ftp.xmission.com/2014.06.ftp.xmission.com.tar/ftp.xmission.com/pub/lists/fractint/archive/fractint.200107

Internet Message Format | 2001-07-30 | 230KB

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  01-07-01  (Pac-Man Strikes Again [6])
Date: 01 Jul 2001 10:22:46 -0400 (EDT)


Classic FOTD -- July 01, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Who can forget Pac-Man?  It was one of the first computer games.
In the game, a yellow ball with a big mouth ran through a maze,
gobbling up energy pills and avoiding ghosts, except when the
ghosts became vulnerable.

I assumed I'd seen the last of the yellow fellow a few years
ago, but what should show up on my screen today but a Pac-Man.
Well, actually it's not a Pac-Man but rather a mis-shapen midget
in the Z^(sqrt2)+C fractal.  If the midget were black, I might
have seen Marvin the Martian when I studied it, but it is
yellow, so "Pac-Man" it is.

Yes, I realize that Pac-Man's mouth is too small, and he
actually seems to be drowning, but it is Pac-Man at the center
of today's image.  There is no doubt of that

I named the picture "Pac-Man Strikes Again".  Just when we
assumed the little gobbler was gone for good, he shows up to
annoy us again.  With the outside set to the normal <iter>, the
image is all right, but just average.  The setting of <tdis>
makes the image just striking enough to qualify as the first
FOTD for the month of July.

The image has been rated at a 6 -- slightly above average.  But
this rating is true for the 640x480 resolution.  At a higher
resolution the bands become better defined, and the rating jumps
to a 7.  The render time of the parameter file is a relatively
slow 29 minutes and 14 seconds on a 200mhz Pentium at 640x480.

As is always the case, the GIF image will soon be available on
the internet at:

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

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was hazy, hot and humid, with a
temperature of 96F (35.5C) and a noisy thunder-storm with heavy
rain in the evening.  The cats took it easy in the yard all
afternoon and hid themselves when the storm came up.

It's now time to enjoy (if possible) a relaxing Sunday.  But
I'll return at the usual time with another fractal to awe and
inspire.  Until then, take care, and fractals are more fun than
a barrel of Pac-Men.


Jim Muth
[e-mail]


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

PacManStrikesAgain { ; time=0:29:12.18--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=1
  center-mag=+0.28719980382691/-0.683275948032916/71\
  42.408/1/-37.5 params=1.414213562373/0/-4/0 float=y
  maxiter=12000 inside=255 outside=tdis periodicity=9
  colors=000GnYFmaEleEkhDjlCipBhsAgwAgzFfvJesNepRdmV\
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  omBvt8poAkkBefC`bDWZEQUFLQGEKHGMHHNHJOHKPHLQHNRHOS\
  HPTHRUHSVHTWHJrKJqNIpRzr0
  }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a
}

END 20.0 PAR-FORMULA FILE==================================


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

From: [e-mail]
Subject: (fractint) Missing FOTD
Date: 02 Jul 2001 11:08:44 EDT

Fractal Enthusiasts:

Due to severe weather and a power outage at Fractal Central, there
will be no FOTD for July 2.  The July 3 FOTD will appear on schedule.

Jim M.

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From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  03-07-01  (The Smallest Midget [7])
Date: 02 Jul 2001 22:45:09 -0400 (EDT)


Classic FOTD -- July 03, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

The FOTD for July 2, which, due to a power failure, was finished
too late to be the FOTD for July 2, now appears as the FOTD for
July 3.  I named the picture "The Smallest Midget", not to be
confused with "The Littlest Angel".  The 'smallest' in the name
refers not to the size of the midget, but to the exponent of Z
in the formula that drew the midget.

With an exponent of only 1.15, the function of today's fractal
is perilously close to being linear, and linear functions do not
produce fractals.  But thanks to the 'Branch Cut' formula, we
can go as far out the logarithmic spiral as necessary to find an
interesting section of the infinite fractal, which seems to
expand and become ever more detailed the farther out we travel.

In today's case, we travel out 320 turns, to where the parent
fractal resembles nothing as much as an egg with just about the
longest tail ever seen.  Today's midget lies about halfway out
that mammoth tail, and finding it was no easy task.

The shape of the midget quite accurately reflects the shape of
the parent fractal, humungous tail and all.  The excessive
maxiter is necessary to fully define the midget, which at a
lower maxiter has sections where the surrounding chaos appears
to blend smoothly into the midget rather than form a well-
defined sharp edge.

I colored the inside of the midget a brilliant white instead of
the normal black.  This way the midget reminds me of the candles
that kept Fractal Central illuminated last night when the entire
area was blacked out.  The stream of chaos trailing from the
midget could almost be taken for the column of heat rising from
a candle flame.

I rated the picture at a 7.  The picture is worth it considering
the extra attention I gave to its coloring.  And with a render
time of 11 minutes, running the parameter file does not try
one's patience beyond endurance.  Of course, the GIF image will
soon be available on the internet at:

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

and:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

But give Paul and Scott a chance to post the image before
visiting.

The fractal weather today was as good as it gets around here,
with the bluest skies and a temperature of 72F (22C).  These
conditions made the fractal cats happy, much in contrast to
yesterday, when a violent thunder-storm struck in the evening,
with winds of near 120kph, torrential rain, continuous lightning
and even a scattering of hailstones.  When the wind and thunder
finally died down, the cats didn't show themselves for over an
hour.  Luckily, it was a Sunday, with little computer work to be
done when the power failed.

It's now Monday evening however -- time to give the cats their
end-of-day snack and shut down the fractal place until tomorrow.
Until then, take care, and weather is supposed to be chaotic and
even fractal in nature, but I saw no fractal midgets in
yesterday's storm.


Jim Muth
[e-mail]


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

TheSmallest_Midget { ; time=0:11:01.14--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=1
  center-mag=-12.88324182229829000/-10.9467020423215\
  4000/4045361/1/150 params=1.15/0/320/800 float=y
  maxiter=75000 inside=255 logmap=94 periodicity=10
  colors=000K0AK0AK0AK0AK0AK0AK0AK0AK0AK4AK7AKBAKEAL\
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  zzTzzSzzSzzRzzRzzQzzQzzQzzPzzPzzOzzOzzNzzNzzMzzMzz\
  LzzLzzKzzRzzYzzdzzkzzlzzz
  }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a
}

END 20.0 PAR-FORMULA FILE==================================


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

From: "O Bd" <[e-mail]>
Subject: (fractint) July's FOTD
Date: 03 Jul 2001 19:15:57 +0800

Jim!

What happened to this...?

--------

On June 15, 2001 Jim Muth wrote...

"I have decided that the month of July will me a midgetless month."

--------

I was kinda looking forward to this. Not that I'm not enjoying what we're getting but...

O Bd.
--

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From: Jim Muth <[e-mail]>
Subject: (fractint) Re: July's FOTD
Date: 03 Jul 2001 09:36:52 -0400 (EDT)

At 07:15 PM 7/3/01 +0800, O Bd wrote:
>Jim!
>
>What happened to this...?
>
>--------
>
>On June 15, 2001 Jim Muth wrote...
>
>"I have decided that the month of July will me a midgetless month."

I meant a month without a *quadratic* midget.

>I was kinda looking forward to this.

There will be enough FOTD's with no 'midgets' of any kind before the
month is finished.

>Not that I'm not enjoying what we're getting but...

...you're a bit disappointed?

Jim M.


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

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) Re: July's FOTD
Date: 03 Jul 2001 16:07:37 -0000

> >On June 15, 2001 Jim Muth wrote...
> >
> >"I have decided that the month of July will me a midgetless month."
>
>I meant a month without a *quadratic* midget.

Now there's a thought... quadratic midgets occur in all sorts of formulas,
but has anyone ever seen, say, a cubic Mandelbrot in any formula other than
z^3+C?

Thanks.
Andrew.

_________________________________________________________________________
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From: [e-mail]
Subject: Re: (fractint) Re: July's FOTD
Date: 03 Jul 2001 10:13:40 -0600

Andrew,

You can find cubic midgets in HalleyNova fractals, which are like
Nova fractals (derived from Newton fractals) but using Halley's
method instead of Newton's method. Newton's method converges
quadratically, but Halley's method converges cubically. You can
extend the technique to use any-degree approximation and thus
produce Newton-like fractals qith any kind of midget you want.

--Damien

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From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Fractal math
Date: 03 Jul 2001 14:33:06 -0400


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> I did the math and roots  in Octave. I hope I haven't made any mistakes=
 but if I did someone will help.
> Respectfully
> Doug Stewart

I have a text file on my disk with all these up to period 8, and to more =
decimal places. :-) From a short C program I wrote that calculates them w=
ith Newton's method.<br clear=3Dall><hr>Get Your Private, Free E-mail fro=
m MSN Hotmail at <a href=3D"http://www.hotmail.com">http://www.hotmail.co=
m</a>.<br></p>

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<HTML><BODY STYLE=3D"background-color:#ffffff;font:10pt verdana; border:n=
one;"><FONT face=3DArial> <BLOCKQUOTE style=3D"PADDING-RIGHT: 0px; PADDIN=
G-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIG=
HT: 0px"> <DIV align=3Dleft> <DIV align=3Dleft> <DIV> </DIV> <DIV>&g=
t; I did the math and roots  in Octave. I hope I haven't made any mi=
stakes but if I did someone will help.</DIV> <DIV>> Respectfully</DIV>=
 <DIV>> Doug Stewart</DIV> <DIV> </DIV> <DIV>I have a text file o=
n my disk with all these up to period 8, and to more decimal places. :-) =
From a short C program I wrote that calculates them with Newton's method.=
</DIV></DIV></FONT></DIV></BLOCKQUOTE></BODY></HTML><DIV><BR><br clear=3D=
all><hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http=
://www.hotmail.com">http://www.hotmail.com</a>.<br></p></DIV>

------=_NextPart_001_0001_01C103CD.138EF700--

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From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) C-FOTD 30-06-01 (Head of Zardoz [4])
Date: 03 Jul 2001 14:39:28 -0400


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> This three-way stretching appears quite often around holes when
> they are sliced in odd directions.  There must be some geometric
> feature of the Julibrot causing the effect, which would be quite
> apparent if we could visualize four-dimensional forms.

The stretching is also a dead giveaway that the image is in an odd slice =
and not merely perturbed. It's because the behavior of the iteration with=
 respect to the screen coordinates is not constrained by the Cauchy-Riema=
nn equations, which it is in slices parallel to the c-plane (fixed z_0) o=
r the z_0 plane (fixed c).<br clear=3Dall><hr>Get Your Private, Free E-ma=
il from MSN Hotmail at <a href=3D"http://www.hotmail.com">http://www.hotm=
ail.com</a>.<br></p>

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<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> This thre=
e-way stretching appears quite often around holes when<BR>> they are s=
liced in odd directions.  There must be some geometric<BR>> featu=
re of the Julibrot causing the effect, which would be quite<BR>> appar=
ent if we could visualize four-dimensional forms.</DIV> <DIV> </DIV>=
 <DIV>The stretching is also a dead giveaway that the image is in an odd =
slice and not merely perturbed. It's because the behavior of the iteratio=
n with respect to the screen coordinates is not constrained by the Cauchy=
-Riemann equations, which it is in slices parallel to the c-plane (fixed =
z_0) or the z_0 plane (fixed c).</DIV></BODY></HTML><DIV><BR><br clear=3D=
all><hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http=
://www.hotmail.com">http://www.hotmail.com</a>.<br></p></DIV>

------=_NextPart_001_0002_01C103CD.F6F4C560--

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From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Fractal math
Date: 03 Jul 2001 14:41:50 -0400


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> But if you just plot all the points in all those infinitesimal bays,
> together they will appear like an outline of the Mandelbrot set (a kind
> of dust that grows ever denser near the "shoreline"...)

I think I mentioned that earlier in the thread, when I said that these po=
ints accumulate on the boundary of M.<br clear=3Dall><hr>Get Your Private=
, Free E-mail from MSN Hotmail at <a href=3D"http://www.hotmail.com">http=
://www.hotmail.com</a>.<br></p>

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<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV><BR></DIV> <DI=
V>> But if you just plot all the points in all those infinitesimal bay=
s,<BR>> together they will appear like an outline of the Mandelbrot se=
t (a kind<BR>> of dust that grows ever denser near the "shoreline"...)=
</DIV> <DIV> </DIV> <DIV>I think I mentioned that earlier in the thr=
ead, when I said that these points accumulate on the boundary of M.</DIV>=
</BODY></HTML><DIV><BR><br clear=3Dall><hr>Get Your Private, Free E-mail =
from MSN Hotmail at <a href=3D"http://www.hotmail.com">http://www.hotmail=
.com</a>.<br></p></DIV>

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From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Fractal math
Date: 03 Jul 2001 14:50:32 -0400


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> But there is only one root per bay so you will see an outline of the
> manelbrot set but the shore line will not be defined, only a dot for ea=
ch
> small bay and there are many small bays on the shore line.

The proof is in 3 steps.
1. A point on the boundary of M with rational internal angle in a compone=
nt in M is where a cardioid cusps or a bud attaches
   to a component -- a "root". In images, the bottom of a "valley". In th=
is valley, other buds form sequences that shrink
   toward the root. The centers of these are in the above set and accumul=
ate on the root. So these points are in the set.
   The set of points with rational external angle with odd denominator in=
 lowest terms thus lies in the closure of these
   centers.
2. The remaining points of rational external angle (even denominator in l=
owest terms) are the Misiurewicz points -- points
   on filaments, often filament tips or branching points. These are easil=
y seen to have sequences of mini Mandelbrots that
   shrink toward them. The centers of their cardioids accumulate to them,=
 and the Misiurewicz points lie in the closure of
   the set of component centers. That takes care of all points with ratio=
nal external angle on the boundary of M.
3. Here we assume that M is locally connected, a conjecture with strong e=
vidence for it, but to the best of my knowledge
   not yet proven (or disproven). If this is true, all points with irrati=
onal external angle are accumulation points of points with
   rational external angle, and lie in the closure of the closure of the =
set of component centers. But the closure of a closure
   is the original closure, which puts the whole of the boundary of M in =
the component centers' closure.<br clear=3Dall><hr>Get Your Private, Free=
 E-mail from MSN Hotmail at <a href=3D"http://www.hotmail.com">http://www=
.hotmail.com</a>.<br></p>

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<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV><BR></DIV> <DI=
V>> But there is only one root per bay so you will see an outline of t=
he<BR>> manelbrot set but the shore line will not be defined, only a d=
ot for each<BR>> small bay and there are many small bays on the shore =
line.<BR></DIV> <DIV>The proof is in 3 steps.</DIV> <DIV>1. A point =
on the boundary of M with rational internal angle in a component in M is =
where a cardioid cusps or a bud attaches</DIV> <DIV>   to a com=
ponent -- a "root". In images, the bottom of a "valley". In thi=
s valley, other buds form sequences that shrink</DIV> <DIV>   t=
oward the root. The centers of these are in the above set and accumulate =
on the root. So these points are in the set.</DIV> <DIV>   The =
set of points with rational external angle with odd denominator in lowest=
 terms thus lies in the closure of these</DIV> <DIV>   centers.=
</DIV> <DIV>2. The remaining points of rational external angle (even deno=
minator in lowest terms) are the Misiurewicz points -- points</DIV> <DIV>=
   on filaments, often filament tips or branching poi=
nts. These are easily seen to have sequences of mini Mandelbrots that</DI=
V> <DIV>   shrink toward them. The centers of their cardioids a=
ccumulate to them, and the Misiurewicz points lie in the closure of</DIV>=
 <DIV>   the set of component centers. That takes care of all p=
oints with rational external angle on the boundary of M.</DIV> <DIV>3. He=
re we assume that M is locally connected, a conjecture with strong eviden=
ce for it, but to the best of my knowledge</DIV> <DIV>   not ye=
t proven (or disproven). If this is true, all points with irrational exte=
rnal angle are accumulation points of points with</DIV> <DIV>  =
 rational external angle, and lie in the closure of the closure of the se=
t of component centers. But the closure of a closure</DIV> <DIV> &nb=
sp; is the original closure, which puts the whole of the boundary of M in=
 the component centers' closure.</DIV></BODY></HTML><DIV><BR><br clear=3D=
all><hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http=
://www.hotmail.com">http://www.hotmail.com</a>.<br></p></DIV>

------=_NextPart_001_0004_01C103CF.82D38B60--

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

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Re: July's FOTD
Date: 03 Jul 2001 14:55:36 -0400


------=_NextPart_001_0005_01C103D0.3779E1E0
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

> I meant a month without a *quadratic* midget.

Someone here seems to be a prime candidate for public office... :-)<br cl=
ear=3Dall><hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D=
"http://www.hotmail.com">http://www.hotmail.com</a>.<br></p>

------=_NextPart_001_0005_01C103D0.3779E1E0
Content-Type: text/html; charset="iso-8859-1"
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<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> I meant a=
 month without a *quadratic* midget.<BR></DIV> <DIV>Someone here seems to=
 be a prime candidate for public office... :-)</DIV></BODY></HTML><DIV><B=
R><br clear=3Dall><hr>Get Your Private, Free E-mail from MSN Hotmail at <=
a href=3D"http://www.hotmail.com">http://www.hotmail.com</a>.<br></p></DI=
V>

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

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Re: July's FOTD
Date: 03 Jul 2001 14:56:48 -0400


------=_NextPart_001_0006_01C103D0.629FB840
Content-Type: text/plain; charset="iso-8859-1"
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> Now there's a thought... quadratic midgets occur in all sorts of formul=
as,
> but has anyone ever seen, say, a cubic Mandelbrot in any formula other =
than
> z^3+C?

Sure. I constructed a quartic years ago to exhibit one. And I did it deli=
berately. And it worked. The only requirement is that the critical point =
you use be a zero of the derivative with multiplicity two.<br clear=3Dall=
><hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http://=
www.hotmail.com">http://www.hotmail.com</a>.<br></p>

------=_NextPart_001_0006_01C103D0.629FB840
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> Now there=
's a thought... quadratic midgets occur in all sorts of formulas,<BR>>=
 but has anyone ever seen, say, a cubic Mandelbrot in any formula other t=
han<BR>> z^3+C?<BR></DIV> <DIV>Sure. I constructed a quartic years ago=
 to exhibit one. And I did it deliberately. And it worked. The only requi=
rement is that the critical point you use be a zero of the derivativ=
e with multiplicity two.</DIV></BODY></HTML><DIV><BR><br clear=3Dall><hr>=
Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http://www.h=
otmail.com">http://www.hotmail.com</a>.<br></p></DIV>

------=_NextPart_001_0006_01C103D0.629FB840--

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

From: Mark Christenson <[e-mail]>
Subject: Re: (fractint) Re: July's FOTD
Date: 03 Jul 2001 21:42:57 -0700

</lurk>

At 04:07 PM 7/3/01 -0000, Andrew wrote:
>> >On June 15, 2001 Jim Muth wrote...
>> >
>> >"I have decided that the month of July will me a midgetless month."
>>
>>I meant a month without a *quadratic* midget.
>
>Now there's a thought... quadratic midgets occur in all sorts of formulas,
>but has anyone ever seen, say, a cubic Mandelbrot in any formula other than
>z^3+C?

No cubics, but I have witnessed z^4 midgets in one of my
gravibrots.  Will advise which if you're interested.  I could
direct you to Bud's Fractal Pages, but they're temporarily
offline...


Aloha,
        Bud

<lurk>


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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  04-07-01  (Mand-Newt Eruption [8])
Date: 04 Jul 2001 10:04:54 -0400 (EDT)


Classic FOTD -- July 04, 2001 (Rating 8)

Fractal visionaries and enthusiasts:

Today's FOTD image has no quadratic midget.  In fact, it has no
midget at all.  It is simply a design created by number 13 in my
series of 14 MandNewt formulae, which use variations of the
famous Ikenaga function to create fractals.  Formula numbers 13
and 14 are recent additions to the MandNewt series, which until
now has consisted of only 12 formulae.

Almost the entire image consists of bof60 inside fill.  This
fill changes an otherwise flat inside area into a series of
overlapping bubbles, which can make interesting images.  Today's
scene is one of these images.

It is a rather stately scene with its left-right symmetry.  Some
may see a series of hot-air balloons filling with a grainy
green-and-pink gas; others may see a scene in some surrealistic
outer space.  I see a kind of eruption, and have therefore named
the picture "Mand-Newt Eruption".

I rather like the hazy effect created by the bright blue areas.
In my opinion, this plus the overall appearance gives the image
an exceptional rating of 8, which may be a bit liberal.

The 4-minute render time of the parameter file at a resolution
of 640x480 is bearable, but this is one of those images that
looks best at the highest resolution possible.

The download of the GIF image will soon be available on Paul's
web site at:

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

and on Scott's site at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today here at Fractal Central was
uneventful, with partly cloudy skies and a temperature of 84F
(29C).  The cats must have approved, for they spent most of the
afternoon lounging in the yard.

Today however is Independence Day in the USA, and that means
fireworks.  The cats don't like noise, so I suppose they'll be
skittish most of the day.  As for myself, I'm simply going to
do as little as possible.  Until next time, take care, and
fractals are fun; arguing politics is not.


Jim Muth
[e-mail]


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

Mand-Newt_Eruption { ; time=0:04:22.60--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandNewt13 passes=1 center-mag=8.84911\
  /-9.84213e-014/3.120633/1/-90 params=-4.159/-3.693\
  /-4.144/-0.685/0.119/-0.783 float=y maxiter=90
  inside=bof60 logmap=yes periodicity=0 colors=000I8\
  UJAXKC_LEbMGeNIhOKkPMnQOqRPtQPwPOxONxNMyMLzLKyKJxJ\
  IwIHuHGsGFqFEoEDmDCkCBiBAgA9e98c87a76_65Y07W06U05S\
  04Q03O02M01K00I00G00E0AC0KW3NX5PZ9R`CSaEWcGXeIZhL`\
  jNclPemRgnShpWhuUjrUjpSlnSlmRllRmjPmhPmgNncNnaLp`L\
  pZLpXKrWKrUIrSIsPGsNGuLEuKEuICvGCvE0w0CvCLuNUsWare\
  jpnrnvymzzmzznzznzznzzpzzpzzpzyrz000<158>000
  }

frm:MandNewt13 {; Jim Muth
z=g=pixel, a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), e=real(p3), f=imag(p3):
h=z^a+(g-b)*z-f
j=c*z^d+g
z=z-e*h/j,
0.000000000000000000000000000001 <= |h|
}

END 20.0 PAR-FORMULA FILE==================================


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

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) C-FOTD 04-07-01 (Mand-Newt Eruption [8])
Date: 05 Jul 2001 12:44:03 -0000

>From: Jim Muth Reply-To: [e-mail] To:
>[e-mail] CC: [e-mail] Subject:
>(fractint) C-FOTD 04-07-01 (Mand-Newt Eruption [8]) Date: Wed, 4 Jul 2001
>10:04:54 -0400 (EDT)
>
>
>Classic FOTD -- July 04, 2001 (Rating 8)
>
>Fractal visionaries and enthusiasts:
>
>Today's FOTD image has no quadratic midget

>I rather like the hazy effect created by the bright blue areas. In my
>opinion, this plus the overall appearance gives the image an exceptional
>rating of 8, which may be a bit liberal.

That is indeed a very cool image!

Thanks.
Andrew.

_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.


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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  05-07-01  (Platform in Space [7])
Date: 05 Jul 2001 10:30:32 -0400 (EDT)


Classic FOTD -- July 05, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

Since the FOTD is already late, and it is a slow one, I'll make
the discussion short.

To begin, in keeping with the theme of a midgetless July, the
image has no midget.  The iterated formula that drew the image
is Z^1.03+C.  I named the picture "Platform in Space" because
that's what it reminds me of.  I rated it at a 7 because I feel
it's above average.

It's an unusually slow image to render, taking over 2 hours of
computer time on a tired old Pentium 200mhz machine.  Therefore
the best way to view it is to give Paul and Scott a chance to
render it and then visit their Web sites at:

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

and:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather on the Independence Day holiday featured
fireworks from nature.  A series of heavy thunder-showers in the
evening put a damper on the man-made variety.  The temperature
of 86F (30C) did little to ease the fractal cats' skittishness.

And it's now time for an active day doing other things.  Until
next time, take care, and hope for the best.


Jim Muth
[e-mail]


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

Platform_in_Space  { ; time=2:01:41.52--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=recip passes=1
  center-mag=-8.54499/-3.05261/4.14962/1/-29.999
  params=1.03/0/-7.53/800 float=y maxiter=12000
  inside=0 logmap=57 symmetry=none periodicity=10
  colors=000ZN`YMaXLbWKcVJdUIfTIgSHhRGiQFjPEkODlODmC\
  5PE7NF9MGBKIDJJEHKGGMIENKDOLCNNENOFNQGNRINSJNUKNVM\
  NXNNYONZQM`RMaSMcUMdVMeWMgYMhZMj_MkaMlbLncLoeLqfLr\
  gLsiLujLvkLxmLynLzoQujVpeZl`cgWheTgcSfbRfaRe_QdZPd\
  YPcXOcVObUNaTMaRM`QL`PL_OKZMJZLJYKIZIJYJIYJIYJIYJI\
  YJHYJHXJHXJHXKGXKGXKGXKGWKFWKFWKFWKFWLEWLEWLEVLEVL\
  DVLDVLDVLDVMCUMCUMCUMCUMBUMBUMBTJCUMBVOBWRAXTAYW9Z\
  Y9_`8`b8ad8`bB_aE_`HZ_JYYMYXPXWRWVUWUXVSZVRaUQdTPf\
  TOiSMlRLnRKqQJtSHuQIvOJvMKvLKvJLwHMwGMwENwCOwAPx9P\
  x7Qx5Rx2Sz4Rz6Rz8QzAQzCPzEPzGPzIOzKOzMNzONzQMzSMzU\
  MzWLzYLz_KzaKzcKzZMzUOzPQzKSzFUzBVzBUzCTzDRzZKzZLz\
  ZLz_Lz_Lz`Mz`Mz`MzaMzaNzaNzbNzbNzbNz`PzZRzXTzVVzTW\
  zRYzP_zNazLbzJdzHfzFhzDizEgzFfzGezHdzIczJbzKazL_zM\
  ZzNYzOXzPWzQVzRUzSSzTRzUQzVPzWOzXNzYMzdMzkMzrMzqLz\
  pLzoLznKzmKzlKzkJzjJziJzhIzgIzfIzeHzdHzcHzbHzaGz`G\
  zeTzdTzcSzbRzbQzaPz`Oz_Nz
  }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a
}

END 20.0 PAR-FORMULA FILE==================================


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

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) C-FOTD 04-07-01 (Mand-Newt Eruption [8])
Date: 05 Jul 2001 20:03:01 -0400


------=_NextPart_001_0001_01C1058D.7ED06A00
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

> Today however is Independence Day in the USA, and that means
> fireworks.

If you like fJuly 4 fireworks, then there's a particularly apt choice of =
sci-fi movie for the night ...<br clear=3Dall><hr>Get Your Private, Free =
E-mail from MSN Hotmail at <a href=3D"http://www.hotmail.com">http://www.=
hotmail.com</a>.<br></p>

------=_NextPart_001_0001_01C1058D.7ED06A00
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> Today how=
ever is Independence Day in the USA, and that means<BR>> fireworks.</D=
IV> <DIV> </DIV> <DIV>If you like fJuly 4 fireworks, then there's a =
particularly apt choice of sci-fi movie for the night ...</DIV></BODY></H=
TML><DIV><BR><br clear=3Dall><hr>Get Your Private, Free E-mail from MSN H=
otmail at <a href=3D"http://www.hotmail.com">http://www.hotmail.com</a>.<=
br></p></DIV>

------=_NextPart_001_0001_01C1058D.7ED06A00--

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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  06-07-01  (Monument to Nothing [7])
Date: 06 Jul 2001 00:30:12 -0400 (EDT)


Classic FOTD -- July 06, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

When I first saw today's fractal, it reminded me of a wooly
mammoth, one of those hairy, elephant-like animals that roamed
much of the earth until early man hunted them to extinction.
But after further consideration, I decided I was looking at a
roughly carved monument, perhaps a religious idol created and
worshipped by some forgotten tribe of hominids.  When I was
unable to decide what the monument commemorated, I named the
image "Monument to Nothing".

The picture rates an above average 7.  I especially like the way
the foreground features stand out in contrast to the vaguely
patterned purplish background.  Actually, the foreground objects
are on the highest iteration.  Fractals are not always what they
seem.

The expression Z^1.009+C was iterated to produce the image.  The
MandelbrotBC1 formula, which displays remote parts of the
infinite complex-log spiral, assured that this near-linear
expression produced at least a little chaos.

Actually, it produces quite a bit of chaos.  The entire
surrounding area, which lies near the shore of the parent
fractal's lake, resembles nothing as much as a crazy quilt, with
apparently random patterns and textures everywhere.

The image renders in considerably less time than yesterday's
2-hour dawdler, but at almost 27 minutes on a Pentium 200mhz, it
is certainly no quickie.  My advice is to give Paul and Scott a
chance to render and post the image to their Web sites at:

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

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

and download the GIF image from there.

The fractal weather today featured a temperature of 85F (29.5C)
followed by a tornado scare.  Luckily, the twister fizzled into
just another heavy thunder-storm by the time it arrived at
Fractal Central.  But the crackling lightning and roaring winds
sent the fractal cats scurrying for safety under the bed.  They
are just now getting over their scare.

That's it for today, fractal fans.  The cats have recovered, and
I'll return in 24 hours or so with another fractal with no
quadratic midget.  Until then, take care, and beware of fractals
lurking in dark places.


Jim Muth
[e-mail]


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

MonumentToNothing  { ; time=0:26:47.66--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=1
  center-mag=+0.6528807149373907/+1.259183430170431/\
  286.6663/1/-49.999 params=1.009/0/120/2400 float=y
  maxiter=1800 inside=255 logmap=645 periodicity=10
  colors=000WUzWUzXUzYUz_Uz`UzaUzcUzbUzbUzaUzaUz`Uz`\
  Uz`Uz_Uz_UzZUzZUzYUzYUzYUzaUzdUzgUzjUzmUzpUzsUzxUz\
  vUztUzsUzqUzoUznUzlUzkUziUzgUzfUzdUzcUzaUz_UzZUzXU\
  zWUzUUzSUzRUzPUzFUzKUzOUzSUzWUz_UzcUzgUzkUzqUzpUzo\
  UznUznUzmUzlUzkUzkUzjUziUziUzhUzgUzfUzfUzeUzdUzfUz\
  eUzdUzcUzbUzaUzaUz`Uz_UzZUzYUzYUzXUzWUzVUzUUzUUzTU\
  zSUzRUzQUzQUzPUzOUzNUzMUzMUzNUzOUzPUzPUzQUzRUzSUzS\
  UzTUzUUzUUzVUzWUzXUzXUzYUzZUz_Uz_Uz`UzaUzaUzbUzcUz\
  dUzdUzeUzfUziUzfUzcUz`UzZUzWUzTUzQUzOUzLUzIUzFUz8U\
  zDUzIUzNUzRUzWUz`UzeUziUznUzsUzWUziUzwUzvUzuUztUzt\
  UzsUzrUzqUzqUzpUzoUzoUznUzmUzlUzlUzkUzjUziUziUzhUz\
  gUztUymUxgUwaUvVUuPZtKcsKhrUmqcmpmrompohnnclmZklUi\
  lPgkJejJdiJbhJ`hJZgIYfIWeIUeISdIRcIPbINaILaIK`II_I\
  GZIEZIDYIBXI9WI7WI5WI2VI0VI0VI0UI0UI0TI0TI0SI0SI0R\
  I0RI0QI0QI0PI0PI0OI0OI0NI0NI0MI0MI0LI0LI0KG0KH0KI0\
  KI0KJ0KJ0KK0KK0KL0KM0KL0K
  }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a
}

END 20.0 PAR-FORMULA FILE==================================


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

From: Gedeon <[e-mail]>
Subject: (fractint) new web site
Date: 06 Jul 2001 11:36:13 -0400

Due to the termination of NBCi's web space hosting, I closed my extensive
web site at that location. My new site is much smaller, for the time being
only a single page, containing both old and new images. The gfp.ufm formula
file is available for download at the site, but, of course, it is also
available at the Ultrafractal Formula database. I regret, however, that due
to space limitations Morgan Owens' chebyshev formula file will no longer be
available at my site. Janet Preslar generously consented to hosting it at
her Ultrafractal Resources page.

I invite you to visit my new site at the address below, and your comments
are welcome.

Best regards,

Gedeon
------
FRACTALS: http://www.geocities.com/gedeonp/fractals/frindex.html
Established: July 5, 2001
Member Infinite Fractal Loop
PHOTOGRAPHY: http://www.geocities.com/gedeonp/photos/phindex.html
Established: July 5, 2001
------



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

From: [e-mail]
Subject: (fractint) C-FOTD  07-07-01  (Mysterious Darkness [6])
Date: 06 Jul 2001 21:35:08 EDT


Classic FOTD -- July 07, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

With today's image, the string of FOTD's without benefit of a
quadratic midget, continues unabated.

Today's image was created by number 14 in my series of 14
formulae based on distortions of the Ikenaga function, a
function that must do little other than make fractals, since its
creator has apparently disowned it.

I had a bit of a problem finding a name for today's fractal.
Some of the names that came to mind as I studied the image are
unmentionable.  But after making my mind a blank, (no problem
for me), I finally centered my attention on the fractal elements
converging on the mysterious dark area at top center.  The
darkness appeared most mysterious, inspiring the name
"Mysterious Darkness".

Actually, most of the image consists of 'inside' area, which has
been colored with an inside fill of bof60.  The few outside
areas are colored with the 'real' option, though this makes
little difference in the overall appearance.

I rated the image at only a 6.  The green and purple color
palette is not really very harmonious, though it is rather
attention-getting.  With a better color scheme, the image might
have rated a 7 or 8.

The image renders from the attached parameter file in a little
under 9 minutes on a rusty old Pentium 200mhz machine optimized
for Fractint fractals.  For those who would rather not fuss with
parameter files, the ready-to-view GIF image will soon be
available on the internet at Paul's web site at the URL:

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

and at Scott's site at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was absolutely perfect, with crystal
blue skies, refreshingly dry atmosphere, gentle winds, and a
temperature of 79F (26C).  The fractal cats relished the
conditions in the shade of the fractal holly tree.

As for me, I'd relish an evening watching a bit of junky TV.
Maybe I'll put on one of my many 'Dark Shadows' tapes to keep
with the dark mood of today's FOTD.  They're always good for a
hoot.  Until next time, take care, and in time of need, a good
fractal may be a life saver.


Jim Muth
[e-mail]


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

MysteriousDarkness { ; time=0:08:43.44--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandNewt14 passes=1 center-mag=6.36546\
  /-1.11022e-016/0.8933869/1.1682/-90
  params=-1.5411/0.5839/4.434/0.6981/-1.545/-5.4089
  float=y maxiter=180 inside=bof60
  outside=real logmap=yes periodicity=0
  colors=000FADDDFAFI8HKDKJHOIKSHOXFS_FXcEZgDbkBfoBj\
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  7K20X00U00R00O00M23K46I7A
  }

frm:MandNewt14 {; Jim Muth
z=g=pixel, a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), e=real(p3), f=imag(p3):
h=z^a+(g-1)*(z-b)
j=c*z^d+g
z=z-e*h/(f*j),
0.000000000000000000000000000001 <= |h|
}

END 20.0 PAR-FORMULA FILE==================================

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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  08-07-01  (N-D-E [6])
Date: 08 Jul 2001 10:21:20 -0400 (EDT)


Classic FOTD -- July 08, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Having posted my FOTD's on the web for several years, my e-mail
addresses are on many mailing lists, and as a result I receive a
lot of unwanted e-mail.  This morning was no exception.  On
opening my e-mail box, I found the expected large number of
'spam' letters.  I usually delete these messages after reading
the first line.  But I was amused this morning by the way every
letter began with an excuse -- a reason why it was not spam.

One letter told me that I had received it because I had 'opted
in', whatever that means.  Two others claimed to be replying to
my previous 'inquiry'.  Another claimed to be from a long-lost
relative.  (Funny that the relative's letter ended with a form,
complete with a space for credit-card number, to fill in if I
wanted to receive the product, which curiously enough was a
program that would let me find long-lost relatives.)  Another
letter, of the highest priority, claimed to contain an urgent
message.  Unfortunately for the seller, I am not desperate to
lose weight just in time for the summer season.  Next, there was
the letter telling me how to get rich quick by telling others
how to get rich quick.  I have never figured out where the
extra money is supposed to come from in these schemes where
everyone gets rich.  Finally, I opened a letter informing me
that I was in imminent danger of losing my soul unless I did as
the well-meaning sender described.

The final letter, about the fate of my soul, inspired the name
for today's FOTD image.  I had been thinking about what to name
the image for almost 1/2 hour when I read the soul-saving
letter.  Since the letter reminded me of an after-death journey
to somewhere, I named the image "N-D-E", which is short for
"Near-Death Experience", an experience that those who have come
close to death sometimes have.  The experience takes many forms.
In one of the most common, the person seems to leave their body
and travel through a tunnel toward a light, frequently meeting
lost loved ones and religious figures at the far end.

Believers feel that the experience is real, that the soul
actually reaches a heaven in these experiences, but is sent back
to earth because the time is not yet right.  Skeptics feel that
the experience is imaginary, a kind of dream produced by the
oxygen-deprived brain.  But both of these views go beyond what
is known for certain, and demand a degree of belief.  Still
searching for the exact meaning of the concepts 'real' and
'imaginary', I am undecided as to the nature of the NDE, and any
connection it might have to a possible 'after'-life.

Well, I see myself wandering from the fractal topic.  Today's
image is one of a midget.  No, it is not a quadratic midget, but
one of the order 1.066.  I found it by breaking out the
JimsCompMand formula, one I have not used in several years.

It may seem hard to believe, but today's midget is what is left
of the midget located at -1.75 on the negative tail of the
classic M-set.  Using the present formula, I kept track of the
midget as I lowered the exponent of Z.  The midget actually
continues below the Z^1.066 of today's image, but the render
time becomes grossly exaggerated as the midget blends into the
very high iteration chaos surrounding the main bay of the parent
fractal.  In a few days, I may present an image of this midget
as it merges into the main bay, but if so, it will be a very
slow image, taking over 12 hours to render.

Even after so much discussion, today's image rates only a 6.
But it's relatively fast and rather pleasant to behold.  And if
running a parameter file is not to your liking, the GIF image
may be found posted to the following two web sites:

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

and

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

But before visiting, give the owners time to render and post the
image.

The fractal weather today (Saturday, July 7) was once again
perfect, with deep blue skies, puffy white clouds, gentle
breezes, dry atmosphere, and a temperature of 84F (29C), which
pleased the fractal cats.

It's now time to have a peaceful Sunday, if possible.  Until
next time, take care, and there's always light at the end of the
tunnel.


Jim Muth
[e-mail]


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

N-D-E              { ; time=0:06:39.36--SF5 on a P200
  reset=2001 type=formula formulafile=jim.frm
  formulaname=JimsCompMand passes=1
  center-mag=-1.123943163353295/+0.1801440422711643/\
  614.4685/1/67.5 params=1.066/0/0.688/0/0/0 float=y
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  z5zz4zz4zz4zz4zz6zz7zz8zz9zzBzzCzzDzzEzzGzzHzzIzzJ\
  zzLzzMzzNzzOzzQzzRzzSzzTzzUzzYzz`zzdzzgzzjzzkzzkzz\
  kzzlzzlzzlzzmzzmzzmzzmzznzznzznzzozzozzozzozzgzz`z\
  zUzzMzzFzz8zz1zz3zz4zz5zz6zz7zz9zzAzzBzzCzzDzzFzzG\
  zzHzzIzzJzzKzzLzzMzzNzzNzzOzzPzzPzzQzzRzzRzzRzzRzz\
  RzzRzzRzzRzzSzzSzz1zz5zzz
  }

frm:JimsCompMand {; Jim Muth
z=c=pixel:
z=z^p1*(c^p2)+c,
|z| <= p3+100
}

END 20.0 PAR-FORMULA FILE==================================


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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  09-07-01  (The Grand Arch [6])
Date: 09 Jul 2001 08:21:02 -0400 (EDT)


Classic FOTD -- July 09, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

My only spam message this morning arrived with the subject
"You've won!"  The message informed me that I had won the first
round of a contest and was now eligible to claim my entry.
Nuts!  What a let-down!  I thought I would be eligible to claim
my prize, but discovered that I am eligible only to enter some
stupid contest, and that I must actually pay for the privilege
of entering.  I wonder how many 'contestants' fail to win the
first round of this 'contest'.  I eased my disappointment by
turning to the world of fractals.

Today's image features the work of another long-forgotten
formula, Mystic2, a formula that I wrote a number of years ago.
Because I rarely add comments to my formulae, the original
purpose of the formula is now a mystery.  Perhaps I wrote it
totally at random, just to see what it would do, and then
discarded it because with the inside set to the usual 0, it
draws nothing but circles.  If so, I acted in haste, for when a
dynamic fill such as bof60 is applied, the formula comes to life.

When the Mystic2 formula is used, all the action is on the
inside.  Today's image is a good example.  Using the bubble-
producing bof60 inside fill, the formula has produced what looks
like a grand double-arch.  The curved boundary at the bottom is
part of the ever-present circle that always appears when this
formula is used.

Since the image resembles an elaborate double-arch, I named it
"The Grand Arch".  I rated the image at a 6.  This is the third
consecutive FOTD with a rating of 6.  The attached parameter
file runs in 4-1/2 minutes, leaving it to the viewer to decide
whether to download the GIF file of the image from:

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

or from:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today began with a mild thunder-shower and
ended with another mild thunder-shower.  In between it was
sultry, with lots of clouds and a temperature of 82F (28C).  The
fractal cats were too busy sleeping to give much notice to the
weather.

It's now time to attend to other things, but the next fractal is
already cooking.  Until the next one is finished, take care, and
have a moderately good day.


Jim Muth
[e-mail]


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

The_Grand_Arch     { ; time=0:04:39.30--SF5 on a P200
  reset=2001 type=formula formulafile=jim.frm
  formulaname=Mystic2 function=sin passes=1
  center-mag=0.698216/6.66134e-016/2.801685/1/-90
  params=-5.499/1.957/7.803/1.028/0.359/-1.367
  float=y maxiter=120 inside=bof60
  logmap=yes periodicity=0
  colors=000Z`OWXLSTJPQHFFFFFFGGGHHHIIIJJJKKKe2Nc2Ma\
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  UXcOPUIGKC8A6moYikVegTbcQ
  }

frm:Mystic2 {; Jim Muth
a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), k=real(p3), f=imag(p3),
g=pixel, z=(pixel)^a+(b*(pixel))^c:
z=(fn1(z)+(d*(g)))^k+(f*(cos(g)))
g=sqr(g),
LastSqr <= 100
}

END 20.0 PAR-FORMULA FILE==================================


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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  10-07-01  (The End of a Midget [6])
Date: 10 Jul 2001 09:44:05 -0400 (EDT)


Classic FOTD -- July 10, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Today's image is very slow.  In fact it's the second slowest
FOTD of all time.  It's so slow because we've gone a long way --
we've followed the largest midget of the M-set until it is
finally ready to be absorbed into the infinite ocean of trapped
points of its parent, the god-like place where midgets go when
they cease to exist.

It's the same midget that appeared in the N-D-E image of July 8,
but what a change lowering the exponent of Z from 1.066 to 1.05
has made.  The N-D-E image renders in 6 minutes, while today's
takes 11 hours.

The big difference is that the midget, or what remains of it,
has been absorbed into the high-iteration random chaos that
stretches (invisibly at normal maxiters) along the shoreline of
the parent fractal, the nearest part of which lies just beyond
the upper right corner of the frame.

Most of the elements in the N-D-E image had iterations in the
hundreds; the blue elements in today's image have iterations in
the hundreds of thousands.  The original negative tail of the
M-set is still vaguely visible as the broad, featureless area of
blue stretching from the midget toward the left edge of the
screen.  The midget itself has degenerated until it is little
more than a distorted circle.  The only remaining recognizable
feature is East Valley, the point on the midget's lower edge,
where the features converge.  No elephants are in the scene
however.  The elephants have long since vanished, to be replaced
by scalloped features that seem to be shedding fractal debris.

The reddish area at the lower left, which eventually leads into
the midget's valley, seems almost not to belong there.  It has
an iteration in the 150 range compared to the 100,000 range of
most of the scene, and is an actual part of the shoreline of the
parent fractal, which is little more than a crooked circle.

To see how today's midget lies in relation to its parent, lower
the maxiter to 300, turn off the logmap, and back out a few
zooms.  It will be immediately apparent that, when viewing the
parent, there is no evidence of the midget's existence.  The
only way to find today's midget is to follow it as the exponent
of Z is reduced.  And even this is difficult, for the exponent
of C in the iterated formula must be adjusted by just the right
amount to keep the midget from slipping out of sight beyond some
branch-cut discontinuity.

I could have taken the process even further, but at lower
exponents of Z, the render time increases apparently without
limit.  Since as far as I can tell, the appearance of the midget
does not change at lower exponents, I decided that Z^1.05 and a
render time of almost 12 hours was a good place to stop.

And that's the story of how a midget came to its end.  I named
the picture "The End of a Midget" and rated it a 6.

For those wise fractalists who decide not to render, but to
download the finished GIF image instead, that image will soon be
available on paul's web site at:

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

It will also be available on Scott's site at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

But give them a chance to do the heavy work before visiting
their sites.

The fractal weather today (yesterday) was summer-like, with hot
sun, a temperature of 90F (32C), and happy cats.

The work today is piling up, so I'd better get busy.  I'll
return in the allotted time with a fractal that is guaranteed to
be faster.  And I might even have some philosophy to cause one
to wonder about things they would rather forget.  Until then,
take care, and don't forget to wonder about those fractals.


Jim Muth
[e-mail]


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

TheEnd_of_a_Midget { ; time=11:01:10.44-SF5 on a P200
  reset=2001 type=formula formulafile=jim.frm
  formulaname=JimsCompMand passes=t
  center-mag=-1.095780444268702/+0.155209794935997/3\
  213.186/1/52.5 params=1.05/0/0.688/0/0/0 float=y
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  zXMzXMzXMzXMzXMzWMzWMzWMz
  }

frm:JimsCompMand {; Jim Muth
z=c=pixel:
z=z^p1*(c^p2)+c,
|z| <= p3+100
}

END 20.0 PAR-FORMULA FILE==================================


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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  11-07-01  (Sea-What [4])
Date: 11 Jul 2001 11:05:02 -0400 (EDT)


Classic FOTD -- July 11, 2001 (Rating 4)

Fractal visionaries and enthusiasts:

July, 2001 has been declared midgetless month, quadratic-
midgetless that is.  So I need a way to follow the theme while
still pampering my obsession with these tiny holes that fill the
border of the Mandelbrot set as well as many other fractals.

Today I have chosen to work around the no-midget theme by
viewing the hole from a different direction.  Those who would
like to see the hole in its full quadratic-midget aspect can do
so by entering either the p3 or p4 coordinates into the Mandel
formula as center coordinates and letting it iterate.

The coordinates show that today's scene lies deep in the
Seahorse Valley area of the Mandelbrot set, or more accurately,
the extension of Seahorse Valley into the four-dimensional
Julibrot.  I'll not try to describe the orientation of today's
image in that 4-D object, since 4-D things are impossible for we
3-D limited beings to visualize.

As is usually the case in the odd slices, the area around the
hole, which in this case has been pulled into a thin slit, is
stretched and distorted.  The 2,4,8... series can be followed to
the 'four' level, but the 'eight' level is nearly lost in the
stretching and distortion closer to the hole.

I named the image "Sea-What" because, though it is a view of a
seahorse, it is like nothing to be found in the familiar
"Seahorse Valley".  And since it's not really an outstanding
image, I could rate it at only an 8.  The image may be viewed by
running the attached 7-minute parameter file or by picking up
the GIF image from Paul's web site at:

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

or from Scott's site at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was sunny and hot until 5pm, when a
very strong thunder-storm moved in, dropping the temperature
from 93F (34C) to 70F (21C).  The fractal cats enjoyed the
sudden coolness, but disliked the noise that accompanied its
arrival.

It's now almost 11am -- time to do something useful.  So until
next time, take care, and just because the fourth dimension
can't be pictured doesn't mean it's not there.


Jim Muth
[e-mail]


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

Sea_What           { ; time=0:07:41.65--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=multirot-XZ-YW-new passes=1
  center-mag=+0.00000327661430389/-0.000000049069920\
  32/1.729035e+007/0.003293/-179.142/88.744
  params=183/92/2/0/-0.749695276287/0.032780202799\
  /-0.749695276287/0.032780202799 float=y
  maxiter=12000 inside=0 periodicity=10
  colors=000ICEJEFKFGLGHMHINIJOJKPKLQLMRMNSNOTOPUPQV\
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  ebZdaXc_VaZT`YS_WQZVOYUMWSLVRJUQHTOFRNEQMCPKAOJ9NI\
  BOKDOLFOMHPNJPOKPPMQROQSQQTSQUURVVRWXRYZSZ`S_bS`dS\
  aeTbgTdiTekUfmUgoUhpUikVlgVnbVqZVsXWrWXrUXrTYqSYqQ\
  ZqPZqO_pM`pL`pKapIaoHboGboEcoDdnCdnAen9en8fm6fm5gm\
  4gm5fl6fl7el7ek8ek9dkAdjAcjBcjCciCbiDbiEbiFahFahG`\
  hH`gH`gI_gJ_fKZfKZfLZeMYeMYeNYeOXdPXdPWdQWcRWcRVcS\
  VbTUbUUbUUaVTaWTaWTaUS`TR`SQ`RP_QP_PO_NN_MMZLLZKLZ\
  JKZIJYGIYFHYEHYDGXCFXBEXAEXBDWCDVDDVECUFCTGCTHCSIB\
  RIBRJBQKAQLAPMAONAOO9NP9MQ9MQ8LR8LS8KT8JU7JV7IW7HX\
  7HX6GY6GZ6F_5E`5Ea5Db5Cc4Cd4Bd4Be3Af39g39h38i27j27\
  k26k26j37j47j47j57j67j67i78i88i88i98iA8iA8hB8hC9hC\
  9hD9hE9hE9gF9gG9gGAgHAgIA
  }

frm:multirot-XZ-YW-new {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p3, c=e*imag(pixel)+p4:
z=z^(p2)+c,
|z| <= 36  }

END 20.0 PAR-FORMULA FILE==================================


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

From: "Morgan L. Owens" <[e-mail]>
Subject: (fractint) Re: [philofractal] C-FOTD  11-07-01  (Sea-What [4])
Date: 12 Jul 2001 19:05:44 +1200

At 03:05 12/07/2001, Jim Muth wrote:

>... just because the fourth dimension
>can't be pictured doesn't mean it's not there.
>

Textures in 3-D software like POV-Ray are four-dimensional (more if you
count colouring).

Morgan L. Owens
"It's just another number."


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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  12-07-01  (An Illegal Midget [8])
Date: 12 Jul 2001 10:44:54 -0400 (EDT)


Classic FOTD -- July 12, 2001 (Rating 8)

Fractal visionaries and enthusiasts:

In yesterday's FOTD, which rated a 4, I mistakenly mentioned
that the image rated an 8.  So to atone for my error, I feel it
is proper for me to present an image today that actually rates
an 8.  But to do so I must renege on my pledge to present no
quadratic midgets in the month of July.  Well, with only one
midget, we'll call July a virtually midgetless month.

I had been saving today's image for the FOTD of August 1, which
will be the first day on which quadratic midgets will again be
permitted.  But due to the circumstances, I found it necessary
to use it today.

As I mentioned, today's image shows a very prominent midget.  It
is therefore illegal.  I named the image "The Illegal Midget"
accordingly.

The parent fractal was created by the MandelbrotMix4 formula
-10(Z^(-1.1))-0.1(Z^(-11))+(1/C), with a bailout radius of 900.
The parameter file is relatively fast, but still slow enough to
cause impatience if the machine is needed for other things.  But
relief will soon be available on the internet at Paul's web site
at:

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

and at Scott's site at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

With a temperature of 86F (30C), the fractal weather today was
near perfect, the only exception coming in the early afternoon,
when a dark cloud dropped a few large raindrops that chased the
fractal cats indoors.  Five minutes later the cloud passed on,
the sun returned, and the cats once again went into the yard.

It's now time to get busy.  Until next time, take care.


Jim Muth
[e-mail]


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

An_Illegal_Midget  { ; time=0:14:15.16--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+5.011007493464664/-0.127916407872741/8\
  75157.1/1/130 params=10/-1.1/0.1/-11/-2/800 float=y
  maxiter=2400 inside=0 logmap=221 periodicity=10
  colors=000AAiAAiAAgAAeAAcBAaCA_DAYEAWFAUGASHAQIBOJ\
  CMKDKJCIJAFI9CI7AH67H44H32F88EDDDIJCNOASU9XZ8ad7fi\
  4lq6kn8jlAijChhDgfFgcHfaJe_LdYMcWObUQbRSaPT`NV_LXZ\
  JZYH`YEaXCcWAeV8gU6hU4iT6jS7kR9lQAmPBnODoNEpMFqLHr\
  KIxMMsKJoJHjIFfHCaGA`D9YF8VH7SJ6PK6ML5JL4GL3DL3AK2\
  7K14L16K58J89KCBLFDLJEMMGLQHLTJMWLM_MMbOMfPLiRKmTK\
  pUJtWIwXIzWMuWPqVSlVVhVYcU`_UcVUgRTjMTmITpDSs9Sv4S\
  y0Qt6OoCMjILeOJ`UHW_DQcGRdJRdLSdOSeQTeTTeVUeYUf_Vf\
  bVfdWfgWgiXglXgnYgqYhsZhvZhxZhtXcqV_nTWkSShQOeOKbN\
  G_LCXJ8ZI4cJ6hK8mLAqLCsMEuNGwOIwOKwNMsNNoNOkNPgMQc\
  MR_MTVMUPLVMLWILXELYBKWBLZBO`BRbBTdBWfBZhBajBclBfn\
  BipBkrFemI`iMVdPQ`RLXUFSWAOY5KW9MWCOXFPXIRXLTYOUXR\
  WWUYWVZWXZVTUUQQTMLSJH_PCgV7pY2n_3m`3lb3kc3id3hf3g\
  g3fh3ej3ck4bm4an4`o4_q4Yr4Xs4Wt4Xu4Yv4Zw5_x6`y6az7\
  bz7cz8cz8cz9czAczAczBczBczCczCczDczEczEczFczOczRcz\
  UczXcz_czbczeczcczgczjczm
  }

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

From: [e-mail]
Subject: (fractint) Re: C-FOTD  11-07-01
Date: 12 Jul 2001 14:04:05 EDT

Morgan Owens wrote:

>Textures in 3-D software like POV-Ray are four-dimensional (more if you
>count colouring).

Yes, but we still see only 3-D variations.  Our minds tell us that the
various
3-D shapes can be taken together to form a single 4-D or 5-D hyperobject,
but that higher form must remain forever unvisualized.  Likewise, when
viewing a computer animation of a rotating 4-D object, depending on the
orientation, I see either a normal 3-D object rotating in the normal manner,
a 3-D object changing shape in a cyclical manner, or a 3-D object both
rotating and changing shape.  At no time do I see the entirety of the
undistorted 4-D object at a single moment of time.  Of course, I would
need eyes with retinas whose surfaces were three-dimensional to do so.

Jim M.

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

From: "Fernando Bresslau" <[e-mail]>
Subject: Re: (fractint) Midgets...
Date: 12 Jul 2001 10:23:19 -0300

I would even suggest you publish  a resulting sequence somewhere. I┤m
curious.
Once I downloaded a prog that would calculate the positon of midgets. It
worked, since I know the author used it to render the deepest midget found
until that time.
Fernando Bresslau

----- Original Message -----
Sent: Tuesday, June 19, 2001 7:43 AM


> Hmm, could you make a command line version that could
> take parameters from the command line or via a batch
> file, then display the results? Is there some way to
> save the results? It sounds like fun!
>
> David
> [e-mail]
>
> On 19 Jun 01 at 4:54, Multiple Bogeys wrote:
>
> > Over the past couple of days I cobbled together a small
> > C program that is possibly the first Mandelbrot
> > autoexplorer designed specifically to home in on midgets
> > -- and if not, then probably the first one that actually
> > works.
> >
> > I'd post the source code here, but there're about two
> > thousand lines of it. I'd stick it on the Web but my
> > pages are in a shambles. Besides, the interface sucks --
> > it's noninteractive with no parameters, you have to
> > actually edit the source and recompile it to change any
> > of the parameters, and without varying the parameters it
> > has a limited repertoire. It produces a short zoom
> > sequence (as many as 20 images) of grey-scaled distance
> > estimator images that look very nice and tend to close
> > in on a midget (occasionally a bud instead).
> > Occasionally it "backs up" a bit and zooms back in in a
> > slightly different spot.
>
>
> --------------------------------------------------------------
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-------------------------------------------------------------------------------

From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD  11-07-01
Date: 13 Jul 2001 15:05:13 +1200

At 06:04 13/07/2001, [e-mail] wrote:
>Morgan Owens wrote:
>
> >Textures in 3-D software like POV-Ray are four-dimensional (more if you
> >count colouring).
>
>Yes, but we still see only 3-D variations.

Funny, I only see 2-D variations. It's my mind that (with practice) puts
these together and inter/extrapolates to give me a 3-D visualisation.

Morgan L. Owens
"What sort of retinas do you have?"


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

From: "Jean-Pierre Louvet" <[e-mail]>
Subject: (fractint) Fractal Art FAQ
Date: 13 Jul 2001 11:48:40 +0200

Version 1.5 of the Fractal Art FAQ is at

http://fractals.iuta.u-bordeaux.fr/F-art-faq/ (main site)
http://www.fractalus.com/fractal-art-faq/ (thanks to Damien Jones
http://www.fractovia.org/F-art-faq/ (will be updated soon).

Any suggestion to improve this document is welcome. I really hope your
contribution. Note that the best address to private mails concerning this
FAQ is [e-mail]
(this address is read by the 3 coordinators), and for a public discussion
about this FAQ the fractal-art discussion list is strongly suggested.

Best regards.

J.P. Louvet                | Phone :  [phone]
IUT Universite Bordeaux 1  |
33405 Talence CEDEX France | email : [e-mail]
Fractales sur serveur Web IUT Universite Bordeaux 1 :
http://fractals.iuta.u-bordeaux.fr


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

From: [e-mail]
Subject: (fractint) C-FOTD  13-07-01  (Fractal Forest [7])
Date: 13 Jul 2001 08:35:05 EDT


Classic FOTD -- July 13, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

I enjoy trees, and since real trees are fractal in nature, it
should be no surprise that tree-like figures are found in
fractals.  Today's image pictures one of these fractal trees.

I originally had named the picture "Tree", but since the tree in
the picture is but one of an infinity, I finally decided on the
name "Fractal Forest".  The image is almost, but not quite, part
of a Julia set of the (-Z)^1.618034+C Julibrot figure.  It is
not a Julia set because the direction of the slice is rotated
1.8 degrees from the Julia direction.  This slight rotation
makes little difference in the overall appearance of the image,
though it does give the 'tree' a more stylized appearance.

This type of image is quite common in the world of fractals, and
it is closely connected to a rocky-landscape type of image that
I occasionally investigate.  In a day or so, I'll give an
example of the rocky landscape hiding in today's tree-like image.

I used John Goering's formula to draw the image and do the
rotating.  This formula can draw more orientations within the
Julibrot than any other I know of, though there are still some
directions that it cannot reach.

The attached parameter file renders in a couple minutes, which
is fast enough for all but the busiest fractaliers.  For those
busy fractaliers, the GIF image will soon be posted on Paul's
web site at:

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

and on Scott's site at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was near-perfect, with blue skies,
puffy clouds, and a happy-cat temperature of 82F (28C).
Unfortunately, the cats were so happy that they spent most of
the day sleeping.

As for me, I'll have to spend most of the day working.  And the
day is just starting.  But I shall return with a new FOTD in 24
hours or so.  Until that glorious moment arrives, take care, and
enjoy the day.


Jim Muth
[e-mail]


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

Fractal_Forest     { ; time=0:02:54.55--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=SliceJB-new-min passes=1 center-mag=0.\
  224291/2.56739e-016/12.49983/1.0776/90 params=0.51\
  /0.5/0.5/0.5/1.618034/0/-1.153365/0/0/0 float=y
  maxiter=1800 inside=0 logmap=5 periodicity=0
  colors=000FFQFFQFFPFFPFFPFFOFDOFDOFDMFDMFDLFDLFDLF\
  DJFDJFDIFDIFCIFCGFCGFCGFCFFCFFCDFCDFCDFCCFCCFAAFAA\
  FAAFA9FA9FA9DA7DA7DA6DA6DA6D94D94D93D93D93D91D91D9\
  1D90D90D90D70D70D70D70D70D70D70D70D70D70D70D60D60D\
  60D60D60D60D60D60D60D60D60D60F70G90IA0JA0JC0LD0MF0\
  OF0PG0PI0QI0SJ0TL0TM0VM0XO0YP0_P0_Q0`S0aT0cT0cV0dX\
  0fX0gY0i_0i`0j`0la0mc0ld0mc0mc0mc0mc0mc1mc1mc3mc3m\
  c4oc4oc6oc6oa7oa7oa9oa9oaAoaApaCpaCpaDpaDpaFpaGp`H\
  p`Ip`Jr`Kr`Lr`Mr`Nr`Or`Pr`Qr`Rr`Sr`Ts_Us_Vs_Ws_Xs_\
  Ys_Zs__s_`s_au_bu_cu_duYeuYfuYguYhuYiuYjvYkvYlvYmv\
  YnvYovYpvXqvXrvXsxXtxXuxXvxXwxXxxXyxXzxXzxXzzYzyXz\
  xXzvXzuXzsXzrXzpXzoXzmXzlXzjXziXzgXzfXzdXzcVzaVz`V\
  z_VzYVzXVzVVzTVzQVzPVzOVzMVzLVzJVzIVzGTzFTzDTzCTzA\
  Tz9Tz7Tz6Tz4Tz3Tz1Tz0Tz0Tz0Tz0Tz0Uz0Uz0Vz0Vz0Wz0Wz\
  0Xz0Xz0Yz1Yz1Zz3Zz3_z4_z4`z6`z6az7az9bzAbzAczCczDc\
  zDczFczGczGczIczJczLczLcz
  }

frm:SliceJB-new-min {; by John R. H. Goering, July 1999
  pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1),
  b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), ca=cos(a),
  cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d),
  sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
  q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg,
  s=v*sin(a), c=p+flip(q)+(p4), z=r+flip(s)+(p5):
  z=(-z)^(p3)+c
  |z|<=100
  }

END 20.0 PAR-FORMULA FILE==================================

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

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) C-FOTD 12-07-01 (An Illegal Midget [8])
Date: 13 Jul 2001 16:38:05 -0000

>From: Jim Muth <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>CC: [e-mail]
>Subject: (fractint) C-FOTD  12-07-01  (An Illegal Midget [8])
>Date: Thu, 12 Jul 2001 10:44:54 -0400 (EDT)
>
>
>Classic FOTD -- July 12, 2001 (Rating 8)
>
>Fractal visionaries and enthusiasts:

This is indeed a special image, well deserving its rating. Thankyou Jim!

Andrew.

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

From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) Re: [philofractal] C-FOTD  11-07-01  (Sea-What [4])
Date: 13 Jul 2001 16:17:07 -0500

"Morgan L. Owens" wrote:

> Textures in 3-D software like POV-Ray are four-dimensional...

In what sense?

--
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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

From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) C-FOTD 12-07-01 (An Illegal Midget [8])
Date: 13 Jul 2001 16:33:26 -0500

Andrew Coppin wrote:

> This is indeed a special image, well deserving its rating. Thankyou Jim!

Ditto!!

I especially liked the "flame" effects!

--
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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

From: Programmer Dude <[e-mail]>
Subject: (fractint) Images of .MAP files
Date: 13 Jul 2001 16:50:11 -0500

Gentle Listers-

I'm curious, and I didn't find anything similar on the FractInt site.
A while back I wanted a way to visual the many, many .MAP files I've
accumulated for FractInt, so I wrote a utility to create small .GIF
files (256 x 100) displaying the .MAP.

Did I miss an existing tool (seems kind of a no-brainer, so I can't
believe I'm the first)?  Is there any interest?

I can offer: a unix-based version that should compile under any decent
C compiler, or a Windows version for VC++ v6.  NOTE: both use the gd 1.3
library that is no longer supported by its author (that GIF legal mess).

I couldn't *fully*legally* make the images I've made available, at least
not as .GIFs.  (Also, the Windows version is a console program.)

So,... if there does seem to be any interest, I might put all the common
.MAP images up as .JPG and/or .PNGs.  It'd be fun, again assuming anyone
wants this, to have an image generator that you could upload a new .MAP
file to and get back an image.

But again, I don't know if anyone cares.

--
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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

From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Re: [philofractal] C-FOTD  11-07-01  (Sea-What
Date: 14 Jul 2001 14:16:51 +1200

At 09:17 14/07/2001, Programmer Dude wrote:
>"Morgan L. Owens" wrote:
>
> > Textures in 3-D software like POV-Ray are four-dimensional...
>
>In what sense?

For each point (X,Y,Z) in space, the texture specifies a fourth number
which which (via the colourmap) gives the colour of that point.

To come at it from the other direction. If you're trying to reconstruct the
texture used on a given set of points (the surface of a sphere, let's say)
you need to know more than just the three spatial coordinates of each
point, you need to know where they lie along the colourmap dimension as well.


Just as you need more than just latitude and longitude to locate an
aircraft, just as Newtonian mechanics uses three numbers for position and
another three for momentum, and just as you need three numbers to position
and another three to orient an object in space unless it's circularly
symmetric along one or more axes.

Morgan L. Owens
"The wind is southerly here, but southwesterly over there. And that's just
at ground level."



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

From: "David Jones" <[e-mail]>
Subject: Re: (fractint) Images of .MAP files
Date: 13 Jul 2001 19:50:02 -1000

On 13 Jul 01 at 16:50, Programmer Dude wrote:

> So,... if there does seem to be any interest, I might
> put all the common .MAP images up as .JPG and/or .PNGs.
> It'd be fun, again assuming anyone wants this, to have
> an image generator that you could upload a new .MAP file
> to and get back an image.
>
> But again, I don't know if anyone cares.

I care - go for it! It would be a lot more helpful for
picking color maps to be able to see the colors in it ...

David
[e-mail]


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

From: "David Jones" <[e-mail]>
Subject: Re: (fractint) Images of .MAP files
Date: 13 Jul 2001 19:50:02 -1000

On 13 Jul 01 at 16:50, Programmer Dude wrote:

> I'm curious, and I didn't find anything similar on the
> FractInt site. A while back I wanted a way to visual the
> many, many .MAP files I've accumulated for FractInt, so
> I wrote a utility to create small .GIF files (256 x 100)
> displaying the .MAP.

[snips]

> I can offer: a unix-based version that should compile
> under any decent C compiler, or a Windows version for
> VC++ v6.

Forget GIF, go with PNG. You can do a Windows version if
you have to, but I'd much rather have the UNIX/Linux
version.

David
[e-mail]


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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  14-07-01  (Monolith Monsters [5])
Date: 14 Jul 2001 09:59:53 -0400 (EDT)


Classic FOTD -- July 14, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

Today's image is a different view of the same forest that held
the tree which appeared in yesterday's FOTD.  But instead of
viewing the scene from close to the Julia direction, today we
view it from the Mandelbrot direction.

I named the picture "Monolith Monsters" after one of my favorite
old sci-fi movies.  I rated it a perfectly average 5.

What once was a figure-eight edged with tree-like shapes has now
become a valley edged with monolithic rocks -- a scene on an
alien planet if you wish.  The alien rocks, which once formed
the crown of a tree, decrease in size as they fade into the
distance, and the alien sky above, not quite like earth's, has
an unearthly rusty tinge near the horizon.

I would estimate the average temperature on this planet, which
is circling an orange class-K star, to be -40F, which is also
-40C.  The atmospheric pressure appears to be about 250mb, 1/4
that of earth's.  But unfortunately, there is no water, and life
never had a chance to get started.

The curious rocks have obviously been formed by volcanism,
though the chemical composition that would crystallize into such
strange shapes is yet to be determined.

Several deep fault lines extend diagonally through the scene,
and even a short way into the sky.  I'll not attempt to explain
how an atmosphere can support fault lines, but the atmospheric
discontinuities *are* there.

Finally, the trip to this exotic place takes only 2-1/2 minutes,
via the parameter-file spaceship.  For those without a ticket,
the scene will soon be showing at the following web sites:

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

and:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was once again perfect, with blue
skies, puffy clouds, (which are also possible to create with
fractals), and a very earth-like temperature of 82F (28C).  The
fractal cats, who really have little interest in fractals, spent
most of the day on the porch, taking it easy.

I've been taking it a little too easy for several days, and I
now find myself with a yard of grass in need of a trimming.  Oh
well, there's only one way I know to get the job done -- and
that's to get started.  So until next time, take care, and do
fractals exist on other planets?


Jim Muth
[e-mail]


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

Monolith_Monsters  { ; time=0:02:36.32--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=SliceJB-new-min center-mag=-1.14927217\
  827850100/-0.00241559409796065/12578.62/1/-27.5
  params=0/0/0/0/1.618034/0/0/0/0/0 float=y
  maxiter=1800 inside=255 logmap=86 periodicity=0
  colors=000ROzROzSOzSOzTOzTOyUOyUOyVOyVOyXOyXOyZOzY\
  QyZQz_Qz`Qz`Qz`QzaQzaQzaRzaRzbRzbSzcSzcTzcTzcTzgTz\
  cUzdUzeUzeVzeVzeVzeVzeWzeWzfWzfWzfXzfXzfXzfYzfYzgY\
  zhYzhZzhZzhZzhZzh_zi_zi_zi`zi`zi`zi`ziazjazjazjazj\
  bzhWHiXIjYJkZKk_Kk`KkaKkbKkcKkdKkeKkfKkgKkhKkiKkjK\
  kkKklKkmKknKlnKmnKnmLolOpkQqjSriUshWtgWsfYsf_reard\
  cqceqcgpbipako`mo`on_qnZsmYumYwlXxlWykVzkVzjUwjTwi\
  SwiSwhRwhQwgPwgPwfOwfNweMweMwdLwdKwcJwcJw_GwXDwUAw\
  R7wO4wM7wL9wKBwJDwIFwGHwFJwELwDNwCPwASw9U`8W`7Y`6_\
  `4a_3c_2e_1g_0i_2gZ4eY6cY8bXA`XCZWDXWFWVHUVJSULQUN\
  PTONTQLSSJSUIRWGRYEQZDQYFRYGSYHSYITYKUYLUYMVYNVYOW\
  YQXYRXYSYYTYYVZYW_YX_YY`YZ`Z__Z`_Za_ZbZZcZZdZZeYZf\
  YZgY_hX_iX_jX_kW_lW_mW_nV_oV_pV`qU`rU`sU`tT`uT`vT`\
  wS`xS`yS`ySaxRbwQbvQcuPctPdsOdrOeqNepNfpMfoMgnLgmL\
  hlKhkKijJiiJjhIjgIkgHlfGleGmdFmcFnbEnaEo`Do_DpZCpZ\
  CqYBqXBrWArVAsU9sT9QghKAR
  }

frm:SliceJB-new-min {; by John R. H. Goering, July 1999
  pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1),
  b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), ca=cos(a),
  cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d),
  sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
  q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg,
  s=v*sin(a), c=p+flip(q)+(p4), z=r+flip(s)+(p5):
  z=(-z)^(p3)+c
  |z|<=100
  }

END 20.0 PAR-FORMULA FILE==================================


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

From: "Morgan L. Owens" <[e-mail]>
Subject: (fractint) Re: C-FOTD  14-07-01  (Monolith Monsters [5])
Date: 15 Jul 2001 03:04:10 +1200

At 01:59 15/07/2001, Jim Muth wrote:
>  do
>fractals exist on other planets?
>

http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10691.jpeg
http://photojournal-a.jpl.nasa.gov/outdir/PIA03000.25354.jpeg
http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10598.jpeg
http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10703.jpeg
http://photojournal-a.jpl.nasa.gov/outdir/PIA03000.25440.jpeg
http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10634.jpeg
http://photojournal.jpl.nasa.gov/archive/PIA01655.gif
http://photojournal-a.jpl.nasa.gov/outdir/PIA01297.25528.jpeg
http://photojournal.jpl.nasa.gov/archive/PIA01651.gif
http://photojournal-b.jpl.nasa.gov/outdir/PIA02556.10681.jpeg
http://photojournal-a.jpl.nasa.gov/outdir/PIA00829.25718.jpeg


Morgan L. Owens
"Come and see the Real Thing."


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

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 14-07-01 (Monolith Monsters [5])
Date: 14 Jul 2001 15:20:54 -0000

>From: "Morgan L. Owens" <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>CC: [e-mail]
>Subject: (fractint) Re: C-FOTD  14-07-01  (Monolith Monsters [5])
>Date: Sun, 15 Jul 2001 03:04:10 +1200
>
>At 01:59 15/07/2001, Jim Muth wrote:
>>  do
>>fractals exist on other planets?
>>
>
>http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10691.jpeg
>http://photojournal-a.jpl.nasa.gov/outdir/PIA03000.25354.jpeg
>http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10598.jpeg
>http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10703.jpeg
>http://photojournal-a.jpl.nasa.gov/outdir/PIA03000.25440.jpeg
>http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10634.jpeg
>http://photojournal.jpl.nasa.gov/archive/PIA01655.gif
>http://photojournal-a.jpl.nasa.gov/outdir/PIA01297.25528.jpeg
>http://photojournal.jpl.nasa.gov/archive/PIA01651.gif
>http://photojournal-b.jpl.nasa.gov/outdir/PIA02556.10681.jpeg
>http://photojournal-a.jpl.nasa.gov/outdir/PIA00829.25718.jpeg
>
>
>Morgan L. Owens
>"Come and see the Real Thing."

Your point being?

_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.


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

From: Bob Margolis <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD  14-07-01  (Monolith Monsters [5])
Date: 14 Jul 2001 11:07:49 -0500

"Morgan L. Owens" wrote:
>
>
>
> http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10691.jpeg
> http://photojournal-a.jpl.nasa.gov/outdir/PIA03000.25354.jpeg
> http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10598.jpeg
> http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10703.jpeg
> http://photojournal-a.jpl.nasa.gov/outdir/PIA03000.25440.jpeg
> http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10634.jpeg
> http://photojournal.jpl.nasa.gov/archive/PIA01655.gif
> http://photojournal-a.jpl.nasa.gov/outdir/PIA01297.25528.jpeg
> http://photojournal.jpl.nasa.gov/archive/PIA01651.gif
> http://photojournal-b.jpl.nasa.gov/outdir/PIA02556.10681.jpeg
> http://photojournal-a.jpl.nasa.gov/outdir/PIA00829.25718.jpeg
>


FYI: For each jpeg there was a "File Not Found" message when I clicked
on them. Only the two gifs were viewable.

Cheers,

Bob
--
************************************************************

  "And now the sequence of events in no particular order."
                              --Dan Rather, tv news anchor

************************************************************

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

From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD  14-07-01  (Monolith Monsters [5])
Date: 15 Jul 2001 16:08:46 +1200

At 04:07 15/07/2001, Bob Margolis wrote:
>"Morgan L. Owens" wrote:
> >
> >
> >
> > http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10691.jpeg
> > http://photojournal-a.jpl.nasa.gov/outdir/PIA03000.25354.jpeg
> > http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10598.jpeg
> > http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10703.jpeg
> > http://photojournal-a.jpl.nasa.gov/outdir/PIA03000.25440.jpeg
> > http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10634.jpeg
> > http://photojournal.jpl.nasa.gov/archive/PIA01655.gif
> > http://photojournal-a.jpl.nasa.gov/outdir/PIA01297.25528.jpeg
> > http://photojournal.jpl.nasa.gov/archive/PIA01651.gif
> > http://photojournal-b.jpl.nasa.gov/outdir/PIA02556.10681.jpeg
> > http://photojournal-a.jpl.nasa.gov/outdir/PIA00829.25718.jpeg
> >
>
>
>FYI: For each jpeg there was a "File Not Found" message when I clicked
>on them. Only the two gifs were viewable.

Well, the proper pages all had the same URL, so it wouldn't have helped
much - so I hoped the images themselves had stable URLs. The site was
JPL's photojournal, http://photojournal.jpl.nasa.gov/, and the images in
question (available via the search query) are PIA03000, PIA01655,
PIA01297, PIA01651, PIA02556, PIA00829, PIA02590, PIA1656, PIA02864,
PIA02253, and PIA03101. (Why the 'PIA' is necessary, since all images appear
to have them, I don't know.)

Morgan L. Owens
"The best way to see if other planets have fractals is to go and have a look."



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

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD  14-07-01  (Monolith Monsters [5])
Date: 14 Jul 2001 23:26:39 -0500

Bob Margolis wrote:
>
> "Morgan L. Owens" wrote:
> > http://photojournal-b.jpl.nasa.gov/outdir/PIA03000.10691.jpeg
> > http://photojournal.jpl.nasa.gov/archive/PIA01655.gif
> >
>
> FYI: For each jpeg there was a "File Not Found" message
> when I clicked on them.  Only the two gifs were viewable.
>

After only entering the directory paths without the file name:

    http://photojournal-a.jpl.nasa.gov/outdir/
    http://photojournal-b.jpl.nasa.gov/outdir/

These were the only images available for "a":

    PIA00403.19219.jpeg    14-Jul-01 21:16    68k
    PIA00558.19035.jpeg    14-Jul-01 21:07    28k
    PIA00567.19064.jpeg    14-Jul-01 21:09    59k
    PIA00567.19175.jpeg    14-Jul-01 21:14    59k
    PIA01301.19419.jpeg    14-Jul-01 21:20   130k
    PIA01309.19209.jpeg    14-Jul-01 21:15   148k
    PIA02879.19085.jpeg    14-Jul-01 21:10    18k
    PIA02879.19125.jpeg    14-Jul-01 21:11    18k
    PIA03101.19168.jpeg    14-Jul-01 21:13   260k
    PIA03149.19114.jpeg    14-Jul-01 21:10    52k
    PIA03150.19023.jpeg    14-Jul-01 21:06    42k

and for "b":

    PIA00558.23523.jpeg    14-Jul-01 21:18    28k
    PIA00567.23453.jpeg    14-Jul-01 21:14    59k
    PIA01081.23629.jpeg    14-Jul-01 21:24    42k
    PIA01669.23507.jpeg    14-Jul-01 21:16    49k
    PIA02099.23485.jpeg    14-Jul-01 21:15    80k
    PIA02099.23568.jpeg    14-Jul-01 21:21    80k
    PIA02314.23348.jpeg    14-Jul-01 21:11    91k
    PIA02879.23372.jpeg    14-Jul-01 21:12    41k
    PIA02879.23384.jpeg    14-Jul-01 21:12    18k
    PIA02879.23406.jpeg    14-Jul-01 21:13    41k
    PIA02879.23448.jpeg    14-Jul-01 21:14    18k
    PIA03000.23426.jpeg    14-Jul-01 21:13    37k
    PIA03223.23578.jpeg    14-Jul-01 21:21    93k
    PIA03451.23279.jpeg    14-Jul-01 21:10    42k

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD  14-07-01  (Monolith Monsters [5])
Date: 14 Jul 2001 23:32:32 -0500

Morgan L. Owens wrote:
>
> Well, the proper pages all had the same URL,
> so it wouldn't have helped much - so I hoped
> the images themselves had stable URLs.

Apparently these images are rotated fairly often, based upon the date
and timestamp for the actual files in those directories.

P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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

From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD  14-07-01  (Monolith Monsters [5])
Date: 15 Jul 2001 17:15:21 +1200

At 16:32 15/07/2001, Paul N. Lee wrote:
>Morgan L. Owens wrote:
> >
> > Well, the proper pages all had the same URL,
> > so it wouldn't have helped much - so I hoped
> > the images themselves had stable URLs.
>
>Apparently these images are rotated fairly often, based upon the date
>and timestamp for the actual files in those directories.

By guess is that they're cached as files for each request, to cut down on
blob queries to the database.

Morgan L. Owens
"Maybe if I faked the form fields in a querystring..."


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

From: [e-mail]
Subject: (fractint) C-FOTD  15-07-01  (Dry Lake [3])
Date: 15 Jul 2001 11:06:24 EDT


Classic FOTD -- July 15, 2001 (Rating 3)

Fractal visionaries and enthusiasts:

The word has come in to Fractal Central that fractals *might*
exist on other planets.  The question now becomes whether a
fractal really exists if no intelligent life is there to be
aware of it.  Perhaps a better way of stating the question is to
ask whether fractals existed on earth 2000 years ago, before we
knew of them.  And this is simply another form of the old philo-
sophical question of whether we create reality by considering
certain things of which we are aware to be real, or whether the
things would be real even if no intelligent life existed to be
aware of them and declare them real.

Today's modest offering most certainly is real.  (I think.)  It
is an example of a very common fractal feature I call a 'dry
lake'.  All too often while tracking down a midget, I come upon
features of a class I call 'dry lakes'.  One of these dry lakes
exists at the exact center of today's image, and is the reason I
named the picture "Dry Lake".

A dry lake is surrounded by the symmetrical type of features
that point the way to a midget, but before the midget is
reached, the basin bottoms out in a saddle-shaped surface.
These saddle surfaces indicate a failed search, and as soon as I
see one, I usually turn away to search elsewhere.

I consider these dry lakes to be near misses.  A midget does
exist nearby in the surrounding Julibrot, but the slice on the
screen misses the midget by a narrow margin.  Still, if the
slice comes close enough to the actual midget, some of these dry
lakes display nearly perfect surrounding features.  In these
cases, the presence or absence of a central midget makes little
difference.  But I sometimes wonder whether a program designed
to automatically track down midgets would be fooled by these dry
lakes.

Today's image, which misses the midget by a rather wide margin,
shows a relatively imperfect dry lake, with symmetry that is
unbalanced and does not go beyond the stage of 2.  Because of
its imperfection, I rated the image a below-average 3.

With a render time of 15 minutes, the parameter file tries one's
patience.  A download of the GIF image is the way to see today's
FOTD.  That download will soon be available at:

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

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today here at Fractal Central may safely be
passed over.  But for those who have an interest in such
unimportant things, it was another perfect day, with blue skies
and a temperature of 84F (29C).  The cats were happy all day.

It's now time to do other things.  So until next time, take
care, and we have the fractal saddle, all we need is the fractal
horse.


Jim Muth
[e-mail]


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

Dry_Lake           { ; time=0:14:59.68--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.63371185168602/+1.1142664608147/1.59\
  2733e+007/1/67.5 params=10/-1.333/1/-13.33/-2/300
  float=y maxiter=1200 inside=0 logmap=246
  colors=000C0AD0AD0AE0AE0AF0AF0AG0AG0AG0AG0AH0AH0AH\
  0AH0AI0AI0AI0AI0AJ0AJ0AJ0AJ0AK0AK0AK0AK0AL0AL0AL0A\
  L0AM0BM0BM09M0CN0CN0CN0CN0CO0CO0BO0BO0BP0BP0BP1BP3\
  CQ4BQ4BQ4BQ6BR6BR69R69R89S89S89S89SA7TA7TA7TA7TC7U\
  C7UC5UC5UD5UD5UD5UD5UF3UF3UF3UF3UH3UH3UH2UH2UI2UI2\
  UI2UI2VK0VK0VK0WK0WM0WM0WM0YM0YO0YO0_O0_O0_P0`P0`P\
  0`R0bR0bR0bR0bT0dT0dT0dT0fU0fU0fU0gU0gW0gW0iW0iW0i\
  Y0iY0kY0kY0k_0l_0l_0l_0na0na0na0pa0pb0pb0pb0rb0rd0\
  rd0td0td0tf0uf0uf0uf0wg0wg0wg0wi0wg0wg0wg0wg0wg0wg\
  0wg0wf0wf0wV0wf0zY0wf0za0wf0wd2wd3wd5wd7wd7wd9wdBw\
  dCwbEwbEwbGwbHwbJwbLwbLwaMwaOwaQwaRwaRwaTwaVxaXx_Z\
  x_Zx__y_ay_cy_dy_dz_fzYhzYjzYkzYkzYmzYozYpzWrzWrzW\
  tzWvzWxzWyzWyzWzzUzzUzzUzyUzxUzwUzwUzyWzwUzwUzuUzu\
  UzuUztUztUztTzrTzrTzrTzpTzpTzpTznTznRznRzlRzlRzlRz\
  nUzpWzrYztWzuWzwWzwWzwUzwUzwUzwUzwTzwTzwTzwTzwRzwR\
  zwRzwRzwPzwPzwPzwPzwOzwOz
  }

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

From: "Ricardo M. Forno" <[e-mail]>
Subject: (fractint) Another use for fractint
Date: 15 Jul 2001 11:11:02 -0300

Some time ago, I discovered another practical use for fractint.
I created a batch file f.bat which simply called fractint.The f.bat file was
under the /bat directory, which I included in the path.
Then, when some program under DOS lets the screen in an abnormal state, for
example with different colors or letter size, I simply type f and when
fractint appears I press Esc. This easily returns the screen to its normal
state.


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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  16-07-01  (Corona [7])
Date: 16 Jul 2001 11:05:11 -0400 (EDT)


Classic FOTD -- July 16, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

With today's image, we rise out of yesterday's abyss.  Today's
image resembles a something -- I am not sure what -- but while
studying it, searching for a name, I had the impression of the
sun during a total eclipse, with the arcing colors surrounding
the central circle being the coronal loops.  True, the central
circle with its horizontal stripes bears little resemblance to
the black disk of the new moon, but with a bit of imagination,
the resemblance to the eclipsed sun with its coronal streamers
is there.

Yes, I have noticed the area at the bottom of the striped
circle, which looks suspiciously like a midget.  Since July is
quadratic midgetless month, this object, if it is in fact a
midget, has no right to be there.  But it is so unobtrusive that
even if it is a midget, it does not violate my pledge to have no
more midgets in July.  Perhaps I'll investigate this area after
the end of this month, when quadratic midgets will once again be
permissible.

The formula behind today's image is number 13 in my series of 14
MandNewt formulae.  Some of the image is outside material, some
is inside colored by the bof60 option, and some is open inside,
which should be colored by the inside fill, but for some reason
is not.  Turning on the logmap adds color to the black areas of
today's image, but I like it better the way it is.

After a short period of pondering, I named today's FOTD
"Corona", and rated it at a 7.  And seven minutes are required
to render the image from the parameter file.  The image will
also soon be available in GIF form on the Web at:

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

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was once again perfect, with blue
skies, puffy white clouds, and a cat-pleasing, wading-pool-
splashing temperature of 86F (30C).

Unfortunately, we've now come to the end of another FOTD, but
additional FOTD's are lined up into the indefinite future, and
the next one will appear within 24 hours.  Until that golden
moment arrives, take care, and fractals are as real as we
consider them to be.


Jim Muth
[e-mail]


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

Corona             { ; time=0:06:56.06--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandNewt13 passes=1
  center-mag=-44.5237/0/0.01512924/1/-90
  params=-1.413/4.324/4.275/-2.475/1.797/4.89
  float=y maxiter=140 inside=bof60 periodicity=0
  colors=000GluGkuHjtIitIhsJgrKfrLeqLdqMcpNboNaoO`nP\
  _nQZmQYlRXlSWkSVkQWjPWiNWhMWgKWgJWfIWeGWdFWcDWcCWb\
  AW`9W`8W`CWZGWYKWWOWVSWUWWS`VRcUQhSOlQNpNMsKKvGJxE\
  IyHJyJJyMJxOJxQJwSJwUJvWJvYJu_JuaJtdJtgJsjJsmJrpJu\
  qIrqJrpKqoKqmLpkMpjMphNofNoeOncPnaPm`QmZRmXRlWSlUS\
  kSTkRUjPUjNVjMVhNWgNXfNYeNZdN_bO_aO``Oa_ObZOcXPcWP\
  dVPeUPfTPgSPgQQhPQiOQjNQkMQlKRlJRmIRnHRoGRpESpDSqC\
  SrBSsASt9StARtAQtAPtAOtBNtBMtBLtBKtCJtCItCHtCHtFJq\
  IKnKLlNMiPNfSOdUPaXQZZRXaSUdSMcTScUXcVabWfbXkbYpaZ\
  ua_za_zbZzcYzcYzdXzeXzfWzfWzgVzhUziUziTzjTzkSzjRzk\
  SzlSzmSzmSznSzoSzpSzpSzqSxrSwrSusSstSruSpuSnvSmwSk\
  xSixShySfzSdzR`zSazSbzScySdwSdvSeuSfsSgrTgpThoTimT\
  jlTkkTkiTlDdzDdzCezBfzBgzAhz9iz9jz8kz6jz8kz9kzAlzB\
  lzCmzDmzEnzGnzHozIozJpzKpzLqzMqzNqzPrzQrzRszSszTtz\
  UtzVuzXuzYvzZvz_wz`wzaxzbxzbzzcxzdwzdvyeuyftxfswgr\
  whqvhpuinujmtjlskksljrliq
  }

frm:MandNewt13 {; Jim Muth
z=g=pixel, a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), e=real(p3), f=imag(p3):
h=z^a+(g-b)*z-f
j=c*z^d+g
z=z-e*h/j,
0.000000000000000000000000000001 <= |h|
}

END 20.0 PAR-FORMULA FILE==================================


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

From: Michael Weitzel <[e-mail]>
Subject: Re: (fractint) Another use for fractint
Date: 16 Jul 2001 20:10:51 +0200

Am Sonntag, den 15. Juli 2001, um 11:11h schrieb Ricardo M. Forno:

> Some time ago, I discovered another practical use for fractint.
> I created a batch file f.bat which simply called fractint.The f.bat file was
> under the /bat directory, which I included in the path.
> Then, when some program under DOS lets the screen in an abnormal state, for
> example with different colors or letter size, I simply type f and when
> fractint appears I press Esc. This easily returns the screen to its normal
> state.
calling "mode co80" would probably have done the same job ;-) but
nothing compares to using Fractint for this ;-))
--
   Michael                  LDKnet / LDK/LUG / Unix-AG
     *Weitzel* /LinuX --- email: michael(at)ldknet.org

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

From: "Multiple Bogeys" <[e-mail]>
Subject: Arbitrary 2D slices was Re: (fractint) C-FOTD 13-07-01 (Fractal Forest [7])
Date: 17 Jul 2001 00:33:32 -0400


------=_NextPart_001_0001_01C10E58.1C348740
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

> I used John Goering's formula to draw the image and do the
> rotating.  This formula can draw more orientations within the
> Julibrot than any other I know of, though there are still some
> directions that it cannot reach.

Here's some math that might be useful to devise a formula to draw any 2D =
slice of a 4D fractal.

Any plane can be exactly specified by two non-collinear vectors. Two 4-sp=
ace vectors can be specified with 8 real values -- 7 if they are normaliz=
ed. Four of the formula parameters, say p1-p4, could be used to give thes=
e vectors.

The cheap way to convert the pixel coordinates into the plane of two vect=
ors v1 and v2 is:

x*v1 + y*v2

Of course, the resulting image is skewed, aspect mangled, or otherwise di=
storted if v1 and v2 aren't equal in magnitude and perpendicular. However=
, if they are not collinear, we can preprocess v2 to be orthogonal to v1 =
by a projection calculation:

v2 <- v2 - (v1*v2)(v1/|v1|)

where (v1*v2) is the dot product of v1 and v2 and |v1| is the magnitude o=
f v1, (the square root of v1*v1). (Observe that if v2 is already perpendi=
cular to v1, the dot product is zero and v2 is not changed. If v2 and v1 =
are collinear, the dot product is |v1||v2|, the term on the right ends up=
 with the direction of v1 (which is that of v2) and the magnitude of v2 a=
nd thus is v2, and v2 becomes zero, so things go wrong.)

Making them equal length is easy -- replace v1 by v1/|v1| and v2 by v2/|v=
2| so both have length 1. A simple procedure is then:

v1 <- v1/|v1|
v2 <- v2 - (v1*v2)v1
v2 <- v2/|v2|

I leave the translation of this into a fractint formula using four comple=
x variables to represent v1 and v2 as an exercise for the reader.

At this point, you get a rectilinear image -- no skew or aspect squashing=
 unless the input coordinates (using the zoom box) are themselves subject=
ed to such distortion. However, one can still rotate the image by playing=
 with v1 and v2 as well as by rotating the zoom box. These effects are ad=
ditive.<br clear=3Dall><hr>Get Your Private, Free E-mail from MSN Hotmail=
 at <a href=3D"http://www.hotmail.com">http://www.hotmail.com</a>.<br></p=
>

------=_NextPart_001_0001_01C10E58.1C348740
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> I used Jo=
hn Goering's formula to draw the image and do the<BR>> rotating. =
 This formula can draw more orientations within the<BR>> Julibrot than=
 any other I know of, though there are still some<BR>> directions that=
 it cannot reach.<BR><BR>Here's some math that might be useful to devise =
a formula to draw any 2D slice of a 4D fractal.</DIV> <DIV> </DIV> <=
DIV>Any plane can be exactly specified by two non-collinear vectors. Two =
4-space vectors can be specified with 8 real values -- 7 if they are=
 normalized. Four of the formula parameters, say p1-p4, could be used to =
give these vectors.</DIV> <DIV> </DIV> <DIV>The cheap way to convert=
 the pixel coordinates into the plane of two vectors v1 and v2 is:</DIV> =
<DIV> </DIV> <DIV>x*v1 + y*v2</DIV> <DIV> </DIV> <DIV>Of course=
, the resulting image is skewed, aspect mangled, or otherwise distor=
ted if v1 and v2 aren't equal in magnitude and perpendicular. However, if=
 they are not collinear, we can preprocess v2 to be orthogonal to v1 by a=
 projection calculation:</DIV> <DIV> </DIV> <DIV>v2 <- v2 - (v1*v=
2)(v1/|v1|)</DIV> <DIV> </DIV> <DIV>where (v1*v2) is the dot product=
 of v1 and v2 and |v1| is the magnitude of v1, (the square root of v=
1*v1). (Observe that if v2 is already perpendicular to v1, the dot produc=
t is zero and v2 is not changed. If v2 and v1 are collinear, the dot prod=
uct is |v1||v2|, the term on the right ends up with the direction of v1 (=
which is that of v2) and the magnitude of v2 and thus is v2, and v2 becom=
es zero, so things go wrong.)</DIV> <DIV> </DIV> <DIV>Making them eq=
ual length is easy -- replace v1 by v1/|v1| and v2 by v2/|v2| so both hav=
e length 1. A simple procedure is then:</DIV> <DIV> </DIV> <DIV>v1 &=
lt;- v1/|v1|</DIV> <DIV>v2 <- v2 - (v1*v2)v1</DIV> <DIV>v2 <- v2/|v=
2|</DIV> <DIV> </DIV> <DIV>I leave the translation of this into a fr=
actint formula using four complex variables to represent v1 and v2 as an =
exercise for the reader.</DIV> <DIV> </DIV> <DIV>At this point, you =
get a rectilinear image -- no skew or aspect squashing unless the input c=
oordinates (using the zoom box) are themselves subjected to such distorti=
on. However, one can still rotate the image by playing with v1 and v2 as =
well as by rotating the zoom box. These effects are additive.</DIV> <DIV>=
 </DIV></BODY></HTML><DIV><BR><br clear=3Dall><hr>Get Your Private, =
Free E-mail from MSN Hotmail at <a href=3D"http://www.hotmail.com">http:/=
/www.hotmail.com</a>.<br></p></DIV>

------=_NextPart_001_0001_01C10E58.1C348740--

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

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Another use for fractint
Date: 17 Jul 2001 00:53:57 -0400


------=_NextPart_001_0003_01C10E5A.F5BE00C0
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

> Some time ago, I discovered another practical use for fractint.
> I created a batch file f.bat which simply called fractint.The f.bat fil=
e was
> under the /bat directory, which I included in the path.
> Then, when some program under DOS lets the screen in an abnormal state,=
 for
> example with different colors or letter size, I simply type f and when
> fractint appears I press Esc. This easily returns the screen to its nor=
mal
> state.

Blind-typing "mode co80" at the prompt will accomplish the same thing :-)
(If you want a single-letter command for it, you can put "mode co80" in a=
n "f.bat". :-))<br clear=3Dall><hr>Get Your Private, Free E-mail from MSN=
 Hotmail at <a href=3D"http://www.hotmail.com">http://www.hotmail.com</a>=
.<br></p>

------=_NextPart_001_0003_01C10E5A.F5BE00C0
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> Some time=
 ago, I discovered another practical use for fractint.<BR>> I created =
a batch file f.bat which simply called fractint.The f.bat file was<BR>>=
; under the /bat directory, which I included in the path.<BR>> Then, w=
hen some program under DOS lets the screen in an abnormal state, for<BR>&=
gt; example with different colors or letter size, I simply type f and whe=
n<BR>> fractint appears I press Esc. This easily returns the screen to=
 its normal<BR>> state.<BR></DIV> <DIV>Blind-typing "mode co80" at the=
 prompt will accomplish the same thing :-)</DIV> <DIV>(If you want a sing=
le-letter command for it, you can put "mode co80" in an "f.bat". :-))</DI=
V></BODY></HTML><DIV><BR><br clear=3Dall><hr>Get Your Private, Free E-mai=
l from MSN Hotmail at <a href=3D"http://www.hotmail.com">http://www.hotma=
il.com</a>.<br></p></DIV>

------=_NextPart_001_0003_01C10E5A.F5BE00C0--

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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  17-07-01  (Fractal Limeade [6])
Date: 17 Jul 2001 11:06:12 -0400 (EDT)


Classic FOTD -- July 17, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

I have no real excuse for naming today's image "Fractal
Limeade".  True, the weather has been warm here lately, and
limeade is one of my favorite summer drinks, but the only
resemblance of today's image to a glass of limeade that I can
find is the vaguely lime-green color of the prominent ring of
features surrounding the non-quadratic midget.

The image is a scene in the Z^1.75+C fractal.  It was found with
the aid of the MandelbrotBC1 formula, which reveals areas in the
remote parts of the infinite logarithmic spirals of fractals
created with fractional exponents.

I rated the image a 6, which is a bit above the average of my
standard offering.  With the parameter file's render time of
almost 9 minutes, running it is not the most efficient way of
viewing the scene.  A more efficient way is to download the pre-
rendered GIF image from:

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

or from:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather was hot and lazy today, with a temperature
of 90F 32C, which kept the fractal cats stretched out on the
porch most of the day.

Unfortunately, with all the work before me, I can't afford to be
lazy.  So until next fractal, take care, and think about those
4-D rotations.


Jim Muth
[e-mail]


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

Fractal_Limeade    { ; time=0:08:49.54--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=b
  center-mag=+0.74278632205274600/-0.079548597538634\
  95/1.830877e+007/1/105 params=1.75/0/-36/0 float=y
  maxiter=1450 inside=255 logmap=368 periodicity=10
  colors=000_6WuVSsTSpRSnPSkMSiKSfIRdGRaDR_BRX9RV7RV\
  5TX6U_6Wb7Yf7_i8al8dp9fs9hvAjyAlwGhuMesRaqXZobVmgS\
  kmOjrLhqOfpRdoUbnX`mZZlaXkdVjgXjkUiiRhhPggMfeJedHd\
  cEcbBb`9a_Hc7G`6GZ6FW5ET5DQ4CN4CL3BI3AF29C2891871C\
  C4FG7IL9LPCOUERYHVbKYfM`kPcoRftUhwWYuNNrECo6Gf8KYA\
  OQCSHEV9GYCJ`ELbHNeJPhLRjOTmQVpSXrVZuX`wZbu_`s`Zqa\
  XobVmcTldSjeQhfOfgMdhKbhIahH_fIYcIX`IVYIUVISSIRPJP\
  MJOJJMGJLDJJAJI8JJCNJFQKITKLWKOZLRbLUeLXhM_kMbnMeq\
  ShkYkfcnabn`bn`geekXikXjkXjkXjkXkkXkkXkhZje_jcai`b\
  iYdiWehTghQhhOjgLkgGmhJlgLkgOkfQjfSjfOihLiiIikEhlB\
  hn8hoCgpGgpKgqOfqRdrVbrZ`sbZsf_ti`tmauqbuucvxdvvZi\
  tUXmDTfEP_FMTGIMHEFIB8J7mbKk`KhZLeXLcVL_XKWYJSWIO`\
  HKfGGqFCjE8kD4lC0mC2XP4cmKXmZ4kYLOXa1Vb5Uc8TdBSeER\
  fHQgLPhONiRMjULkXKl`JmcInfHoiGolImdJkXLiPMgHNfAac8\
  bZ8cV8cQ8cM8dH8eD8fF7gG6iI6kJ5mK4oM4qN3sO3uP3wQ6yR\
  AzSDzSFzTHzTJzUMzUOzVQ000
  }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a
}

END 20.0 PAR-FORMULA FILE==================================


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

From: "Jonathan Osuch" <[e-mail]>
Subject: (fractint) Fractint version 20.1.13
Date: 17 Jul 2001 20:28:11 -0500

Fractint version 20.1.13 is now available at www.fractint.org.

New features include:

Added parameters p4 and p5 to the evolver.  This required splitting the
  tweak central screen into two pages.

  Fixed an evolver bug that was causing the evolver to not exit cleanly.

  Changed the compile options on evolve.c to eliminate aliasing, which
  started to cause problems with this patch.

I haven't updated the Xfractint sources yet.

Jonathan



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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  18-07-01  (The Lost Rotation [4])
Date: 18 Jul 2001 10:55:50 -0400 (EDT)


Classic FOTD -- July 18, 2001 (Rating 4)

Fractal visionaries and enthusiasts:

The world is filled with lost things -- lost files, lost
computers, lost chords, and last but not at all least, lost
fractals.  Today's modest fractal offering is lost.  It's simply
another view of the East Valley area of the Julibrot figure, but
the direction in which the scene has been sliced is one I have
yet to write a formula to reach.

Yes, I know you're wondering how I produced the image if I have
no formula that can draw the rotation.  The answer is that I
have no formula designed specifically for 4-D rotations that can
draw this particular angle.  The formula that drew today's image
was written many years ago, back when Fractint had only 4
variable parameter entries for type=formula.  I wrote it at
random, with a now forgotten name, just to see what it would do.
When I realized it could draw oblique slices of the Julibrot I
changed its name to ObliqueMan.  Finally, when the 5th and 6th
variable parameters were added to Fractint, I changed the name
to ObliqueManPlus.

The Julia aspect of the image is evident in the familiar East
Valley shape of the outer dark rusty red border.  The Mandelbrot
aspect appears as the brilliant green wedge within and seemingly
behind the outer border.  This green wedge is the East Valley
itself, and a careful examination will reveal the valley's
elephants in various stages of formation and not yet able to
find their proper buds.

The equal stretching of two dimensions of the hypercylindrical
East Valley because of the oblique direction of the slice is
something that can happen only in four or more dimensions.  In
three dimensions only one dimension of a cylindrical object can
be stretched by an oblique slice.

I named today's image "The Lost Valley" not because the valley
itself has been lost, but because this particular aspect of it,
with the valley at an oblique angle, has not yet been found with
a formula specifically designed for the purpose.  I rated the
image a 4 because it's only moderately attractive.

The image's greatest advantage is its speed.  The parameter file
renders in only 30 seconds -- that is after the minute or so it
takes to change this letter into a Fractint parameter file ready
for running.  Those who would rather surf the Web can find the
image at:

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

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

But give Paul and Scott a chance to post it before visiting
their sites.

Today's fractal weather, (How did weather get to be a part of
the FOTD?), was the average summer fare for this part of the
world.  The temperature of 94F 34.5C, and the high humidity,
slowed the fractal cats to a crawl, causing them to spend nearly
all the day sleeping.

There's no time for me to sleep however, not with air
conditioning and a full day's work waiting to be finished.  So
until next FOTD, take care, and become one with the universe.


Jim Muth
[e-mail]


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

The_Lost_Rotation  { ; time=0:00:30.05--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=ObliqueManPlus
  center-mag=-0.291733/-0.00378091/1.103753/1/90
  params=0.28/0/0.28/0/0.015/0.015 float=y
  maxiter=6000 inside=0 logmap=yes periodicity=10
  colors=000HHCHGBJEALD9NB8PA8RBCTBFVCIXCLXCOYDRZDU_\
  EY`E``EcbFfdFifGlhGoiGrhIohKlhLigNfgOcgQ`fSYfTVfVS\
  eWPeYMe_Jd`GdbDdcAf`FgYKiWPjTUlQZmOcoLhpImqGrhKo_N\
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  NfLZhLjiLlhHfjFalEWmDRoBLqAGr9At75v60w52r74m96mB8m\
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  jiSlhTngUpgVnhUlhTjhShhSfiRdiQbiP`iPZjOXjNVjMTjMWi\
  OZhQagScfUfeWidXlcZnb`qabt`dv_epabjb_ddYZeVTgTNhQI\
  iOPgPWePRhVMk_IneDqj9toCwkFzhIzeLzbOz_RzXUzTXzQ_zN\
  bzKezHgzEoz_kzYgzXczV_zUWzSSzROzPKzOGzMCzL8zJ5zI6z\
  H7zH8zH9zGAzGAzGBzGCzFDzF
  }

frm:ObliqueManPlus {;Jim Muth
z=p1+pixel, c=p2+(p3*pixel):
z=sqr(z)+c,
|z| <=100
}

END 20.0 PAR-FORMULA FILE==================================


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

From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) Fractint version 20.1.13
Date: 18 Jul 2001 18:10:51 -0500

> I haven't updated the Xfractint sources yet.

It's done.

Jonathan



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

From: "Ricardo M. Forno" <[e-mail]>
Subject: Re: (fractint) Another use for fractint
Date: 17 Jul 2001 20:23:52 -0300

This is a multi-part message in MIME format.

------=_NextPart_000_002E_01C10EFE.64ECB100
Content-Type: text/plain;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Of course. I only remarked that the same file I used to call fractint =
solves this little problem.
  ----- Original Message -----=20
  From: Multiple Bogeys=20
  To: [e-mail]=20
  Sent: Tuesday, July 17, 2001 1:53 AM
  Subject: Re: (fractint) Another use for fractint


  > Some time ago, I discovered another practical use for fractint.
  > I created a batch file f.bat which simply called fractint.The f.bat =
file was
  > under the /bat directory, which I included in the path.
  > Then, when some program under DOS lets the screen in an abnormal =
state, for
  > example with different colors or letter size, I simply type f and =
when
  > fractint appears I press Esc. This easily returns the screen to its =
normal
  > state.

  Blind-typing "mode co80" at the prompt will accomplish the same thing =
:-)
  (If you want a single-letter command for it, you can put "mode co80" =
in an "f.bat". :-))



-----
  Get Your Private, Free E-mail from MSN Hotmail at =
http://www.hotmail.com.



------=_NextPart_000_002E_01C10EFE.64ECB100
Content-Type: text/html;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 5.50.4611.1300" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY=20
style=3D"BORDER-RIGHT: medium none; BORDER-TOP: medium none; FONT: 10pt =
verdana; BORDER-LEFT: medium none; BORDER-BOTTOM: medium none"=20
bgColor=3D#ffffff>
<DIV><FONT face=3DArial>Of course. I only remarked that the same file I =
used to=20
call fractint solves this little problem.</FONT></DIV>
<BLOCKQUOTE dir=3Dltr=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
  <DIV style=3D"FONT: 10pt arial">----- Original Message ----- </DIV>
  <DIV=20
  style=3D"BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>=20
  <A title=[e-mail] =
href=3D"mailto:[e-mail]">Multiple=20
  Bogeys</A> </DIV>
  <DIV style=3D"FONT: 10pt arial"><B>To:</B> <A =
title=[e-mail]=20
  =
href=3D"mailto:[e-mail]">[e-mail]</=
A>=20
  </DIV>
  <DIV style=3D"FONT: 10pt arial"><B>Sent:</B> Tuesday, July 17, 2001 =
1:53=20
AM</DIV>
  <DIV style=3D"FONT: 10pt arial"><B>Subject:</B> Re: (fractint) Another =
use for=20
  fractint</DIV>
  <DIV><BR></DIV>
  <DIV>> Some time ago, I discovered another practical use for=20
  fractint.<BR>> I created a batch file f.bat which simply called=20
  fractint.The f.bat file was<BR>> under the /bat directory, which I =
included=20
  in the path.<BR>> Then, when some program under DOS lets the screen =
in an=20
  abnormal state, for<BR>> example with different colors or letter =
size, I=20
  simply type f and when<BR>> fractint appears I press Esc. This =
easily=20
  returns the screen to its normal<BR>> state.<BR></DIV>
  <DIV>Blind-typing "mode co80" at the prompt will accomplish the same =
thing=20
  :-)</DIV>
  <DIV>(If you want a single-letter command for it, you can put "mode =
co80" in=20
  an "f.bat". :-))</DIV>
  <DIV><BR><BR clear=3Dall>
  <HR>
  Get Your Private, Free E-mail from MSN Hotmail at <A=20
  href=3D"http://www.hotmail.com">http://www.hotmail.com</A>.<BR>
  <P></P></DIV></BLOCKQUOTE></BODY></HTML>

------=_NextPart_000_002E_01C10EFE.64ECB100--


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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  19-07-01  (Midget by Starlight [4])
Date: 19 Jul 2001 10:31:45 -0400 (EDT)


Classic FOTD -- July 19, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

I named today's rusty-red-and-turquoise FOTD image "Midget by
Starlight" because of the very prominent 8-pointed star
surrounding the midget.  Instead of a star I sometimes see two
crossed concave squares with rounded corners surrounding the
midget, but "Crossed Squares" just doesn't sound as classy as
the actual name.

The image has been rated a 6, though some of its worth is due to
the presence of the star, which is a result of the coloring, and
not something the numbers have done.

Yes, I realize that it's a quadratic midget at the center of
today's image, and that July is a month with no quadratic
midgets, but due to a schedule change made necessary by a train
derailment, hazmat spill and fire in a tunnel under the downtown
area of the city, I was forced to use one of the images in my
vast archives.  And those archives are filled with mostly
midgets.

The formula that drew the image is a mess.  For the benefit of
the curious, it is: 0.00001(Z^(-1100))+10.1(1/Z)+(1/C), a
whimsical expression that means nothing beyond the fractal it
creates.

The render time of almost 1/4-hour on a Pentium 200mhz machine
makes a download of the GIF image the better way of viewing the
stellar scene.  In an hour or so, the download will be available
on the Web at:

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

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was cloudy with occasional heavy
showers and a temperature of 75F 24C.  The cats found the
temperature fair enough, though the rain kept them stranded
indoors.

As for me, I've still got some catching up to do.  The best way
to finish is to get busy, so that's what I'll be doing for a
good part of the day.  Until next time, take care, and keep your
cool while having sympathy for a fire department that must fight
an underground fire that it can't reach, which has half the city
shut down and has been burning for 20 hours already.


Jim Muth
[e-mail]


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

MidgetBy_Starlight { ; time=0:14:26.94--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-315.0304695202377/+33.89218968206931/7\
  59.3559/1/7.499 params=0.00001/-1100/10.1/-1/0/800
  float=y maxiter=3600 inside=0
  logmap=127 periodicity=10
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  zBmzFmzKmzEmzHmzLmzOmzRmz
  }

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

From: [e-mail]
Subject: (fractint) C-FOTD  20-07-01  (Negative is Positive [6])
Date: 20 Jul 2001 11:21:21 EDT


Classic FOTD -- July 20, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

It's another hectic day here at Fractal Central, so this will
have to be a short one.

The image was created by the formula
-2.5(Z^(-0.4))-25(Z^(-4.4))+(1/C), obviously a whimsical
expression.

I named the image, which comes from the Fractal Central
archives, "Negative is Positive".  I gave the image this name
because in it, two negative exponents have been added and
produced something positive.  Then I rated it a 6.

The 20-minute render time of the parameter file makes the
download more efficient.  The download may be found on the Web
at:

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

and:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was partly cloudy with a temperature
of 82F 28C.  The cats must have approved, though I had little
time to observe their approval.

And now it's back to work.  Until next FOTD, take care, and
endure.


Jim Muth
[e-mail]


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

NegativeIsPositive { ; time=0:20:42.09--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-5.577462512835426/-2.6019781270348/430\
  8367/1/150 params=-2.5/-0.4/-25/-4.4/0/800 float=y
  maxiter=3000 inside=0 logmap=367 periodicity=10
  colors=000mKzkIyjGwhEuiDsgCqfCodBncBlbBj`Ai_AgYAeX\
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  JuaHwa6xZFyaNzdVzgbzjjzldznZzpTzrNztIzxHzvHzuHztHz\
  sHzqHzpHzonz_tzZrzapzcozf
  }

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

From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) Re: [philofractal] C-FOTD  11-07-01  (Sea-What[4])
Date: 20 Jul 2001 11:18:50 -0500

"Morgan L. Owens" wrote:

>>> Textures in 3-D software like POV-Ray are four-dimensional...
>>
>> In what sense?
>
> For each point (X,Y,Z) in space, the texture specifies a fourth number
> which which (via the colourmap) gives the colour of that point.

Ah, I see what you mean.

In that sense, I'd think there was more than four dimensions, because
there are other attributes (filtering, transparency, surface normal,...)
that are also a part of each X,Y,Z point....

--
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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

From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Re: [philofractal] C-FOTD  11-07-01
Date: 21 Jul 2001 15:27:32 +1200

At 04:18 21/07/2001, Programmer Dude wrote:
>"Morgan L. Owens" wrote:
>
> >>> Textures in 3-D software like POV-Ray are four-dimensional...
> >>
> >> In what sense?
> >
> > For each point (X,Y,Z) in space, the texture specifies a fourth number
> > which which (via the colourmap) gives the colour of that point.
>
>Ah, I see what you mean.
>
>In that sense, I'd think there was more than four dimensions, because
>there are other attributes (filtering, transparency, surface normal,...)
>that are also a part of each X,Y,Z point....

More or less; certainly a fully-implemented texture could have an
(arbitrary?) number of layers, each with its own colourmap (which in the
case of POV-Ray at least maps one quantity into RGBF space - itself
four-dimensional!). I think what I really meant to refer to was a pigment like:

pigment
  {granite
   turbulence 0.4
   color_map
    {[0.000, 0.153   color rgbf <0.729, 0.502, 0.451, 0.000>
                     color rgbf <0.769, 0.686, 0.592, 0.000>]
     [0.153, 0.398   color rgbf <0.769, 0.686, 0.592, 0.000>
                     color rgbf <0.843, 0.753, 0.718, 0.000>]
     [0.398, 0.559   color rgbf <0.843, 0.753, 0.718, 0.000>
                     color rgbf <0.780, 0.667, 0.561, 0.000>]
     [0.559, 0.729   color rgbf <0.780, 0.667, 0.561, 0.000>
                     color rgbf <0.741, 0.659, 0.576, 0.000>]
     [0.729, 1.001   color rgbf <0.741, 0.659, 0.576, 0.000>
                     color rgbf <0.729, 0.502, 0.451, 0.000>]
    }
  }
                                    /* T_Grnt0, by Mike Miller */


To be precise: the "granite turbulence 0.4" part, specifying a
three-dimensional surface embedded in a four-dimensional space, just as a
sphere is a two-dimensional surface embedded in 3-space.

The rest is (as the name suggests) the colour map, specifying a (piecewise
linear) curve embedded in another four-dimensional space.

Morgan L. Owens
"Oh, how Euclidean."


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

From: [e-mail]
Subject: (fractint) C-FOTD  21-07-01  (Iterative Serenade [5])
Date: 21 Jul 2001 11:12:00 EDT


Classic FOTD -- July 21, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

With a normal 20-minute trip across town now taking 2 or 3
hours, things are still somewhat hectic here in the Fractal
Central part of the world.  This leaves little time for fractal
fun, but being one who enjoys fun, I somehow managed to find a
fractal.  Actually, I would not call the discovery 'finding' a
fractal.  Finding a fractal is like going to the beach and
finding a grain of sand.  I simply took one of the infinity of
fractals that I knew were there.

However, with the appearance of yet another July midget, it no
longer makes much sense to claim that July will be a midgetless
month.  Searching for a reason, I can always unroll the old
excuse that fate was against me.  But the effort to have a month
with no midget was not totally futile, for I did produce a few
worthwhile fractals with no midgets at the center.

Today, we declare the FOTD midgets to once again be legitimate.
The formula behind today's image is
6Z^(-1.68)+3.6Z^(-3.11)+(1/C), a whimsical expression that I
pecked out totally at random.

I colored the scene with the <tdis> option, and for no obvious
reason named the result "Iterative Serenade".  Actually, the
name is probably the best part of the image, which on its own
merit rates only a perfectly average 5.

The 6-minute render time from the parameter file is a bit slow
for such an average image.  The download, which will soon be
available at:

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

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

is far more efficient.

The fractal weather today was perfect, with brilliant sun and a
temperature of 82F 28C.  The fractal cats were happy with the
perfection, doing nothing all day but sleep.

And I'll be happy when I get the rest of the graphic work
wrapped up.  But regardless of how other things go, I'll be back
next time with another fractal and a few words.  Until then,
take care, and where did the philosophy go?


Jim Muth
[e-mail]


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

Iterative_Serenade { ; time=0:06:00.53--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.67175138564879/+6.985289718906726/2.\
  182875e+007/1/-139.999 params=6/-1.68/3.6/-3.11/0/0
  float=y maxiter=1200 inside=0
  outside=tdis periodicity=10
  colors=000Y_9_Z7`Y6bW8cUAdSCeQEgOFhMHiKJjILkGMbLLV\
  PLNTKFXK7`KA_PDZTGYXJXaLWeOViRUnUTrXSvZRzjUoZZqObr\
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  dsWiyQmvTltWkrZjpaimdhkfgiifgledodbrc`ubZwaYw_XwZW\
  wYVwXUwVTwUSwTRwSQwRNj6Ll7Km8Jn9HoAGpBFqCErDCsEBtF\
  AuG9vGCsFEqEGnEIlDKiCMgCPeBRbAT`AVY9XW8ZU8YXEX_JXb\
  OWdTVgZVjcUmhUomXeoVaDW`B
  }

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

From: "David Jones" <[e-mail]>
Subject: Re: (fractint) Re: [philofractal] C-FOTD  11-07-01  (Sea-What[4]
Date: 21 Jul 2001 09:16:11 -1000

Scientifically speaking, any measurable quantity about
something is a dimension - so there are lots of
multidimensional things around. Just not to be confused
with spatial dimensions.

David
[e-mail]

On 20 Jul 01 at 11:18, Programmer Dude wrote:

> "Morgan L. Owens" wrote:
>
> >>> Textures in 3-D software like POV-Ray are four-dimensional...
> >>
> >> In what sense?
> >
> > For each point (X,Y,Z) in space, the texture specifies a fourth number
> > which which (via the colourmap) gives the colour of that point.
>
> Ah, I see what you mean.
>
> In that sense, I'd think there was more than four
> dimensions, because there are other attributes
> (filtering, transparency, surface normal,...) that are
> also a part of each X,Y,Z point....


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

From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Re: [philofractal] C-FOTD  11-07-01
Date: 22 Jul 2001 11:48:14 +1200

At 07:16 22/07/2001, David Jones wrote:
>Scientifically speaking, any measurable quantity about
>something is a dimension - so there are lots of
>multidimensional things around. Just not to be confused
>with spatial dimensions.

Mathematically speaking there's no distinction.

Morgan L. Owens
"Who insisted on spatial dimensions anyway?"


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From: "Osher Doctorow" <[e-mail]>
Subject: (fractint) Fractals and Cross-Term Dimensional Analysis
Date: 21 Jul 2001 23:53:40 -0700


I have been proving several theorems on [e-mail],
[e-mail], real-analysis, anzap-l
(Australian-New Zealand Applied Probability), and elsewhere which appear to
relate fractals to cross-term-dimensional analysis (which I also discovered
recently).

Ordinary dimensional analysis in (mathematical) physics and engineering
(including chemical engineering) and even astrophysics and other fields is
mostly concerned with factors inside a single term of a physical equation
except to check that different terms reduce to the same dimensions. The
products of integer exponents of the dimensions of the factors in a single
term, including negative integers corresponding to division by integer
powers form an abelian group under multiplication.  For example, speed or
velocity has dimensions L/T which is usually written LT^(-1) where ^
represents exponent here.  L is the dimension of length, T is the dimension
of time.  Three other dimensions are in common use: M (mass), Q (charge,
usually electric), THETA (temperature).  If objects behave differently in
different spatial directions, the dimension of length is often subdivided
into three *independent* dimensions of Lx (backward-forward, say), Ly
(left-right, say) and Lz (up-down, say).   A typical problem that can be
solved in hydrodynamics, for example, is to find how the variables are
organized as factors in a single term (whether division or multiplication,
and what exponents are involved), provided that one knows the relevant
variables or has some theoretical (and hopefully experimental) basis for
choosing the variables.   Bluman and Kumei in their volume Symmetries and
Differential Equations, Springer-Verlag: N.Y. 1989, and the papers on which
it is based, revolutionized the study of ordinary and partial differential
equations largely by using a generalization of the fact that dimensional
analysis in such equations is a special case of Lie Groups.

What, then, is Cross-Term Dimensional Analysis (CTDA for short), and why is
it needed?   Dimensional analysis provides no clue as to why terms in a
physical equation have plus or minus (positive or negative) signs.
Suppose, for example, that x, y, z, and w are nonnegative variables, and
that some equation holds among them which in homogeneous form (all variables
moved to the left side of the equation and the left side is set equal to 0)
is:

1)  w - y + x - z = 0

Where do the + and - signs come from?   CTDA attempts to answer this
question, and the somewhat remarkable answer appears to be that the signs of
terms under the above types of conditions reflect whether a variable is a
causing/influencing or a caused/influenced variable as well as (when
combined with the enumeration of the number of variables involved) how many
steps are involved in the causation or influence.

What does all this have to do with fractals?   It has to do with the
fractals which are generated by iteration, e.g., by composition
f(f(....   ).   Notice here that the same function is composed with itself.

Now look at this rather strange expression: p1(p1(x, y), p1(z, w)).   This
looks a lot like the above iterated function, especially if we keep
iterating (e.g., x = p1(u, w), etc.).  However, there is already something
remarkable, just with this one expression.   Here p1 is the proximity
function p1(x, y) = 1 + y - x with y < = x and all variables x, y, z, w
between 0 and 1.   By evaluating the above expression, we find that:

2)  p1(p1(x,y), p1(z,w)) = 1 + p1(z, w) - p1(x, y) = 1 + (1 +(w - z)) - (1 +
(y - x)) = 1 + (w - z) - (y - x)

This is beginning to look awfully like equation (1).  In fact, if we set the
left hand side of (2) equal to 1, then we get (1) above:

3)  p1(p1(x,y),p1(z,w)) = 1

Moreover, if we go deeper and deeper inward in iteration of (2), we get
successively an expression like (2) with 8 variables instead of just 4 (x,
y, z, w being 4 variables), and so on (double each time), although there is
a specific pattern of + and - differences which yields an algorithm for the
n+1 st iteration in terms of the nth iteration.

I do not know how many readers recall my original contributions to fractint,
but I discussed here and elsewhere the fact that p1(x, y) = 1 + y - x for y
< = x and both x, y between 0 and 1 has three simultaneous interpretations
(although the objects referred to are not necessarily the same objects in
the three interpretations): (1) it is the probable/statistical (Logic-Based
Probability or LBP) influence of x on y (or the sets whose probabilities are
represented by x and y), in that order, (2) it is the Lukaciewicz fuzzy
multivalued logical implication x-->y (*x implies y*) = 1 + y - x (see P.
Hajek, Metamathematics of Fuzzy Logics, Kluwer Academic: Dordrecht 1998 for
excellent presentations of Lukaciewicz, Product-Goguen, and Godel fuzzy
multivalued logics) when x and y are fuzzy multivalued logical propositions,
(3) it corresponds geometrically to (one-sided) *nearness* of x to y when x
and y are 1 dimensional coordinates, just as ordinary Euclidean
distance-function or metric d(x, y) is the two-sided *farness* between x and
y.   Both have n-dimensional generalizations for n any positive integer.
In fact, p1(x, y) is a one-sided partial inverse of d(x, y) which is maximum
when d(x, y) is minimum subject to the constraints y < = x and x, y in [0,
1], and vice versa the former is minimum when the latter is maximum.  For n
dimensions, x and y become n-dimensional vectors and the expressions above
are the same except that x and y are replaced in the equations by the
average of their respective components, and yi < = xi for i = 1 to n, and
all xi, yi components of x, y are between 0 and 1.

Notice that we could generate iterated fractals as a special case of an
iterated p1 function by setting one of the p1 arguments equal to 0 and
possibly changing the range of the p1 function and the other constraint.
However, the most interesting part is not this but the fact that fractals
appear to be related to the basic causal or influence structure of the
mathematical and physical universe through (1) mathematical logic, (2)
probability/statistics, (3) geometry.  Only by combining fractals or their
p1 double-argument generalization and non-fractal or non-p1 expressions do
we obtain a complete dimensional analysis of both factors and terms of all
physical equations.

Osher Doctorow Ph.D.
Doctorow Consultants
Formerly (and still intermittently in parts) California State Universities
and Community Colleges




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From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  22-07-01  (Silk and Satin [8+])
Date: 22 Jul 2001 09:55:22 -0400 (EDT)


Classic FOTD -- July 22, 2001 (Rating 8+)

Fractal visionaries and enthusiasts:

Things are finally calming down here in the Fractal Central
area, though one would never guess it from the unchanged
behavior of the fractal cats, who rarely are anything but calm.
The disruption has already done its damage however -- my goal of
a month without a midget has failed.

But now that we've abandoned the goal of a month with no
quadratic midgets, the FOTD's are starting to improve.  I
couldn't decide whether to rate today's image an 8 or a 9, so I
decided on an 8+.

The expression 1.5(Z^(0.9))-1.35(1/Z)+(1/C) was iterated by the
MandelbrotMix4 formula to produce the parent fractal, which
appears as a very twisted Mandeloid, with a period-2 main bud so
shrunken and misplaced that even identifying it is difficult.

But there is no difficulty identifying the area that corresponds
to East Valley in this fractal, and today's scene is located way
down deep near the tip of a spiral that resembles but fails to
actually duplicate an elephant trunk.

I named the picture "Silk and Satin".  The name was inspired by
the satin-like effect, which is especially prominent in the
amber areas.  This satiny effect is far easier to achieve with
several specially designed Fractint coloring options, but as is
usually the case, I prefer to do it the hard way, with the good
old classic equal-iteration bands.

Rendering in 17 minutes, the image is a bit slow, but salvation
is on the way in the form of the finished GIF image, which will
soon be posted on the Web at:

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

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was perfect, one by-product being
happy cats.  The temperature of 86F 30C and sunny skies seemed
just right for the hottest time of year.

Now I see it's time to start thinking of the next FOTD, so until
then, take care, and see you soon.


Jim Muth
[e-mail]


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

Silk_and_Satin     { ; time=0:17:14.19--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-0.21103269278124330/+0.604572415492978\
  40/9.458008e+009/1/37.5 params=1.5/0.9/-1.35/-1/0/0
  float=y maxiter=1800 inside=0
  logmap=310 periodicity=10
  colors=000NNBLNAKPAJR8IT8IV7GX6FZ6E`5Cb5Bd3Bf3KhBS\
  jJ_lPgnWopcpriqnnlgsgVwcKz`NxZOuWQqVSnSSkQVgPWdNZ`\
  K_ZJ`VGcSEgOCjLFnQIqVKu_NxdPzlNzkLwkKujJsjIpjGniFk\
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  glggigeegdbibZi`Vi_SiZOiYKkVGnUCpS8sS5uQ2wS7zVBzYG\
  z_Kz`PzcSzeYzg`zjezkizjiziizgizgizeizdizcizbiz`iz_\
  izZizYizWizVizUizUizdEzgC
  }

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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From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) C-FOTD 20-07-01 (Negative is Positive [6])
Date: 23 Jul 2001 11:59:40 +0000

>From: [e-mail]
>Reply-To: [e-mail]
>To: [e-mail]
>CC: [e-mail]
>Subject: (fractint) C-FOTD  20-07-01  (Negative is Positive [6])
>Date: Fri, 20 Jul 2001 11:21:21 EDT
>
>Classic FOTD -- July 20, 2001 (Rating 6)
>
>Fractal visionaries and enthusiasts:

Dam boy, that is HOT! It's worth more than 6, if only because of the very
funky colour scheme!

Thanks.
Andrew.


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From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) C-FOTD 22-07-01 (Silk and Satin [8+])
Date: 23 Jul 2001 12:06:31 +0000

>From: Jim Muth <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>CC: [e-mail]
>Subject: (fractint) C-FOTD  22-07-01  (Silk and Satin [8+])
>Date: Sun, 22 Jul 2001 09:55:22 -0400 (EDT)
>
>
>Classic FOTD -- July 22, 2001 (Rating 8+)
>
>Fractal visionaries and enthusiasts:
>
>I
>couldn't decide whether to rate today's image an 8 or a 9, so I
>decided on an 8+.

Let me help you: That is a pure 9 image. It's lovely!

Thanks.
Andrew.


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From: Jim Muth <[e-mail]>
Subject: Re: (fractint) C-FOTD 22-07-01 (Silk and Satin [8+])
Date: 23 Jul 2001 10:21:41 -0400 (EDT)

At 12:06 PM 7/23/01 +0000, Andrew Coppin wrote:

>Let me help you [rate the image]: That is a pure 9 image.
>It's lovely!

Andrew:

Thanks for the praise.  Only my humility keeps me from admitting
that it's true.  ;-)

Jim M.


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From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) C-FOTD  21-07-01  (Iterative Serenade [5])
Date: 23 Jul 2001 10:05:38 -0500

[e-mail] wrote:

> ...and where did the philosophy go?

Same place the light goes when you turn off the switch??

--
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  23-07-01  (Crystal Devils [7])
Date: 23 Jul 2001 10:14:56 -0400 (EDT)


Classic FOTD -- July 23, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

Just after 7am this morning, after 5 days of intense effort, our
intrepid firemen extinguished the last burning car in the train
tunnel that stretches under the center of town.  Now it's a
matter of inspecting for structural damage to the tunnel, and
also the roads, buildings, storm drains, water mains, utility
lines etc. above, and doing repairs.  We are told that within a
month or so, things will be back to normal, and the cross-town
roads will once again be passable.  Until then, to get from the
east side to the west side, it will be necessary to go around,
which is nearly impossible because everyone else wants to do it,
and there are not enough roads.  Considering conditions on the
west side, some say this is a good thing.  I am neutral.
Fractals are far more fun.

Today's FOTD image, which appears to have several layers but
actually has only one, pictures another midget, this one lurking
in the fractal created by the formula:
      -1*(Z^(1.1))+Z^(-0.7)+(1/C).

This simple expression creates a fractal that consists of two
Mandeloids, a large, relatively undistorted figure, with a
smaller figure in its northwest suburbs.  The smaller figure is
quite distorted.

For today's FOTD, we dive into an arm of a star of a bud on the
southeast shore of the large figure.  Well, we don't actually
dive into the arm, we go directly to its tip.  Of course, the
point of the exact end of the arm exists in a fractal fuzziness,
which, like quantum objects, cannot be given a precise location.
One can come as close as they wish to the end of the arm, but
more precision will always show that it is possible to come even
closer.

In today's image, I have colored the outside parts with the
<fmod> option, an option which, as today's effort shows, I use
all too infrequently.  The smaller features in the picture
remind me of crystals; the large rusty-red background shapes
remind me of devils.  I therefore named the image "Crystal
Devils".  I rated it a 7 because I consider it above average.

With a render time in the 5-minute range, running the parameter
file is not too bad a choice, but in an hour or so the finished
GIF image will be available on the Web at:

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

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The download from there would be more efficient.

The fractal weather today was typical summer, with sunny skies,
a temperature of 86F 30C, and lazy cats.

It's now time for me to do some un-lazy work, so until next
time, take care, and fractals are just as good as we want them
to be.


Jim Muth
[e-mail]


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

Crystal_Devils     { ; time=0:05:38.12--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.026683029720186/-0.41544346140642/2.\
  748383e+008/1/-177.499 params=-1/1.1/1/-0.7/0/800
  float=y maxiter=1200 inside=0 proximity=0.0645
  outside=fmod symmetry=none periodicity=10
  colors=000zhJzhEzh8zoGztLrzTkzZdzPXzIRzAVrNXkZ`dib\
  XtfPzhIzdPzbVz`bzZhzXmzZkxZkrZimZihZib`hX`hR`hL`fG\
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  qZVo`XobZmdbmfdkhfkihiikikmhmohoqfqtfrvdtxdtzftxht\
  xhtxitxktxktvmtvmtvotvqtvqttrttttttttvttvttkxfbzRR\
  zCIz0VzCfzP`zRXzRTzRPzTLzTIxTExTAxV6vV1vV0vX0tX0tX\
  0tX0q`0md0if0fi0bk0Zo0Vq0Rt0Nv0Js0Ip0Gm0Ej0Cg0Ad08\
  a16`33Y61V80SA0P30M30Jf1G
  }

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

From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) C-FOTD 22-07-01 (Silk and Satin [8+])
Date: 23 Jul 2001 12:34:32 -0500

Andrew Coppin wrote:

> That is a pure 9 image. It's lovely!

Hear! Hear!

--
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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From: [e-mail]
Subject: Re: (fractint) C-FOTD 22-07-01 (Silk and Satin [8+])
Date: 23 Jul 2001 19:08:07 -0500

fortunately Jim's humility is exceeded only by his talent. ;-)

Jim Muth wrote:

> At 12:06 PM 7/23/01 +0000, Andrew Coppin wrote:
>
> >Let me help you [rate the image]: That is a pure 9 image.
> >It's lovely!
>
> Andrew:
>
> Thanks for the praise.  Only my humility keeps me from admitting
> that it's true.  ;-)
>
> Jim M.
>
> --------------------------------------------------------------
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From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  24-07-01  (Internet Spy program [6])
Date: 24 Jul 2001 00:25:18 -0400 (EDT)


Classic FOTD -- July 24, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

BUG ALERT!!

Well, it's not actually a bug, but before getting into my
regular discussion, I must point out that today's parameter file
requires special attention before it will draw the correct
image.  To see today's image correctly, run the parameter file
as it is, but when the image is finished, do one maximum in-zoom
into the center.  You will then be viewing the correct image.
This extra step is necessary because the extreme magnitude of
the full-sized image causes strange and unpredictable
inaccuracies when the parameter file is directly written from it.

The very simple formula -1*(Z^(1.1))+Z^(-0.7)+(1/C) drew the
parent fractal, which consists of a large Mandeloid with a
smaller satellite nearby.  Today's scene lies way out at the tip
of the negative tail of the large Mandeloid.  Actually, it's not
really a negative tail, but only the center filament attached to
a period-2 bud.

Though the magnitude of the image is extreme, the maxiter is a
remarkably modest 256, making the logmap feature meaningless.
The small maxiter also makes the parameter file a very fast one,
which is a good thing, considering that two steps are necessary
to draw the correct image.

The name "Internet Spy Program" came about when I noticed the
many eye-like features surrounding the midget.  I had just
deleted 4 e-mails that wanted me to buy those learn-anything-
about-anyone internet 'spy' programs.  I rated the image a 6
because that's what I think it's worth.

Running the parameter file and zooming into the resulting image
may be the best way of viewing today's finished product.  The
image will also soon be available at:

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

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

though I cannot guarantee that the correct image will be posted.

The fractal weather today was the normal summer fare for this
part of the world.  The hot sun and 90F 32C degree temperature
had the fractal cats lazy but happy all day.

And it's time for me to get on with other projects, such as
watching TV.  I'm sorry about the inconvenience of the 2-step
parameter file, but it's one of those freaky things that will
probably never again be necessary.  Until tomorrow, take care,
and I wouldn't be surprised if the universe proved to be
composed of fractals.


Jim Muth
[e-mail]


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

InternetSpyProgram { ; time=0:01:30.30--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.02429494176869804/-0.118024956696030\
  00/6.248276e+011/1/32.522/-0.001 params=-1/1.1/1\
  /-0.7/0/800 float=y maxiter=256 inside=0
  periodicity=10 mathtolerance=/1
  colors=000IkhIrmIxq4UX2Sd1Ql0PtCZcOhO_q8cmDgjIjgNn\
  cSr`XuY`gkbUxdSudRsdPpdOndMkdLidJfdIddKaeL_fMYgNIZ\
  OJePPiQXi`NVkDGv42wVAzwInlOfdTYUYQZbHcg9hlNmMOmKPm\
  JQmIMmLJmOGmQDmTAmW7mYBmVEmTImRLmPPmNSmLVmJbmLjmNr\
  pPLwRFuM9sH3oDFoGKpJKqMKrRMsWOt_Qu`SvaUwaWxbYyb_zc\
  azcczSezNgzIizDkz8mzIozSqzaszkuztwzkyzbzzVzzMzzDzz\
  5zzZzzazzdzzgzzjzzlzzizzfzzczz`zzYzzVzzZzzbzzfzzjz\
  znzzszzxzzpzzhzzazzUzzNzzFzz8zzDzzIzzNzzSzzWzzXzzX\
  zzXzzYzzYzzYzzazzezzhzzlzzpzzszzwzzzzzxzzwzzuzztzz\
  szzqzzpzzozzrzztzzwzzyzzuzzqzznzzjzzfzzczzfzzhzzjz\
  zmzzozzqzzrzzszzszztzzuzzuzzszzqzzozzmzzkzzizzgzze\
  zzvzzdzzOzzUzzZzzczzhzzmzzrzzwzzMzzMzzMzzLzzLzzZzz\
  UzzOzzJzzXzzizzvzzhzzVzzHzzFzzEzzDzzCzzBzzAzzIzzQz\
  zXzzczzjzzqzzbzzOzzAzzBzzBzzCzzCzzCzzDzzDzzDzzJzzP\
  zzUzz_zzdzzjzzozzJzzOzzTzzYzzazzWzzQzzKzzEzz9zzBzz\
  CzzEzzFzzGzzLzzQzzVzzZzzc
  }

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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From: "Cerridwen Connelly" <[e-mail]>
Subject: (fractint) saving files
Date: 24 Jul 2001 11:04:44 +0100

Does anyone know how to (or if it is possible to) save frames from Fractint
as .JPG or .GIF?

When I attempt this on my Pentium II/Windows 98, and try to open the saved
images in Photoshop or PaintshopPro, they do not open.

Back when I was on a 386/windows3.1, it was possible to save files in these
formats (can't remember how though) and tweak them in a photo-editor program
or art program to obtain the effects on the website listed below.

I would like to continue doing this artwork:-)

Any help greatly appreciated.


Cerridwen
http://www.users.bigpond.com/catfishy/CERRIDWEN.HTM




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

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) saving files
Date: 24 Jul 2001 05:23:54 -0500

Cerridwen Connelly wrote:
>
> Does anyone know how to (or if it is
> possible to) save frames from Fractint
> as .JPG or .GIF?

Not as a JPEG format, but GIF has been the way for most all images since
the creation of FractInt.  Once the image has completed, just hit the
"S" (for Save) on your keyboard and it will be written to whatever
directory path you have specified for GIF files in your SSTOOLS.INI
file.  The first image file save will automatically be called
FRACT001.GIF and if you save any others, then they will be sequentially
numbered from there.

>
> When I attempt this on my Pentium II/
> Windows 98, and try to open the saved
> images in Photoshop or PaintshopPro,
> they do not open.

Which version/release/level of FractInt are you using??  And what is the
file that you are trying to open in your graphics editor??  How did you
create that image file??

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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

From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) C-FOTD  21-07-01  (Iterative Serenade [5])
Date: 24 Jul 2001 23:23:39 +1200

At 03:05 24/07/2001, Programmer Dude wrote:
>[e-mail] wrote:
>
> > ...and where did the philosophy go?
>
>Same place the light goes when you turn off the switch??

You mean the same place dropped Internet packets go?

Morgan L. Owens
"The landscape here must be littered with 'em"


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

From: "Cerridwen Connelly" <[e-mail]>
Subject: Re: (fractint) saving files
Date: 24 Jul 2001 14:08:19 +0100


> Cerridwen Connelly wrote:
> >
> > Does anyone know how to (or if it is
> > possible to) save frames from Fractint
> > as .JPG or .GIF?
>
> Not as a JPEG format, but GIF has been the way for most all images since
> the creation of FractInt.  Once the image has completed, just hit the
> "S" (for Save) on your keyboard and it will be written to whatever
> directory path you have specified for GIF files in your SSTOOLS.INI
> file.

SSChoice.exe is the closest thing in the list of program parts to
SSTOOLS.INI (which isn't there at all).

>The first image file save will automatically be called
> FRACT001.GIF and if you save any others, then they will be sequentially
> numbered from there.

This FRACT001.GIF does not appear on the bar with flashing dos-like cursor.
Nothing appears until I type something in.
>
> >
> > When I attempt this on my Pentium II/
> > Windows 98, and try to open the saved
> > images in Photoshop or PaintshopPro,
> > they do not open.
>
> Which version/release/level of FractInt are you using??

20.0

>  And what is the
> file that you are trying to open in your graphics editor??

ONE.GIF

>  How did you
> create that image file??

I ran (for example) mandel, cycling and altering colours with Enter key,
then hit spacebar to capture a still, pressed s, and saved on that bar with
the blinking cursor as ONE.GIF

The error message in Photoshop reads: "could not open because the
file-format module cannot parse the file".


Cerri
http://www.users.bigpond.com/catfishy





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

From: "cybersue" <[e-mail]>
Subject: Re: (fractint) saving files
Date: 24 Jul 2001 10:59:00 -0400

Hello, Cerridwen (what a wonderful Celtic (?) name!) , The easiest way to do
what you want is perhaps to save just the frame layers as a separate UPR,
deleting all others (after saving, of course! :-)). Then render the frame
UPR using the "Render to disk" command! The result will be a jpg file which
you could then put into Photoshop and erase the center background black to
transparent to use as a second layer over your own photos! (I'm assuming
that's what you want to do?)

I hope my humble answer helps you a little bit! I believe every little bit
helps some! :-)

Sharon
[e-mail]

"Freedom Rules!"


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From: "cybersue" <[e-mail]>
Subject: Re: (fractint) saving files
Date: 24 Jul 2001 11:02:24 -0400

So sorry, Cerridwen, I just realized that I was reading my "Fractint" mail,
not my "UltraFractal" mail! the solution I gave works in UF but I'm not
experienced enough to know is there is a similar procedure for Fractint! I'm
sorry I jumped too soon. Perhaps someone else on this list knows the answer
to this one. Good luck.

Sharon
[e-mail]

"Freedom Rules!"


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

From: [e-mail]
Subject: Re: (fractint) saving files
Date: 24 Jul 2001 18:58:26 +0100

Hi Cerridwen,


>
> I ran (for example) mandel, cycling and altering colours with Enter key,
> then hit spacebar to capture a still, pressed s, and saved on that bar with
> the blinking cursor as ONE.GIF

I see your problem, when you colour cycle and then hit space to pause you are
actually still in colour cycle mode in fractint (some video modes will
show this by having a white border oin the screen)  and when you hit
's' in colour cycle mode you actually end up saving the pallette (just the
colour set, not the image itself) which is in fractint's own .map format.

What you need to do is hit escape once after pausing the cycle, then
when you hit 's' it will save the image for you (without asking for a file name)

to go back into colour cycle mode hit 'c' to continue where you left off.


Hope this helps,
              Robin.

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

From: "Les St Clair" <[e-mail]>
Subject: Re: (fractint) saving files
Date: 24 Jul 2001 19:27:31 +0100

Hi Cerridwen,

OK, problem solved!

As Paul said, pressing "s" will save the current fractint screen image as a .gif file in your Fractint directory (unless
another location was specified in sstools.ini).

However, as you were in colour cycling mode at the time, pressing "s" will save the colour palette as a ".map" file.
As you called the file "one.gif" this has overwritten the default ".map" extension.
Your graphics viewer could not open the "gif" file because it wasn't really a .gif file at all.

The way to do what you want is to hit "c" instead of spacebar to pause colour cycling, then press "Esc" to leave colour
cycling mode. Now press "s" to save the gif image. BTW, press "x" to get to the "basic options" screen. Here you can
change the savename of the gif file to whatever you want.

I hope you understood my garbled explanation.

cheers,

Les

> I ran (for example) mandel, cycling and altering colours with Enter key,
> then hit spacebar to capture a still, pressed s, and saved on that bar with
> the blinking cursor as ONE.GIF
>
> The error message in Photoshop reads: "could not open because the
> file-format module cannot parse the file".



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

From: "Cerridwen Connelly" <[e-mail]>
Subject: (fractint) thanks and another stupid question
Date: 24 Jul 2001 21:35:20 +0100

Thank you Robin and Les!!!

It works  now:-)

Stupid question two:

I can't recall how to make the square box appear on the screen to crop the
fractal and "go in deeper". Does anyone know from this appalling description
what I am talking about and which keys to press?:-)

*This is my final stupid question, I promise:-)


Yn y Gwe,

Cerridwen
http://www.users.bigpond.com/catfishy




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

From: "Les St Clair" <[e-mail]>
Subject: Re: (fractint) thanks and another stupid question
Date: 24 Jul 2001 22:03:17 +0100


Hi again,

> I can't recall how to make the square box appear on the screen to crop the
> fractal and "go in deeper". Does anyone know from this appalling description
> what I am talking about and which keys to press?:-)

Use the "Page Up" key.
It's not easy to remember all the keystrokes for old-fashioned DOS apps is it!!

Help is at hand though... Just press "F1" while running Fractint to get all the on-line help you need!
The first help screen - four pages worth summarising the main commands - can be navigated using the cursor keys.
Press F1 again to get the main help mega index!

Have fun.

- Les



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

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) thanks and another stupid question
Date: 24 Jul 2001 16:05:20 -0500

Cerridwen Connelly wrote:
>
> I can't recall how to make the square box
> appear on the screen to crop the fractal
> and "go in deeper".

You are probably speaking about the Zoom Box, which may be reached by
using the PAGE_UP keep on your keybaord.  You will then have many
options available while in that mode.  At this point, I suggest hitting
the F1-Key to acquire the various instructions.

You may wish to also runt the following from the Command Line:

      fractint.exe makedoc

This will generate a multi-page document with almost everything that you
would care to know about FractInt.

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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

From: "Doug Stewart" <[e-mail]>
Subject: Re: (fractint) thanks and another stupid question
Date: 24 Jul 2001 17:06:59 -0400

Try  "page up" or "page down"

----- Original Message -----
Sent: Tuesday, July 24, 2001 4:35 PM


> Thank you Robin and Les!!!
>
> It works  now:-)
>
> Stupid question two:
>
> I can't recall how to make the square box appear on the screen to crop the
> fractal and "go in deeper". Does anyone know from this appalling
description
> what I am talking about and which keys to press?:-)
>
> *This is my final stupid question, I promise:-)
>
>
> Yn y Gwe,
>
> Cerridwen
> http://www.users.bigpond.com/catfishy
>
>
>
>
> --------------------------------------------------------------
> Thanks for using Fractint, The Fractals and Fractint Discussion List
> Post Message:   [e-mail]
> Get Commands:   [e-mail] "help"
> Administrator:  [e-mail]
> Unsubscribe:    [e-mail] "unsubscribe fractint"
>


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

From: "Doug Stewart" <[e-mail]>
Subject: Re: (fractint) thanks and another stupid question
Date: 24 Jul 2001 17:06:59 -0400

Try  "page up" or "page down"

----- Original Message -----
Sent: Tuesday, July 24, 2001 4:35 PM


> Thank you Robin and Les!!!
>
> It works  now:-)
>
> Stupid question two:
>
> I can't recall how to make the square box appear on the screen to crop the
> fractal and "go in deeper". Does anyone know from this appalling
description
> what I am talking about and which keys to press?:-)
>
> *This is my final stupid question, I promise:-)
>
>
> Yn y Gwe,
>
> Cerridwen
> http://www.users.bigpond.com/catfishy
>
>
>
>
> --------------------------------------------------------------
> Thanks for using Fractint, The Fractals and Fractint Discussion List
> Post Message:   [e-mail]
> Get Commands:   [e-mail] "help"
> Administrator:  [e-mail]
> Unsubscribe:    [e-mail] "unsubscribe fractint"
>


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

From: Mark Christenson <[e-mail]>
Subject: Re: (fractint) JPEGs & layers (was "saving files")
Date: 24 Jul 2001 17:32:00 -0700

At 10:59 AM 7/24/01 -0400, cybersue wrote:
>Hello, Cerridwen (what a wonderful Celtic (?) name!) , The easiest way to do
>what you want is perhaps to save just the frame layers as a separate UPR,
>deleting all others (after saving, of course! :-)). Then render the frame
>UPR using the "Render to disk" command! The result will be a jpg file which
>you could then put into Photoshop and erase the center background black to
>transparent to use as a second layer over your own photos!

At 11:02 AM 7/24/01 -0400, cybersue wrote:
>So sorry, Cerridwen, I just realized that I was reading my "Fractint" mail,
>not my "UltraFractal" mail!

For anyone who *is* doing layers in Fractint, I wish to share a
trick which has made my JPEGs much better.  The program
I use to merge my layers has the annoying trait of having a
minimum compression ratio (won't generate a completely
non-compressed JPEG).  I have learned to save it first as a
24-bit color TIFF (I have no PONG-capable software), and
then do final adjustments and conversion to a mildly
compressed JPEG in a program with better compression
characteristics (in my case, PSP 2.0. Yes, 2.0!)  You still
have to live with artifacts, but they are less severe.


Happy fractalling,
        Bud


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

From: [e-mail]
Subject: (fractint) C-FOTD  25-01-00  (What a Midget [5])
Date: 25 Jul 2001 08:12:08 EDT


Classic FOTD -- July 25, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

Today's image is a harsh one, which takes 1-1/2 hours to render
from the parameter file.  Looking at it, I get the impression
that it could have been an 8-rated image, but somewhere along
the way something went wrong.  Maybe there's just too much muddy-
looking black.  In the end, I rated the image at an average 5
and named it "What a Midget".  The name is to be taken more as a
question than as an exclamation.

The image is part of the Z^(sqrt(2))+C fractal.  In today's
case, the pictured section of the fractal is located 6.283185307
out the infinite fractal spiral.  This number is two times pi.
I chose it because setting real (p2) of the MandelbrotBC1
formula to pi produces fractals with X-axis symmetry, and I
wanted to see what 2pi would do.  I found that it did nothing
extraordinary

The slow render time and less than great quality of today's
image make a download of the GIF image the better choice.  But
before visiting their web sites, give paul and Scott a chance to
render and post the image.  Those sites may be found at:

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

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was once again summer-like, with
humidity as high as the temperature, which reached 94F (34.5C).
The public complained, but the cats approved.

And I wish I had nothing to do, but the day is young and the
work is waiting.  Until next time, take care, and be efficient.


Jim Muth
[e-mail]


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

What_a_Midget      { ; time=1:27:57.45--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=1
  center-mag=-0.30392296144667660/-0.870386112464632\
  30/7.247228e+008/1/-72.5 params=1.414213562373/0/6\
  .283185307/0 float=y maxiter=15000 inside=0
  logmap=2481 periodicity=10
  colors=0008R6AR7CR9ERAHRCJRDLRFNRGQRHSRJURKWRMZRN`\
  RPbRQbOMcQPdRReSUfUWfVZgW`hXbiZej_gj`jkbllcomdqmes\
  idqfcpcco`bmXalUakR`iO_hL_gK`fK`fK`eKaeJadJadJbdJb\
  cIbcIcbIcbIcbHdaHdaHd`Hd`Ge`Ge_Ge_GfZFfZFfZFgYFgYE\
  gXEhXEhXEhWDiWDiVDiV7gSDiVIkXOmZTo`Zqbcsdiufmxfnwg\
  nwhnvhnvinvinujnukntkntlotlosmosnosnoroorooqpoqpoq\
  qoprpprppspospotpnupnupnvpmvpmwpmwqnwrpxqnwqlvqjvq\
  hupftpdtpbsp`soZroXqoVqoTpnRonPonNnnLnmJmmHlmFlmDk\
  lBjl9jl7im4jl5ik5hj5gi5fh5fg5ef5de5cd5cc5bb5aa6``6\
  `_6_Z6ZY6YX6YW6XV6WU6VT6VS6UR7TQ7SP7SO7RN7QM7PL7PK\
  7OJ7NI7MH7MG8LF8KE8JD8JC8IB8HA8G98G88F78E68D53C68D\
  6CD7HD7LD8QE8UE9YE9bEAfFAkFBoF9yDBsFDmGFgIHbJJXKLR\
  MNLNLFNNGOOGOPGORGOSHOTHOVHOWHOXIPZIP_IP`IPbJPcJPe\
  JPgJPiKQjKQmKQnKQpLQrLQtLQzJSwKRuLQrMQpNPmOOkOOhPN\
  fQMdRMaSLZTKXTKVUJSVIPWINXHKYGIYGGZFD_EB`E9aD7bC3d\
  B4cC5bC5bC6aD6aD7`D8`E5R4
  }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a
}

END 20.0 PAR-FORMULA FILE==================================

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

From: "Cerridwen Connelly" <[e-mail]>
Subject: (fractint) thanks - up and down:-)
Date: 26 Jul 2001 10:42:54 +0100

Thank you Paul, Les and David for the "Page Up and Down" replies.

It works fine now and I am happily generating new additions to my art link
pages:-)

Yn y Gwe,

Cerridwen
http://www.technopagans.co.uk
http://www.pagantours.co.uk
http://www.users.bigpond.com/catfishy




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

From: [e-mail]
Subject: (fractint) C-FOTD  26-07-01  (A Skeletized Scene [5])
Date: 26 Jul 2001 10:28:09 EDT


Classic FOTD -- July 26, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

Due to a rush, today's discussion will be short.

Today's fragmented scene has a nearly-lost midget at the center.
The unusual effect is caused by coloring the outside area with
<fmod> rather than the usual <iter>.

The formula behind the image is (Z^2)+(0.2(Z^3))+C.  The parent
fractal is a figure with a string of bays, with many new valleys
to explore between the bays.  Today's scene lies in one of the
new valleys.  Noticing the skeletal effect of the picture, I
named it "A Skeletized Scene".  Due to the haste in which the
image was produced, I could rate it no higher than a 5.

The parameter file renders in 29 minutes on a Pentium 200mhz
machine.  The download of the GIF image from:

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

or from:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

is far faster.  But give Paul and Scott a chance to render and
post the image before visiting their sites.

The fractal weather today was sunny and quite hot and humid
today, with a temperature of 97F 36C.  The fractal cats ignored
the heat and slept most of the day.

But I've got a bit of work to accomplish, so until next time,
take care, and patience is rewarded, but too much patience gets
nothing done.


Jim Muth
[e-mail]


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

A_Skeletized_Scene { ; time=0:29:49.15--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-3.517795082582847/-0.172268355153175/5\
  .450818e+011/1/-154.935/-0.116 params=1/2/0.2/3/0/0
  float=y maxiter=3000 inside=0
  proximity=0.047 outside=fmod periodicity=10
  colors=000DITDITCISCISCISBIRBIRBIRAIQAIQAIQ9JP9JP9\
  JP8JO8JO8JO7JN7JN7JN6JM6JM5HN6JM6KM6LM6NL6OL6PL6RL\
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  RADPAAHAAKAAMAAPAARAAUAAT
  }

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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From: [e-mail]
Subject: (fractint) C-FOTD  27-07-01  (Billowing Billows [6])
Date: 27 Jul 2001 10:09:50 EDT


Classic FOTD -- July 27, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

My opinion of the <tdis> outside fill option grows more
favorable every time I use it.  However, due to its flaw, the
tendency to revert to a flat color at high iteration levels, I
doubt that it will ever become my default method of exploration.
But it certainly can bring life to some otherwise nearly dead
fractals.

Today's image is a good example of the new life which the <tdis>
option can sometimes bring to ho-hum fractals.  When rendered in
the usual manner, with the usual equal-iteration bands, today's
image is just another fractal, the likes of which we've seen
hundreds of times before.  But when the new <tdis> option is
used, the image takes on a striking, almost three-dimensional
quality that makes it well worth being named Fractal of the Day.

The parent fractal of today's image is a Mandeloid with several
extra bays and valleys.  It was created by a simple combination
of small portions of Z^4 and Z^5.  On the surface it appears to
have little potential, and indeed, were it not for the <tdis>
option, I would have given up on the fractal before reaching the
scene of today's image.

I named today's picture "Billowing Billows" partly as a joke,
and partly because I like the sound of the words.  The rating
of 6 is fair.

The parameter file runs in 17 minutes.  The file of the GIF
image, which will be posted in an hour or so to:

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

and to:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

will download in less than one minute.

The fractal weather today was cloudy, with a temperature of 88F
(31C) and a light shower in the afternoon.  The fractal cats
approved of everything but the rain.

And I'll approve of today's work once it's behind me.  The only
way I know to get the work behind me is to start, so that's what
I'm now ready to do.  But I'll return in the proper time with
another fractal.  The philosophy is also once again stirring, so
it stands to reason that it will soon make a long overdue re-
appearance.  Until tomorrow, take care, and search for fractals.


Jim Muth
[e-mail]


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

Billowing_Billows  { ; time=0:17:09.36--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-4.13027890934321500/+0.608256133526089\
  10/12033.82/1/-164.999 params=0.05/4/0.01/5/0/0
  float=y maxiter=1200 inside=0
  outside=tdis periodicity=10
  colors=000YTAXV9XX7XZ6X_5_c6bf6di6gm6jp6ls6gt8cu9Z\
  uBVvCRwDMwFIxGExHRhNbUTcTWcTYcT_cTacTcdSfdShdSjdSl\
  dSneUmfWmgYmh_mialjclkellglmhlnkfomapoXqqSrsNmrOir\
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  HbjMgrR`oOUmLNkJLjKKiLIhLHgMGfNEeNDdOBdPAcP9bQ7aR6\
  `R4_S3ZT2ZTGROUJJgBEt3As69s98sC7rF6rH6rK5qN4qQ3qT2\
  qV2oY3n_3lb4kd4jg4hi5gl5en6dq6cs6YqAToEOnIIlLDkPJ`\
  tKbtKdsLfsLhsZMGYOEYQDYSB
  }

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

From: [e-mail]
Subject: (fractint) C-FOTD  28-07-01  (Midget and a Half [6])
Date: 28 Jul 2001 11:13:37 EDT


Classic FOTD -- July 28, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Today's fractal has been named "Halfway Midget".  I gave it this
name not because of its behavior, but because the generating
formula of its parent fractal is Z^(2.5)+C, and 2.5 of course is
halfway between 2 and 3.

Midgets in this range come in all shapes.  The shape of the
midget in today's picture, with the midget splitting along its
East Valley, is one of the most frequently seen.

I originally found today's midget by using the MandelbrotBC
formula.  But when the image was completed, I realized that the
second parameter was set to pi, and the formula was therefore
drawing the same image as Fractint's built-in manzpower formula
would draw.  I then rendered the image with the manzpower
formula, but found it too slow.  I finally turned to my own
MandelbrotN formula, and found that this formula draws the
identical image in 2/3 the time of the manzpower formula.

In my opinion, the most notable thing about the image is the
inconspicuousness of the branch cut discontinuities.  The breaks
are there, but they are so well hidden that unless looked for,
they would never be noticed.  All in all, it's a slightly-above-
average image, well worth the rating of 6.

Rendering the image with the fastest formula, MandelbrotN, takes
4-1/2 minutes.  Downloading the GIF image file is even faster,
but before going for the download, give Paul and Scott a chance
to post the image file to their web sites.

The GIF image will be available for download at:

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

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was perfect.  The sunny skies, low
humidity, and temperature of 81F 27C made the cats as well as
myself happy.

Until next time, take care.


Jim Muth
[e-mail]


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

Midget_and_a_Half  { ; time=0:04:34.35--SF5 on a p200
  reset=2001 type=formula formulafile=slices.frm
  formulaname=MandelbrotN passes=1 center-mag=-0.923\
  23411769327450/-0.00079409795476115/2.610506e+008/\
  1/-14.999 params=2.5/0/0/0/0/0 float=y maxiter=3500
  inside=0 logmap=106 periodicity=10
  colors=000AfgAfhAeiAdiAcjAbkAakA_lAYl9Wm9Un8Sn8Qm8\
  Pk8Ni8Lg8Je8Ic8Ga8E_8CY8BW7AU7AS79Q79O68M68K67I67G\
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  BzXBzYBzZAz_Az`AzaAzbAzc9zc9zc9zc9zc9zc8zc8zc8zc8z\
  c8zc7zc7zc7zc7zc7zc6zc6zc6zc6zc6zc5zc5zc5zc5zc5zc4\
  zc4zc4zc4zc4zc4zc6zc7zc9zcAzcCzcDzcFzcGzcHzcJzcKzc\
  MzcNzcPzcQzcRzcTzcUzcUzcU
  }

frm:MandelbrotN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=z^(b)+c,
|z| <= 16
}

END 20.0 PAR-FORMULA FILE==================================

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

From: [e-mail]
Subject: (fractint) C-FOTD  29-07-01  (Creature Feature [7])
Date: 29 Jul 2001 10:57:24 EDT


Classic FOTD -- July 29, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

I named today's picture of a Z^(sqrt(2))+C midget "Creature
Feature" because I found it on a Saturday evening, just as I was
ready to settle down to watch my traditional Saturday night
junky old creature feature on TV.  The image rates a 7 because
it shows a relatively new kind of midget.

But what is a creature feature?  To qualify as a creature
feature, a movie needs to meet certain low standards.  Most
importantly, it must violate so many scientific principles as to
be totally unbelievable.  A typical plot might be to have the
planet Earth torn in half by a magnitude 15 earthquake,
(impossible), and the two halves drift off in their own orbits.
(Also impossible.)  Of course, we would need a 'scientist' to
exclaim something like, "wow! what a trembler!", as the quake
happened.  (The word is temblor.)

Next, the special effects must be immediately obvious and
totally unconvincing.  Any invading alien monsters must look
like men in rubber suits, and not like actual alien life forms.
This leaves out most current movies with their computerized
effects that can be quite convincing.  These modern films can be
enjoyable, but they're not creature features.

The dialog of course must be so stereotyped as to be
predictable.  A line such as, "look George, an alien from outer
space!", can bring a dying movie back to life in a hurry.

Finally, in case all else fails, and to interest the ladies, the
movie must have a human relationship of the proper man-woman
kind.  And the viewers must spot the lovers before the lovers
recognize each other.

What does all this have to do with today's image?  Well, today's
image reminds me of an alien fungus growing on a man's arm,
which will soon turn the man into another alien fungus.

The fungus is actually the filaments shooting out from the
midget, which is located at the edge of a bay of its parent
fractal.  The parent is shaped quite like its child.

The parameter file renders in a quick 2-3/4 minutes, and is
about as much work as downloading the GIF image from:

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

or from:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The choice is left to the viewer.

The fractal weather today was pleasant but uneventful, with
partly cloudy skies and a temperature of 79F 26C.  The cats must
have approved, though they slept most of the afternoon.

Until next time and next fractal, take care, and see you then.


Jim Muth
[e-mail]


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

Creature_Feature   { ; time=0:02:42.30--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=1
  center-mag=-0.56270101574334630/+0.915160418848623\
  90/160.9974/1/-155 params=1.414213462373/0/75.3/800
  float=y maxiter=3600 inside=0 logmap=47
  colors=00006R06R07S18T29U3AV4BW5CX6DY7EZ8F_9G`AHaB\
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  zpQzqNzrKzsHztEzwBzv8zw6zxAzzDzzGzzJzzMzzPzzSzzWzz\
  Zzzazzdzzgzzqzzpzzpzzozzo
  }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a
}

END 20.0 PAR-FORMULA FILE==================================

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

From: [e-mail]
Subject: (fractint) C-FOTD  30-07-01  (Illusory Minibrot [7])
Date: 30 Jul 2001 10:34:05 EDT


Classic FOTD -- July 30, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

Today's fractal is a zoom into a curious image sent to me
yesterday by Lee Skinner.  I have named it "Illusory Minibrot"
because of the deceiving nature of its symmetry.  I rated it a 7
because in addition to its mathematical interest it is a
striking image.

A quick glance seems to show 32 filaments entering from the
border of the image, but by the time the reddish teeth jutting
into the blue area are reached, the symmetry has dropped to 16.
Things are not as they appear however, for both of these
apparent symmetries are false.  The symmetry of the whole
picture is one big illusion.

Out beyond the 16 encircling yellowish arms, the actual symmetry
is 8.  Look closely at those 16 rusty-red teeth.  They are not
identical, but alternate between two different varieties, making
the complete circle consist of 8 groups of 2.  The smaller teeth
have one long filament attached, while the larger teeth have 3,
giving a total of 32 filaments extending out beyond the image
border.

The reason for this pseudo-symmetry is not altogether clear,
though it is certainly connected to the periodicity of the area
and perhaps to the value of the exponents of the generating
formula.  Regardless, it is a promising area to investigate,
which I will likely be exploring in the not-too-distant future.

The image takes 18 minutes to render on my machine, which is an
old-style Pentium running at 200mhz.  Within an hour or two, the
file of the completed GIF image will be posted to:

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

and to:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today featured clouds, light rain, and a
most un-summer like temperature of 64F 18C.  The cats complained
a bit, then went to sleep.  I notice that the cats are romping
less and sleeping more as the months and years pass.  They must
be starting to feel their age.

As for myself, I'm feeling the need to get some work done.  So
until next time, take care, and don't write off the philofractal
list as dead yet.  I've got a lot of controversial stuff yet to
discuss.  All I need is the time to sit down and write it.


Jim Muth
[e-mail]


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

Illusory_Minibrot  { ; time=0:18:34.17--SF5 on a p200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-4.28968168524079100/+0.751079008850680\
  90/1.517355e+012/0.9996/-175.008/-0.043
  params=0.05/4/0.01/5/0/0 float=y maxiter=1800
  inside=0 logmap=373 periodicity=10
  colors=000M6FL4EK2CJ0BI1DI1EH2FH2GG2HG3IF3JF3KE4LE\
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  zKmzKmzKmzKmzKmzLmzLmzOmz
  }

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:   [e-mail]
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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  31-07-01  (Smoky Joe Midget [7])
Date: 31 Jul 2001 09:14:43 -0400 (EDT)


Classic FOTD -- July 31, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

Long ago, before the bridge across the Chesapeake Bay was built,
there used to be a ferry that carried travelers to the eastern
shore.  That ferry was named "Smoky Joe".  I never had the
pleasure, or displeasure, of riding on that ferry, but my father
rode it often, and frequently told of the thick black clouds of
oily smoke that belched from the funnel whenever the ancient
engines were running, sometimes choking the passengers and
always marking the ferry's position even when the boat itself
was below the horizon.

For some strange reason, today's fractal reminds me of a ferry
boat that I have seen only pictures of.  The outer features
surrounding the central midget do have a rather smoky effect,
and the streaks of orange-red could be the reflection of a fire
in a coal furnace, so I guess the name is justified.

The formula Z^3+0.225(Z^5)+C is responsible for the smokiness,
as well as everything else in the image, except for the
coloring, which was created by the <tdis> inside fill option
aided by myself.  The rating of an above-average 7 is justified.

The render time of a little over 8 minutes is slightly slow, but
worth the wait.  And as always, those who lack the computer time
to render from the parameter file may see the image by visiting
Paul's web site at:

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

or Scott's at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

and downloading the GIF image from there.  Give Paul and Scott a
chance to first post the image of course.

The fractal weather today was average, with a temperature of 81F
27C and big puffy white clouds that occasionally dropped a few
large raindrops but never released their full potential.  The
fractal cats showed their approval by spending several hours in
the yard, dodging the few raindrops.

It's now 9am of the last day of July, and time to get a bit of
work done.  I'll return as always at the proper time.  Until
then, take care, and brace yourself for imminent philosophy.


Jim Muth
[e-mail]


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

Smokey_Joe_Midget  { ; time=0:08:17.96--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+0.02671087209221384/-1.928837536631981\
  00/6.528213e+012/0.9999/-127.48/-0.023
  params=1/3/0.225/5/0/0 float=y maxiter=1200
  inside=0 outside=tdis periodicity=10
  colors=000CbSAXU8OWELSKJPQHLWFI_DFUHMZKTYOhWRmVVrU\
  YwVTrWPcWKWXGPYBHY7A_KObQVQFsPKoOPkNTgMYcL``MYdMVg\
  NSjNOmOLpOIsQKnSLiUMdWN`YOW_PRaQMbRINDR70_I7_TE_cL\
  _KK_7J26IC6HL6GU5Fb5Ek5EtBGpGIlLKhQLdVN`_PXdQTeUXe\
  Y`eadfegfikfmofqreopcnoblmfIsiItkItmItnMuoPupTuqWu\
  rZusbuteuuiuvluwouxsuyvuyyuruskqqdnpYjnRgmKckD`j6X\
  h0Ug9ehIphFneDlcAj`8iZH`VPYRTYXXba_hfcmkgspjxuhulf\
  rddoWclORnHEoA1p36mBBjIGgQKdXPadUZkZWsbTzdVtfXnhZi\
  j`clbZndToeOibMd`KZYJUWHPTFJREEOC9MBCODEQFGSHIUJON\
  QTGXY9c_2jT6iJAhADg9Gf8If8Ke7Ne7Pe6Rd6Td5Wd5Yc4_c4\
  ac3Z`3WY3TV2RSRS6TV6VX6XZ7Za7ac7ce7eh7gj7il7ln6oo5\
  rp5uq4xr4pm7hhA`dDaeEafFafGbgGbgHbhIchJciJciKdjLdj\
  MdkMekNelOelOchKbeG`bC__8YX4XU0MD2OE4KF5RL7QJ9PHAN\
  FAMDALBAJ9AI7AH5AO8CUAD`CEfEFjGDpICuKBzLAyN9xO8wP8\
  vQ7uR7rS6rT6jV8bXAVZCN`EGbG8QX1Dm3If5N`6SV8XOAaIBf\
  CDhEEiGFjIHkKIlMJmOHzOEpQ
  }

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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