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fractint-digest       Thursday, January 29 1998       Volume 01 : Number 090




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

Date: Sat, 24 Jan 1998 01:35:23 -0600
From: "Justin A. Kolodziej" <[e-mail]>
Subject: Re: (fractint) Duplicate messages (DUPLICATE)

Gedeon Peteri wrote:

> These past couple of days I received approximately 20 messages which
> were duplicates of postings I already received once several days ago.
> And they keep coming; two just this morning. The duplicates do not bear
> current dates, but those of the original posting. Is anyone else
> experiencing this phenomenon?
> Gedeon

Yep, this is a duplicate.  Here's my new theory now that the Netscape one
is shattered...

"I repeat myself when under stress
I repeat myself when under stress
I repeat myself when under stress
I repeat myself when under stress
I repeat myself when under stress" -King Crimson, "Indiscpline"


> -
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- --
Justin A. Kolodziej
Why pay for an OS when you can get a clearly superior one for free?
Justin Kolodziej is [e-mail]
Marquette University is www.mu.edu




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

Date: Wed, 28 Jan 1998 17:11:34 -0600
From: "Tim Wegner" <[e-mail]>
Subject: (fractint) Hi Folks

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Date: Wed, 28 Jan 1998 15:46:08 -0800
From: "Jay Hill"<[e-mail]>
Subject: (fractint) Is this still a great list or what?

Hi Fractintiers,

You can still follow the adventures of Dr. J, the mad scientist of
fractal space at

http://home.san.rr.com/jayrhill/FotN/FotNindx.html

Last we heard he may have over consumed on some beverage
after the FractoBowl Game.

Hopefully there are some useful formula hints there from
someone who is also learning about this from this list.

Enjoy
Jay




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

Date: Wed, 28 Jan 1998 18:59:38 -0500
From: Gedeon Peteri <[e-mail]>
Subject: (fractint) gravijul formula

Mark Christenson wrote:

> Enjoy, and please post interesting results (I already have about
> 20 of my own) !
>
>         - Bud

Bud, I liked your formula and played around with it a good bit - that
"super-generalization" you spoke of offers a lot of choices. I posted
the first four pars a few days ago, but the list was down and it did not
seem to get through. Since then I added two more. I hope you'll find
them interesting. Gedeon

==================================

Here is Mark Christenson's formula:

gravijul { ; r^(-2) Mark Christenson 1/25/98
; defaults: p1 = (1,0) p2 = (0,0) p3 = (4,0)
   z = pixel:
   w = fn1(z)
   z = fn3(p1/fn2(w*w)) + p2
    |z| < p3
  }

and six of my pars:

gp-gj09-01         { ; Mark Christenson's formula
                     ; Gedeon Peteri, Jan 25, 1998
                     ; Wizzle deeps2 map
  reset=1960 type=formula formulafile=*.frm formulaname=gravijul
  function=recip/cotan/asinh passes=b
  center-mag=4.44089e-016/-3.10862e-015/0.4026667/1/27.498
  params=4/0/0/0/2.95/0 float=y inside=epsiloncross outside=atan
  colors=000EXU<4>0IE<15>kuz<10>K0S<10>zzm<22>L29<18>\
  wwm<4>pmenkcmjblha<20>O88N76M55K33K36K29K2DK1GK0K<9>\
  cru<15>00P<7>cru<16>V3WU0US0U<9>C0U<6>c0U<18>60u40w40t\
  <11>7CI7DF7EC8F8AIBCLE<13>fzz<9>HZX
  }

gp-gj09-02         { ; Mark Christenson's formula
                     ; Gedeon Peteri, Jan 25, 1998
  reset=1960 type=formula formulafile=*.frm formulaname=gravijul
  function=recip/sin/atanh passes=b
  center-mag=1.21207/-0.721783/8.83661/1/27.5 params=1/0/0/0/2.95/0
  float=y outside=atan
  colors=0007O0uQB<16>X1wW0zX1w<22>zW0JOP<13>bfgchhbgg\
  <14>JOP00z<22>z0z<23>00zNMK<6>jjh<7>NMK0G0<6>Nh1<7>\
  0G0WWz<21>yW3zW0yW2<22>WWzV8R<6>pQk<7>V8RLLL<14>llm\
  <15>LLLzW0yU2xT5
  }

gp-gj09-03         { ; Mark Christenson's formula
                     ; Gedeon Peteri, Jan 25, 1998
  reset=1960 type=formula formulafile=*.frm formulaname=gravijul
  function=recip/cotan/asinh passes=b
  center-mag=4.44089e-016/-3.10862e-015/0.4026667/1/27.498
  params=4/0/0/0/2/0 float=y inside=epsiloncross outside=atan
  colors=000BWN8SJ4NF00c<6>0Wz<7>00cV5H<6>uVg<7>V5H0G0\
  <6>WzW<7>0G0S24<6>wRT<7>S24000<6>kkk<7>0008LM<6>Pkl\
  <7>8LMJN4<6>ntS<7>JN4L5Z<6>fQu<7>L5ZW00<6>z00<7>W0000W\
  <6>0zz<7>00WS24<6>wRT<7>S24L5Z<6>fQu<5>O8aL5ZG0W<6>\
  zWz<7>G0WIF7<6>mfU<6>MIAIF7G00<6>z00<7>G004NF<6>Wti<4>F_R
  }

gp-gj09-04         { ; Mark Christenson's formula
                     ; Gedeon Peteri, Jan 25, 1998
  reset=1960 type=formula formulafile=*.frm formulaname=gravijul
  function=recip/atanh/atan passes=t
  center-mag=-3.55271e-015/1.77636e-015/0.3743325/1/20
  params=1/0/0/0/2/0 float=y inside=period outside=atan decomp=256
  colors=G00M00G004NF<6>Wti<7>4NF00c<6>0Wz<7>00cV5H<6>\
  uVg<7>V5H0G0<6>WzW<7>0G0S24<6>wRT<7>S24000<6>kkk\
  <7>0008LM<6>Pkl<7>8LMJN4<6>ntS<7>JN4L5Z<6>fQu<7>\
  L5ZW00<6>z00<7>W0000W<6>0zz<7>00WS24<6>wRT<7>S24L5Z\
  <6>fQu<5>O8aL5ZG0W<6>zWz<7>G0WIF7<6>mfU<6>MIAIF7G00\
  <6>z00<4>Y00M00
  }

gp-gj09-05         { ; Mark Christenson's formula
                     ; Gedeon Peteri, Jan 26, 1998
  reset=1960 type=formula formulafile=*.frm formulaname=gravijul
  function=flip/flip/log passes=b
  center-mag=1.77636e-015/-6.21725e-015/0.1813158
  params=2/-1.5/0/0/8/0 float=y outside=atan
  colors=000N5B<17>wwm<4>pmenkcmjblha<20>O88N76M55\
  K33K36K29K2DK1GK0K<9>cru<15>00P<7>cru<16>V3WU0US0U\
  <9>C0U<6>c0U<18>60u40w40t<11>7CI7DF7EC8F8AIBCL\
  E<13>fzz<7>MdbKa_HZXEXUBUR8RO<2>0IE<15>kuz<10>K0S\
  <10>zzm<22>L29
  }

gp-gj09-06         { ; Mark Christenson's formula
                     ; Gedeon Peteri, Jan 26, 1998
  reset=1960 type=formula formulafile=*.frm formulaname=gravijul
  function=recip/cotan/asinh passes=b
  center-mag=-4.44089e-016/-1.55431e-015/0.9432784/1/27.499
  params=4/0/0/0/2.95/0 float=y maxiter=1023 fillcolor=255
  inside=epsiloncross outside=atan invert=0.596820086519159/0/0
  colors=000M00<5>z00<7>G004NF<6>Wti<7>4NF00c<6>0Wz\
  <7>00cV5H<6>uVg<7>V5H0G0<6>WzW<7>0G0S24<6>wRT<7>S2\
  4000<6>kkk<7>0008LM<6>Pkl<7>8LMJN4<6>ntS<7>JN\
  4L5Z<6>fQu<7>L5ZW00<6>z00<7>W0000W<6>0zz<7>00WS24\
  <6>wRT<7>S24L5Z<6>fQu<5>O8aL5ZG0W<6>zWz<7>G0WIF7\
  <6>mfU<7>IF7000
  }




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

Date: Mon, 26 Jan 1998 11:56:15 -0500
From: Gedeon Peteri <[e-mail]>
Subject: Re: (fractint) hearts and flowers

Mark Christenson wrote:

> Enjoy, and please post interesting results (I already have about
> 20 of my own) !
>
>         - Bud

Here is Mark's formula:

gravijul { ; r^(-2) Mark Christenson 1/25/98
; defaults: p1 = (1,0) p2 = (0,0) p3 = (4,0)
   z = pixel:
   w = fn1(z)
   z = fn3(p1/fn2(w*w)) + p2
    |z| < p3
  }

and four of my pars:

  gp-gj09-01         { ; Mark Christensen's formula
                     ; Gedeon Peteri, Jan 25, 1998
                     ; Wizzle deeps2 map
  reset=1960 type=formula formulafile=*.frm formulaname=gravijul
  function=recip/cotan/asinh passes=b
  center-mag=4.44089e-016/-3.10862e-015/0.4026667/1/27.498
  params=4/0/0/0/2.95/0 float=y inside=epsiloncross outside=atan
  colors=000EXU<4>0IE<15>kuz<10>K0S<10>zzm<22>L29<18>\
  wwm<4>pmenkcmjblha<20>O88N76M55K33K36K29K2DK1GK0K<9>\
  cru<15>00P<7>cru<16>V3WU0US0U<9>C0U<6>c0U<18>60u40w40t\
  <11>7CI7DF7EC8F8AIBCLE<13>fzz<9>HZX
  }

gp-gj09-02         { ; Mark Christensen's formula
                     ; Gedeon Peteri, Jan 25, 1998
  reset=1960 type=formula formulafile=*.frm formulaname=gravijul
  function=recip/sin/atanh passes=b
  center-mag=1.21207/-0.721783/8.83661/1/27.5 params=1/0/0/0/2.95/0
  float=y outside=atan
  colors=0007O0uQB<16>X1wW0zX1w<22>zW0JOP<13>bfgchhbgg\
  <14>JOP00z<22>z0z<23>00zNMK<6>jjh<7>NMK0G0<6>Nh1<7>\
  0G0WWz<21>yW3zW0yW2<22>WWzV8R<6>pQk<7>V8RLLL<14>llm\
  <15>LLLzW0yU2xT5
  }

gp-gj09-03         { ; Mark Christensen's formula
                     ; Gedeon Peteri, Jan 25, 1998
  reset=1960 type=formula formulafile=*.frm formulaname=gravijul
  function=recip/cotan/asinh passes=b
  center-mag=4.44089e-016/-3.10862e-015/0.4026667/1/27.498
  params=4/0/0/0/2/0 float=y inside=epsiloncross outside=atan
  colors=000BWN8SJ4NF00c<6>0Wz<7>00cV5H<6>uVg<7>V5H0G0\
  <6>WzW<7>0G0S24<6>wRT<7>S24000<6>kkk<7>0008LM<6>Pkl\
  <7>8LMJN4<6>ntS<7>JN4L5Z<6>fQu<7>L5ZW00<6>z00<7>W0000W\
  <6>0zz<7>00WS24<6>wRT<7>S24L5Z<6>fQu<5>O8aL5ZG0W<6>\
  zWz<7>G0WIF7<6>mfU<6>MIAIF7G00<6>z00<7>G004NF<6>Wti<4>F_R
  }

gp-gj09-04         { ; Mark Christensen's formula
                     ; Gedeon Peteri, Jan 25, 1998
  reset=1960 type=formula formulafile=*.frm formulaname=gravijul
  function=recip/atanh/atan passes=t
  center-mag=-3.55271e-015/1.77636e-015/0.3743325/1/20
  params=1/0/0/0/2/0 float=y inside=period outside=atan decomp=256
  colors=G00M00G004NF<6>Wti<7>4NF00c<6>0Wz<7>00cV5H<6>\
  uVg<7>V5H0G0<6>WzW<7>0G0S24<6>wRT<7>S24000<6>kkk\
  <7>0008LM<6>Pkl<7>8LMJN4<6>ntS<7>JN4L5Z<6>fQu<7>\
  L5ZW00<6>z00<7>W0000W<6>0zz<7>00WS24<6>wRT<7>S24L5Z\
  <6>fQu<5>O8aL5ZG0W<6>zWz<7>G0WIF7<6>mfU<6>MIAIF7G00\
  <6>z00<4>Y00M00
  }




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

Date: Wed, 28 Jan 1998 19:20:22 EST
From: Nature102 <[e-mail]>
Subject: Re: (fractint) Reuse of previous zooms

In a message dated 1-28-98 6:01:39 PM Central Standard Time, [e-mail]
writes:

<< For example, if the zoom box is half as wide and half as high as the old
 image, then one in four of the pixels in the new image have already been
 calculated.  Using some kind of guessing algorithm, most of the others
 could be worked out very quickly.

 This would make zooming into fractals a great deal faster. >>

  Well, yah, but I personally zoom in with the box as small as possible. It's
true that if you were to use a relatively big box, there would be a major
speed increase, but for small boxes, the speed increase would be negligible
::Shrugs:: Oh well. It's a cool idea. Let's bomb the Fractint people with it.
:-)

  BTW, does anyone know about how long it is between versions of Fractint on
the average? I just got into the fractal world with 19.6, so I don't really
know how often it gets updated.

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

Date: Wed, 28 Jan 1998 04:19:52 -0500
From: davides <[e-mail]>
Subject: (fractint) Re: simple par

Posting only a simple par; for whatever reason I rather like the colors in
this - something of a quiet fractal. Forward flames to your local tax
collection agency...  :)

pastel_blue2       { ; (c) Copyright David Shanholtzer, 1998
  reset=1960 type=phoenixcplx
  center-mag=0.45827/0.312116/6.94316/1.2136 params=0.2/0/0.3/0/0
  maxiter=5000 inside=255 logmap=75 decomp=256
  colors=rqvnourqv<62>6Ia5I`4H`4H`4Ia4Jb<31>CmrDnsEnr<8>TgoUgoWhp<13>vvw<1\
  5>UUhVVhWXhYZh<43>omspnspnsqotpmrokp<11>cRTZ00<11>mfjoinpmrrqvrnv<14>m0m\
  3Km<8>Ycraerdgsgjtklu
  }

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

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

Date: Wed, 28 Jan 1998 19:46:01 -0800
From: Peter Jakubowicz <[e-mail]>
Subject: (fractint) 2 Dumb ??

1)What does the Farey series have to do with the Mandelbrot set?
2)How long is the coast of the Mandelbrot set?
Thank you.


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

Date: Wed, 28 Jan 1998 16:52:11 -0800
From: "Jay Hill"<[e-mail]>
Subject: Re: (fractint) Re: simple par

David wrote

>Posting only a simple par; for whatever reason I rather like the colors in
>this - something of a quiet fractal.

The image seems a little pale, so I panned down to this

pastel_blue2a      { ; (c) Copyright David Shanholtzer, 1998
                     ; nearby image
  reset=1960 type=phoenixcplx
  center-mag=0.491675/-0.344382/3.471483/1.2137 params=0.2/0/0.3/0/0
  maxiter=5000 inside=255 logmap=75 decomp=256
  colors=rqvnourqv<64>4H`4H`4Ia<32>CmrDnsEnr<8>TgoUgoWhp<13>vvw<15>UUhVVhW\
  XhYZh<45>pnsqotpmr<12>cRTZ00<11>mfjoinpmrrqvrnv<14>m0m3Km<9>aerdgsgjtklu
  }

Jay



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

Date: Wed, 28 Jan 1998 19:56:14 EST
From: Nature102 <[e-mail]>
Subject: Re: (fractint) 2 Dumb ??

In a message dated 1-28-98 6:52:10 PM Central Standard Time,
[e-mail] writes:

<< 1)What does the Farey series have to do with the Mandelbrot set?>>

  Umm... They both have standard scientist names that aren't exactly normal
human names like Smith or Jones? They both involve plus signs? I give up. :-P
(What IS the Farey series, for that matter? :-P)

<< 2)How long is the coast of the Mandelbrot set? >>

  Ooh, ooh, I know! It's really long! Infinite, to be exact! Same length as
the coast of anything! (Hmm... Iraq's border is infinitely long. Bet that
would boost our friendly mad dictator with weapons of mass destruction's ego
some. :-P)

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

Date: Wed, 28 Jan 1998 17:06:39 -0800
From: "Jay Hill"<[e-mail]>
Subject: (fractint) 2)How long is the coast of the Mandelbrot set?

What measure would you like to use?

There is the boundary of the Cardoid with the attached buds.
In this case, it is a fractal whose dimension I measured a few
years ago. I calculated the circumference as a function of
limiting bud size.

These is also the boundary around all of the set. I measured
this using the arc length of the contours.

There may be even other measures.

I don't have the numbers handy.

Jay



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

Date: Mon, 26 Jan 1998 18:57:27 -0600
From: "Tim Wegner" <[e-mail]>
Subject: Re: (fractint) Astrophysical Lunacy

Mark wrote:

> Geez, I almost wish you hadn't pointed that out, but I guess
> it's best I know the ugly truth.  I should have been suspicious
> of integer artifacts from the nearly-hyperbolic "biomorph" spikes
> in ap-102.  Sadly, I find that all of the half-dozen images I
> genned from jul1-138 lose their best features when generated
> in their "true" form, which means they're not really fractals.

From a philosophical point of view, images that depend on integer
artifacts can still be fractals. Fractals can be generated from
discontinuous functions with strange rounding and multiple cases as
easily as from iterating simple, elegant, differentiable nonlinear
functions.

To take the point further, one of the points of fractal theory is
to break the prejudice that prefers the well behaved, smooth
functions of elemntary calculus, and sneers at the others as
unimportant counter examples. Perhaps we have just pushed the same
prejudice one level deeper when we acknowlege highly "ill behaved"
fractal functions as long as they are defined by iterating nice,
friendly, smooth, well-defined functions like z^2+c.

That's my view as a philosopher, but not my view as a programmer. A
good programmer takes backwards compatability very seriously, because
the alternative is to create huge problems for users every time a
new software version is released. Integer artifacts give programmers
fits when they happen accidently, because they are hard to control. I
would prefer that artists use floating point and the various rounding
functions, because then the software behaves more robustly when the
internals change. Perhaps we need some new functions proposed that
satisfy those who enjoy exploring artifacts.

Integer math surely is going to be removed from fractint. We're
just not sure how soon.

Tim

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

Date: Wed, 28 Jan 1998 21:21:05 -0800
From: Peter Jakubowicz <[e-mail]>
Subject: Re: (fractint) 2)How long is the coast of the Mandelbrot set?

At 05:06 PM 1/28/98 -0800, you wrote:
>
>What measure would you like to use?
>
>These is also the boundary around all of the set. I measured
>this using the arc length of the contours.

That's what I want to know. What did you do about the arc length of the
contours to determine the boundary?

BTW, thanks for those FOTNs. Good exercise for both halves of the brain.
Unfortunately, the March Astronomy is not out in my part of the world.


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

Date: Wed, 28 Jan 1998 18:40:11 -0800
From: "Jim sellers" <[e-mail]>
Subject: (fractint) Virus

 This was received from a friend and it sounds important.
Jim Sellers
> > > Subject:
> > > Date: Fri, 23 Jan 1998 10:52:17 -0500 (EST)
> > > Message-ID: <l0310280db0ee27e83074@[140.103.60.92]>
> > >
> > > VIRUS WARNING
> > > If you receive an email titled "JOIN THE CREW," DO NOT open it. It
will erase everything on your hard drive. Forward this letter out to as
many people as you can. This is a new, very malicious virus and not many
people know about it. This informatio
n was announced Wednesday morning from IBM;

 please share it with everyone that might access the internet. Once
again, pass this along to EVERYONE in your address book so that this may
be stopped.

Also, do not open or even look at any mail that says
"RETURNED OR UNABLE TO DELIVER." This virus will attach itself to your
computer components and render them useless. Immediately delete any mail
items that say this.

AOL has said that this is a very dangerous virus and that
there is NO remedy for it at this time. Please practice cautionary
measures and forward this to all users.
> > >
> > > Gloria Litteral
> > > Administrative Assistant to the Dean
> > > Dean of Students' Office
> > > The College of Wooster
> > > Galpin Hall
> > > Wooster, Ohio   4469l
> > > Telephone: [phone]ll
> > > FAX: [phone]
> > > e-mail:  [e-mail]
> > >
> > > --------- End forwarded message ----------
> > Received this from a friend, and have no reason to doubt it.  I've
> > already had a couple of messages that were returned that should have
> > gone through.
> >
> > Pat Cline



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Date: Wed, 28 Jan 1998 21:19:28 -0600 (CST)
From: [e-mail]
Subject: Re: (fractint) Reuse of previous zooms

On Mon, 26 Jan 1998, Edward Avis wrote:

> If you zoom in to a fractal there is potential for part of the old image to
> be used to calculate the new one.
>
> For example, if the zoom box is half as wide and half as high as the old
> image, then one in four of the pixels in the new image have already been
> calculated.  Using some kind of guessing algorithm, most of the others
> could be worked out very quickly.
>
> This would make zooming into fractals a great deal faster.
Yes, it would... IF you zoom in by half.  If you zoom in by, say, making
the zoom box .084637745656 as wide and .084637745656 as high (random
numbers), there is a very high likelyhood that NONE of the pixels will have
been calculated already.

You would have to limit zooming in to simple rational numbers, like 1/3,
1/4, 1/10... for it to work.

Justin A. Kolodziej


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Date: Wed, 28 Jan 1998 21:32:15 -0600
From: Bob Margolis <[e-mail]>
Subject: Re: (fractint) Virus (There is none!)

Jim sellers wrote:
>
>  This was received from a friend and it sounds important.
> Jim Sellers
> > > > Subject:
> > > > Date: Fri, 23 Jan 1998 10:52:17 -0500 (EST)
> > > > Message-ID: <l0310280db0ee27e83074@[140.103.60.92]>
> > > >
> > > > VIRUS WARNING

The virus you're talking about is the message you're sending. E-Mail
messages don't spread viruses; software programs do. You've sounded an
alarm for nothing.

Bob Margolis

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Date: Wed, 28 Jan 1998 21:41:15 -0600
From: "Tim Wegner" <[e-mail]>
Subject: Re: (fractint) Virus

> > > > VIRUS WARNING
> > > > If you receive an email titled "JOIN THE CREW," DO NOT open it.

Please don't post messages like this to the fractint list!!! ONLY
post messages to this list that have to do with fractals. The "virus"
message was a fraud, but even if it weren't a fraud, this is not a
virus discussion list!

Sorry to bother everyone with this, but I felt this message needed a
response. Also, folks, if you see off topic messages, you don't need
to personally take care of it by posting a response; as list
administrator, I will. (Feel free to email me personally
if yopu think I missed something.)

Thanks for your patience, and glad to see things are getting back to
normal. back to fractals!

Tim


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Date: Wed, 28 Jan 1998 21:54:37 -0600
From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Virus

Jim sellers wrote:
>
> This was received from a friend and it sounds important.
> Jim Sellers
> > > > Subject:
> > > > Date: Fri, 23 Jan 1998 10:52:17 -0500 (EST)
> > > > Message-ID: <l0310280db0ee27e83074@[140.103.60.92]>
> > > >
> > > > VIRUS WARNING
> > > >

Those are bogus virus email messages.  If you want to know about the
"real" viruses going around:

____________________________________________________________________
Welcome to the Virus Alert of the Day for Tuesday, January 27, 1998.

The following new viruses are expected to activate tomorrow:
PS-MPC
VCL
Victor
Girafe

Viruses scheduled to activate today are:
Ah
Emo-899
Demon variants
Murphy variants

All of the above viruses can be detected and removed with regular
antiviral agents.

Ongoing alerts for the month of January:
Plastique
Major
Manzon
Tentacle
Ripper
Baby New Year: e-mail hoax
____________________________________________________________________

The rest of the information may be obtained on a daily basis by going to
the following and subscribing:

         http://www.tipworld.com

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

Date: Thu, 29 Jan 1998 17:02:49 +1300
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Astrophysical Lunacy and Integer Arithmetic

At 18:57 26/01/98 -0600, Tim Wegner wrote:
>
>Integer math surely is going to be removed from fractint. We're
>just not sure how soon.
>
>Tim
>
I've been expecting this myself for a while now - Fractint's integer
arithmetic was after all introduced for the sake of speed, and I for one
find that the floating-point algorithms are much _faster_ on my machine,
and have been since my 486. (My 386/IIT was faster at floating point than
integer for that matter).

These days I only ever use integer arithmetic for deliberately introducing
artefacts. The thing is, I really _like_ some of these artefacts (my
Astro.frm formulae are cases in point). So when integer arithmetic is
removed from Fractint (Fractfloat? Ouch...) I would like to see some sort
of fossil support retained.

MLO

circuitry          { ; It's an artefact and I don't care!
  reset=1950 type=unity passes=b float=n
  center-mag=0/0/0.25 maxiter=256 inside=255
  potential=255/300/150 periodicity=0 colors=@headache.map
  }



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

Date: Wed, 28 Jan 1998 21:20:33 -0700 (MST)
From: Kerry Mitchell <[e-mail]>
Subject: Re: (fractint) 2 Dumb ??

The Farey series provides a convenient way to identify the disks along the
cardioids in the Mandelbrot set.  For review, the Farey sequence starts:

0/1, 1/1 in the first generation, followed by
0/1, 1/2, 1/1;
0/1, 1/3, 1/2, 2/3, 1/1; etc.

For each subsequent level, every second term is a combination of two terms
from the previous generation.  For example, the 1/3 comes from (0+1)/(1+2)
from the previous step.

For the Mandelbrot set, let 0/1 represent the cusp (0.25,0), 1/2 is the
large disk at -1, and 1/1 is back to the cusp.  Looking at the third level
above, between 0/1 and 1/2 is 1/3.  This corresponds to the large disk at
the top of the cardioid (and 2/3 is the other disk at the bottom).
Between any two disks with adjacent Farey entries at generation j, the
largest disk between those two has the Farey number between those two at
generation j+1.  In other words, the largest disk between disks 1/3 and
1/2 is disk (1+1)/(2+3) = 2/5.

Aside from labelling, the Farey numbers also serve as a coordinate.  Let

theta = 2 * pi * m/n, where

m/n is the Farey fraction for the given disk.  Then,

r = 0.5 * (1 - cos(theta)),
x = r * cos(theta) + 0.25,
y = r * sin(theta),
c = x + i*y

c is the point of tangency between the main cardioid and the m/n disk.
Since all fractions eventually show up in the Farey series, all fractions
have corresponding disks.  Also, if we replace the rational number m/n
with an irrational number (such as phi = 0.618034...), then the
corresponding c will be a cardioid boundary point with no tangent disk.
Therefore, it will have a chaotic orbit.  (An easier way to get chaotic
points is to use a rational number for theta.  Since pi is irrational,
that guarantees that the factor (m/n in the Farey case) will also be
irrational.)

The point abouve above chaotic orbits brings up another Farey connection.
Each disk has a corresponding Farey number m/n, which is in lowest terms.
The denominator, n, indicates the periodicity of the disk tangent to the
cardioid at the point c.  For example, with m/n = 1/2, the tangency point
is at the disk of periodicity 2 at -1.  The 1/3 and 2/3 disks are tangent
to the period 3 disks at the top and bottom.

These are the connections between the Farey sequence and the Mandelbrot
set of which I'm aware.  Any others?

- -------------------------------------------------------------------------------
Kerry Mitchell
[e-mail]
- -------------------------------------------------------------------------------

On Wed, 28 Jan 1998, Peter Jakubowicz wrote:

> 1)What does the Farey series have to do with the Mandelbrot set?
> 2)How long is the coast of the Mandelbrot set?
> Thank you.
>
>
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>


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

Date: Wed, 28 Jan 1998 21:20:33 -0700 (MST)
From: Kerry Mitchell <[e-mail]>
Subject: Re: (fractint) 2 Dumb ??

The Farey series provides a convenient way to identify the disks along the
cardioids in the Mandelbrot set.  For review, the Farey sequence starts:

0/1, 1/1 in the first generation, followed by
0/1, 1/2, 1/1;
0/1, 1/3, 1/2, 2/3, 1/1; etc.

For each subsequent level, every second term is a combination of two terms
from the previous generation.  For example, the 1/3 comes from (0+1)/(1+2)
from the previous step.

For the Mandelbrot set, let 0/1 represent the cusp (0.25,0), 1/2 is the
large disk at -1, and 1/1 is back to the cusp.  Looking at the third level
above, between 0/1 and 1/2 is 1/3.  This corresponds to the large disk at
the top of the cardioid (and 2/3 is the other disk at the bottom).
Between any two disks with adjacent Farey entries at generation j, the
largest disk between those two has the Farey number between those two at
generation j+1.  In other words, the largest disk between disks 1/3 and
1/2 is disk (1+1)/(2+3) = 2/5.

Aside from labelling, the Farey numbers also serve as a coordinate.  Let

theta = 2 * pi * m/n, where

m/n is the Farey fraction for the given disk.  Then,

r = 0.5 * (1 - cos(theta)),
x = r * cos(theta) + 0.25,
y = r * sin(theta),
c = x + i*y

c is the point of tangency between the main cardioid and the m/n disk.
Since all fractions eventually show up in the Farey series, all fractions
have corresponding disks.  Also, if we replace the rational number m/n
with an irrational number (such as phi = 0.618034...), then the
corresponding c will be a cardioid boundary point with no tangent disk.
Therefore, it will have a chaotic orbit.  (An easier way to get chaotic
points is to use a rational number for theta.  Since pi is irrational,
that guarantees that the factor (m/n in the Farey case) will also be
irrational.)

The point abouve above chaotic orbits brings up another Farey connection.
Each disk has a corresponding Farey number m/n, which is in lowest terms.
The denominator, n, indicates the periodicity of the disk tangent to the
cardioid at the point c.  For example, with m/n = 1/2, the tangency point
is at the disk of periodicity 2 at -1.  The 1/3 and 2/3 disks are tangent
to the period 3 disks at the top and bottom.

These are the connections between the Farey sequence and the Mandelbrot
set of which I'm aware.  Any others?

- -------------------------------------------------------------------------------
Kerry Mitchell
[e-mail]
- -------------------------------------------------------------------------------

On Wed, 28 Jan 1998, Peter Jakubowicz wrote:

> 1)What does the Farey series have to do with the Mandelbrot set?
> 2)How long is the coast of the Mandelbrot set?
> Thank you.
>
>
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>


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

Date: Wed, 28 Jan 1998 22:40:13 -0800
From: "Jay Hill" <[e-mail]>
Subject: (fractint) F.O.T.N. (Fractal of the Night) 29 Jan 1998 (Garden Path)

F.O.T.N. (Fractal of the Night) 29 Jan 1998 (Garden Path)

Finally, contact with Dr. J.  He just cannot resist those technical
questions.  Alas, he won't answer my email questions about the
FractoBowl games. Since he won't say anything, we can assume
his favorite team lost. Tonight, it would seem, he has been reading his
email and saw something of interest. So I'm taking a break from
the sequence of panoramas, like last nights panorama.

Peter Jakubowicz asked about the perimeter of the Mandelbort
set lakes. I replied, in the usual way, "Been there, done that". Just
kidding, got to stall somehow. But Dr. J put me to shame as only
someone from that fractal space can. He just went for his evening
stroll around the grounds and counted his steps. After all, isn't that
the definition of a fractal perimeter. He says he can take big steps
following the lower count escape contours, which should be obvious.
But as he huffed and puffed around the higher iteration count
contours (see Big Fatso to see why he huffs and puffs)

http://home.san.rr.com/jayrhill/FotN/FotN20.html

he reported he had to take steps about half as long for each contour.
That  is so he can follow the curves. He sent along the following
picture, Figure 1, showing his garden pathways.

http://home.san.rr.com/jayrhill/FotN/FotN29.html
http://home.san.rr.com/jayrhill/FotN/FotNindx.html

Figure 1. Dr. J's paths around the ground of his home.

  n     perimeter
 1  12.5663606457797931
 2   8.8944950515498699
 3   7.7383729769791320
 4   7.4436432355331474
 5   7.7000303808066779
 6   8.1421088527093027
 7   8.9862442676535721
 8   9.9311532506364844
 9  11.2267264962016062
10  12.7021596574680396
11  14.5645917174476154
12  16.6181359097436469
13  19.2297329357505035
14  22.1410545197811443
15  25.6606374585242084

The perimeter seems to  be a function of n, the iteration count for
the contour, namely, a one fifth power.

P = C1*2^(n/5)

Since Dr. J had to take steps half as long to insure getting around
every wrinkle in the path, we know his step lengths are

L=C2*2^(-n)

Therefore, the dimension must be the exponent in P/L.

P/L = C*2^(6/5)

and the dimension is 6/5.

Enjoy
Jay
PS. Newton's method was used to follow the contour around the
MSet. Approximate halving the step size was required to prevent
straying from the path. Following the path to higher order is of
ever more difficulty.  I have reached the limits of 80 bit floats and
weekend runs on a P200.  If the trend is real, the dimension
using this measure is 6/5.



Dr_Js_grounds { ; A simulation of Dr. Js garden pathways.
reset=1960 type=mandel center-mag=-0.5/0/0.6666667
params=0/0 maxiter=16 float=y colors=@default.map
}


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

Date: Thu, 29 Jan 1998 05:05:30 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Hi Folks

That's a big ten-four.


- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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End of fractint-digest V1 #90
*****************************