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fractint-digest         Thursday, July 5 2001         Volume 01 : Number 580




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

Date: Sun, 1 Jul 2001 10:22:46 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  01-07-01  (Pac-Man Strikes Again [6])

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\
  cjZcg`_bbWZdSVfPQhLMjHIkEEiHDhKCgNBfQAeT9dW9bZ8aa7\
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  FdLIbNK`PMZROYTQWVSUXUSZWR_YPa_NcaMecKgeIigGkiFmkD\
  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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------------------------------

Date: Mon, 2 Jul 2001 11:08:44 EDT
From: [e-mail]
Subject: (fractint) Missing FOTD

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

Date: Mon, 2 Jul 2001 22:45:09 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  03-07-01  (The Smallest Midget [7])

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\
  IAOLARPAUSAXVA_ZAbaAeeAhhAklAnoAqrApm9pi8pd8p`7pX7\
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  zCyzCzzBzzBzzBzzAzzAzzYzzXzzXzzWzzWzzVzzVzzUzzUzzT\
  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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------------------------------

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

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

Date: Tue, 3 Jul 2001 09:36:52 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) Re: July's FOTD

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

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

> >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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------------------------------

Date: Tue, 3 Jul 2001 10:13:40 -0600
From: [e-mail]
Subject: Re: (fractint) Re: July's FOTD

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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Date: Tue, 3 Jul 2001 14:33:06 -0400
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Fractal math

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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>

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Date: Tue, 3 Jul 2001 14:39:28 -0400
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) C-FOTD 30-06-01 (Head of Zardoz [4])

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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>

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Date: Tue, 3 Jul 2001 14:41:50 -0400
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Fractal math

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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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Date: Tue, 3 Jul 2001 14:50:32 -0400
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Fractal math

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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>

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Date: Tue, 3 Jul 2001 14:55:36 -0400
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Re: July's FOTD

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> 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>

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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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Date: Tue, 3 Jul 2001 14:56:48 -0400
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Re: July's FOTD

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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>

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<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>

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

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

</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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------------------------------

Date: Wed, 4 Jul 2001 10:04:54 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  04-07-01  (Mand-Newt Eruption [8])

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

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

>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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------------------------------

Date: Thu, 5 Jul 2001 10:30:32 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  05-07-01  (Platform in Space [7])

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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Date: Thu, 5 Jul 2001 20:03:01 -0400
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) C-FOTD 04-07-01 (Mand-Newt Eruption [8])

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> 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>

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<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>

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End of fractint-digest V1 #580
******************************