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fractint-digest        Monday, October 29 2001        Volume 01 : Number 607




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

Date: Tue, 23 Oct 2001 22:22:04 +0500
From: "Tony (Anthony) Hanmer" <[e-mail]>
Subject: Re: (fractint) FOTD 23-10-01 (Maltese_Minibrot[7])

Jim, the ONLY unsuccessful thing about this image is your rating of it:  too
bad you're not as "clever" with real integers as you are with complex
numbers!  Try a 9.  I'm so glad that Sept. 11 didn't permanently knock you
out of interacting with all of us in your amazing way.  Thank you.

Tony Hanmer
Tbilisi, (Republic of) Georgia

_________________________________________________________________
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Date: Wed, 24 Oct 2001 10:58:55 EDT
From: [e-mail]
Subject: (fractint) FOTD  24-10-01  (Mandelbrot Mania [6])

FOTD -- October 24, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Once again I must let down my faithful readers, who were
(hopefully) waiting with bated breath for further adventures on
the hypersphere.  Unexpected work arrived, leaving me no time to
write.  But I did find time to dredge up a quickie fractal.

(In the future, I will not promise an article until I actually
have it written and composed.)

The formula of today's fractal subtracts 1.3 parts of Z^(0.9)
from 1.3 parts of Z^(-1.1) and adds 1/C, producing a 3-lobed
figure that is quite sensitive to the bailout radius.  The scene
of today's image is deep on the left side of the right valley.

I named the image Mandelbrot Mania because of the appearance of
the parent fractal more than the appearance of the image itself.
I rated it a 6 because it's a little better than a 5 and not
quite worth a 7.  The render time of 44 minutes is a bit much to
ask for an image that rates only a 6, so I recommending
downloading the GIF image from:

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

or from:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

where the image will soon be posted.

The day began cloudy and foggy here at Fractal Central, but by
noon the sun burned off the dampness, leading to a warm
afternoon with a temperature of 79F 26C.  The fractal cats
enjoyed much of their time outdoors, but still managed to find
something to fight about.  All ended well however, with the
dynamic duo sleeping together peacefully on the porch.

(For a bit of philosophy, check the philofractal list.)

With a day's work waiting to be done, I must now close the FOTD
and get busy on other matters.  But I'll return in the proper
time.  Until then, take care, and hope for the best.


Jim Muth
[e-mail]


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

Mandelbrot_Mania   { ; time=0:45:23.09--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.07345537336418037/+0.042097568866235\
  17/3.724103e+007/1/-115.000000007003862/5.70113192\
  766008581e-009 params=1.3/-1.1/-1.3/0.9/0/50
  float=y maxiter=6000 inside=0 logmap=745
  colors=000WffVjmVjkVjjUjiUjhUkfTkeTkdTkbSkaSk`Sk_R\
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  zRjzSjzTjzUjzVjzWjzXizWjz
  }

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: Thu, 25 Oct 2001 09:39:11 EDT
From: [e-mail]
Subject: (fractint) FOTD  25-10-01  (Threads of Infinity [6])

FOTD -- October 25, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

It's another very busy day here at Fractal Central, which means
another brief FOTD discussion.  I view such days with mixed
emotions, of course.  On the one hand, busy days mean more money
to buy a faster fractal-finding machine, but on the other hand,
busy days mean little time to actually search for the fractals.

Also due to the rush, the continuation of the misadventures on
the hypersphere will have to wait at least two more days.

Today's fractal, which takes 13 minutes to render, took about
1/2 hour to find.  This is about the average time that passes
between going into fractal mode and actually finding the midget
of the day.  To this time must be added the render time of the
image.  Luckily, I can write the discussion on a separate
machine.

The formula that created today's image takes 10 parts of 1/Z and
subtracts one part of Z before adding 1/C.  The resulting parent
fractal appears as a half-obscured Mandeloid standing on its
nose.  The midget in today's image is located in a spiral on the
left shore of the East Valley of the Mandeloid, which in today's
case is actually a North Valley.

The elements of the spiral are unusually rope-like, inspiring
the name "Threads of Infinity".  The name also could have been
inspired by the name of an old TV program about fractals, which
is titled "Colors of Infinity".

The image rates a 6, and renders in 13 minutes.  The GIF image
downloads in only one minute.  The image may be found at the
URL's:

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

and:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was very summer-like, with warm sun
and a temperature of 83F 28C.  The fractal cats, who have been
quarreling lately, enjoyed an afternoon in the yard, and
actually managed to get through the entire afternoon without
getting into a fight.

And I'm about to 'enjoy' a busy day, so until next FOTD, take
care, and the less you try to make sense of things, the more
sense they'll make.


Jim Muth
[e-mail]


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

ThreadsOf_Infinity { ; time=0:13:19.83--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-0.00007793807533362/+0.112392194825511\
  90/5.776346e+008/1/22.5000000881690916/-2.05411887\
  214956845e-007 params=10/-1/-1/1/0/0 float=y
  maxiter=1200 inside=0 logmap=178
  colors=0000JdTWYegThfMldHpcAsc5ig6`j6VgCOdHIbMC`Q5\
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  TjuVkuWluXmuYou_pu`quasuctudvudvudvudvudvudvudvudv\
  udvudvudvuevugvuhvuivukvu
  }

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

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

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

Date: Fri, 26 Oct 2001 11:06:45 EDT
From: [e-mail]
Subject: (fractint) FOTD  26-10-01  (A Chilling Chiller [6])

FOTD -- October 26, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Another rushed day brings another short discussion.  I gave
today's image the name "A Chilling Chiller" because of the
somewhat ominous feeling it produces.  This effect would work as
the starting point for the cover of a cheap horror novel.  The
brownish elements around the midget, with their sharp points,
have a vague resemblance to a colony of roosting bats, and with
the lack of strong reds, the remaining blues and greens add to
the ominous overall feeling.

The formula of the parent fractal is a simple Z^(2.1)+C, with
the resulting figure being sliced a bit up the infinite
logarithmic spiral.  The rating of 6 is perhaps a bit high for
this hasty image, which rendered while I tended to other tasks.
The render time of 34 minutes is slow enough to make a trip to
Paul's web site at:

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

or Scott's site at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

worth the effort.

The fractal weather today was once again summer-like, with blue
skies and a temperature of 77F 25C.  But the brisk winds had the
fractal cats uneasy, cutting their outdoor time by well over
half.

It's now time to return to the daily grind, and do what needs to
be done.  One of these days I'll get around to that hypersphere,
but today is not the day.  I shall return tomorrow however, with
the next FOTD.  Until then, take care, and worry not.  (If
possible)


Jim Muth
[e-mail]


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

A_Chilling_Chiller { ; time=0:34:43.34--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=1
  center-mag=-0.47311802838614140/+0.585934696010908\
  20/1.223377e+010/1/-122.5000875222524/0.0002730490\
  83844949247 params=2.1/0/0/0 float=y maxiter=10000
  inside=0 logmap=790 periodicity=25
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  wDcwEcwFcwGcwGcwHcwXcwVcw
  }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a
}

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

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

Date: Fri, 26 Oct 2001 16:44:34 -0500
From: [e-mail]
Subject: Re: (fractint) FOTD  25-10-01  (Threads of Infinity [6])

> The elements of the spiral are unusually rope-like, inspiring
> the name "Threads of Infinity".  The name also could have been
> inspired by the name of an old TV program about fractals, which
> is titled "Colors of Infinity".

Was this program narrated by Arthur C. Clarke?  The first time I ever
heard of fractals was a show on PBS about them.  All I remember was a
zoom into the Mandelbrot set with Arthur C. Clarke talking.  A few months
later, I got internet access and came across a (not very good) Mandelbrot
explorer almost by accident.  I remembered the word Mandelbrot from the
show, downloaded it, and I was hooked.

If anyone can name the show based on this vague description, tell me.

Jon K.
________________________________________________________________
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------------------------------

Date: Sat, 27 Oct 2001 12:57:08 +1300
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) FOTD  25-10-01  (Threads of Infinity [6])

At 16:44 26/10/2001 -0500, [e-mail] wrote:
> > The elements of the spiral are unusually rope-like, inspiring
> > the name "Threads of Infinity".  The name also could have been
> > inspired by the name of an old TV program about fractals, which
> > is titled "Colors of Infinity".
>
>Was this program narrated by Arthur C. Clarke?  The first time I ever
>heard of fractals was a show on PBS about them.  All I remember was a
>zoom into the Mandelbrot set with Arthur C. Clarke talking.  A few months
>later, I got internet access and came across a (not very good) Mandelbrot
>explorer almost by accident.  I remembered the word Mandelbrot from the
>show, downloaded it, and I was hooked.
>
>If anyone can name the show based on this vague description, tell me.

"Colours of Infinity: Exploring the Fractal Universe", published in 1994
(with a soundtrak by David Gilmour). It grew out of a speech Clarke had
given in 1989.

An extract of the speech is at the end of Clarke's 1990 novel _The Ghost
 From the Grand Banks_, where he introduces it thus:

In November 1989, when receiving the Association of Space Explorers'
Special Achievement Award in Riyadh, Saudi Arabia, I had the privilege of
addressing the largest gathering of astronauts and cosmonauts ever
assembled at one place. (More than fifty, according to Apollo 11's Buzz
Aldrin and Mike Collins, and the first "space walker" Alexei Leonov, who is
no longer embarrassed at sharing the dedication of _2010: Odyssey Two_ with
Andrei Sakharow.) I decided to expand their horizons by introducing them to
something _really_ large, and, with astronaut Prince Sultan bin Salman bin
Abdul Aziz in the chair, delivered a lavishly illustrated lecture "The
Colours of Infinity: Exploring the Fractal Universe".
The material that follows is extracted from my speech; another portion
appears at the beginning of Chapter 15. I'm only sorry that I cannot
illustrate it with the gorgeous 35-millimetre slides - and videos - I used
at Riyadh.

Try "http://klru.worldpost.com/publicarea/ViewProgram.asp?VsnID=45398"

Morgan L. Owens
"Yet the most astonishing feature of the M-set is its basic _simplicity_."



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Date: Fri, 26 Oct 2001 20:38:50 -0500
From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) FOTD  25-10-01  (Threads of Infinity [6])

[e-mail] wrote:
>
> Was this program narrated by Arthur C. Clarke?
>    ........
> If anyone can name the show based on this vague
> description, tell me.

I acquired a copy of the video quite some time ago, but I hear that it
can now be purchased from the following (at a much higher price):

         http://www.films.com/item.cfm?bin=4976

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

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

Date: Sat, 27 Oct 2001 10:17:12 EDT
From: [e-mail]
Subject: (fractint) FOTD  27-10-01  (Electric Minibrot [9])

FOTD -- October 27, 2001 (Rating 9)

Fractal visionaries and enthusiasts:

Due to the continuing rush, the discussion will once again be
short.  But the rush is nearly finished, so hopefully, in the
next FOTD, I'll return to the hypersurface (curved 3-D space) of
the hypersphere to explain how one might find their way from one
place to another.  Today's FOTD is not a total loss however, for
the image is one of the select few to have rated a 9.

The formula behind the image adds a tiny negative portion of 1/Z
to a much larger portion of Z, then adds 1/C.  The resulting
parent fractal is a curious Mandeloid with broad bands of chaos
on its east side, but only very narrow bands on its west side.
Today's midget is located near the tip of a meandering, curving
chaotic area in the narrow band of chaos on the northwest shore
of the main west bud.

I named the picture "Electric Minibrot" when the zig-zag
filaments reminded me of stylized lightning.  The glowing white
balls could also be seen as samples of those rare glowing blobs
of plasma known as ball lightning, which by the way I have never
observed.

Whether the rating of 9 is justified is up to the viewer to
decide.  The 13-minute, 13-and-13-hundredths seconds render
time, which consists of a string of unlucky 13's, is a bit slow.
The wise and lucky choice would be to download the GIF image
from:

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

or from:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today (Friday) here at fractal central was
chilly and blustery.  The temperature of 59F 15C was not too
cold, but combined with the brisk wind, it was enough to keep
the sensitive cats house bound.  The cats got grouchy.

As for me, I'm going to wrap up the last of the serious work so
that I can get to the even more serious work of searching for
the next fractal.  That next fractal will appear as tomorrow's
FOTD.  Until then, take care, be patient, but not so patient
that you become a patient.


Jim Muth
[e-mail]


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

Electric_Minibrot  { ; time=0:13:13.13--SF5 on a P200
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  formulaname=MandelbrotMix4 function=recip passes=1
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  OgNNgRMhWLh_KicJigIjhPjiWkjbkkillpllwkfojahiWahUVg\
  UOfUHeUAdU3eU5fT7gW9gYAh_CiaEicGjeHkgJkhLliNmjOnkQ\
  nlSomUpnVpoXqpZrq`rrassastasuatvatwatxarybqzcpzdoz\
  enzemzflzgkzhKzVGzQBzM6zI
  }

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: Sun, 28 Oct 2001 09:56:52 EST
From: [e-mail]
Subject: (fractint) FOTD  28-10-01  (Midget in the Woods [8])

FOTD -- October 28, 2001 (Rating 8)

Fractal visionaries and enthusiasts:

My first impression of today's fractal scene was one of a mass
of dense alien foliage, perhaps starting to turn yellow with the
approach of alien Autumn.  Then, when I saw the Mandelbrot
midget in the midst of the brush, I named the image "Midget in
the Woods".

The most unusual feature of the 8-rated image may be the totally
different nature of the areas north and south of the midget.
North of the midget, the surroundings appear solid, like a more
or less normal fractal scene.  But to the south, the features
resemble an archipelago of islands interlaced with open areas of
water.  The dividing line cuts straight through the center of
the midget.

This dividing line is explained by examining the parent fractal,
which is a circular open hole filled with fractal debris.  The
chains of debris extend beyond the open area and continue well
into the solid area surrounding the hole.  The size of the hole
is dependent on the bailout, which is specified by the imag(p3)
parameter.  The greater the bailout value, the larger the hole.

Knowing that the size of the hole varies with the value of the
bailout, I found it simple to take a reasonably interesting
midget on the outside of the open area and increase the bailout
until the edge of the open area expanded to cut straight through
the center of the midget.  It took a few trials to find the
exact bailout, but the image is a very fast one, so this was no
problem.  Once I had fixed the bailout, it was only a matter of
finding a reasonable color palette.

Not counting the set-up time, the attached parameter file runs
in 1-1/2 minutes.  Not counting the time required to go on-line,
retrieving the GIF image will take about the same time.  Those
who decide to download the GIF image will find it waiting at:

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

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

But before going there, give Paul and Scott a few minutes to
render and post the image.

The fractal weather today was quite chilly, with brisk winds,
heavy clouds, occasional spits of rain, and a temperature of 52F
11C.  These conditions limited the fractal cats to only a few
minutes outdoors, but they didn't complain too much, and were
actually rather refined cats most of the day.

I've been thinking much (a rare event) about the fourth
dimension and the hypersphere lately, and have decided that the
best place to start is at the surface.

The surface (or hypersurface) of a hypersphere is a three-
dimensional space of constant positive curvature.  Limited
portions of this curved space appear exactly like our familiar
'real' space, though as the range of vision grows larger,
strange differences appear.

One of the most intuitive features of the 'real' world is that
the farther away an object lies, the smaller it appears, until
it finally disappears altogether.  To our everyday minds, it
must be this way.  Common sense dictates that it could not
possibly be any other way.

If our space were the surface of a hypersphere however, common
sense would lead to a wrong conclusion.  An object would first
appear smaller with increasing distance in the expected manner,
but then, once it passed beyond a distance of one quadrant (90
degrees), it would begin to appear larger, until it reached the
antipode (opposite point) of the hypersphere, when the object
would appear horrendously magnified, surrounding us in all
directions.

Of course, the motion of objects, the finite speed of light, and
the ripples in space caused by the presence of mass would
prevent the ultimate view from being the back of our own head.
But the apparent increase in size with increasing distance
should easily be observable.

To my knowledge, we have not observed this effect in our
universe.  This may be because we cannot observe a large enough
volume of space, but most likely it is because our universe is
not shaped like the hypersurface of a hypersphere, but rather
more like a pseudosphere.  But a pseudosphere is a different
animal entirely, which makes a different story.  We'll not get
into that story -- at least not yet.

In the next FOTD I'll lay out the latitude, longitude and
altitude grid on the hypersurface of a hypersphere.  Until then,
when we'll all have our bearings, take care, and don't get lost.


Jim Muth
[e-mail]


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

MidgetInTheWoods   { ; time=0:01:31.61--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+1.81788303560401100/+0.010023098963900\
  95/3360.9/1/80.0000000001628422/-1.592690701546217\
  72e-010 params=1/-1.5/2/-15/0/245400000 float=y
  maxiter=275 inside=0 logmap=20
  colors=000dSWh`XifVilTjrRjxPdrM_lJVfHP`EKVCFP9AJ7I\
  J6QJ5YJ4jJ3rJ3zP7mUAgZDedHciKbnNWgOQaPKWQJTRIRSHPT\
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  izbjzclzdmzfnzgozhpziqzjrzkkzldzmbzn`znZzoXzoVzpUz\
  pSzqQzrOzrMzsLzsJztHztFzuDzuCzvDzvEzwFzwGzxHzxIzyJ\
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  hQzcXzZbzUizPozNpzKqzIrzGszDtzBuz9vzJmzTezaYzXUzTR\
  zPOzLKzHHzDEz9BzCEzEGzGIzIKzKMzMOzOQzQSzSUzUWzWYzY\
  _z_bzadzcfzehzgjzilzknzmp
  }

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: Sun, 28 Oct 2001 16:39:02 -0500
From: "Phil DiGiorgi" <[e-mail]>
Subject: (fractint) Fractint on Windows XP

Is it possible?   I've been unsuccessful so far.   I still have a win 98
partition I can boot with, but don't need it for anything else anymore.

Anyone?



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

Date: Mon, 29 Oct 2001 13:09:38 +0000
From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) FOTD 28-10-01 (Midget in the Woods [8])

>From: [e-mail]
>Reply-To: [e-mail]
>To: [e-mail]
>CC: [e-mail]
>Subject: (fractint) FOTD  28-10-01  (Midget in the Woods [8])
>Date: Sun, 28 Oct 2001 09:56:52 EST
>
>FOTD -- October 28, 2001 (Rating 8)

encore! encore!

Thanks.
Andrew.


_________________________________________________________________
Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp


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

Date: Mon, 29 Oct 2001 10:54:39 EST
From: [e-mail]
Subject: (fractint) FOTD  29-10-01  (Randomized Colors [6.5])

FOTD -- October 29, 2001 (Rating 6-1/2)

Fractal visionaries and enthusiasts:

I named today's image for its basically random color palette.
Except in the areas near the center, where I emphasized the
midget's surroundings with a soft green glow, the entire scene
is colored with one on the random palettes created with the
<enter> key.  The resulting fractal is vivid, though the
disorganization of its colors holds its rating to no more than
a 6-1/2.  The name "Randomized Colors" needs no explanation.

The parent fractal of today's scene has perhaps the most
irregular shape that I have yet come upon, and likely will
produce several more FOTD's before being discarded to the
fractal archives.  It is well worth an outzoom and a look.  But
before doing an outzoom, reset the logmap to 0.

The 17-minute render time from the attached parameter file is a
bit trying.  The better choice is to download the GIF image from
Paul's web site at:

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

or from Scott's site at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

With the fractal image under control, it's time to return to the
four-dimensional abstraction known as the hypersphere.  Like a
spherical 3-D planet, a hyperspherical 4-D planet has an
equator, a great circle that lies in the plane of rotation.  But
unlike a 3-D planet, a hyperplanet also has a polar great
circle.  This polar circle marks the axis of rotation.  As the
hyperplanet rotates, the points of the equator rotate in the
normal 3-D manner, but every point along the polar circle turns
on itself, remaining fixed in position exactly like the two
polar points of earth.

In the case of a 3-D planet, the rotation is simple.  Due to the
gyroscopic effect, the axis and its orientation will remain
fixed unless an outside force is applied, which will cause the
axis to rotate.  With a 4-D hyperplanet however, the situation
is far more complicated.  The simple single rotation is a
special idealized case, which would almost never be realized.

The complication lies in the polar circle, which, even while
acting as the axis of rotation of the equator, may itself begin
rotating exactly as the equator is already doing, putting the
hyperplanet into an entirely new state known as a double
rotation.  If the two rotations are equal, every point of the
hyperplanet but the center point moves in a circle, while the
center point remains fixed.  If the rotations are unequal, every
point spirals around and moves along a circular line, in a screw
motion, tracing out a path known as a surface of double
revolution, which is a two-dimensional surface curved in four
dimensions.  This surface somewhat resembles a doughnut.  This
hyperdoughnut shape is also the shape of the latitude surfaces
of a hyperplanet.  And in the next FOTD we'll actually lay out a
latitude, longitude and altitude grid on our hyperplanet.

The fractal weather today (Sunday) was brilliantly sunny but
with a chilly temperature of 51F 10.5C.  The winds were lighter
however, and this permitted the fractal cats to sleep for over
an hour in the warm sun of the porch.

Unfortunately, being neither a fractal nor a cat, I cannot sleep
in the sun.  Instead, I find myself with a day's work that needs
to be done before I turn to the fantasy world of fractals and
hyperspace.  But despair not, for the probability is 99.975325
percent that I shall return tomorrow around this same time with
another glorious fractal and a few words not quite as glorious.
Until then, take care, and if you take perfect care, nothing
more will be needed.


Jim Muth
[e-mail]


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

Randomized_Colors  { ; time=0:16:53.15--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-1.02460269414871400/+0.015803598960749\
  27/7397888/1/37.5000008972091194/-4.40023098798036\
  916e-007 params=0.439/2.466/1.265/1.372/0/0
  float=y maxiter=1800 inside=0 logmap=315
  colors=000PcnLXcHPUCKKXEco7vz1zl0rU0Y90CMEMYRVhcds\
  olZprFrw7nz1kz0nz0pz4050as0O`09HdzhIcL0zz0iw0Uc0CI\
  FKAzszzdxdPdI9ILzv7`SzH2wA0c40I00UaSCICPmXAIEziMoU\
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  00R0MezFUl9IX15E91r40c10P00AKAz71c0Ve0CKzzaHzV5XE7\
  t41R01zzszz`peHOKzz1sp0RO0zKnwC`c5OI09rF7P417zc2dP\
  0IAE1a90R40H0055IV19K017zCpi5YL0FIV0CL05C0020OcgHK\
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  gzzzzzvzwazcHzIOzsEz`4zHczpzzMezEKz4SzzSzdHzP5zAzz\
  0azxRzhHzU5zC0zzzz`czHzzt
  }

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, 29 Oct 2001 21:59:44 +0100
From: Guy Marson <[e-mail]>
Subject: Re: (fractint) Fractint on Windows XP

At 16:39 28/10/01 -0500, you wrote:
>Is it possible?   I've been unsuccessful so far.   I still have a win 98
>partition I can boot with, but don't need it for anything else anymore.
>
>Anyone?

but Fractint don't run very fast under Win XP, I must push [Enter] when
generating a fractal, then it run fast for c. 10 lines and slow down until
the next [Enter] get pushed...

cheers,


Guy

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

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

Date: Mon, 29 Oct 2001 17:35:31 -0500
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) FOTD 23-10-01 (Something Different [7])

- ------=_NextPart_001_0001_01C160A0.1BF724A0
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<snip>

Two problems with that description. First of all, if a hyperplanet accret=
ed in 4-space it would most probably have angular momentum about every po=
ssible axis -- a rotation matrix like

| cos a   sin a       0       0|
|-sin a   cos a       0       0|
|     0       0   cos b   sin b|
|     0       0  -sin b   cos b|

describes a rotation a 4-sphere with no fixed points on the surface. Such=
 a planet would have no poles at all.

The more serious problem is that it would spiral into its sun in finite t=
ime, or spiral away into deep space. There are no stable orbits in a four=
- -space (inverse-cube) gravity.<br clear=3Dall><hr>Get your FREE download =
of MSN Explorer at <a href=3D'http://go.msn.com/bql/hmtag_itl_EN.asp'>htt=
p://explorer.msn.com</a><br>

- ------=_NextPart_001_0001_01C160A0.1BF724A0
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV><snip></=
DIV> <DIV> </DIV> <DIV>Two problems with that description. First of =
all, if a hyperplanet accreted in 4-space it would most probably have ang=
ular momentum about every possible axis -- a rotation matrix like</DIV> <=
DIV> </DIV> <DIV>| cos a   sin a    &n=
bsp;  0       0|</DIV> <DIV>|-sin a&nb=
sp;  cos a       0   &n=
bsp;   0|</DIV> <DIV>|     0   &n=
bsp;   0   cos b   sin b|</DIV> <DIV>| =
;    0       0  -s=
in b   cos b|</DIV> <DIV> </DIV> <DIV>describes a rotation=
 a 4-sphere with no fixed points on the surface. Such a planet would have=
 no poles at all.</DIV> <DIV> </DIV> <DIV>The more serious problem i=
s that it would spiral into its sun in finite time, or spiral away into d=
eep space. There are no stable orbits in a four-space (inverse-cube) grav=
ity.</DIV> <DIV> </DIV></BODY></HTML><DIV><BR><br clear=3Dall><hr>Ge=
t your FREE download of MSN Explorer at <a href=3D'http://go.msn.com/bql/=
hmtag_itl_EN.asp'>http://explorer.msn.com</a><br></DIV>

- ------=_NextPart_001_0001_01C160A0.1BF724A0--

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End of fractint-digest V1 #607
******************************