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fractint-digest        Friday, October 20 2000        Volume 01 : Number 501




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

Date: Mon, 16 Oct 2000 16:31:07 +1300
From: <[e-mail]>
Subject: Re: (fractint) Fractal greeting cards

> Sweetests Day, Oct. 21
> in the States.
>
Never head of it, myself.

Morgan L. Owens
"Me and 5.8 billion other people, I'd guess"

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

Date: Mon, 16 Oct 2000 00:22:21 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD  16-10-00  (Fractal Foliage [6])

FOTD -- October 16, 2000 (Rating 6)

Fractal visionaries and enthusiasts:

The midget in today's FOTD appears to be peeking through a
forest of foliage.  What better name than "Fractal Foliage"
could be given to such a scene?

The parent fractal of today's image consists of three circles,
the whole thing surrounded on the west side by a series of
concentric arcs.  Today's scene lies deep in the outermost arc
on the southwest side.

The expression that created the parent fractal is so whimsical
that I'll not bother repeating it here, but for those who are
interested, the parameters are given in the parameter file that
appears at the end of this discussion.

The render time of just under 7 minutes makes a download of the
GIF image file the wiser choice.  That download may be found on
the Usenet group:

          <alt.binaries.pictures.fractals>

and on the W.W.Web at:

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

If the FOTD web site is not working as it should, contact Paul
Lee, who maintains the site.  I only find the fractals and write
the discussions.

And speaking of things to discuss, we have the fractal weather
in particular.  It was another perfect day here in Fractal Land.
The sunny skies and temperature of 81F (27C) were ideal for cats
and their pet humans alike.

The philosophy is still brewing, though an eruption is still a
number of days in the future.  But keep in touch; you wouldn't
want to miss the excitement when the eruption inevitably happens.

A glance at the wall clock shows that the time has come to shut
down the fractal shoppe and call it a night.  Until 24 hours
from now, take care, and perhaps the best thing of all about
fractals is that they're absolutely free.


Jim Muth
[e-mail]


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

Fractal_Foliage    { ; time=0:06:50.51 -- SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-8.938876274351706/-9.976549500589202/452\
  .3876/1/-79.999 params=-11/-1.1/-1.11/-2.222/-0.9/200
  float=y maxiter=1800 inside=0 logmap=98 periodicity=9
  colors=000S0SvAuo7rg3o`0mS0jL0gD0d60cC0dI6fMGgSQiX`j\
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  g0Qv0IzC9zY0zF0z00v0<3>0T00M00G0DFMTFgiFzcDv_CoVCgQA\
  `L9TG9MC7F777<2>FGfIJrJLz9Lc0LF0L00O30QD0TO0XY0_i0as\
  0dz0gz3da6a09f6AjCDoIFsOGvSP0iQQXQzLMrJ<3>AGD77CFYFM\
  vGJpTGlfDgso07j71<2>as0<3>mg1pd6sc9mQPgFcc3rY6rT9sOC\
  sIFuCIu7LuDOvIPxMQxTSy`TzgVzoYzz_zz`zzazvczzdzyizylz\
  xoxxruxurvxpvzmvzluzjszj<2>oximxilvgjvgiuggsffsfdrfc\
  pdapd`od`odapccpccpadradr`fr`<2>gs_dma<3>YVmXQpTLrSG\
  uQCxO6zM1zL0zJ0zL0vM7lOFaPLSQSIS_7Sd0OV7LMGGDPD3_90g\
  60p70r71s99u9Iv9PxAXyAczAlzCszCzzCzz<3>PzzTzyXzx_zva\
  zufzs<3>szmvzlyzjzziszgjzgczfVzfMzfFzd6zd0zd<3>0zj0z\
  l0zl<2>0zp0zr0zr<2>0zv0zx0zx0zs4zo9zjDzfIzcMz_QzVVzQ\
  YzOPzGGzA7z40z00z00z01z46zACzGIzMMzSSzY
  }

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, 16 Oct 2000 03:08:45 -0500
From: DeBow Freed II PhD <[e-mail]>
Subject: Re: Re: Re: Re: [Fwd: (fractint) Another fractal greeting card URL]

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
Dear Bob,
<p>Again, my post was nothing more than a gratuitous comment, offered in
the hope that some of your more conventionally "accessible" images would
be offered as Cards. I <b>LIKE</b> your images.
<p>I had hoped the statistically insignificant - "anecdotal" if you wish
- - report of one small "patient group" would be accepted in the spirit it
was offered: gratitude to you, and a sense of humor (boy do we need to
invent something better than smiley faces to render e-mail more expressive
than it is).<b>{;-(|) </b>- whatever that means].
<p>I am - thank you very much - fully aware of the other discussion groups,
Damien- and non-Damien-associated, and intentionally steer a wide course
around them - although I enjoy Jim Muth's contributions. My intent was
to ask YOU to consider the implications of thei ssues which you elect to
classify as "philofractal", based on the reaction of a small - and probably
un-focused - "focus group".
<p>How's about accepting the compliment and providing a simple response
to a simple question?: Can/will you provide some of your more <u>conventionally
"accessible</u>" fractal images as cards, or not? That's all. Lets's not
glorify it into some tangential "philofractal" issue, make it sexist, or
otherwise evade the issue. Guess I should have sent it via back channels.
<p>D. Freed
<br>
<br>
<p>Bob Margolis wrote:
<blockquote TYPE=CITE>Dear Dr. Freed;
<p>I am forwarding to you this message sent nine hours ago to the FractInt
<br>mail list. I did not see it come up on the mail list since I sent it,
<br>hence this repeat. New information is added at the end of this message.
<p>Bob Margolis
<p>===================
<p>Bob Margolis wrote:
<br>>
<br>> Dear Dr. Freed;
<br>>
<br>> Before I respond I want to say that I do not have a Web site, and,
<br>> therefore, I in no way made any of the fractal designs exhibited
at both
<br>> fractal postcard Web sites.
<br>>
<br>> With that out of the way, I found you're e-mail very interesting
and
<br>> thought provoking. I would suggest that you subscribe to an e-mail
<br>> discussion group that deals with the philosophical aspect of fractals
<br>> and repost your e-mail addressed to me there.
<br>>
<br>> I do not subscribe to that forum so I don't have available the
<br>> subscription address for you. I'm hoping someone with this (FractInt)
<br>> mail server will read this message and tell you how to subscribe
to that
<br>> forum. I'm leaving the house now and won't be back until later this
<br>> evening. If I see that no one has provided you with the philosophical
<br>> forum e-mail address, I will get it for you from one of several people
<br>> who I know are list members.
<br>>
<br>> I think you will be well rewarded in discussing the effects of fractal
<br>> colors and shapes upon the non-fractal public in that forum.
<br>>
<br>> Best regards,
<br>>
<br>> Bob Margolis
<p>Since that message was written, I asked someone for the e-mail address
<br>of that fractal philosophy discussion group I mentioned. Here is his
<br>response:
<p>Bob,
<p> - What is the e-mail subscription address for the fractals philosphy
<br> - group?
<p>[e-mail]
<p>So if you want to subscribe, send mail to this address:
<p>[e-mail]
<p>...and follow the instructions you're sent.
<p>Damien M. Jones   \\
<br>[e-mail]  \\  Fractalus Galleries & Info:
<br>
\\  <a href="http://www.fractalus.com/">http://www.fractalus.com/</a>
<p>Please do not post my e-mail address on a web site or
<br>in a newsgroup.  Thank you.</blockquote>
</html>


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

Date: Mon, 16 Oct 2000 21:09:25 -0400
From: "Damien M. Jones" <[e-mail]>
Subject: Re: (fractint) Fractal greeting cards

Morgan,

 - > Sweetests Day, Oct. 21
 - > in the States.
 - >
 - Never head of it, myself.

It's a new "holiday" cooked up by various commercial interests to be a fall
Valentine's Day. It's so commercialized right from the start it makes me
gag, but I had one woman tell me flat-out that she didn't care, an excuse
for her man to be thinking of her was what mattered.

*sigh*

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: Mon, 16 Oct 2000 21:09:29 -0400
From: "Damien M. Jones" <[e-mail]>
Subject: Re: Re: Re: Re: [Fwd: (fractint) Another fractal greeting card URL]

D. Freed,

 - I am - thank you very much - fully aware of the other
 - discussion groups, Damien- and non-Damien-associated, and
 - intentionally steer a wide course around them - although I
 - enjoy Jim Muth's contributions.

Then you need not fear the philofractal list. Although it runs through my
server, I don't personally run it. In fact I'm not even a subscriber.

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



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

Date: Mon, 16 Oct 2000 21:07:16 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD  17-10-00  (A Nice Fractal Midget [8])

FOTD -- October 17, 2000 (Rating 8)

Fractal visionaries and enthusiasts:

In the world of science, things that are long assumed to be true
sometimes prove to be untrue.  Why should fractals be any
different?  Take for example the often stated assumption that
there are many Julia sets but only one Mandelbrot set.  Even
when the perturbed Mandelbrot sets are ignored, this assumption
is untrue.  It is untrue because there are at least two 'true'
Mandelbrot sets, with all their parts intact.

The familiar M-set cuts through the four-dimensional Julibrot
along the plane where Z equals zero.  But there is a second
slice that cuts through the Julibrot in a perfect M-set -- the
plane where the values of Z and C are equal.

This second M-set, which I call the shadow set, is oriented
exactly halfway through the double rotation between the
Mandelbrot orientation and the Julia orientation.  It lies at an
absolute angle of 45 degrees to the classic M-set, every line in
the shadow set lying at an angle of 45 degrees to every line in
the classic set.

This shadow set appears exactly like the classic set, though its
linear dimensions are 1.4 times those of the classic set and its
associated perturbed sets are strangely different.  And yes, it
is possible to enlarge its features to 1.4 times the size of the
identical features in the classic set before reaching the limit
of math precision.

Is this second M-set the only oblique Julibrot slice that gives
a spurious Mandelbrot set?  I think so, but I'm not sure.  One
of these days I'll do some serious investigating, perhaps along
the surface where Z equals the square root of C, but for the
present I've got a rather exceptional FOTD to talk about.

The math expression that drew the image is a totally whimsical
journey into the land of fractional negative exponents.  A quick
check of the parameters will show the exact values.

Try as I might, even after spending 1/2 hour coloring the
picture, I could think of no suitable name for it, so I settled
on the generic description "A Nice Fractal Midget".  A second
look convinced me that the rating of an exceptional 8 is fully
justified.

The parent fractal is the latest in my series of 'parent'
images, which are characterized by a prominent 'fan' and lots of
rings.  The scene of today's image is located at the edge of the
fan.

The parameter file takes 9-1/2 minutes to render, making a
download of the GIF image file the wise choice.  The image file
has been posted to the Usenet binary group:

          alt.binaries.pictures.fractals

and to Paul Lee's web site at:

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

The fractal weather today was less perfect than yesterday, but
still perfect enough to keep the cats happy.  The partly cloudy
skies and temperature of 73F (23C) lured them onto the porch,
from where they bounded down into the grass to chase butterflies.

The philosophy is smouldering, and could burst into flames at
any time.  I'm currently pondering the relation between fractals
and the mind.  Something may come of my thoughts, or perhaps
nothing will.  Regardless, I'll be here again tomorrow with
another fractal and more gossip.  Until then, take care, and be
happy in your fractaling.


Jim Muth
[e-mail]


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

A_NiceFractlMidget { ; time=0:09:36.66 -- SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+4.39976788244362300/+0.25116878814085030\
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  Yhx<4>Mgx
  }

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, 17 Oct 2000 22:05:02 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD  18-10-00  (A Fractal Gone Batty [6])

FOTD -- October 18, 2000 (Rating 6)

Fractal visionaries and enthusiasts:

That time of the year is fast approaching when we turn our
thoughts to the supernatural world of witches, vampires,
mummies, wolf-men, ghosts, and monsters of various and sundry
appearances.  Of course, we know that these things are mere
entertaining distractions, and fun for children.  They certainly
do not actually exist -- well, after seeing today's picture, I
should change that statement to they *almost* certainly do not
exist.

Today's fractal image is a serendipitous discovery.  I zoomed in
on the wrong area by mistake, but my mistake turned out to be no
mistake, for there in an area I would never have suspected of
harboring a midget, I found today's image.

After a few minutes of coloring the picture, I settled on the
present palette.  I studied the image for several more minutes
before recognizing the spooky aura to the scene.  Those dark
sharp-angled shapes floating around the midget could be vampire
bats out for a quick snack.  Or the shapes could be a group of
less-sinister bats flitting before the midget, which could well
be a full moon.  Regardless, I named the picture "A Fractal Gone
Batty".

The parameter file renders in a slow 14-1/2 minutes.  Since the
GIF image file downloads in only one minute, I strongly
recommend going to Usenet at:

          <alt.binaries.pictures.fractals>

or to the Web at:

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

where the GIF file has been posted, and downloading it from
there.

The fractal weather today was cloudy, with just enough rain to
dampen the grass.  The wet grass, along with a temperature of
59F (15C), confined the fractal cats to the indoors, where they
managed to pass the day sleeping.

I've still got the fractal philosophy on hold, while I work up
the energy for a major eruption.  But before I philosophize, I
must decide exactly what fractal philosophy is.  I'll have at
least 24 hours to make that decision.

Until next time, which by a rare coincidence will be in 24
hours, take care, and why do we enjoy fractals?


Jim Muth
[e-mail]


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

A_FractalGoneBatty { ; time=0:14:32.72 -- SF5 on a P200
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  formulaname=MandelbrotMix4 function=recip passes=1
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  }

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, 18 Oct 2000 01:20:23 -0400
From: JoWeber <[e-mail]>
Subject: (fractint) updated website

Hi All,

I rebuild my website for faster loading and easier navigation and added a=

lot of new stuff.
Feel free to visit it, comments are welcome.

Cheers --Jo Weber--

http://www.joweber.de

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

Date: Thu, 19 Oct 2000 01:08:41 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD  19-10-00  (Convoluted Fractal [5])

FOTD -- October 19, 2000 (Rating 5)

Fractal visionaries and enthusiasts:

Things got a little busy again today here at Fractal Central,
which doubles as a graphic design shop when it's not busy being
the fractal shoppe.  With enough work to keep me hopping like a
rabbit, I found little time to search for fractals, but in the
brief time I found, I generated the sqrt(Z)+C Mandeloid.

The default image of this expression drawn by the MandelbrotBC
formula is quite interesting, with a spectacular main stem
extending well beyond the default screen, and many promising
side filaments.  I did my searching along one of these side
filaments.

The midgets become quite difficult to locate when the exponent
of Z is much less than two.  In these cases, the filaments are
the easiest places to find the midgets.  As is the case with
midgets in all low-order fractals, the midget in today's image
is surrounded by sharp, almost dagger-like discontinuities,
though the sharpness is somewhat offset by the mass of convolu-
ted, twisting filaments.

When I saw the convolutions, I named the picture "Convoluted
Fractal" and gave it the honor of being a FOTD.  The 7-minute
render time is a bit excessive for an image that rates only a 5.
Therefore, my advice is to go to the Usenet group:

          <alt.binaries.pictures.fractals>

or to Paul Lee's web site at:

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

and download the GIF image file from there.

The fractal weather today was rainy in the morning, followed by
a clearing in mid-afternoon.  Despite the late sun and tempera-
ture of 66F (19C), the grass remained too wet for the fractal
cats, who amused themselves indoors by sleeping and eating.

My fractal philosophy remains suppressed, but may arise at any
moment.  Don't miss tomorrow's FOTD.  If the philosophy rises
between now and then, you'll want to be in on the action.

And that's it for this evening fractal fans.  Until next time,
take care and fractals are just as real as we make them.


Jim Muth
[e-mail]


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

Convoluted_Fractal { ; time=0:07:13.72 -- SF5 on a P200
  reset=2001 type=formula formulafile=branchct.frm
  formulaname=MandelbrotBC passes=1
  center-mag=-0.84997772846451300/+0.37369015583381380\
  /11165.74/1/140 params=1.414213762373/0/0/0 float=y
  maxiter=15000 inside=0 logmap=130 periodicity=10
  colors=000IEcICc<3>FCcHE_JFYKFUMGRNGPPHPQKMRLJTMHUOD\
  WQBYS8YUB<3>YYIYZJY_MY`NY`PY`QZ`TZ`UZ`WZ`Y``_```````\
  ``abcabdacfacgacjadkbdlccmbao<3>cVrcTrcRsdQudOueNveK\
  weJweGxfGyfDy<2>g9zhByiDwhEuiGrjHqjKokLllNjlOimQgoSe\
  <2>qYbq``r`ZsbXscWudTveRvgPwhOxjL<2>ynG<4>zaIzZJzXJz\
  ULzSLzOLzNMzJLzHLxIKwIKvIIuHI<3>pIHoIGlIGkIGjHE<2>fI\
  DeIDdIBcHB`HB_IAZIAYI9WH8VH8UH8TI7QH6NG6KE5ID4<2>A92\
  8817817916A06C07E0<3>7J06K05L07O09Q2BR3CT4FR5GT7<2>L\
  UAMUBPUDQUESUFTTGVUIWUIZWJ<5>h`RjaTlcUmcVpdXqeYsfZuf\
  `whaxhb<11>wpfwqgwrg<2>wthwthvtj<3>vvkvwkwxlwxlwylwz\
  n<3>xzoxzoxzpxzpxznxzluziozg<3>VzXPzVIzS<2>MzMOzOQzP\
  QzQ<2>UzSWzTXzV<4>bz_dz`dz`<3>jzflzgmzh<2>pzlqzmrzm<\
  2>pzq
  }

frm: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|<100
}

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


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Date: Thu, 19 Oct 2000 01:40:32 -0400
From: Mike Traynor <[e-mail]>
Subject: Re: (fractint) updated website

Jo,
>
> Hi All,
>
> I rebuild my website for faster loading and easier navigation and added a
> lot of new stuff.
> Feel free to visit it, comments are welcome.

This one will be:  Those mandelbrot zooms are AMAZIMG!!! Wonderful colour!

Mike

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

Date: Thu, 19 Oct 2000 01:45:01 EDT
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) FOTD 19-10-00 (Convoluted Fractal [5])

For some reason, this one isn't linked from the October 2000 index page.
However, it's still accessible by directly punching in the filename. (Using
the URL for yesterday's and a little prestidigitation...)
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------------------------------

Date: Thu, 19 Oct 2000 00:51:40 -0500
From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) FOTD 19-10-00 (Convoluted Fractal [5])

Multiple Bogeys wrote:
>
> For some reason, this one isn't linked from
> the October 2000 index page.

Yes, it is.    :-)

>
> However, it's still accessible by directly
> punching in the filename.

You might try refreshing your browser's cache.  Both pages get uploaded
at the same time, and tested afterwards.

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

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

Date: Thu, 19 Oct 2000 09:06:43 -0500
From: Bob Margolis <[e-mail]>
Subject: (fractint) Rayleigh Quotient iteration

Are any of the formulas writers among you familiar with the Rayleigh
Quotient iteration?

I was reading a four-page article about it last night in Chaos and
Fractals: A Computer Graphical Journey, which came out two years ago and
was edited by Clifford Pickover.

The article says, "The Rayleigh Quotient Iteration is a numerical
technique for estimating eigenvalues. It typically converges to an
eigenvalue quadratically, but the convergence is cubic when the matrix
is Hermitian. While there is a sense of unpredictability in the
convergence, distinct basins of attraction often have smooth
boundaries."

Twelve illustrations accompany the article and some of them appear to be
similar to Newton basins. The illustrations were colorful and I thought
they could lead toward interesting FractInt-generated pictures.

You can see what what I'm writing about by referring to an illustration
I found at

http://ww2.lafayette.edu/~reiterc/aa/index.html.

I found a lengthy article at http://etna.mcs.kent.edu/ In Volume 7
(1998) entitled "A Block Rayleigh Quotient Iteration with Local
Quadratic Convergence" in pdf and postscript format. I printed out the
pdf version, and, upon reading it, exclaimed, "Duhhhhhhhhhhhh."

What I was hoping to do was write a formula for FractInt based upon the
RQI, but I see my Duhhhhhhhhhh prevents that. Can anyone help me in that
regard?

Bob

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

Date: Fri, 20 Oct 2000 00:06:51 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD  20-10-00  (The Oddest Angle [4])

FOTD -- October 20, 2000 (Rating 4)

Fractal visionaries and enthusiasts:

Today's fractal is a new view of an old friend.  The friend is
the classic Mandelbrot set, which is one of only two of its
kind.  Actually, since the Z parameter is equal to the C
parameter, today's fractal is a scene in the second M-set, the
one I call the shadow set.

The strangely stretched and twisted object is an unfamiliar view
of the last midget out on the negative tail that is within reach
of the double-precision math routine.  This midget is located at
C=-1.999999117... on the tail.

When seen as a Mandelbrot midget or a Julia set, this object is
surrounded by the neat, symmetrical pattern of a midget near the
escape radius, with features bifurcating in a 2,4,8,16... series
as they approach the midget.  But today's picture is neither a
Mandelbrot midget nor a Julia set.

The plane of today's image is oriented within a few degrees of
the Rectangular direction of the Julibrot.  This Rectangular
plane is determined by imag(z) and imag(c).  At this odd angle,
(which is the name I gave to the picture), the nice neat
2,4,8... series has been stretched and twisted into a grotesque
parody of itself.  Even the 2,4,8... series has been
obliterated, and replaced by an indescribable series of ever-
smaller features.

The whole thing makes more of a mathematical curiosity than a
work of art, so I could rate the image at only a 4.  But despite
the low rating, it is not without its merit, and the render time
of 11 seconds is fast enough to make the parameter file the most
efficient way to view the image.

For those who would prefer to download the GIF image, that image
is available at:

          alt.binaries.pictures.fractals

and at:

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

The fractal weather today was perfect, with brilliant Autumn sun
and a temperature of 70F (21C), which pleased the two fractal
cats immensely.

The cats are still pleased, but they would be even more pleased
if I were to feed them, so I guess it's time to shut down the
fractal shoppe and call it a day and a night.  Until the next
time, which is coming in 24 hours, take care, and exalt in your
fractals.


Jim Muth
[e-mail]


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

The_Oddest_Angle   { ; time=0:00:11.50 -- SF5 on a P200
  reset=2001 type=formula formulafile=multirot.frm
  formulaname=multesc4-XZ-YW passes=t center-mag=-0.00\
  000000000271445/-0.00000000001024659/5.033505e+011/0\
  .07201/106.91/-79.243 params=99.3/107.3/-1.999999117\
  587294/0/-1.999999117587294/0 float=y maxiter=550
  inside=0 outside=real logmap=36 periodicity=10
  colors=000RYbXcY_jSZbJZXAUK0cMEgIRmFbqBomIUwSozkczzS\
  nrNafIOUDBF87MH4OO2SX0Vc0Zk0as0cz8RvQFqNHoMUoJZnIMmF\
  NmEOkBQkARj2F03H03I23I44J84KD4KF6MJ6NN6NQ7OU7QY7Q_8R\
  c8SgYegXci<3>RaiQaiO_iN_iMZiKZiKYjJYjjN8qNA0zw_6izez\
  0SkMKqiDvz4zgDkKKY0RJAZKKfKXmMfuMqzMoeKoJJo0J8z0Hz0N\
  w4VrBamHggNobSvYZzSczQjzNqzMvvRw<3>akwXqwRvwMzw<2>2Z\
  r0Qq0Ho0QfBZYKgOMaUMXYMRaNKf<2>N4rZDejJSvQFzX2gEifHc\
  <3>fMJfNEeMEbKDaKD_JBSoaXrbZubbwcfzeizemzfozfgsb_cZU\
  OXM8SF0QUAegQsuczDIE8JF6JF2KF0KF0MF0MF0MF0RSAVeJZrJX\
  nJUkJSi<2>Q8II8XA8j38w4Hs4Oo4Vm6bi6if6qb6w_Ayc<2>Mzm\
  QzqUzsXzv0UX6X_HYbHYbHXbFXcFXcFXcEVe<2>DVfDVfBUgBUgB\
  UgAUiASiASi8Sj8SjzzHzzJzzKwzMuwNquQnsRjqSgnUcmVajYYi\
  ZVf_RcaObbQzYNuV<2>JeNMfOOgQRiRSjR<2>_nVym8siAnfBjcB\
  eaD_ZEXXEbaUifinky6_fESaMMYUFUa8Qg2M_MkHXS0e830z87zE\
  EuIKnNRi
  }

frm:multesc4-XZ-YW {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p2, c=e*imag(pixel)+p3:
z=sqr(z)+c,
|z| < 4  }

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


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

Date: Fri, 20 Oct 2000 01:15:10 EDT
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) FOTD 19-10-00 (Convoluted Fractal [5])

>You might try refreshing your browser's cache.  Both pages get uploaded
>at the same time, and tested afterwards.

Can't be. I thought that was it, but I refreshed it twice and the link
didn't appear.
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------------------------------

Date: Fri, 20 Oct 2000 01:23:07 EDT
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) FOTD 20-10-00 (The Oddest Angle [4])

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

There's definitely something flaky about home.att.net lately. Tonight, I
clicked this link, and got an RST instead of an ACK from my SYN. When I
tried again, I got in, but the index list only went up to "Convoluted
Fractal". I refreshed it -- twice -- to no avail. Then I went to "Convoluted
Fractal", altered the URL (producing
http://home.att.net/~Paul.N.Lee/FotD/FotD_00-10-20.html), and got a 404, so
the fractal is not even there this time!

I suggest hitting the home.att.net Webmaster over the head with a nastygram,
and if the server isn't acting less flaky in a day or two, moving your site
to a more reliable and better-run host. (This, unfortunately, would probably
mean an annoyingly tedious change of ISPs -- I'd use the occasion as an
opportunity to make the changeover to broadband...)
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------------------------------

Date: Fri, 20 Oct 2000 01:31:19 EDT
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) FOTD 20-10-00 (The Oddest Angle [4])

Because of home.att.net's flakiness, I tediously copied the parameter entry,
pasted it into Notepad, saved it, and ran it to see the results...

>the render time of 11 seconds is fast enough to make the parameter
>file the most efficient way to view the image.

It took 39 seconds on my machine, at 1024x768 resolution. What resolution do
you usually use (the Web images tend to be 640x480) and what kind of
computer are you using? Mine cranks at 400 MHz and isn't a Cyrix or a
Celery...

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

Date: Fri, 20 Oct 2000 01:34:05 EDT
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) updated website

> > Hi All,
> >
> > I rebuild my website for faster loading and easier navigation and added
>a
> > lot of new stuff.
> > Feel free to visit it, comments are welcome.
>
>This one will be:  Those mandelbrot zooms are AMAZIMG!!! Wonderful colour!

Damn. I deleted the original message, now I read this and it sounds
interesting enough to be worth taking a look (in the last few years, it's
gone from too few fractal sites to find many worth looking at to too many to
exhaustively look at them all without prior indications of quality by
word-of-mouth), but Hotmail recycled the original message so I can't
retrieve it, and you didn't quote the URL. Could someone please re-post the
URL?
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------------------------------

Date: Fri, 20 Oct 2000 02:01:48 EDT
From: [e-mail]
Subject: Re: (fractint) updated website

In a message dated 00-10-18 01:21:47 EDT, you write:

<<
 Hi All,

 I rebuild my website for faster loading and easier navigation and added a
 lot of new stuff.
 Feel free to visit it, comments are welcome.

 Cheers --Jo Weber--

 http://www.joweber.de
  >>
there ya go, have fun!

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

End of fractint-digest V1 #501
******************************