 2000 22:45:57 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 24-05-00  (A Nice Fractal [7])

FOTD -- May 24, 2000  (Rating 7)

Fractal visionaries and enthusiasts:

The day started with a blaze of glory as the deep fat cooker at
the local McDonalds restaurant erupted into flames just as I was
finishing reading my newspaper and eating my junk breakfast.
Luckily, the manager had the presence of mind to grab the fire
extinguisher and douse the flames even before the fire brigade
arrived.  No serious damage was done, but it was an exciting
start to what otherwise would have been just another dull
Tuesday.  Today's fractal is not nearly as exciting as a large
pan of burning fat, but it's still worth seeing.

People use the word 'nice' when they wish to praise something,
but can find nothing specific to praise.  It's one of those
vague, broad, good-sounding, all-purpose adjectives such as
'great', 'fantastic', 'amazing', 'superb', 'outstanding', and
'exquisite', which writing teachers tell tyro writers never to
use.  Even so, it is all I could think of to describe today's
image.

Today's FOTD is a nice fractal, so I named it "A Nice Fractal".
It is so nice that I rated it a somewhat exaggerated 7, which
translates to above average on my 0-to-10 scale of FOTD
worthiness.  The colors are nice; the sinuous elements
surrounding the midget are nice; the sinuous holes in the image
are nice; the formula that drew the image, which is
0.5Z^(-0.3)+0.5Z^(-3)+(1/C), is nice and neat; the mild 3-D
effect adds a nice touch, as does the slightly askew aspect of
the inner pattern.  And it is nice that the proper 2,4,8...
number of elements are to be found around the midget.

The formula that created the image continues the theme of the
past few days, which is to take a low-value negative power of Z
and add the negative power with ten times the value, and then
add the reciprocal of C.  When this is done, the resulting
fractal resembles a lake rather than the expected island, and
the fractal is loaded with midgets.

The midget in today's image lies in a minor valley of the parent
fractal.  This parent fractal is filled with other interesting
places that hold other interesting midgets, some of which will
eventually be seen by human eyes, but an infinite 100 percent of
which will never be seen.  (Infinity is paradoxical.)  And there
are an unlimited number of possible fractals with midgets.  In
fact, if I found a new midget for every minute of eternity, I
would still have found exactly zero percent of all the midgets
that exist.

The parameter file of today's image takes 17-1/2 minutes on a
Pentium 200mhz machine.  On the fastest machines that time may
be cut to 5 minutes or so, but the most efficient way to see the
picture is to download the image file from Usenet, where it has
been posted to the binary newsgroup:

          <alt.binaries.pictures.fractals>

The image may also be seen on the Web, where Paul has or soon
will post it to his FOTD web site at the URL:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

The fractal weather today was overcast with occasional sprinkles
of rain.  The temperature of 68F (20C) felt comfortable enough,
but the wet grass kept the fractal cats confined to the porch,
where they showed their displeasure by passing the afternoon
hunkered down in their sulkiest attitudes.

The fractal philosophy is still cooking, but the time will soon
arrive when it will ready for the world to see, and when that
time comes anything could happen.  I may even answer the riddle
of the universe, (but don't count on it).

One certain thing is that it's time to get serious and tackle
the day's work.  Until next time fractal fans, take care, and
may nothing but nice things happen.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

A_Nice_Fractal     { ; time=0:17:33.52 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+2.84571875602007300/+5.79283748228003700\
  /10053.87/1/45 params=1/-0.3/1/-3/-0.5/0 float=y
  maxiter=10000 inside=0 logmap=162 periodicity=10
  colors=0005GL5OL<3>4SL4KL4TL8PNBVPFYRIWT<3>WZ`__bb`d\
  e`e<2>sqUQ9uVDvZHwbLx<2>wTf<3>YdnSfoMiq<2>3qv<4>FcaH\
  aYJZU<3>SPE<2>5Cj<3>GOnJRoLUp<3>WetYcu`kvcnzeqxttyjw\
  y<8>WPfUMdSIb<2>N6XM3VN7Y<5>RUiRYkSam<2>UmsUpuWqs<8>\
  jvgkwemwd<3>sy_<3>VbLiYIMZJW_JI`KGOKEaK<3>6dM4dM9`M<\
  3>QOMVLMZIM<3>o5M<3>k5WgKZw5`h5c<3>d5mc5ob5r<2>_5y<3\
  >NEfKGaGJY<3>4Ra<6>GKhIJiKIj<3>QEn<2>h_q<3>lZumFv<3>\
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  bw<11>mdwmdwmcw<3>mdwmdwmdw<10>mcw
  }

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==================================


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

Date: Wed, 24 May 2000 20:39:10 EDT
From: [e-mail]
Subject: (fractint) Lake Transform

Hi,
I just love the "Lake Transform" by Sylvie Gallet.
It is a fabulous piece of work.

Does it depend on Fractint and its formula parser
to work its magic, or could it be implemented
as a Photoshop filter, so it could be applied
to any picture?

Or does such a filter already exist?

Thanks,
Lee Fairbanks

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

Date: Thu, 25 May 2000 00:53:38 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 25-05-00  (Tangerine Minibrot [6])

FOTD -- May 25, 2000  (Rating 6)

Fractal visionaries and enthusiasts:

Take an unlikely fractal-type formula -- Z^(-0.5)+Z^(-5)+(1/C)
for example -- and see if you can get it to make a fractal.
That's what I did, and today's fractal is what I got.

The parent of today's rather unusual midget is another of those
grossly mis-shapen negative-exponent Mandeloids with a lake at
the center, and more spurious valleys than one can shake their
stick at.  The midget in today's image lies in one of the less
obvious valleys on the WNW edge of the lake.

I am becoming quite interested in these double-negative
fractals.  The existence of the almost perfect equal-iteration
bands in many of them came as an almost total surprise.  And the
flexibility of these fractals is incredible, with all six
parameters having noticeable effects on the image.  In view of
the great variety, I'll probably be investigating this type of
fractal for a week or so.

The unusual coloring of today's picture is a lucky accident.  I
made only a few fine-tuning changes once the final color palette
appeared.  The striking orange disk and spiral arms that stand
out so obviously are of significantly higher iteration than the
rest of the scene, which explains the unusual coloring effect.

At first I could think of no name for this picture.  Then I
noticed a tangerine lying nearby.  Taking my cue from that
reddish-orange fruit, I named the picture "Tangerine Minibrot".

Once again the parameter file just dawdles along, requiring over
an hour on a 200mhz Pentium and an inconveniently long time on
even the fastest machines.  Being a merciful person, I have
posted the JPEG image file to the Usenet binary group:

          <alt.binaries.pictures.fractals>

And Paul Lee has posted it to his web site at the URL:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

The fractal weather today, (This paragraph was written at 11pm
Wednesday the 24th, 14 hours after the main body.), was partly
sunny for a change, with a light thunder-shower in mid-afternoon
and a temperature of 82F (28C) that brought out the best in the
fractal cats.

And now it's time to put away the fractals and get busy making
some customers satisfied.  Until next time, take care, and
dreams of fractals are most mysterious dreams of all.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Tangerine_Minibrot { ; time=1:01:21.99 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-0.13011235422442010/+0.45932225027365970\
  /6.934382e+011/1/25.055/-0.084 params=1/-0.5/1/-5/0/0
  float=y maxiter=15000 bailout=25 inside=0 logmap=1140
  symmetry=none periodicity=10
  colors=000rgm<3>ddPacJYbDVa7Sa1_URfNo<5>mZ_n`XobU<3>\
  sjKZgOFdR<17>_Bqa9rb7t<3>f1y<3>nCjpFgrIcsK`<3>tcDth8\
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  <3>o0c<3>YRPUYLQdHMjE<14>nXRpWSrVT<3>ySWwRWrSWlUWdVT\
  VWS<4>`TObSNcRNdQMfPLgOK<3>lLHmKHoJG<2>sGEqADuKCxXBz\
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  mU_mU`mUamUbm<21>Ucm
  }

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==================================


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

Date: Thu, 25 May 2000 23:00:43 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 26-05-00  (Thriving Bacteria [7])

FOTD -- May 26, 2000  (Rating 7)

Fractal visionaries and enthusiasts:

Assuming that the digits of the golden ratio would create a
golden fractal when used as negative exponents of Z, I entered
Z^(-1.618) into the M-Mix4 formula.  Then I added Z^(-16.18),
which has ten times the negative value.  Adding (1/C) completed
the expression.  When I saw the image that resulted, I was
neither surprised nor disappointed.

On my screen was the expected grossly distorted Mandeloid, with
the right end a bit out of the frame, causing me to immediately
adjust the view.  In this case the figure is so distorted that
it is impossible to tell by a casual glance which end should be
up.  Examining the inner nature of the various parts of the
figure can sometimes give a hint as to where one is located in a
Mandeloid, but in this case my attention was drawn by a smaller
midget very near the northeast shore of the main lake.

This midget lies so close to the main figure that it has been
stretched almost beyond recognition, and it in turn is
stretching the part of the main figure closest to it.  Only a
narrow and fragile isthmus separates the two features.  It is in
this isthmus that I did my searching.

I began my search by seeking the exact point where the basins of
the two features meet in a tiny saddle-shape.  When I found the
point I noticed that a smaller midget lay very close to it.
This smaller midget is the one that appears in today's picture.

The purplish color palette reminds me of some kind of repulsive
purple bacteria growth I once saw thriving in a petri dish.  I
named the picture "Thriving Bacteria", but don't let the name be
a put-off.  There is nothing repulsive in the image, which rates
a 7 even without exaggeration.

If anyone feels that the near 18-minute render time is too long,
I don't blame them.  I feel it's too long myself.  But that's
the nature of fractals.  The faster our machines become, the
more difficult will be the fractals we seek, and as a result, a
fractal will always be a slow thing.  This is why I have posted
the JPEG file of the image to:

          <alt.binaries.pictures.fractals>

and Paul has posted it to:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

After a brief but heavy thunder-shower during the night, the day
dawned cloudy.  The clouds hung around until early evening, when
they cleared just in time for a glorious sunset.  The
temperature of 77F (25C) was ideal for everything including the
cats, who made up for lost time by romping in the yard.

The philosophy, (if that's what the stuff I have to say can be
called), is simmering.  The results of my ponderings will be
revealed in the near future on the philofractal list.  So keep
checking and you may learn something you never suspected.  You
might also learn something you always suspected.  ;-)

Until next time, take care, and when the itch to go fractaling
strikes, scratch the issue.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Thriving_Bacteria  { ; time=0:17:41.60 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+1.94099720531588100/+0.60075721046998280\
  /3.394908e+007/1/104.999 params=1/-1.618/1/-16.18/0/0
  float=y maxiter=8000 bailout=25 inside=0 logmap=267
  symmetry=none periodicity=10
  colors=000A0KA0KA0MA0O<3>H0SJATLFUNFWPLYRRZTUgVXf<4>\
  _bf`ceade<2>dgeehedid<2>cidbjcbjcakcakc<8>YoaXo`Xo`<\
  4>Vr_Ur_Us_TtZTuZSuZ<3>Tq_Tp_To_Tn_<3>Um`Um`Um`Um`<6\
  >VgaVfaVeb<12>XZdXYdXYd<2>XWdXWdWVcVVc<25>EJYDJXDJXC\
  IX<3>9GU9GT8GR<3>5EM5DL4DK4DK5EM6ER<3>AGXBGZCG`<5>IJ\
  eJJfKJgLKhMKh<3>PMoQMqRMsSNuTNw<4>YPwZPw_Qw<2>bRwcRx\
  dQycOz<3>gGz<2>jMskOslQs<3>mYrm_roarpcrqdr<33>PllOlk\
  NmkMmkLmk<3>JnkJnjAmkAml<5>DmmDmmEmm<4>Emm
  }

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==================================


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Date: Fri, 26 May 2000 23:38:53 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 27-05-00  (Baubles and Beads [7])

FOTD -- May 27, 2000  (Rating 7)

Fractal visionaries and enthusiasts:

As I studied today's fractal image, I was reminded of a box of
those nearly worthless trinkets known as baubles.  The midget,
with its surrounding spots and patches, has a surface gaudiness
that is striking at first glance, but diminishes with further
study -- a perfect effect to be described by the name "Baubles
and Beads".

The unlikely parameters entered as real(p1), real(p2) and
real(p3) tell that I used the Fractint evolver to find the
scene.  But though I am a fractal purist of the strictest kind,
I find nothing wrong with using the evolver to find fractals,
for the evolver produces true undistorted fractals, and is
merely a faster way of entering trial values by hand.  For
today's fractal I rounded the unnecessarily precise evolver
values to a much more tidy 3 decimal places.

The midget itself is perhaps the most unlikely one I have yet
found.  I have no idea what led me to this particular spot of
the parent fractal.  Sometimes I just get a feeling that a
midget is down there, and sometimes I am right.  Today's picture
is irrefutable evidence that my non-patented intuitive method
works.  (sometimes works that is)

The parent fractal is one of those grossly oversized ones that
appear near the point where the entire image turns inside out.
The center coordinates in the parameter file are not an error;
they accurately define the location in the parent fractal of
today's midget.

With a rendering time of a few seconds under 5 minutes, today's
parameter file is slightly slow.  It's not unbearably slow, but
it's slow enough to make the download from:

          <alt.binaries.pictures.fractals>

or from:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

worth the slight effort.

The fractal weather today was not fractal -- there was not
enough of it to be fractal.  In fact, it was so perfect that it
was boring.  It was boring because I find it impossible to get
excited about a deep blue, totally cloudless sky, a light
northwest wind, pleasantly low humidity, and a temperature of
80F (26.6C).  But at least the fractal cats enjoyed the perfect
day.

Though today's weather was perfect, the weather over the next
three days (27th, 28th, 29th) should be more interesting.  This
weekend is the first big holiday of summer here in the USA, and
the local weather is due to be rainy all three days.  Luckily,
fractal searching is an indoor activity, so the expected rain
will put no damper on my holiday.

The philosophy is still ripening, and will not be ready for a
few days.  The current topic of my pondering is the order in the
universe.

Until next time, which will arrive in 24 hours, take care, and
when the going gets tough, the tough get going and search for
fractals.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Baubles_and_Beads  { ; time=0:04:40.50 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+20827.97209153728/+7055.944158089405/693\
  .4634/1/92.5 params=0.654/-0.4/-0.213/-4/0.201/0
  float=y maxiter=1500 bailout=25 inside=0 logmap=67
  symmetry=none periodicity=0
  colors=000KVG0TG4PK7GKAHRD`OGsLQjRZrW<2>zqkxd_vSPFLN\
  <3>A49906D7C<3>SV_V`eZfkalp<3>0IV<3>Z9Ff7CjJSnVfqfu<\
  3>kopjqoisnhumaveVwY1ET<3>YGVeHVmHVued<3>BNe0Je6Ni<2\
  >OXshJ8<3>Ug4Qm3Ms2Jy2<2>Me5N_6MZ8LYALYB<3>ThWVk`Wme\
  <3>QcEPa7O_1<3>GQEEOHDMK<3>52`<3>Y5Zd6Yk6Ym2ak8_jEZo\
  `d<3>wqgyuhzyhRd8<2>45d<3>SfVYpSbyQ<2>B4F<3>ngHwpHpm\
  L<3>Ra_KZcEXfVUd<2>9E2NBx<3>eRrjVqnZosbnwfm<2>P3j<3>\
  GCcDEaBG_9IY7KX5XK<2>v6_WId<2>IdM<2>5g3<3>QkGJlj<3>U\
  pOWqJSrI<3>FvICwIWxZoyn<3>RzcLz`FzZ9zW3zU<3>4zh5zl5z\
  o5zs5zv<3>4zb4zY9zX<3>SzU<2>NzhMzlIzf<2>9zR<3>FzDHzA\
  Iz7MzPPzeszL<2>szezzV<2>fzI<4>ZzgfzOLzGEzG
  }

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==================================


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

Date: Sat, 27 May 2000 11:35:45 -0300
From: "Fernando Henrique Bresslau" <[e-mail]>
Subject: Re: (fractint) FOTD, 27-05-00  (Baubles and Beads [7])

- ----- Original Message -----
From: Jim Muth <[e-mail]>
Sent: Saturday, May 27, 2000 12:38 AM

> The center coordinates in the parameter file are not an error;
> they accurately define the location in the parent fractal of
> today's midget.

Hi, Jim. I once used two programs (I don┤t remember the names or where I
found the progs, they should be archived in my pc somewhere). These programs
would calculate the center coordinates of a midget if you fed them with a
point you knew it was near to such a midget center point. It used numerical
cauculus do do this. One prog would use normal float precision and the other
would use double-float.
But (there┤s allways a but) they would work only for the real-true-vanilla
mandelbrot.
So, my question is, how can you guarantee that these center coordinates are
the center coordinates of your midget (if this is what you tried to tell
with the above sentence)?

Fernando Bresslau
USP - Brazil
http://www.ozdobe.org/bresslau


__________________________________________________
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Talk to your friends online with Yahoo! Messenger.
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Date: Sun, 28 May 2000 00:36:18 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 28-05-00  (A Blue Beauty [7])

FOTD -- May 28, 2000  (Rating 7)

Fractal visionaries and enthusiasts:

Earlier today I began playing with the digits 4,1,4, which are
the first three digits of the fractional part of the square root
of two.  I tried several combinations before trying the formula
Z^(-0.414)+Z^(-4.14)+(1/C).  The resulting fractal required one
out-zoom to fit on the screen, but since the fractal looked
interesting, I started investigating deeper.

After giving the image a 90-degree CW rotation, the open lake
reminded me of a yogi in meditation, squatting with crossed
legs.  I saw many places that could hold midgets of a type never
before seen.  The place I decided to investigate was the
shoreline of the broad valley where the yogi's legs cross.

At first glance, it's a relatively normal Mandel-type shoreline,
with its endless procession of circular buds.  However, some
unusual things happen just inland of the water line, where the
landscape consists of a series of hummocks connected by an
intricate network of lacy filaments.  I chose one of these
filaments to examine more closely.

Inside the filament all was a confusion of criss-crossing
networks and lacy converging spirals.  Spirals are usually
interesting, so I looked closer at one.  I had the feeling that
midgets were there, but had no idea where to search.  With no
better ideas, I began searching at random.  After a few minutes
of fruitless search, I found a spot that looked suspiciously
2-way symmetrical, and began zooming.

My instinct once again proved correct.  It soon became apparent
that I was in the outer part of the basin of an as-yet-unseen
midget.  The rest of the story can be seen in today's picture,
which rates another 7 on my arbitrary scale of fractal
worthiness.

A named the image "A Blue Beauty" -- a name which is a pretty
good description.  The beauty will take 11 minutes to become
visible to those who chose to run the parameter file.  It will
appear much sooner to those who go and seek the JPEG image file
at:

          <alt.binaries.pictures.fractals>

or at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

The fractal weather today was cloudy with a steady light rain
that made things totally miserable for those planning outdoor
activities.  The temperature of 59F (15C) kept the would-be
bathers out of the water and kept the fractal cats indoors.  Bad
weather however has no adverse effect on fractaling, which is
what I did for a good part of the afternoon.

I did not philosophize today, but I may do so tomorrow.  Check
then, and if there is no philosophy, there certainly will be
another fractal.  Until 24 hours from now, take care, and the
sun always shines on exactly one-half of the world.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

A_Blue_Beauty      { ; time=0:10:57.95 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+5.502844144327801/+0.6715408407749046/1.\
  403758e+009/1/40/-0.001 params=1/-0.414/1/-4.14/0/0
  float=y maxiter=1800 bailout=25 inside=0 logmap=208
  symmetry=none periodicity=10
  colors=000ZcoZdpZeqahu<3>RZfOWcMU_<2>ENPBKM6DG6FF3DB\
  0A6<20>8Ee8Ef9Fh<2>AFmAFo9Go<14>GCtGCuHBu<3>IBv<3>SS\
  pUXnW`m<3>eqglufryewwdzuc<3>nn`kl_hkZeiYbgX_dW<2>XXU\
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  5Ja5Fe<2>51u<10>55i55h56f56e56d57c<4>58h59i59j47k<6>\
  7Hr7Is8Kt<3>9Px5Py<8>aRzeRziSz<3>wSz<3>vQzuQzuQz_Pza\
  Nz<21>Zcz
  }

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==================================


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

Date: Sun, 28 May 2000 08:29:32 -0400
From: Sylvie Gallet <[e-mail]>
Subject: (fractint) MandelbrotMix4 Lakes

Hi All,

  A formula file that contains all of the MandelbrotMix4-lake formulas I
made from Jim Muth's parameters (+ some of mine) is available on the
Downloads page of my web site (check out Mmix_lak.zip):

    <http://www.fractalus.com/sylvie/homepage.htm>

  Here's some examples:

6ml06101           { ; .                           t=3D  0:03:41.86
                     ; Copyright Sylvie Gallet, May 10, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
                     ;  Version 2000 Patchlevel 6
  reset=3D2000 type=3Dformula formulafile=3Dmmix_lak.frm
  formulaname=3DMMix4-lake-0061 function=3Dident passes=3D1
  center-mag=3D+1.44519368957052900/+0.14160825065617150/76615.3\
  3/1/-34.999 params=3D0/0/36/0/0.2/200 float=3Dy maxiter=3D2500
  inside=3D0 periodicity=3D0 sound=3Doff
  colors=3D000<3>20530630840950B<10>O76Q85S85<3>ZC3`D3aF3<7>nQ5o\
  S5qT5rV5tW5vY6<9>xiCxjDylE<2>yoGzqHzqJ<16>xufxuhxvi<2>wwnwwp\
  vvqvvsuuu<171>mcK
  }

6ml13902           { ; .                           t=3D  1:35:22.02
                     ; Copyright Sylvie Gallet, May 01, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
                     ;  Version 2000 Patchlevel 6
  reset=3D2000 type=3Dformula formulafile=3Dmmix_lak.frm
  formulaname=3Dmmix4-lake-0139b function=3Dident passes=3D1
  center-mag=3D+1.88255488398907100/-0.02668502674302770/1.76539\
  1e+010/1/30 params=3D0/0/27/0/0.3/200 float=3Dy maxiter=3D2000
  inside=3D0 cyclerange=3D0/255 sound=3Doff
  colors=3DYHE<2>cGI<3>kTXmX`o_drch<13>KITIGSFFR<3>58M26L38M<3>5\
  HR6JS7LU<4>DW`EYbF_cGaeHcfJfhLhi<3>Zmoanpeor<3>stw<2>rrrrqpq\
  qnppl<17>edHdcFcbE<3>``6`_4_Z2ZY0<16>HJ0GI0FH0EG0CF0<8>C60C5\
  0C40C30C20D10C01<3>N05Q07S08V09Y0B`0C<8>hKOiNQjPRkSSlUUmWVnZ\
  X<3>rgZsi_tk_<3>xubyxbzzc<3>zuRztOzrK<3>vgEudCtaB<3>pQ4nN2mM\
  2<5>dG4cF4aE5<3>XA6W97U87T77<3>iV9m`AqfAulBzrC<9>aiD_hEXgE<2\
  >QdENcFNbF<3>JXCJVBIUB<3>CM4AK28H0<3>9C19B19A1A82<2>A21A00C3\
  1<4>OI9<3>WHD
  }

6ml22701           { ; Feerie a Versailles         t=3D  0:07:12.15
                     ; Copyright Sylvie Gallet, Apr 24, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
                     ;  Version 2000 Patchlevel 6
  reset=3D2000 type=3Dformula formulafile=3Dmmix_lak.frm
  formulaname=3DMMix4-lake-0227 function=3Drecip passes=3D1
  center-mag=3D+2.86077719777997400/+0.00103133600044388/715138.\
  4/1/7.5 params=3D0/0/37/0/0.7/200 float=3Dy maxiter=3D1000
  bailout=3D25 inside=3D0 logmap=3D15 symmetry=3Dnone
  periodicity=3D10 sound=3Doff
  colors=3D00040C<3>709808808<3>C04E14H24<8>fF3hG2kI2nJ2qL2tM2uO\
  2wQ1<7>xf5yh6yj6yl7yn7zq8<6>zvDzwEzwEzxFzyG<3>zzNzzPzzR<5>yy\
  `yybyycxxexxfxxh<3>wwnwwpvvqvvsuuu<3>sttrttqtt<18>SljRliQkiP\
  khNjh<12>6ea5e`3d`2d_0cZ<104>02L02L01L<3>00KFFF00K<6>00G00F0\
  0F<3>00C00G<3>30D
  }

6ml30001           { ; Wildfire I                  t=3D  0:16:25.36
                     ; Copyright Sylvie Gallet, May 21, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
                     ;  Version 2000 Patchlevel 6
  reset=3D2000 type=3Dformula formulafile=3Dmmix_lak.frm
  formulaname=3Dmmix4-lake-0300 function=3Drecip passes=3D1
  center-mag=3D+1.92711632140873700/+0.06885607469174922/1352.02\
  8/1/-32.499 params=3D0/0/35/0/0.3/150 float=3Dy maxiter=3D2000
  inside=3D0 periodicity=3D0 sound=3Doff
  colors=3D000<5>403504604<3>907500<5>M71P81S92<3>cF2fG2iI2<3>vO\
  2<9>wh5xj6xl6<2>xr7yu8yuA<14>xvhxvkxvm<2>xvtwwwwww<10>uuutuu\
  tuutuu<3>qttpttnss<10>_nnZnmXmm<4>RliQkiPkh<3>JifIifGhe<4>Ag\
  c9fb7fb<3>2d_0cZ0cZ<103>02L02L01L<3>01K01K01K<6>00G00F00E<3>\
  00C00G
  }

6ml30301           { ; .                           t=3D  0:59:25.38
                     ; Copyright Sylvie Gallet, May 24, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
                     ;  Version 2000 Patchlevel 6
  reset=3D2000 type=3Dformula formulafile=3Dmmix_lak.frm
  formulaname=3DMMix4-lake-0303 function=3Drecip passes=3D1
  center-mag=3D+2.79125975335705300/+5.69700602216168700/7496.93\
  7/1/140 params=3D0/0/34/0/0.25/180 float=3Dy maxiter=3D2000
  inside=3D0 logmap=3D90 periodicity=3D0 sound=3Doff
  colors=3Dzz0zK66P8AUA<15>dmNfnNhoO<2>nsRpuSpuU<8>vxlvxowxq<2>y\
  ywzzzyzz<11>boz`nzZmz<3>RiyPhxNgx<3>EcvBauB`rA_o9ZlAZl<10>Rg\
  sShtUiu<5>cowdqxfqxhsxisykuymvz<3>mwqlwolvl<15>isChsAhs7hs5h\
  s3gr0<5>co0bn0an0am0`m0_l0<20>M`2L`2L_2<4>GX3FW3EV3DU3CT3BT3\
  <3>7P46P46P4<3>6O46O46N4<7>3F22E22D1<2>1A10901A0<8>DP1FR1GT1\
  <2>KY1M_2N_2<24>kt8lu8mv9<2>py9rzArzD<12>wzp
  }

6ml30401           { ; .                           t=3D  0:15:27.15
                     ; Copyright Sylvie Gallet, May 25, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
                     ;  Version 2000 Patchlevel 6
  reset=3D2000 type=3Dformula formulafile=3Dmmix_lak.frm
  formulaname=3DMMix4-lake-0304 function=3Drecip passes=3D1
  center-mag=3D+4.02785545745316800/+1.79514268564319900/167449.\
  1/1/10 params=3D0/0/34/0/0.3/200 float=3Dy maxiter=3D2000
  inside=3D0 periodicity=3D0 sound=3Doff
  colors=3D000L11K000CP<3>0BO0BO0BO<48>829819819<2>818907B07<3>J\
  46L55N65<3>XA3_B3bC3dE2gF2<3>pK1rM0rO0<4>uZ3v`4vb5<2>xi6xk7x\
  k7<6>yrCysDytDyuEyvF<16>zwczwdzwfzwh<3>zwmzvozvpzvrzvszuu<11\
  7>L11
  }

  Enjoy!

        - Sylvie

- -----------------------------------------------
 E-mail:
   [e-mail]
 Web site:
   http://www.fractalus.com/sylvie/homepage.htm
- -----------------------------------------------

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

End of fractint-digest V1 #477
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