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fractint-digest         Friday, April 14 2000         Volume 01 : Number 467




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

Date: Mon, 10 Apr 2000 08:31:09 -0400
From: Barry N Merenoff <[e-mail]>
Subject: (fractint) Branch Cuts

Andrew, try this:

p=3Dreal(p1)+PI
q=3D2*PI*floor(p/(2*PI))
r=3Dreal(p1)-q
Z=3DC=3DPixel:
Z=3Dlog(Z)
IF(imag(Z)>p) Z=3DZ+flip(2*PI) ENDIF
Z=3Dexp(2.5*(Z+flip(q)))+C
|Z|<4
}

Note: I don't know if Fractint has a floor function, but it should have
something equivalent to it.

Sincerely,
        Collin Merenoff

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

Date: Mon, 10 Apr 2000 14:06:22 -0700 (PDT)
From: Kenneth Childress <[e-mail]>
Subject: Re: (fractint) Branch Cuts

Collin,

> p=real(p1)+PI
> q=2*PI*floor(p/(2*PI))
> r=real(p1)-q
> Z=C=Pixel:
> Z=log(Z)
> IF(imag(Z)>p) Z=Z+flip(2*PI) ENDIF
> Z=exp(2.5*(Z+flip(q)))+C
> |Z|<4
> }
>
> Note: I don't know if Fractint has a floor function, but it should have
> something equivalent to it.

Is there a typo or mistake in the above?  I notice that the assignment
to r is never used.


Ken...




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Date: Tue, 11 Apr 2000 01:17:41 -0400
From: Barry N Merenoff <[e-mail]>
Subject: Re: (fractint) Branch Cuts

OOPS!!!

That should be IF (imag(Z)>r)

Sincerely,
        Collin Merenoff

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

Date: Tue, 11 Apr 2000 02:51:47 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 11-04-00 (The Mandelbrot Set [7]) (c)

FOTD -- April 11, 2000  (Rating 7)

Fractal visionaries and enthusiasts:

The formula for today's fractal is -(Z)-3(Z^(-2))+C, and like
most of my FOTD formulas, (Formulae is the spelling for the
over-educated.), its apparent simplicity belies its potential
for creating fractals.

The parent fractal of today's scene is a lopsided circle with a
skewed hyperbola with fractal edges inside -- a rather
unpromising image.  However I consider unpromising scenes a
challenge, and I gladly accepted today's challenge.

I named the picture "The Mandelbrot Set" after that most famous
of all fractals, whose outline appears in glowing bronze at the
center of today's picture.

I devoted a little extra time to coloring today's image, finally
working out a palette that I feel rates an honest 7.  To see the
above-average picture, either run the parameter file and wait 9
minutes, or download the completed image and wait one minute.
That download may be found at:

          <alt.binaries.pictures.fractals>

and at:

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

The fractal weather today was sunny and 63F (17C), barely warm
enough for the fractal cats to sneak outside.

Until next time, which will really come in 22 hours, take care.


Jim Muth
[e-mail]


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

The_Mandelbrot_Set { ; time=0:08:54.00, SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=3.57871498151/1.535460434974/281530.3/1/55
  params=-1/1/-3/-2/0/0 float=y maxiter=1200 bailout=25
  inside=0 logmap=80 symmetry=xaxis periodicity=10
  colors=000mcKphmrUZzenwjznsonkomlzmlp<11>hsugsugtv<3\
  >evwKzzdwxzsUcxycyydzz<59>8Fl7El7Dl6Cl<73>328328327<\
  2>326325114<24>S6BU6BV6C<3>Z7D_BD<4>dAEeAEfAEgAEhAE<\
  7>pHEqIErJE<3>vNFwOGxPGyQG<2>zTHzUHzUKzUI<13>zUN
  }

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

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


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

Date: Tue, 11 Apr 2000 09:16:12 GMT
From: "Andrew Coppin" <[e-mail]>
Subject: (fractint) Branch Cuts

Thankyou people!!! I now have two working formulas:

- ---BEGIN
MandelbrotBC = { ; Z = Z^E + C
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(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|<4
}

JuliaBC = { ; Z = Z^E + C
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  C=p3
  Z=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<4
}
- ---END

Plug these into the evolver, with real(p1) changing from 2 to 3 along the X
axis and real(p2) changine from -6 to +6 along the Y axis and you have a
real treat of an image (depending on the other parameters; I used p3=-1).
Now, if I can just remember how to do that IsMand() stuff...

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

Date: Wed, 12 Apr 2000 00:22:20 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 12-04-00 (Edge-on Galaxy [7]) (c)

FOTD -- April 12, 2000  (Rating 7)

Fractal visionaries and enthusiasts:

Today's FOTD image, which was once again created by the omni-
present MandelbrotMix4 formula, reminds me of a telescopic view
of two overlapping galaxies, one face-on, the other edge-on.  I
named the picture "Edge-on Galaxy" because it is the edge-on
effect that makes the picture.

The iterated formula is (1/Z)+(Z^(-1.1))+(1/C), an expression
that I chose purely on a whim, having nothing particular in
mind.  Most of the scene consists of bof61 inside fill, and the
maxiter is 6000, a combination that means a slow parameter file.
The most patient fractalists will run the parameter file and
wait 1/2 hour to see the GIF image, which in this case is more
brilliant than the JPEG image posted to:

          <alt.binaries.pictures.fractals>

and to:

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

Before getting to the all-unimportant weather report, I must
comment on the "branch cut" formulas worked out by Andrew Coppin
with help from several other list members.  The formulas very
efficiently do what they are designed for, and open an entire
new door for exploration.  When I have done a little experimen-
ting with the formulas, I'll likely have a few FOTD's created by
them.

Now on to what you've all been waiting for -- the weather.  It
was cloudy and cool all day, with a temperature of 55F (13C),
which was too chilly for the cats to venture out of doors.  In
the evening a light rain began.  Now isn't that report thrilling?

The latest burst of philosophy has just about exhausted itself,
so there will be a short break before I return with more words
of wisdom.  But wise or not, I'll return tomorrow with another
wonderful fractal and some notable words.  Until that time
comes, take care, and without fractals the world just wouldn't
be the same.


Jim Muth
[e-mail]


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

Edge-on_Galaxy     { ; time=0:32:02.82, SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=mandelbrotmix4 function=recip passes=1
  center-mag=-3.08437/8.85332/2.418791/1/80
  params=1/-1/1/-1.1/0/0 float=y maxiter=6000
  bailout=25 inside=bof61 logmap=87 periodicity=10
  colors=0000z0<9>0z0<4>0z00z20z40z7<2>0zC0zG<3>0yO0yP\
  0yR0yT0yX0yY0y`<3>0yg0yi0ym<3>0yt0yv0yw0zr0yy0Vz00z0\
  Az0It0Pk0Xd0dV0kO0rE0y70z0<11>0z0<4>0z0000<40>000<4>\
  00000200200400700700200400700700800800A00A00C00C00E0\
  0E00G00G00I00I<2>00O40M70MA0KC0KG0II0IM0GO0GP0GT0EV0\
  EY0C`0Cd0Ae0Ai08k08n07p07r27v74wA4zE2zI2zM0<2>zX0<2>\
  zw0zz0zz0zz0zz2zz2zz4zz7IEkIGmIGmKGmKGmMImMImMImOImO\
  KmOKnPKnPMnPMnRMnRMnROnTOnTOnVMpTOn<2>TPmTPmTRkTRkTT\
  iTTiTTiTVgRVgRXe<3>RYdRYdR`bR`bRb`Rb`Pb`PdY<2>PeXPeX\
  PgVPgVPiTPiTPiTOkROkROkROmP<2>OnOOnOOpMOpMOyCKy8Iy7E\
  y4Cy28y07z02z0
  }

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, 12 Apr 2000 09:14:55 GMT
From: "Andrew Coppin" <[e-mail]>
Subject: (fractint) Branch Cuts

I know that Log is multivalued with complex numbers, and therefore X^Y can
be multivalued... but are there any other formulas that are? I think Sin,
Cos, etc are all true function even in complex space, aren't they?

PS. I tell you what would be usefull in the formula parser... We have a
real() function, an imag() function, but it would be nice to have mag() and
arg() functions too. And if the GUI could be changed to allow the input of
complex numbers in polar form... But I guess if I want that I'll have to
code it myself (shiver!)

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

Date: Thu, 13 Apr 2000 13:11:39 +1200
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Branch Cuts

At 09:14 12/04/2000 GMT, you wrote:
>I know that Log is multivalued with complex numbers, and therefore X^Y can
>be multivalued... but are there any other formulas that are? I think Sin,
>Cos, etc are all true function even in complex space, aren't they?
>

sqrt is multivalued... sqrt(x^2) = +/-x ... but of course that's x^(1/2).
x^(1/3) is triple-valued (and Fractint's Newton type will help you locate
them), x^(1/4) is quadruple-valued, ....

Since the sine, cosine, hyperbolic sine, ... functions are periodic (the
hyperbolic ones with imaginary period), their inverses are multiple-valued.

Eg, sin(y)=x, Arcsin(x)=y+2n*pi

but again, one can expand arcsin in terms of logs and noninteger exponents,
so that's not so surprising. sin itself can be expanded without such
beasties, as a series using only divisions, multiplications, and
natural-number exponents. Since all of these are single-valued, a sum of
such (in of course those cases where the sum exists) is also single-valued.

In short, it's nonintegral exponents that give you your multiple values. If
the exponent is a rational number, then its denominator (when the fraction
is written in lowest terms) specifies the number of possible values. If the
function has a number of such exponentiations, the multiplicity of the
function is determined by the lowest common multiple of these denominators.
And of course, if there are an infinite number of distinct exponents in the
expansion of a function (such as those for Log, Arcsin, etc.) then there
are an infinite number of "sheets in the Riemann surface" to lapse into
technical argot at the end.

Well, maybe not that short. Shorter:
z is a complex number, n and m are nonnegative integers with no common
factor, v is an irrational number

z^n => single-valued
z^n/m => m-valued
z^v => infinitely-valued

When the exponent is itself complex, consider z^(x+iy) = z^x*z^(iy) - the i
rotates the graph of the function 90 degrees in the complex plane, so
doesn't alter its multiplicity.

Morgan L. Owens
"But what's a good way of drawing a Riemann surface?"





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

Date: Wed, 12 Apr 2000 21:26:07 -0600
From: Tim Wegner <[e-mail]>
Subject: Re: (fractint) Branch Cuts

Andrew wrote:

> PS. I tell you what would be usefull in the formula parser... We have a
> real() function, an imag() function, but it would be nice to have mag() and
> arg() functions too.

That's not too hard, though I'd want to make sure it would really be
useful.

>And if the GUI could be changed to allow the input of
> complex numbers in polar form

That would take more work, not hard, but work.

Tim


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

Date: Thu, 13 Apr 2000 01:45:05 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 13-04-00 (Utter Chaos [5]) (c)

FOTD -- April 13, 2000  (Rating 5)

Fractal visionaries and enthusiasts:

Finding some spare time this afternoon, I brought up Andrew's
Branch-Cut formula to see what it can do.  The first thing I
noticed is that the images the formula creates extend far beyond
the bailout of 4, but raising the bailout to 100 (a minor
adjustment) solved this problem.

Then I noticed something strangely familiar with the images the
formula creates when e=2.5.  I had seen these shapes somewhere
before.  A moment later, I recalled the default Z^2.5+C fractal,
which is filled with midgets of the most extraordinary shapes.
The shapes created by the new formula are identical to the
various shapes of the midgets in the default Z^2.5 fractal.  And
not surprisingly, its close relative, the symmetrical (-Z)^2.5+C
fractal, is one of these shapes.

I also noticed that exponents which produce boring images with
the default complex-log value become very interesting as one
examines farther out the corkscrew.  The formula for today's
fractal is Z^1.005+C, which draws a tiny bean-shaped hole at the
center of a series of concentric circles when the default log is
calculated.  As today's image shows, some of the other log-
slices of this formula are far more interesting.

This is the most unusual chaotic fractal image I have yet
encountered.  It is "Utter Chaos" yet with enough traces of
order to produce a curiously surrealistic effect.  I was a bit
hasty on the coloring, so I doubt that the present palette would
be difficult to improve upon.

The parameter file runs unusually slowly.  Only the most
steadfast will fail to download the completed JPEG image from:

          <alt.binaries.pictures.fractals>

or from:

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

The fractal weather today was sunny but quite chilly, and
tonight will see a late season frost.  The temperature of 54F
(12C) was too cold for the cats.

With such an interesting new formula to play with, I did no
pondering today.  And since I'll likely be playing with the
formula again tomorrow, I'll do no pondering then either.  But
in a few days the urge to philosophize will once again arise,
and then watch out world.

Until tomorrow, take care, and I wonder how many dimensions the
hypercomplex-log figure exists in.


Jim Muth
[e-mail]


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

Utter_Chaos        { ; time=1:21:04.48, SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=branchct.frm
  formulaname=MandelbrotBC passes=1
  center-mag=-0.0437149579/0.1523876687/605.378/1/4.999
  params=1.005/0/15.9/0 float=y maxiter=50000
  bailout=25 inside=0 logmap=1063 periodicity=10
  colors=000zZKscd<13>vgivgiwgi<2>whjwhjuii<10>gmbfnad\
  n`co`bo_bp`<49>TMPTLPTLP<31>FCFECFEBE<4>CCFCCFCDFCDF\
  BDFBEF<7>AGF9HF9HF<3>8IFKJF<3>KKFKKFMLFOLFQLF<4>QNGQ\
  NGQNG<2>QOGQPGQPIPPK<2>AQQ8RS3RU<3>2Ra2Rc2Re2Rg<2>1R\
  k0Rl1Rm1Rn1Ro<3>CRsFRtIRuKRv<3>IRz7Rz<3>8Rz8Rz8Rz8Rz\
  8Rz<16>TTzUTzVTz<3>ZTz<4>MTzKTzIUz<2>AUz8Uz4Uz<6>CUz\
  AUzAUzAUz
  }

frm:MandelbrotBC   {; Z=Z^E+C  (formula by Andrew Coppin)
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(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|<100
}

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


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

Date: Thu, 13 Apr 2000 09:24:30 -0400
From: "Damien M. Jones" <[e-mail]>
Subject: Re: (fractint) Branch Cuts

Tim, Andrew,

 - > PS. I tell you what would be usefull in the formula parser... We
 - > have a real() function, an imag() function, but it would be nice
 - > to have mag() and arg() functions too.

You already have mag()--use cabs(). atan() is less convenient as arg()
because you have to check for quadrant. Perhaps implementing atan2() like
C? Or just calling it arg()? This *would* be useful, IMO. I vote for
calling it atan2(), but that's the programmer in me...

Damien M. Jones   \\
[e-mail]  \\  Fractalus Galleries & Info:
                    \\  http://www.fractalus.com/

Please do not post my e-mail address on a web site or
in a newsgroup.  Thank you.


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

Date: Fri, 14 Apr 2000 10:36:57 +1200
From: "Karl Scherer" <[e-mail]>
Subject: (fractint) fractals for art competitions

This is a multi-part message in MIME format.

- ------=_NextPart_000_0005_01BFA5FD.5BB71FA0
Content-Type: text/plain;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Hi Fractal friends,

I have two questions today:

1.    Can somebody tell me some art competitions
on the net=20
   - where I can send fractals (as gif files or otherwise) and
   - where I do not have to disclose the formula
     and/or give away my copyright?=20

Thanks for any help on this.


2.   Does any of you guys do exhibitions with framed art work?
=20
I just had two exhibitions with 100 framed fractals with lots of good =
feedback=20
and quite good sales. (framed, size A2 go for US$100, size A3 for US$50)

Furthermore, I now have permanent exhibitions at the Articus Cafe, Upper =
Symonds Str, Auckland, NZ
and at the Chess Parlour, Verrans Corner, Northshore.

I would like to hear from your experiences with selling fractal art.
I am trying to find a producer for a calendar as well.
Any feedback is appreciated.
Thank you!

Karl Scherer
11 Utting Str, Auckland, New Zealand
[e-mail]
Seen my homepage lately?
http://www.kiwi.gen.nz/~karl


- ------=_NextPart_000_0005_01BFA5FD.5BB71FA0
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 content=3D"text/html; charset=3Diso-8859-1" =
http-equiv=3DContent-Type>
<META content=3D"MSHTML 5.00.2919.6307" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>Hi Fractal friends,</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>I have two questions =
today:</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=3DArial size=3D2>1.    C</FONT><FONT =
face=3DArial=20
size=3D2>an somebody tell me some art competitions</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>on the net </FONT></DIV>
<DIV><FONT face=3DArial size=3D2>   - where I can=20
send fractals (as gif files or otherwise) and</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>   - where I do not have =
to disclose=20
the formula</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>     and/or give =
away my=20
copyright? </FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=3DArial size=3D2>Thanks for any help on =
this.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2><FONT face=3DArial =
size=3D2></FONT></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2><FONT face=3DArial =
size=3D2>2.   Does any of=20
you guys do exhibitions with framed art work?</FONT></FONT></DIV>
<DIV><FONT face=3DArial size=3D2> </FONT></DIV>
<DIV><FONT face=3DArial size=3D2>I just had two exhibitions with 100 =
framed fractals=20
with lots of good feedback </FONT></DIV>
<DIV><FONT face=3DArial size=3D2>and quite good sales. (framed, =
size=20
A2 go for US$100, size A3 for US$50)</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=3DArial size=3D2>Furthermore, </FONT><FONT face=3DArial=20
size=3D2>I now have permanent exhibitions at the Articus Cafe, =

</FONT><FONT face=3DArial size=3D2>Upper Symonds Str, Auckland, =
NZ</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>and at the Chess Parlour, Verrans =
Corner,=20
Northshore.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=3DArial size=3D2>I would like to hear from=20
your experiences with selling fractal art.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>I am trying to find a producer for =
a calendar=20
as well.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Any feedback is =
appreciated.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Thank you!</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=3DArial size=3D2>Karl Scherer<BR>11 Utting Str, =
Auckland, New=20
Zealand<BR><A =
href=3D"mailto:[e-mail]">[e-mail]</A><BR>Seen my=20
homepage lately?<BR><A=20
href=3D"http://www.kiwi.gen.nz/~karl">http://www.kiwi.gen.nz/~karl</A><BR=
></DIV></FONT></BODY></HTML>

- ------=_NextPart_000_0005_01BFA5FD.5BB71FA0--


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Date: Thu, 13 Apr 2000 21:23:48 -0400
From: John R Goering <[e-mail]>
Subject: (fractint) Prime numbers and the M-set

Hi to all,

I recently received a question concerning prime numbers and the
Mandelbrot set.  So, does anyone know if there is a meaningful
relationship between the M-set and the prime numbers?

I appreciate your help,

John Ralph


Visit my homepage at http://homestead.juno.com/johnrhg
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John Ralph H. Goering
[e-mail]
- -------------------------------------
Jesus says, "Behold, I am coming soon!" (Revelation 22:12, NIV)

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Date: Fri, 14 Apr 2000 00:00:06 EDT
From: [e-mail]
Subject: (fractint) Zoom limit?

Hi,
While using Fractint v20.0, after I zoom in about ten times or so,
I seem to reach a level where the image is no longer sharply defined
but just colored squares about a quarter inch or so in size.
I must be overlooking something.  What should I do in order to
zoom to deeper levels?
Thank you,
Lee Fairbanks

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Date: Fri, 14 Apr 2000 00:02:26 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 14-04-00 (Silver Pilgrimage [7]) (c)

FOTD -- April 14, 2000  (Rating 7)

Fractal enthusiasts and visionaries:

Today's fractal is another one created with the Mandel BranchCut
formula, which I spent some time with today, as I expected I
might do.  The formula is Z^1.33+C, an extremely simple
expression that works wonders when some of its more remote parts
are calculated.

The bud in the image is of order 1.33, which means it should
have 1/3 lobe.  Actually, the bud is the most perfect 1/3-lobed
bud I have yet found.  And those radiating branch cuts add just
the touch to rate today's FOTD a stately 7.

The bud in the picture is on the southeast shore of the main
fractal, a lopsided bay with chaotic debris extending far into
the northwest suburbs.  Many smaller buds dot the shore in the
vicinity.  I'll investigate these smaller buds tomorrow, and if
I find anything of interest that makes a presentable picture,
I'll declare it FOTD for 15-04-00.

I named the picture "Silver Pilgrimage" for poetic reasons
rather than as a description.  The slight silvery effect around
the edges was all the excuse I needed.

At 4-1/2 minutes, the parameter file is a welcome relief from
yesterday's marathon file.  And of course the JPEG'd image has
been posted as always to:

          <alt.binaries.pictures.fractals>

and to:

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

The fractal weather, for anyone who for some reason is
interested, was partly cloudy and 49F (9.5C), ideal for
strenuous outside work, not so good for fractal cats, who
complained as they turned back indoors.

As forecast, the philosophy went nowhere today.  It's simmering
just under the surface however, and could erupt into a paroxysm
of wisdom any day now.  To see whether that day could be
tomorrow, check back then, when I'll return with a new fractal
and some old words.

Until next time, take care, and I've never seen a real fractal
- -- I've seen only pictures of fractals.


Jim Muth
[e-mail]


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

Silver_Pilgramage  { ; time=0:04:32.92, SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=branchct.frm
  formulaname=MandelbrotBC passes=t
  center-mag=0.784669/-0.335969/3.197277/1/117.5
  params=1.33/0/-3/0 float=y maxiter=25000 inside=0
  logmap=9 periodicity=10
  colors=00075B93CC7FFAHHDJ<6>MYXM`ZNc`<2>PlfPohOmg<14\
  >DWfDVfCUf<2>AQf9Pf7Pe<16>YDq_Dr`Cs<3>fAu<19>mdXmfWm\
  gU<3>nmQonQpoQ<3>stQtuQuvQvwQvxQ<2>hlY<3>RmfNmhImkEm\
  m7mw<3>HmSKmKIm5<3>XmV_m`YmRXnHVt5Wx7<19>`QV`OW`MY<3\
  >aGa<3>THeRHfOIg<3>GIj<17>cOpePqfPq<2>jQrkQrmPt<24>S\
  eJReIQfG<3>NhBVfFbdIpdL<3>SXLMVLOXN<9>Zfa`gbahd<2>dk\
  hfmjeli<3>aih`ih`hgaihbjickjblkaml
  }

frm:MandelbrotBC  {; Z=Z^E+C (formula by Andrew Coppin)
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(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|<100
}

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


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

Date: Fri, 14 Apr 2000 00:32:21 -0600
From: Tim Wegner <[e-mail]>
Subject: Re: (fractint) Zoom limit?

> While using Fractint v20.0, after I zoom in about ten times or so,
> I seem to reach a level where the image is no longer sharply defined
> but just colored squares about a quarter inch or so in size.
> I must be overlooking something.  What should I do in order to
> zoom to deeper levels?

First of all, Fractint is designed to stop you when the zoom limit is
reached, but the zoom limit detection doesn't always work right,
especially if the zoom box is rotated or skewed.

Arbitrary precision will kick in for the Mandelbrot and a few other
types and let you zoom all the way to 10^1500 or so. But for most
fractal types, ten  or so zooms is about the limit of double
precision.

Tim


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

Date: Fri, 14 Apr 2000 17:38:00 -0400
From: Sylvie Gallet <[e-mail]>
Subject: (fractint) Pars: Nacht und Nebel...

Hi All,

  Here's some Mandelbrotmix4's.  Some of them use the same parameters as
Jim's "Jungle of Fractals" (Feb 25).

6041302.GIF        { ; Nacht und Nebel                      t=3D  0:39:57=
.97
                     ; Copyright Sylvie Gallet, Apr 14, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
  reset=3D2000 type=3Dformula formulafile=3Dfractint.frm
  formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1
  center-mag=3D-3.05548/9.30136/3.942029/1/-109.999
  params=3D-1/1/2/-1.5/0/0 float=3Dy maxiter=3D2000 bailout=3D25 inside=3D=
0
  symmetry=3Dnone periodicity=3D0 sound=3Doff
  colors=3DRRRTTT<41>FFFFFFFFF<3>DDDCCCCCC<3>888777666<3>555555555<2>555\=

  555666777<18>HHHIIIIII<4>MMMMMMNNN<41>_________<4>bbbbbbccc<5>dddeee\
  eeeffffff<19>llllllmmm<2>nnnnnnmmm<69>TTT
  }

60311002.GIF       { ; .                                    t=3D  0:47:42=
.59
                     ; Copyright Sylvie Gallet, Apr 11, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
  reset=3D2000 type=3Dformula formulafile=3Dfractint.frm
  formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1
  center-mag=3D+2.88673055761374900/-3.59466658910688800/2.528976e+011
  params=3D1/-1.5/-3/0.5/0/0 float=3Dy maxiter=3D1600 bailout=3D25
  inside=3D0 logmap=3D104 symmetry=3Dnone periodicity=3D10 sound=3Doff
  colors=3D0A54F6<9>FU8GW9HX9<2>KaALbAOcA<4>elEhnFlpG<3>zwJ<8>zeFzcEzaE<\=

  3>zUB<7>zi5zk4zm4<2>zs1zu0zu1<24>zynzypzyr<2>zyxzzzzzz<163>3E5
  }

60401A03.GIF       { ; .                                    t=3D  0:24:32=
.45
                     ; Copyright Sylvie Gallet, Apr 11, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
  reset=3D2000 type=3Dformula formulafile=3Dfractint.frm
  formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1
  center-mag=3D+72.39005639767717000/+0.00000005358312205/18109.86
  params=3D1/100/-2/0.01/35/0 float=3Dy maxiter=3D1800 bailout=3D25
  inside=3D0 logmap=3D47 symmetry=3Dnone periodicity=3D10 sound=3Doff
  colors=3D000zzz046<8>0MX<3>0Uh1Xk1Wi<8>7FM7EK8CH<2>A69B46D46<18>nAJpAK\=

  rAL<2>xBNzCOzDO<17>zjOzlOznO<3>zvO<22>zKPzIPzHP<3>z9Qz7Qz6Rz4Rz2Rz0S\
  <25>C3AA39838<2>236045046<17>0DK0EK0EL0FL0FM<21>2Q`2Ra2Rb2Sb2Sc2Td<7\
  >AYfBZfCZf<23>_kd`ldald<3>end<15>07B
  }

60401A08.GIF       { ; .                                    t=3D  1:01:32=
.91
                     ; Copyright Sylvie Gallet, Apr 11, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
  reset=3D2000 type=3Dformula formulafile=3Dfractint.frm
  formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1
  center-mag=3D+72.39004428961769000/-0.00001110987082908/1.185761e+011/\=

  1.0003 params=3D1/100/-2/0.01/35/0 float=3Dy maxiter=3D1800 bailout=3D2=
5
  inside=3D0 logmap=3D144 symmetry=3Dnone periodicity=3D10 sound=3Doff
  colors=3D000<9>0KU0MX0O_<3>1Xk<5>4MX5LU5JS<3>8CH9AF98CA69B46<5>N5BP6CR\=

  6D<10>m9Ko9Lq9M<2>wAOzBPzCP<16>zfUzhVzjVzlWznW<2>ztXzvYzv_<4>zwizxkz\
  xm<3>zzv<9>zVbzS`zOZ<2>zFTzBRz9Q<3>z2Rz0Sx0R<24>C3AA39838<2>23604504\
  6<15>0CI0DJ0DK0EK0EL0FL<22>2Q`2Ra2Rb2Sb2Sc<2>4Ue5Ve6We7We8Xf<27>_kd`\
  ldald<3>end<15>07B
  }

60401B04.GIF       { ; .                                    t=3D  2:29:42=
.95
                     ; Copyright Sylvie Gallet, Apr 11, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
  reset=3D2000 type=3Dformula formulafile=3Dfractint.frm
  formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1
  center-mag=3D+72.47170030731296000/-0.04740244275976058/1503.494/1/-90
  params=3D1/100/-2/0.01/35/0 float=3Dy maxiter=3D1800 bailout=3D25
  inside=3D0 logmap=3D75 symmetry=3Dnone periodicity=3D10 sound=3Doff
  colors=3D000zzz0Sb<23>0CI0BH0BG<2>09E08D08D08D<9>059058058<2>047047058\=

  <15>0DK0EK0EL0FL0FM<21>2Q`2Ra2Rb2Sb2Sc2Td<9>CZfD_fE_f<13>SflTflUgmVh\
  m<3>Zjo_jp`kpakqblrcmrcmr<26>HTbGSbFRa<2>CO_CNZCMX<7>BDKBBJBAH<2>B7C\
  A5AB46<3>J59L5AN5B<3>T5DV5EX5E<4>d7Hf7Ih7J<3>o8Lq8Ls9M<2>x9OzAPzCP<1\
  4>zhZzjZzm_<3>zvb<2>zqazpazpb<12>www
  }

60401B07.GIF       { ; .                                    t=3D  2:18:43=
.14
                     ; Copyright Sylvie Gallet, Apr 11, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
  reset=3D2000 type=3Dformula formulafile=3Dfractint.frm
  formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1
  center-mag=3D+72.47183790716201000/-0.04891345439138522/75333.13/1/119\=

  .999 params=3D1/100/-2/0.01/35/0 float=3Dy maxiter=3D1800 bailout=3D25
  inside=3D0 logmap=3D140 symmetry=3Dnone periodicity=3D10 sound=3Doff
  colors=3D000000025<86>1P_1P`1P`1Q`1Qa<3>2Sc3Tc4Td<3>6Ud7Ve8Ve<26>Zlt_m\=

  t`nu<2>cpwcpwbov<17>NZgMYfLXe<3>IUcHTbGSb<3>CO_CNZCMX<7>BDKBBJBAH<2>\
  B7CA5AB46<3>J59L5AN5B<3>T5DV5EX5E<4>d7Hf7Ih7J<3>o8Lq8Ls9M<2>x9OzAPzC\
  P<14>zhZzjZzm_<3>zvb<2>zqazpazpb<12>www
  }

6041301.GIF        { ; .                                    t=3D  2:54:43=
.98
                     ; Copyright Sylvie Gallet, Apr 14, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
  reset=3D2000 type=3Dformula formulafile=3Dfractint.frm
  formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1
  center-mag=3D+1.16611516126891800/+0.26169401064720740/3.96582e+007
  params=3D1/1.8/-1/-0.5/0/0 float=3Dy maxiter=3D4000 bailout=3D25
  inside=3D0 logmap=3D378 periodicity=3D0 sound=3Doff
  colors=3D000zzz05F<29>8IR8IR9JS<29>IR_JS`JS`KSaKSa<2>LTbLUbNWd<3>VclYe\=

  n_gp<3>hpy<4>UajQYg<32>_fp`gq`gq`hqahq<2>birbirdks<3>lsxnuzksx<3>_gp\
  WdmUbl<9>COYANX8LV<2>2HR0FP0GQ<3>8NXAPZCR`<3>KZh<3>CTbASa8Q_<3>0KU<2\
  >L0B<11>kCNmDOpEPrFQtGRwHS<25>xnXxoXxpYxrYxsYxtYyvZzx_<21>www
  }

6041307.GIF        { ; .                                    t=3D  1:07:14=
.20
                     ; Copyright Sylvie Gallet, Apr 14, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
  reset=3D2000 type=3Dformula formulafile=3Dfractint.frm
  formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1
  center-mag=3D-1.02154424034962000/+3.34908648639290700/1.443724e+008
  params=3D-1/1/2/-1.5/0/0 float=3Dy maxiter=3D2000 bailout=3D25 inside=3D=
0
  symmetry=3Dnone periodicity=3D0 sound=3Doff
  colors=3D00PTgv<3>WiwXjwYjx<23>nwynwyoxy<3>qyyryxryxsywsyw<3>uzuuzuvzt\=

  <3>wztwzsxzs<4>xypxyoxynxxnxxmxxl<13>xsbxrbxraxraxr`<3>wpYwpYwoX<5>t\
  lStkRsjQsiPshO<2>rgNqfMqeLpdKpcJ<4>n_HmZGlYFkYEjXD<3>hUBgTAfS9<8>_L5\
  ZK4ZK4<4>UG2UG2TF1<2>QC1PC1PB1OB1NA1<8>H60G50F40<2>E41D31D32C22C22<2\
  >A12913913814814<3>606506507<2>307308208209209<7>12D12E02E<3>03H03I0\
  3J<3>05L06M06N<3>28R29R29S<2>2BU3CV3DX<7>7Jb8Kc8Ld<3>ANfBNgBOg<6>GTm\
  HUnHVn<3>LZqM_rM`r<3>PctPcuQduQdvRevSfv
  }

6041403.GIF        { ; .                                    t=3D  0:57:25=
.08
                     ; Copyright Sylvie Gallet, Apr 14, 2000
                     ; <[e-mail]>
                     ; t=3Dcalc time using a PII 300 at 1600 x 1200
  reset=3D2000 type=3Dformula formulafile=3Dfractint.frm
  formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1
  center-mag=3D+2.53408422974110600/-5.58614796935317300/786.2559/1/105
  params=3D1/0.55/-1/0.65/8/0 float=3Dy maxiter=3D5000 inside=3D0
  logmap=3D74 symmetry=3Dnone periodicity=3D0 sound=3Doff
  colors=3D000`NC<22>rgOshOsiP<3>wmRxnRxoSypSzqT<3>xoPxnOwlN<4>qeIodHnbG\=

  <2>jZDiXCjYE<23>vtpwuqwvs<2>yyxzzzyxx<14>bSNaQL_NI<2>WHBUE8UF8<4>ZLC\
  _ND`OE<3>cTHcUIdVJ<11>oidpkeqlgrnisoj<2>vspwurvsp<2>pkinhfmfclda<8>W\
  KFUHDSFA<2>M83K50K50<8>RA9SAASBB<5>XEHYFIZGJ_HK_HK<4>cLPdMQdNR<2>fQT\
  gQUgRUgRV<59>zzw
  }

frm:MandelbrotMix4 {; Jim Muth
a=3Dreal(p1), b=3Dimag(p1), d=3Dreal(p2), f=3Dimag(p2),
g=3D1/f, h=3D1/d, j=3D1/(f-b), z=3D(-a*b*g*h)^j,
k=3Dreal(p3)+1, l=3Dimag(p3)+100, c=3Dfn1(pixel):
z=3Dk*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

  Cheers,

        - Sylvie

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

End of fractint-digest V1 #467
******************************