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fractint-digest         Monday, April 10 2000         Volume 01 : Number 466




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

Date: Tue, 04 Apr 2000 05:43:27 -0400
From: davides <[e-mail]>
Subject: Re: (fractint) Amy Grant uses Fractint?

At 08:43 PM 4/3/2000 -0700, you wrote:

(Amy Grant...)

I downloaded the clip, listened a couple of times (nice voice, I haven't
heard her), but I do not hear fractint in there. Sorry...   :)

OTOH, maybe I'll pick up that cd. :>



[e-mail]
Back up my hard drive?
How do I put it in reverse?

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

Date: Tue, 4 Apr 2000 06:25:53 -0400
From: "James R. McKenzie" <[e-mail]>
Subject: Re: (fractint) list archive

For my $.02 it's not a big risk (so far as I can tell) so my vote (for now)
is no.  Leave it as is.
                             T H A N K   Y O U


                             James R. McKenzie


                         [e-mail]

- ----- Original Message -----
From: "Tim Wegner" <[e-mail]>
To: <[e-mail]>
Sent: Monday, April 03, 2000 10:13 PM
Subject: (fractint) list archive


> Discussion of list management issues is officially off topic except
> for me, the benevolent dictator :-) If anyone has an opinion on the
> issue mentioned below, please *email me* (but don't post to the
> list). I would like to get opinions, but not clutter the list with
> discussion on this topic.
>
> Some of you may be aware that the archive of the digest version of
> this list is publically visible at:
>
> http://www.xmission.com/pub/lists/fractint/archive/
>
> It is possible that automatic webcrawlers can scavange email
> addresses from the archive. I have no evidence that this actually
> happens, and I have heard a point of view that web crawlers
> probably don't check ftp files, which is what the archive consists of.
>
> I could make the archive inaccessible to the public. SHould I?
>
> Pro: This might reduce the exposure of your email to potential
> spammers.
>
> Con:  Availablilty of the archive is useful for folks who are returning
> to the list after an absence or want to search for a topic, so we'd
> lose this capability if the archive were not public.
>
> If you have an opinion, email me. I'm leaning toward the status quo.
>
> Tim
>
>
> --------------------------------------------------------------
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> Unsubscribe:    [e-mail] "unsubscribe fractint"
>


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

Date: Tue, 4 Apr 2000 23:49:15 EDT
From: [e-mail]
Subject: (fractint) Blue Ribbon Fractal ~

 Hi Everyone~

  I submitted 2 fractal images in a judged spring showing at the Victoria Art
League Center in Victoria,Tx., only because they happened to have a computer
art category, along with oils, acrylics, charcoal, sculpting, etc., and was
rewarded with 1st and 2nd place!!  Not overall mind you, just for PC art
(intermediate). This par is of the 1st place pic which was printed in
portrait style  and the other is a UF image which can be seen at
.....members.aol.com/JimBeau549/jim3.htm    title is...."LOVE IS..."
 Fractals are SOOO cool! <G>

  Enjoy ~

 Jim Weaver

________________________________


Ivory02.gif        { ; image(c)2000 Jim Weaver
  reset=1960 type=formula formulafile=fractint.frm formulaname=prn_02
  function=log/tanh/sqr passes=t
  center-mag=-12.4833/-2.13163e-014/0.04731381 params=-0.03624/0/0.4/0
  float=y invert=1/0/0 periodicity=0
  colors=000hoxksynvz<15>F8I<9>c_ffbiiellhookrrnu<17>LDD<13>yll<17>B5G<13>\
  rcu<15>444<17>kkw<27>EJODIMCHLAFJBFK<29>zgz<15>13M<22>MCrAFp9Jp<6>05g<12\
  >dlv
  }


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

Date: Wed, 05 Apr 2000 00:44:26 -0400
From: Paul DeCelle <[e-mail]>
Subject: Re: (fractint) Blue Ribbon Fractal ~

Hi, Jim--

>  I submitted 2 fractal images in a judged spring showing at the Victoria Art
> League Center in Victoria,Tx., only because they happened to have a computer
> art category, along with oils, acrylics, charcoal, sculpting, etc., and was
> rewarded with 1st and 2nd place!!  Not overall mind you, just for PC art
> (intermediate). This par is of the 1st place pic which was printed in
> portrait style  and the other is a UF image which can be seen at
> .....members.aol.com/JimBeau549/jim3.htm    title is...."LOVE IS..."
>  Fractals are SOOO cool! <G>

Congratulations - Very nice work!

Regards, Paul



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

Date: Tue, 4 Apr 2000 22:41:55 -0700
From: "Jason Hine" <[e-mail]>
Subject: (fractint) Re: Amy Grant uses Fractint?

Thanks to all those who took a listen... seems the general consensus is that I'm
hearing things.  Well, it's not the first time, that's for sure...

Amy Grant, for those unfamiliar with her, writes contemporary secular Christian
songs, and has been doing so for around the past 20 years.  A quick web browse
will tell you more if you're curious...

... and if anyone else listens to the clip and _does_ hear Fractint's sound in
there, I'd be delighted to hear from you!

Cheers,
Jason Hine


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

Date: Wed, 5 Apr 2000 01:48:53 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 05-04-00 (The Enclosed World [7]) (c)

FOTD -- April 05, 2000  (Rating 7)

Fractal visionaries and enthusiasts:

Today's fractal midget was generated by another apparently
uninteresting formula.  But the formula,
3.48(Z^0.7)-2.32(Z^0.5)+C, is uninteresting only on the surface.
When iterated it draws a most unusual little Mandelbrot set with
all the convolutions of the classic set.

Today's scene is located in the area of the period-10 radical on
the northeast shore of the main bay of the little M-set, deep in
the spiral of a minor elephant trunk.  I devoted a little extra
effort the coloring, which accounts for the picture's rating of
seven.

At a rendering time of over seven minutes, running the parameter
file is the slow way of seeing the image.  A far better way is
to download the pre-rendered JPEG file from:

          <alt.binaries.pictures.fractals>

or from:

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

The weather was rainy and muggy in the morning, and clearing and
colder in the evening, with the temperature falling from 66F
(19C) to 44F (6.5C) through the day.  The fractal cats chose to
stay indoors, where the temperature remained a relatively
constant 69F (20.5C).

Tomorrow I'll delve deeper into the world of fractals.  For this
evening the hour grows late, the cats are growing hungry and it's
time to post this FOTD.  Until next time, take care, and take
life one fractal at a time.


Jim Muth
[e-mail]


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

The_Enclosed_World { ; time=0:07:20.62, SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=mandelbrotmix4 function=ident passes=1
  center-mag=+0.1446730940127774/+0.01040684926964369/\
  3.308281e+010/1/-12.499 params=-0.4/0.5/0.6/0.7/4.8/0
  float=y maxiter=1200 bailout=25 inside=0 logmap=140
  symmetry=none periodicity=10
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  >Oz4<4>Qz3
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

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


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

Date: Wed, 05 Apr 2000 05:54:03 -0400
From: davides <[e-mail]>
Subject: Re: (fractint) Blue Ribbon Fractal ~

At 11:49 PM 4/4/2000 EDT, you wrote:
>
> Hi Everyone~
>
>  I submitted 2 fractal images in a judged spring showing at the Victoria
Art
>League Center in Victoria,Tx.,


Very nice! And congratulations on your winning!  I'll have to cruise by
your site and look at the UF image.

David
[e-mail]
Back up my hard drive?
How do I put it in reverse?

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

Date: Wed, 5 Apr 2000 17:07:31 EDT
From: [e-mail]
Subject: Re: (fractint) Blue Ribbon Fractal ~

Jim,

Congratulations!  That's great news!

Bill

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

Date: Thu, 6 Apr 2000 01:31:03 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 06-04-00 (Protobud [5]) (c)

FOTD -- April 06, 2000  (Rating 5)

Fractal visionaries and enthusiasts:

Where do Mandelbrot buds come from? . . . why, they come from
protobuds.  Today's rather striking image shows a protobud
caught in the act of emerging from the universal sea of fractal
protoplasm, but not yet fully formed into a mature Mandelbrot
bud.

Making this birth scene visible required extraordinary measures.
To begin, the entire action takes place in the unreal world of
totally trapped points.  This required that a nonflat inside
fill be applied to the image to make the invisible visible.
Several inside fills did an acceptable job, but the atan fill
worked the best.

The formula behind the image is 999(Z^-0.26)-999(Z^-0.25)+1/C,
another of my whimsical, very simple but very surprising
concoctions.  After a slight overall contrast boost in a graphic
program, I named the final result "Protobud", a purely descrip-
tive and at the same time poetic name.

Since the image consists entirely of inside areas, and the
periodicity has been turned off, the image is not a fast one.
It requires 6-1/2 minutes on an average 200mhz Pentium.  As
always, the JPEG'd image file has been posted to:

          <alt.binaries.pictures.fractals>

The image is also available at:

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

The day's fractal weather was partly cloudy with a brisk wind
and a chilly temperature of 54F (12C).  The cats ventured out
briefly, but asked to come indoors when a cloud obscured the sun.

Until next time, take care.


Jim Muth
[e-mail]


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

Protobud           { ; time=0:06:31.42, SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=mandelbrotmix4 function=recip
  center-mag=0.0665663/0.0150862/2813.113/1/67.499
  params=1/-0.25/-1/-0.26/-1000/100000 float=y
  maxiter=300 bailout=25 inside=atan logmap=yes
  symmetry=none periodicity=0 sound=off
  colors=000p_D<4>oSDoQCoPCmOC<3>lIClGClFClDCjCCjACj9C\
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  Fy0Dy1Dy4Cx7Cx9AxCAvF9vIraDr`D
  }



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


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

Date: Thu, 06 Apr 2000 08:35:29 -0400
From: Tom Conally <[e-mail]>
Subject: (fractint) where oh where

Sorry but I can't find the address to get patch 9 of Fractint 20.
Help me out please.
Tom Conally

In every boomerang there is a perfect throw.
Your life, Grasshopper, is to practice
till you find that throw
and become one with that boomerang!
http://fly.to/boomerangs  " Flying Frog Boomerangs"
http://www.vstore.com/vstorehardware/flyingfrogtools/  "Flying Frog Tools"
http://www.netpath.net/~conally   My greater internet index

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

Date: Thu, 6 Apr 2000 11:17:02 -0500
From: "Scott D. Boyd" <[e-mail]>
Subject: Re: (fractint) where oh where

On Thu, 06 Apr 2000, Tom wrote:
> Sorry but I can't find the address to get patch 9 of Fractint 20.
> Help me out please.
> Tom Conally
>
http://www.fractint.org for the Development Team home page or
ftp://ftp.fractint.org/2000p09.zip to download the file directly.

Scott Boyd
- --
email:  [e-mail]
http://www.fastlane.net/~sdboyd/
Introducing Windows 2000 !! -- Reduced to only 65,000 bugs !!



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

Date: Thu, 6 Apr 2000 17:24 0000
From: [e-mail]
Subject: RE: (fractint) where oh where

Hi Tom,

>Sorry but I can't find the address to get patch 9 of Fractint 20.
>Help me out please.

Sure! check out:
ftp://ftp.fractint.org/fractdev.zip

this should always link to an executable at the latest patch level. To get
the patch itself just knock the filename off the end of that path and take
a look at what's there.

Cheers,
         Robin.





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

Date: Thu, 06 Apr 2000 12:44:07 -0400
From: Tom Conally <[e-mail]>
Subject: Re: (fractint) where oh where

Thank you all, I have it now.

At 11:17 AM 4/6/2000 -0500, you wrote:
>On Thu, 06 Apr 2000, Tom wrote:
>> Sorry but I can't find the address to get patch 9 of Fractint 20.
>> Help me out please.
>> Tom Conally
>>
>http://www.fractint.org for the Development Team home page or
>ftp://ftp.fractint.org/2000p09.zip to download the file directly.
>
>Scott Boyd

Tom Conally

In every boomerang there is a perfect throw.
Your life, Grasshopper, is to practice
till you find that throw
and become one with that boomerang!
http://fly.to/boomerangs  " Flying Frog Boomerangs"
http://www.vstore.com/vstorehardware/flyingfrogtools/  "Flying Frog Tools"
http://www.netpath.net/~conally   My greater internet index

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

Date: Fri, 7 Apr 2000 02:08:28 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 07-04-00 (Melismatic Midget [5]) (c)

FOTD -- April 07, 2000  (Rating 5)

Fractal visionaries and enthusiasts:

We have a slight trace of northern lights visible here at
Fractal Central this evening -- not an unheard-of event, but
rare enough to call for a look at the northern horizon.  We also
have a melismatic midget.

While searching for today's fractal, I was listening to middle-
eastern music, which is filled with those decorative phrases
known as melismas.  For some reason, today's image with its
intricate patterns reminded me of that music.  I then named the
picture "Melismatic Midget".

The formula behind the scene is 6(Z^1.333)-6(Z^1.667)+C, a very
simple expression, as are all expressions calculated by the
MandelbrotMix4 formula, which outperforms its apparent potential
by several orders of magnitude.

The eight minutes required to run the parameter file can be
avoided by downloading the pre-rendered JPEG file from Usenet at:

          <alt.binaries.pictures.fractals>

or from the WWW at Paul Lee's web site at:

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

The fractal weather today was unexpectedly warm and sunny,
though the wind was a bit too brisk for the fractal cats, who
grow cautious when the wind blows.  The temperature of 79F (26C)
was perfect for anything.

Right now it's already time to shut down the fractal place for
another evening and call it a day.  Until next time, take care,
keep your feet on the ground and your head in the stars.


Jim Muth
[e-mail]


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

Melismatic_Midget  { ; time=0:08:19.44, SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=mandelbrotmix4 function=ident passes=1
  center-mag=+0.824444041338745/+0.000121906568368/8.2\
  94846e+008/1/79.999 params=-1/1.667/1/1.333/5/0
  float=y maxiter=2200 bailout=25 inside=0 logmap=163
  symmetry=none periodicity=10
  colors=000_Sd_Sd<3>cWldXneYp<2>h`v<3>ld_meUnfOchMRkK\
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  >mRRnNNoJJ<2>s87<9>`KO_LQYMS<2>SPXRQYOJ`<2>F1h<3>FQS\
  FWOFaK<2>Fs8<2>qxZ<3>nyQmyOlyM<2>jyGjyEkuH<6>lZXlWZm\
  T`<2>mJgmGioIe<3>sMT<3>PYTI_TPsz<3>RhjRefSbb<3>TTN<3\
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  pOzsNzi
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

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


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

Date: Fri, 07 Apr 2000 10:01:53 GMT
From: "Andrew Coppin" <[e-mail]>
Subject: (fractint) Branch Cuts

Some time ago I mentioned that if you ask FractInt to render something like
Z^2.5 + C you get a "fractured" image due to branch cuts in the formula... I
wondered if it was possible to move these branch cuts...

Anyway, I seem to have found out where these things originate from. A look
at FractInt's trig identities confirms that FractInt calculates A^B by
taking the natural logarithm of A, multiplying it by B, and then taking the
natural antilogarithm of the product thus obtained.

Now, the complex antilogarithm function *is* a "function", i.e. it produces
a single value. But the logarithm function has multiple solutions; this is
where the branch cuts are comming from.

The FractInt docs don't make this very clear, but basically, to take the
natural logarithm of a complex number Z, you calculate a new number K with
Re(K) = e^(Mag(Z)) and Im(K) = Arg(Z). It's this second part that introduces
the multiple possibilities.

FractInt works out the argument of a complex number using C's atan2()
function. This returns results +/- pi. By just adding 2pi on to the
imaginary part of the result, you get a different, but still legal result.

So I can move the branch cuts "one full circle"... but how do I move then by
just, say, half a turn? Adding on a fraction of pi won't do it... then I'd
just have nonsense answers. Any ideas? Anyone?

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Date: Fri, 7 Apr 2000 10:42:43 -0400
From: Barry N Merenoff <[e-mail]>
Subject: (fractint) Branch Cuts

You can multiply the number by some unitary complex number,
take the logarithm, then subtract the logarithm of your multiplier.

Sincerely,
        Collin Merenoff

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Date: Sat, 8 Apr 2000 01:31:57 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 08-04-00 (Midget with Pancake [3]) (c)

FOTD -- April 08, 2000  (Rating 3)

Fractal visionaries and enthusiasts:

Today turned unexpectedly busy, cutting my fractal hunting time
to the bare minimum.  But despite the rush, I did find a
fractal, and the fractal is worth being declared Fractal of the
Day for April 08.

The less-than-spectacular fractal reminds me of a midget in the
center of a pancake, most likely covered with strawberry syrup.
I named the picture "Midget with Pancake" when I noticed the
resemblance.

The formula that caused all the excitement is Z+2(1/Z)+C, a
formula far too simple and uninteresting to do anything of
value.  But the formula doesn't know this, and produces
interesting fractals anyway.  Perhaps the worthless formula is
the reason I rate the picture only a significantly-below-average
3 on my 1-to-10 scale of fractal worth.

The image might not be gold or silver, or even bronze, but it is
strawberry, and it is posted to:

          <alt.binaries.pictures.fractals>

and to:

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

The fractal weather today was a bit cooler than yesterday, but
still pleasant.  The temperature of 68F (20C) was perfect for
the cats as well as the dogs.

Until next time, take care, and take a brief fractal break.


Jim Muth
[e-mail]


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

Midget_withPancake { ; time=0:05:17.00, SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-2.06274581089187400/+0.68669116186631770\
  /1.940765e+011/1/147.502/-0.002 params=1/1/2/-1/0/0
  float=y maxiter=1500 bailout=25 inside=0 logmap=106
  symmetry=none periodicity=10
  colors=000KC1A01A01A04A06<3>L0GO0JR0LU0NX0QZASa2V<3>\
  l0c<9>gYPg`NfcM<3>epG<3>nfCqdBsbA<2>yW8<3>dYAZYBUZBP\
  ZCKZC<7>SPDTODUND<3>YJD<6>KXUIZXG`Z<3>9gg<3>WaZ``Xf_\
  VkZT<3>NdXHfYBgZ5hZ<3>RlQXlOamM<3>wpE<7>hYXfVZeT`<3>\
  ZKiwxP<5>kwMivMgvL<2>avK`vKYuL<6>HsSFrTCrU<3>3qX<3>T\
  QIZJFdCBj68<2>icjX8r<3>nePrmInnN<3>bne_njXnoUns<4>_c\
  j``iaZg<3>eRa<5>mJcoIcpHc<3>uCd<3>`SOWVJRZF<2>Ci3Glq\
  <6>Q`ZSZWTXT<3>YRJ<3>`gVakYao`bscbwebydHME<3>PI8RH6T\
  G5VF3XF2<8>nNQpNTrOW<3>yRe<5>icCc_IYWN
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

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


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Date: Sat, 08 Apr 2000 11:43:43 -0600
From: Tim Wegner <[e-mail]>
Subject: Re: (fractint) Branch Cuts

Andrew wrote:

> Now, the complex antilogarithm function *is* a "function", i.e. it produces
> a single value. But the logarithm function has multiple solutions; this is
> where the branch cuts are comming from.

Exactly. So Fractint's logarithm formula (and any other complex
valued logarithm formula) has to arbitrarily select from among the
multiple values. This creates a discontinuity somewhere in the
values. You cxan visualize the log function as an infinite corkscrew.
A function has to be single valued, so only one 360 degree piece of
the corkscrew is used by the function, so the corkscrew has to be
cut somewhere.

>
> The FractInt docs don't make this very clear, but basically, to take the
> natural logarithm of a complex number Z, you calculate a new number K with
> Re(K) = e^(Mag(Z)) and Im(K) = Arg(Z). It's this second part that introduces
> the multiple possibilities.

Th docs give the formula for logarithm making it clear it has
multiple values:

    log(x+iy) = (1/2)log(x^2 + y^2) + i(atan(y/x) + 2kPi)
       for k = 0, -1, 1, -2, 2, ...

However the docs don't say anything about the visual discontinuity
except that we know it is supposed to be there. The book Fractal
Creations does discuss this.

> So I can move the branch cuts "one full circle"... but how do I move then by
> just, say, half a turn? Adding on a fraction of pi won't do it... then I'd
> just have nonsense answers. Any ideas? Anyone?

Hmmm, I don't know if this is worthwhile or not, but we could add
the fraction of PI within fractint itself, effectively giving you alternate
logarithm formulas. However you can do this yourself in the formula
parser. Just add some multiple of 2*PI to the imaginary part of the
log function in a formula and see what happens (see formula for log
above). Let us know if you get any interesting results.

Tim


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Date: Sun, 9 Apr 2000 10:20:09 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 09-04-00 (Branch Cuts [3]) (c)

FOTD -- April 09, 2000  (Rating 3)

Fractal visionaries and enthusiasts:

The lateness is due to a short power failure and the fact that
I fell asleep while waiting for the power to return.

I recently noticed a few letters on the fractint list under the
topic "branch cuts", which discussed the discontinuities in
fractals that contain a fractional exponent in their formulas.
It was correctly pointed out that because the complex logarithm
function is multi-valued, these discontinuities must always
appear.  This discussion prompted me to bring out a formula that
I wrote some time ago in an effort to investigate the multi-
valued nature of the complex logarithm.

The expression (x^x)^(1/x)=x, is true when x is a real number.
But when x is a complex number, strange things happen due to the
multi-valued nature of the complex log function.  The basic
iterated expression in the MultValLog2 formula is (Z^Z)^(1/Z),
which appears as though it should equal Z, but doesn't.  I'm not
quite sure what the initial z=p1*(1e-100) was supposed to do,
but p2 and p3 control the portions of (^Z) an (^1/Z).

Since Z+C draws no fractal, the fractals created by this formula
theoretically consist of only artifacts arbitrarily created by
the parser as it decides which log value to use.  I'm not sure
whether the images can be considered fractals at all, but they
certainly are fractured.

And surprisingly, the fractals, which are unusually slow,
contain midgets of an unusual kind, resembling sort of a cross
between a quadratic midget and a midget of a high order.  I
don't know enough about this formula and its fractals to say
much more, so I'll let it go at this, but I'll be further
exploring this forgotten formula in the days to come.

I named the image "Branch Cuts" after the topic line of the
letters that led me to remember the formula.  The artistic
rating of today's effort is only a 3, though the mathematical
interest may be a bit higher.  The parameter file is a rather
slow one, so a download is recommended.  That download can be
found on Usenet at:

          <alt.binaries.pictures.fractals>

and on the WWW at:

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

The weather today was sunny and 80F (26.5C).  Tonight it is
snowing.  The fractal cats are totally confused by the rapid
changes.

The day's philosophy will have to wait until tomorrow's FOTD,
much to the chagrin of those waiting for (IMO) enlightenment.
But as I have often said, don't feel too disappointed.  After
all, one person's enlightenment is another person's nonsense.

I see that it's time to end today's FOTD.  So until next time,
which will be in only 15 hours or so, take care, and brush the
snow from your tulips.


Jim Muth
[e-mail]


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

Branch_Cuts        { ; time=0:36:35.34, SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=multival.frm
  formulaname=MultValLog2 passes=1
  center-mag=-1.15934761779311800/-0.06686366463112242\
  /4458813 params=0/0/-2.5/0/-2.5/0 float=y
  maxiter=12000 bailout=25 inside=0 logmap=328
  symmetry=none periodicity=10
  colors=000bJHlWL<8>nTCnSBnSA<2>oR7oR6pS5<37>i8Ki8Ki7\
  Ki7Li6L<72>PsnPtnPuo<2>OwpOwpNuo<3>LpojlUcUoXcoJko<3\
  2>37k26k25k<2>01k00k11j<66>LTK
  }

frm:MultValLog2 {; Jim Muth
z=p1+(1e-100), c=pixel:
z=(p2*(z^z))^(p3*(1/z))+c,
|z| <= 100
}

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


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

Date: Mon, 10 Apr 2000 01:42:20 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 10-04-00 (Semi-Spiral Scene [6]) (c)

FOTD -- April 10, 2000  (Rating 6)

Fractal visionaries and enthusiasts:

With no power failure today, I'm writing the FOTD discussion on
time.  The fractal in question is an improvement over the past
two days' offerings, which rated only a three.

Today's FOTD, which not surprisingly was found with the
MandelbrotMix4 formula, rates a somewhat-above-average 6 on my
scale of fractal quality.  The exact fractal formula being
iterated in today's image is -1(Z^2.5)-Z+C, another
uninteresting expression that holds quite a few surprises.

I named the picture "Semi-Spiral Scene" because I couldn't
decide whether I was looking at a series of spirals or an
octagon.  I finally decided on the spiral theme, since the
apparent octagon is an artifact of coloring.

The parameter file runs slowly enough to make a download the
better choice.  That download may be found at:

          <alt.binaries.pictures.fractals>

or at:

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

The fractal weather today was partly sunny but blustery and
chilly.  The 3cm of snow that fell overnight vanished by midday,
but the temperature, which remained in the high 40's (around 9C)
was too chilly for the cats, who passed the day eating and
sleeping.

And sleeping is what I'll be doing before much longer, preparing
myself for what promises to be an active week, both in the work
and the fractal departments.  Until next time, take care, and
there's no such thing as a bad fractal.


Jim Muth
[e-mail]


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

Semi-Spiral_Scene  { ; time=0:09:29.02, SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-0.89728782155468800/-0.41895782132379090\
  /5768086/1/-55 params=-1/2.5/-1/1/0/0 float=y
  maxiter=1200 bailout=25 inside=0 logmap=149
  symmetry=none periodicity=10
  colors=00070K80K90Kc0Kc1Nf3Qf4Tc5Wa6ZG7aH8dKJ`NTYMaJ\
  <2>TcpSSlRGiS2g<8>DIaBK`9M_<3>3SY<3>hmi<3>LMGZERGG9<\
  2>eFCsFDzBFyFDuIBqLA<3>fZ4ca2ad1iaJpZ_ybw<2>sLdwGb<3\
  >_GOUGKOGGIGCAC7<3>KRDNVEPYGSaHTcH<6>VeLVfMVfN<3>WgP\
  UlQ<3>aTPcPPeKPhFPjAPn6PsANwQMnILmMKkQIjXHhcG<2>frCe\
  wBezAdwD<3>acN`YP_VS<3>XJaWGcS9j<3>eMThQOkTK<2>ua7rQ\
  NpEbjVUejL<3>gZJhWJhTJkOK<3>bXG`_FZaEXcDUk3<3>YP`ZKh\
  WNj<4>JXoH_pEaq<3>4iu1pw<3>3_s3Vs3Rr<2>4Fp<3>8N`9PYA\
  RU<3>DZF<3>aKVgHZmDbvBj<4>i7Sg6Od5K<3>W36<3>kAOp8Q<4\
  >mNYmP_lS`<2>k`ekbfmbipclqdlren<3>QitGjv<4>UouXpu_qu\
  <3>iuuXvvKwvJxsIyp`zFZz8
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

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


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

Date: Mon, 10 Apr 2000 09:21:10 GMT
From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) Branch Cuts

>>The FractInt docs don't make this very clear, but basically, to >> take
>>the natural logarithm of a complex number Z, you calculate a >> new number
>>K with Re(K) = e^(Mag(Z)) and Im(K) = Arg(Z). It's this >> second part
>>that introduces the multiple possibilities.
>
>The docs give the formula for logarithm making it clear it has
>multiple values:
>
>     log(x+iy) = (1/2)log(x^2 + y^2) + i(atan(y/x) + 2kPi)
>        for k = 0, -1, 1, -2, 2, ...
>
>However the docs don't say anything about the visual discontinuity
>except that we know it is supposed to be there. The book Fractal
>Creations does discuss this.

No, I just ment that (unless you know about these things) it isn't all that
clear that atan(y/x) is Arg(Z) and (1/2)log(x^2 + y^2) is Log(Mag(Z)).

PS.
Nice shortcut with the logarithm there actually... I would have taken the
sqare root then the log, but your way *is* quicker!

>Tim

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Date: Mon, 10 Apr 2000 10:22:48 GMT
From: "Andrew Coppin" <[e-mail]>
Subject: (fractint) Branch Cuts

So log(Z) is a cork screw, and you have to take a 360 degree slice of it.
Hmmm... This formula (I think) varies the slice taken, but only by another
360 degrees. If k is below -3 then you get what the formula parser normally
does. If you now raise k, you get a nice branch cut shift... until you reach
+3, and thereafter there is no further change. Any ideas how to correct
this?

- --BEGIN
comment
{
  Andrew Orphi Coppin, 10 May 2000AD
}

BrotBC = { ; Z^2.5 + C
           ; real(p1) = phase shift.

  p = real(p1)
  Z = C = Pixel:
    Z = log(Z)
    IF(imag(Z) > p) Z = Z + flip(2*PI) ENDIF
    Z = exp(2.5*Z) + C
  |Z| < 4
}
- --END

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End of fractint-digest V1 #466
******************************