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fractint-digest         Tuesday, May 16 2000         Volume 01 : Number 475




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

Date: Sat, 13 May 2000 01:27:25 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 13-05-00  (Col [5])

FOTD -- May 13, 2000  (Rating 5)

Fractal visionaries and enthusiasts:

It's once again late and I'm once again groggy after a hectic
day, so this one will be short.  Today's fractal image, which
was created with the aid of that workhorse M-Mix4 formula, is
the slowest in quite some time, taking almost four hours to
render on a P200.  A glance at the maxiter and logmap values in
the parameter file will reveal the reason for the slowness.

I named the picture "Col" because that's exactly what it's a
picture of.  A col is a saddle-shaped contour, like a mountain
pass.  Today's fractal has a saddle-shaped contour, with the
seat of the saddle lying at the center of symmetry.

The fractal scene is a close-up of the point where the basins of
attraction of two very close midgets bump together.  A few
out-zooms will reveal the two kissing midgets, which are
interestingly distorted by their nearness to each other.

As I mentioned previously, the parameter file is excruciatingly
slow.  No one but the most masochistic should try to run it,
when the pre-rendered image has been thoughtfully posted to:

          <alt.binaries.pictures.fractals>

and to:

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

The fractal weather today was once again hot, hazy and humid,
with a temperature of 90F (32C) that was perfect for doing
nothing.  Unfortunately, not being a cat, I couldn't get away
with doing nothing.

On such sultry days the philosophy gets stifled.  But I give my
word that I'll try again in the next FOTD.

I think this will be the last FOTD I'll write at the end of the
day when I'm all worn out.  Starting with the FOTD for May 14,
I'll do the writing in the morning when I'm fresh, and post the
discussion before noon, (Fractal Central time).  The result will
be livelier and hopefully more profound discussions.

So until next time, which will be in about 33 hours, take care,
and don't worry about the FOTD.  It isn't nearing the end of its
run.


Jim Muth
[e-mail]


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

Col                { ; time=3:56:22.34, SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-0.16762174763149920/+0.03653716755766197\
  /5514.852/1/117.5 params=0.2005265/2/-5/-0.5/0/0
  float=y maxiter=50000 bailout=25 inside=0 logmap=3861
  symmetry=none periodicity=10
  colors=000d4F<3>d4Ad49d48<2>d44c02<8>eG5fI5fK6fL6fN6\
  <3>gY7g`8hc8hf8<3>io9iqAisAiuAjw9izA<4>ikFihG<6>h`Nh\
  _Oh_P<3>hWThVUhUVkTT<10>VXgUXiSXj<2>OYnNYoOXn<22>OAS\
  O9RO8QO7PO6OP4M<29>I9mI9nH9o<2>H9rI9sH9t<2>H9w<5>F9U\
  F9PF9K<3>E90<3>D90D90D90E82<38>b3Bc3Bc3B<2>e2Cf2Ch2C\
  <3>p1Dr1Et1Ev1Ex1Ez0Dz1Ez2E<3>m6Fj6Gh7G<24>UTN
  }

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, 13 May 2000 02:28:10 -0400
From: Barry N Merenoff <[e-mail]>
Subject: (fractint) The Wonderer Returns

A complex derivative is a combination of the real and imaginary partial
derivatives along an
axis. The Cauchy Criterion, which holds for any function constructed
algebraically using
common functions such as Sin, Cos, etc. (but not for "artificial" functio=
ns
such as Abs,
Real, Flip, etc.), states that the complex derivative, when adjusted
according to a formal
substitution, will be the same for any axis.

Ordinary Fourier series probably would not work well in a complex domain
because they
do not produce the expected result of bounded waves. To produce bounded
waves in a
complex domain without violating the Cauchy Criterion, you can use Jacobi=

functions.
Jacobi functions take two arguments: an "angle" and a "type". When the ty=
pe
is zero,
they are trigonometric functions; when the type is one, they are hyperbol=
ic
functions.
I have found that a type of -1 gives, for the Jacobi "SN" function, bound=
ed
waves that
are periodic on both the real and imaginary axes, with a period of about
5.24412. Tim
might think about implementing this in a future version of Fractint.

Sincerely,
        Collin Merenoff

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

Date: Sat, 13 May 2000 11:13:16 -0700
From: "Robert Woods" <[e-mail]>
Subject: RE: (fractint) New Here

switch your video settings to 256c for color cycling

- -----Original Message-----
From: [e-mail]
[mailto:[e-mail]]On Behalf Of Angela Wilczynski
Sent: Friday, May 12, 2000 7:59 PM
To: [e-mail]
Subject: Re: (fractint) New Here


Ammon...

No clue.....I'm art, not technical support...

wizzle

Ammon Cooke wrote:
>
> At 07:44 PM 5/11/00 -0700, you wrote:
> >See several tutorials at....
> >
> >http://wizzle.simplenet.com/fractals/hints/graphic_hints.htm
> >
> >wizzle
> OK I looked found what I was looking for but when I tried it I got this
> error message: I'm sorry but color-cycling requires a palette based video
> driver
>
> Is there a work around for this?
> Thanx.
>
> >Ammon Cooke wrote:
> > >
> > > Hi guys, (& gals) I'm new to fractint & would like to know how to
build
> > > color maps.
> > >
> > > Thanks in advance.
> >
> >--------------------------------------------------------------
> >Thanks for using Fractint, The Fractals and Fractint Discussion List
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>
> --------------------------------------------------------------
> Thanks for using Fractint, The Fractals and Fractint Discussion List
> Post Message:   [e-mail]
> Get Commands:   [e-mail] "help"
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> Unsubscribe:    [e-mail] "unsubscribe fractint"

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_____________________________________________
NetZero - Defenders of the Free World
Click here for FREE Internet Access and Email
http://www.netzero.net/download/index.html

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

Date: Sat, 13 May 2000 12:37:56 -0600
From: Ammon Cooke <[e-mail]>
Subject: RE: (fractint) New Here

OK now I get color-cycling,but when I do what the tutorial tells me it just
starts the cycling it doesn't open a color map.

At 11:13 AM 5/13/00 -0700, you wrote:
>switch your video settings to 256c for color cycling
>
>-----Original Message-----
>From: [e-mail]
>[mailto:[e-mail]]On Behalf Of Angela Wilczynski
>Sent: Friday, May 12, 2000 7:59 PM
>To: [e-mail]
>Subject: Re: (fractint) New Here


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

Date: Sun, 14 May 2000 00:21:10 +0100
From: "Les St Clair" <[e-mail]>
Subject: (fractint) Web Site Re-launched!

Hi Fractal Fans,

Just a note to say that my web sites have been consolidated and  re-launched at the following URL:

http://www.les.stclair.btinternet.co.uk

All of the old Fractal galleries are there (follow the "Fractal Panorama" link), some have been enhanced and improved
with larger images behind the thumbnails.
(Sorry there's no actual new content yet:)

Fractint fans will find fully updated parameter collections from the Fractint List as well as Jim's FOTD (all complete
to the end of April 2000).

Enjoy your visit(s).

- - Les St Clair


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

Date: Sun, 14 May 2000 08:24:37 +0900
From: neko <[e-mail]>
Subject: Re: (fractint) Web Site Re-launched!

>Hi Fractal Fans,
>
>Just a note to say that my web sites have been consolidated and
>re-launched at the following URL:
>
>http://www.les.stclair.btinternet.co.uk
>
>All of the old Fractal galleries are there (follow the "Fractal Panorama"
>link), some have been enhanced and improved
>with larger images behind the thumbnails.
>(Sorry there's no actual new content yet:)
>
>Fractint fans will find fully updated parameter collections from the
>Fractint List as well as Jim's FOTD (all complete
>to the end of April 2000).
>
>Enjoy your visit(s).

...and my backlog of pars to generate grows ever steadily...:)
thanks les!

 -- neko *meow*

 "capital letters were always the best way of dealing with
  things you didn't have a good answer to." -- douglas adams



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

Date: Sat, 13 May 2000 17:24:32 -0700
From: "Robert Woods" <[e-mail]>
Subject: RE: (fractint) New Here

go to Colors | Load Color Map... (in Winfract.exe)

- -----Original Message-----
From: [e-mail]
[mailto:[e-mail]]On Behalf Of Ammon Cooke
Sent: Saturday, May 13, 2000 11:38 AM
To: [e-mail]
Subject: RE: (fractint) New Here


OK now I get color-cycling,but when I do what the tutorial tells me it just
starts the cycling it doesn't open a color map.

At 11:13 AM 5/13/00 -0700, you wrote:
>switch your video settings to 256c for color cycling
>
>-----Original Message-----
>From: [e-mail]
>[mailto:[e-mail]]On Behalf Of Angela Wilczynski
>Sent: Friday, May 12, 2000 7:59 PM
>To: [e-mail]
>Subject: Re: (fractint) New Here


- --------------------------------------------------------------
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_____________________________________________
NetZero - Defenders of the Free World
Click here for FREE Internet Access and Email
http://www.netzero.net/download/index.html

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

Date: Sun, 14 May 2000 07:44:38 -0700
From: "Angela Wilczynski" <[e-mail]>
Subject: Re: (fractint) New Here

Ammon....

To load a new color map...

1.  Enter color editing mode by hitting e or color cycling mode by hitting c
2.  Hit l to take you to your list of maps
3.  Highlight the map you want.....hit enter....the new pallet will be loaded

wizzle



Ammon Cooke wrote:
>
> OK now I get color-cycling,but when I do what the tutorial tells me it just
> starts the cycling it doesn't open a color map.
>
> At 11:13 AM 5/13/00 -0700, you wrote:
> >switch your video settings to 256c for color cycling
> >

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

Date: Sun, 14 May 2000 11:21:09 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: Re: (fractint) FOTD, 14-05-00  (To Mother [5])

FOTD -- May 14, 2000  (Rating 5)

Fractal visionaries and enthusiasts:

This is the first FOTD to be written and posted at the new
time, at the start of the day of its title, rather than at the
end of the day before.  We'll give it a fair trial and see how
it goes for a while.  If it doesn't work out, we'll return to
the old way.

It's the morning of Mother's Day here in the USA.  In honor of
the mothers of the world, I prepared a fractal just for mom.  I
named the picture "To Mother" so that its intent would be clear.

It's another image with a midget, which was created by the
MandelbrotMix4 formula.  This time the expression calculated was
0.125*(Z^4)-(Z^(-2))+C.  The shapes around the midget resemble
stylized hearts closely enough so that the feeling of a greeting
card is there.

The parameter file takes 12 minutes to run.  Downloading the
image file is far faster.  The image may be found as usual
posted by me to Usenet at:

          <alt.binaries.pictures.fractals>

and by Paul Lee to his web site at:

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

The fractal weather yesterday was as warm and humid as it ever
gets around here in May.  The temperature of 92F (33.3C) kept
the cats in the coolness of the shady side of the porch all
afternoon.  But in the late afternoon a whopper of a thunder-
storm came up, which turned day into night, brought down
numerous tree limbs, flooded the fractal basement, and sent the
cats scurrying under the bed for cover from the crashing thunder.

The philosophy, fractal and otherwise, is heating up again on
the philofractal list, and I'll be posting a reply to the latest
reply in a couple hours.  As for the next FOTD -- it will appear
in its full glory in only 24 hours.  Until then, take care, and
enjoy your day.


Jim Muth
[e-mail]


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

To_Mother          { ; time=0:12:21.72, SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+0.312546676762343/+0.5411558771878988/1.\
  048282e+011/1/49.994/0.014 params=-1/-2/0.125/4/0/0
  float=y maxiter=1800 bailout=25 inside=0 logmap=237
  symmetry=none periodicity=10
  colors=000eXPqb0<5>YKCVGESDG<3>F1N<6>a2Pd2Ph2Q<3>t2Q\
  <3>RCAJE6CG3<8>UeAWhBYkC<3>evE<8>MhVKfXIeZ<3>A_e<8>d\
  _Rg_Qk_O<3>x_I<2>9cP<3>PlVTnXXpY`r_ct`<3>ijVjgUleT<3\
  >qWO<3>dbU`cVYeW<2>Pi_<4>`hfcghegi<3>ngnmenmdnSRp<3>\
  fOljOkmNj<2>xMg<3>YD`RBZK9YD7W75V<8>JXlK_nLbp<3>Qnx<\
  9>IZtHXtHWt<2>ERsEQsEQs<3>ESsESsFRr<20>YEqZEq_Dq<3>b\
  BqORS<42>`Dm`DnaCn<3>bBpUQm
  }

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, 15 May 2000 11:13:55 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 15-05-00  (Rhapsody in Blues [4])

FOTD -- May 15, 2000  (Rating 4)

Fractal visionaries and enthusiasts:

If one negative portion of Z^(-2) is added to three negative
portions of Z^(-4) and one portion of C, the resulting fractal
resembles a distorted 5-pointed star with north-south symmetry
and the long point facing east.

Like all fractals that involve negative powers of Z, this
fractal consists of scattered, disconnected bits and pieces of
fractal stuff rather than the nice neat equal-iteration bands of
the images generated from positive powers of Z.

Fractals generated from a simple formula with negative exponents
of Z such as Z^(-2)+C are notoriously boring.  Regardless of how
deep one looks into them, only the same flat circular disks are
there.  The occasional feature that looks promising turns out to
be just another disappointment when checked.  In other words,
after seeing for yourself what these fractals look like, don't
waste your time searching for interesting inner details.  The
details are just not there.

Fractals generated from a formula such as Z^(-2)+Z^(-3)+C are
equally disappointing.  If the exponents are fractional, such
as Z^(-2.5)+Z^(-3.5)+C, the bits and pieces of stuff are broken,
but the result is the same -- just another boring fractal.

A strange thing happens however when a formula such as
Z^(-2)+Z^(-3)+C is iterated with Z initialized to a critical
point of the formula.  And this is what all that weird cauculus
stuff in the second and third lines of the MandelbrotMix4
formula does.  At a critical point, a function momentarily
freezes, and this gives midgets a chance to appear before being
cut off.

A formula such as Z^(-2)+C has no midgets, so the critical point
is irrelevant, but a formula like today's does have midgets, and
if those midgets are to be found, Z must be initialized to a
critical point.  Since the M-Mix4 formula does this, the first
problem has been solved.  The only problem remaining is to find
the midgets.  Not all formulas draw fractals that contain
midgets, and not all parts of the good fractals contain midgets.

I know of no general rule telling where to look for midgets.  I
start by searching the fractals for areas that resemble intact
buds of the Mandelbrot set.  These bits and pieces of Mandelbrot
stuff tell us that the area is critical and therefore likely
to hold midgets.  But intact midgets are sometimes found where
least expected, such as areas that appear obviously perturbed.

In tomorrow's FOTD I'll go into some of the methods that I've
found most effective for locating these elusive midgets.  For
today, we have a picture that I've named "Rhapsody in Blues".
It's a picture of a lively midget I found in a Mandelbrot-like
valley of the parent fractal.  It's also a rather slow image, so
I advise downloading the JPEG file from:

          <alt.binaries.pictures.fractals>

or from:

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

The fractal weather yesterday after the big storm Saturday was
perfect.  The sunny skies and temperature of 74F (23C) brought
out the best in the cats.  Today is starting out equally fine.

The philosophy is once again active on the philofractal list,
where fans of fantistic philosophy will find enough to keep them
thinking for days.  For me, I've got a day's work to do, and I'm
starting to cut into the time I have to do it.  So until next
time, take care, and when a fractal is in critical condition,
unlike people, it's in perfect health.


Jim Muth
[e-mail]


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

Rhapsody_in_Blues  { ; time=0:34:52.85, SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+1.16081437444318100/-0.29199831471349990\
  /266820.4/1/149.999 params=-1/-2/-3/-4/0/0 float=y
  maxiter=3600 bailout=25 inside=0 logmap=350
  symmetry=none periodicity=10
  colors=000cAVc3ae0hg0og0vc0ua0uY0uX0uT0uR0uN0uL0uH0u\
  G0uC0uA0u<2>00u00u00u00u00s00u<2>00v01v13v38x6AxAExC\
  GzEJzGLzHPzLRzNVzPXzR_zVazXezYgz_jzclzeozgqzhuzjvznz\
  zozz<3>xzzzzzzzz<3>zzzzzzxzzvzxuzuszqqznozlozjozhozh\
  ozgozeozcozcnxanv_nuYnuXnsXnqVnoTnnRnlRnjPnjNnhLngJn\
  eJ<2>n_Eja0l_0n_6n_Eo_NoYVqYaqYjsYquXzsYzsYxq_vq_vqa\
  uoasocqocqneonenngnlgllhjjhhjjhjjghlehlehncgnago_go_\
  eqYeqXcsVcsVcuTauRavRavP_xN_xL_zLYzJYzHazN_zJYzHXvGX\
  qEVlCThARc6RY3PT1NN0LH0PC0NA0L80L60J31H13H08G0AE0EE0\
  GC0JA0LA0P80R61V63X36_18a1Ae0Cg0Ej0Gl0Go0Eo0Gq0Gq0Gq\
  0Gq0Gs<2>0Gs0Gs0Gu<5>0Gv0Gv0Gv0Hx0Hx0Hx0Hx0Hz<6>0Hz0\
  Hz0Hz<2>0Hz0Hz0Jz<10>0Jz0Jz0Jz<2>0Jz0Jz0Lz<4>0Lz0Lz0\
  Lz<2>0Lz0Lz0Nz0Lz0Rz<2>0Xz0Yz0Yz<6>0Yz
  }

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, 15 May 2000 10:34:24 -0600
From: Ammon Cooke <[e-mail]>
Subject: Re: (fractint) New Here

Wizzle...

Ok, I didn't make my self clear I know how to load a color map, but I don't
know how to edit it.

Thanks.

At 07:44 AM 5/14/00 -0700, you wrote:
>Ammon....
>
>To load a new color map...
>
>1.  Enter color editing mode by hitting e or color cycling mode by hitting c
>2.  Hit l to take you to your list of maps
>3.  Highlight the map you want.....hit enter....the new pallet will be loaded
>
>wizzle
>


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

Date: Mon, 15 May 2000 22:23:59 -0700
From: "Angela Wilczynski" <[e-mail]>
Subject: Re: (fractint) New Here

Read Linda's Tutorials....remember...I gave you the url....sheesh

Ammon Cooke wrote:
>
> Wizzle...
>
> Ok, I didn't make my self clear I know how to load a color map, but I don't
> know how to edit it.
>
> Thanks.
>
> At 07:44 AM 5/14/00 -0700, you wrote:
> >Ammon....
> >
> >To load a new color map...
> >
> >1.  Enter color editing mode by hitting e or color cycling mode by hitting c
> >2.  Hit l to take you to your list of maps
> >3.  Highlight the map you want.....hit enter....the new pallet will be loaded
> >
> >wizzle
> >
>
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Date: Tue, 16 May 2000 07:48:19 -0400
From: Lee Skinner <[e-mail]>
Subject: (fractint) New Here

>> Read Linda's Tutorials....remember...I gave you the url....sheesh


And you can also RTFM (Read the Fractint Manual) on how to use the color
palette editor.  Use the Following command in a DOS box:

Fractint makedoc

and then print out FRACTINT.DOC, which has several hundred pages of usefu=
l
details about frractint.

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Date: Tue, 16 May 2000 13:16:40 GMT
From: "Andrew Coppin" <[e-mail]>
Subject: (fractint) Re: The Wonder Returns

Hmm... All good stuff!

As I understand it (mostly from BOF), the magnitude of the derrivative of a
complex function is the total slope. What's the significance of the
argument? Does it tell you which way the graph slopes? Or is there some much
more complicated explanation?

As I recall, the descrete Fourier transform is defined in complex numbers.
It's

  f[X] = 1/n * Sum[Y=0..n-1] exp(2*pi*X*Y/n)*S[X]

or something. Loosly it's a matter of drawing an "osciliscope flower" and
taking the average of all the points, adjusting the number of twists in the
flower for each frequency component. Thus, for each frequency we get a
complex number where the magnitude is the frequency's amplitude, and the
argument is the wave's phase (IMHO). I'll try throwing this into FractInt
and see what happens.

What on earth is a Jacobi function?

Would it be possible to "engineer" a function with specific critical points?
If you write something like (x-a)(x-b)(x-c)=0, you could then integrate the
result and have a function with any critical points you like. Can an
algebraic function have critical lines (not just points)?

PS. Is there any other tome like BOF that describes the inner wonders of
complex dynamics (without assuming that you're a God-like)?

________________________________________________________________________
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Date: Tue, 16 May 2000 07:08:14 -0700 (PDT)
From: erdal mazlum <[e-mail]>
Subject: (fractint) hello to all..!

hi,

i just joined this group and wanted to say hello. i
have been using fractint for a long time and enjoying
it. world of fractals is really amazing and
interesting. if you ask me, one can define the things
more realistically by using this complex functions.
hope you all have a good day and enjoy yourself...

erdal.

__________________________________________________
Do You Yahoo!?
Send instant messages & get email alerts with Yahoo! Messenger.
http://im.yahoo.com/

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Date: Tue, 16 May 2000 10:48:44 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 16-05-00  (Ruby-Red Minibrot [4])

FOTD -- May 16, 2000  (Rating 4)

Fractal visionaries and enthusiasts:

Today's fractal, which shows a midget surrounded by ruby-red
elements, and the ruby-red elements surrounded by a celestial
blue background, is named "Ruby-Red Minibrot".  The name is
purely descriptive.

I confess, I did post-process the image just the slightest.  I
did so to liven the colors, which in the un-intensified version
were muddy and dull.  But the sin is not as great as it seems,
for with a bit more effort, I could have achieved the same
result with the Fractint color editor.

In yesterday's FOTD I mentioned fractals that are created by
formulae that contain negative powers of Z.  Today's image,
which was drawn by the formula Z^(-2)+Z^(-23)+(1/C) is a typical
example.

Normally, the fractals of negative powers appear as an ocean
dotted with islands.  This is in contrast to the positive
powers, where the fractals appear as a landscape dotted with
lakes.  But by juggling C, a fractal may be turned inside-out.
The landscape can be turned into an ocean and vice-versa.  By
calculating 1/C instead of C, I have turned the ocean of today's
fractal into a landscape with a big lake.

When a fractal is turned inside-out, the overall appearance
totally changes, though the inner details usually remain
unchanged.  But sometimes, for reasons I cannot determine,
fractals of the M-Mix4 variety that have no midgets when they
appear as oceans with islands, do have midgets when they are
reversed and become landscapes with lakes.  The effect is
probably only apparent, but some fractals do appear far richer
when turned inside-out.

The parent fractal of today's image is a curiously distorted
hodge-podge of Mandelbrot sections.  In it, the normally
near-circular negative-power disks have been distorted into
shapes that almost seem to be trying to form themselves into
equal-iteration bands.  I may further investigate this fractal
when the day's business is completed.

On my P200, the parameter file rendered in 10 minutes plus
1/100th of a second.  On the internet, the JPEG'd image file
will download in far less time.  That image may be found posted
to the Usenet newsgroup:

          <alt.binaries.pictures.fractals>

and to Paul Lee's web site at:

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

The weather yesterday finished as perfectly as it started, the
partly-cloudy skies and afternoon temperature of 68F (20C) being
just warm enough for the cats to enjoy.  Today is starting out
the same.

And now, I must put fun and games aside, and turn to things that
are far less enjoyable but far more profitable.  Until next
time, take care, and keep those fractals coming.


Jim Muth
[e-mail]


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

Ruby-Red_Minibrot  { ; time=0:10:00.01, SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+1.71209342945824300/-0.00604668420008057\
  /46921.65/1/-37.499 params=1/-2/1/-23/0/0 float=y
  maxiter=1400 bailout=25 inside=0 logmap=75
  symmetry=none periodicity=10
  colors=000H3SD7_8Ag5Dn0Fv0Iz0Lz5TzH_tQfl_mcitVqyOpvS\
  otUnpXmnZmjalhdjdgibihZlhXnYMYOBFD00H20L20P30S30V50Z\
  50a72d72h83j85nA5qA7tA7uBFuBMuBUuB_uDguDmuDtuDyuDznH\
  zgKzaOzUQzOTzQSzSQxTPtVOpXMmYLh_KdaI_bHXdFTfEOgDKiBE\
  jAAlA5gDLcFZbLX<2>aXPa_M_dK_hH<2>Zr8aqEbpKcoOdnTfmY<\
  3>lhnmgrnfv<3>qYqrVprUptSotQnuOmvLlvKlwHjxEixDhyAgy8\
  gbdXDzLLzXTvgZppfjzlfz<4>q_zrZztYztYz<3>xTyySxzQwzQw\
  zbyznzzyzzzzzzuzunwnfrgZqiYpjXolXnmVmnVloUjpUjrTitTh\
  uSgvSfwQdxQcyPczPayPZxQXwQUwSSvSPuThMLdLOaKQYITVIVSH\
  YOF_KEbHEdDDg8Bi3Al0AnFFlSLiYKf<3>pchuhiymizpizol<3>\
  worvntunvtnwrny<3>nmzmmzlmzjmz<3>aczZayXZwUXv<3>KMmH\
  KjI0YEIiBYu8lzLnzXozirzfpzbowZmrVlnSiiOhdKg_FdVBcQ7a\
  L2_F0X50ZA2_E7bIBcMEdPIfO<4>VgHYgF_gEchD<3>mi7oi5qi3\
  ti3vl5xm7zn8M5XK5VI3T
  }

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, 16 May 2000 10:49:02 -0400
From: Barry N Merenoff <[e-mail]>
Subject: (fractint) Re: The Wonder Returns

The simple part is that the derivative indicates, in its separate real an=
d
imaginary parts, the
slope of a slice through the x-direction of the surfaces representing the=

real and imaginary
parts of the function. The complicated part is that in order for the
complex derivative to
exist, these two surfaces must be related to each other in such a way tha=
t
the complex
derivative makes sense in terms of other directions of slicing. This
requires that if the
real surface is rotated 90 degrees counterclockwise about the z-direction=

at any point at
which the complex derivative is defined, and then slid along the
z-direction until it inter-
sects the imaginary surface at that point, it will share a tangent plane
with the imaginary
surface at that point.

Your description of the complex Fourier series sounds correct.

The function I am referring to is a solution to the differential equation=

f'(x)^2+f(x)^4=3D1
It can be found using Mathematica as JacobiSN[x,-1]

Yes, you could engineer functions with critical points in specific places=

like this. You
could also raise a factor to a power before integrating to get a
higher-order critical point.

As far as I know, a critical line or curve would be impossible.

You could try reading "Chaos and Fractals: the Mathematics Behind the
Computer
Graphics" by the Symposia in Applied Mathematics.

Sincerely,
        Collin Merenoff

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Date: Tue, 16 May 2000 09:59:40 -0600
From: Ammon Cooke <[e-mail]>
Subject: Re: (fractint) New Here

Sorry for being such a bother but pressing the e key & enter like she says
to doesn't work for me the colors just start cycling.

P.S. if it is a bother to reply by all means DON'T reply if I am asking
this question at the wrong place PLEASE redirect me.


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Date: Tue, 16 May 2000 12:07:41 -0400
From: "Parracho, Rui" <[e-mail]>
Subject: RE: (fractint) New Here

its color cycling because your in color cycle mode.
don't press C.

From the normal fractal generation screen press E, position the grid on the
screen where you want it and then press enter.

Try F1 (help), its very thorough and quick.


- -----Original Message-----
From: Ammon Cooke [mailto:[e-mail]]
Sent: Tuesday, May 16, 2000 12:00 PM
To: [e-mail]
Subject: Re: (fractint) New Here


Sorry for being such a bother but pressing the e key & enter like she says
to doesn't work for me the colors just start cycling.

P.S. if it is a bother to reply by all means DON'T reply if I am asking
this question at the wrong place PLEASE redirect me.


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Date: Tue, 16 May 2000 10:30:38 -0600
From: Ammon Cooke <[e-mail]>
Subject: RE: (fractint) New Here

ok, I am running winfract because I cannot get fractint(dos) to work on my
machine. When I press e like the help says to do nothing happens if I press
enter like Linda's tutorial says to I get color-cycling. How do I avoid this?


At 12:07 PM 5/16/00 -0400, you wrote:
>its color cycling because your in color cycle mode.
>don't press C.
>
> >From the normal fractal generation screen press E, position the grid on the
>screen where you want it and then press enter.
>
>Try F1 (help), its very thorough and quick.
>
>
>-----Original Message-----
>From: Ammon Cooke [mailto:[e-mail]]
>Sent: Tuesday, May 16, 2000 12:00 PM
>To: [e-mail]
>Subject: Re: (fractint) New Here
>
>
>Sorry for being such a bother but pressing the e key & enter like she says
>to doesn't work for me the colors just start cycling.
>
>P.S. if it is a bother to reply by all means DON'T reply if I am asking
>this question at the wrong place PLEASE redirect me.
>
>
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>
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End of fractint-digest V1 #475
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