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fractint-digest        Wednesday, March 4 1998        Volume 01 : Number 121




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

Date: Tue, 3 Mar 1998 11:32:43 -0800 (PST)
From: [e-mail]
Subject: Re: (fractint) gravijul-v3

Mark Christenson wrote:
>
> Seeing Sylvie's gravijul-v3 has reminded me of a question that
> has been in the back of my mind for some time.  I have a basic
> understanding of complex math; mulitiplication is no problem,
> but raising to fractional or complex powers is a total mystery
> to me.  Can anyone point me to a good tutorial?  No need to bore
> the whole list, please just send the URL or book/article title.

But I like boring the whole list :)

Actually, raising complex numbers to a fractional power is not as
tricky as it sounds.  A complex number in cartesian coordinates (ex
3+4i) can be converted into a polar form (magnitude=5, angle= ~.972
rad in this case).  You can also write this in the form m*exp(i*t)
where m is the magnitude and t is the angle theta.  This is because exp(i*t)=cos(t)+i*sin(t).

Raising this to any power (whole or fractional) can be done:

z=m*exp(i*t)

z^x=(m*exp(i*t))^x
   =m^x*exp(i*t*x)
   =m^x*(cos(t*x)+i*sin(t*x))

Raising a number to a complex power can be done by remembering that:

z^(a+b)=z^a*z^b

Now all we have to do is figure out how to raise a number to an
imaginary power.  I can't exactly remember how do to this right now.
Perhaps someone else on the list will pick up the baton.

Ocie


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

Date: Tue, 3 Mar 1998 12:03:23 -0800
From: "Jay Hill" <[e-mail]>
Subject: Re: (fractint) gravijul-v3

Hi Ocie,

Are you the Ocie Mitchell from Claremont Colleges and Harvey Mudd?

Jay Hill

- ----------
> From: [e-mail]
> To: [e-mail]
> Subject: Re: (fractint) gravijul-v3
> Date: Tuesday, March 03, 1998 11:32 AM
[...]
> But I like boring the whole list :)
>
> Actually, raising complex numbers to a fractional power is not as
> tricky as it sounds.  A complex number in cartesian coordinates (ex
> 3+4i) can be converted into a polar form (magnitude=5, angle= ~.972
> rad in this case).  You can also write this in the form m*exp(i*t)
> where m is the magnitude and t is the angle theta.  This is because
exp(i*t)=cos(t)+i*sin(t).
>
> Raising this to any power (whole or fractional) can be done:
>
> z=m*exp(i*t)
>
> z^x=(m*exp(i*t))^x
>    =m^x*exp(i*t*x)
>    =m^x*(cos(t*x)+i*sin(t*x))
>
> Raising a number to a complex power can be done by remembering that:
>
> z^(a+b)=z^a*z^b
>
> Now all we have to do is figure out how to raise a number to an
> imaginary power.  I can't exactly remember how do to this right now.
> Perhaps someone else on the list will pick up the baton.
>
> Ocie
>


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

Date: Tue, 3 Mar 1998 13:21:00 -0800 (PST)
From: [e-mail]
Subject: Re: (fractint) gravijul-v3

Jay Hill wrote:
>
> Hi Ocie,
>
> Are you the Ocie Mitchell from Claremont Colleges and Harvey Mudd?
>
> Jay Hill

I sure am.  Actually, I am now an alum.

Ocie

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

Date: Tue, 3 Mar 1998 14:40:15 -0800 (PST)
From: [e-mail]
Subject: Re: (fractint) gravijul-v3

ocie wrote:
>
> Mark Christenson wrote:
> >
> > Seeing Sylvie's gravijul-v3 has reminded me of a question that
> > has been in the back of my mind for some time.  I have a basic
> > understanding of complex math; mulitiplication is no problem,
> > but raising to fractional or complex powers is a total mystery
> > to me.  Can anyone point me to a good tutorial?  No need to bore
> > the whole list, please just send the URL or book/article title.
>
> But I like boring the whole list :)
>
> Actually, raising complex numbers to a fractional power is not as
> tricky as it sounds.  A complex number in cartesian coordinates (ex
> 3+4i) can be converted into a polar form (magnitude=5, angle= ~.972
> rad in this case).  You can also write this in the form m*exp(i*t)
> where m is the magnitude and t is the angle theta.  This is because exp(i*t)=cos(t)+i*sin(t).
>
> Raising this to any power (whole or fractional) can be done:
>
> z=m*exp(i*t)
>
> z^x=(m*exp(i*t))^x
>    =m^x*exp(i*t*x)
>    =m^x*(cos(t*x)+i*sin(t*x))
>
> Raising a number to a complex power can be done by remembering that:
>
> z^(a+b)=z^a*z^b
>
> Now all we have to do is figure out how to raise a number to an
> imaginary power.  I can't exactly remember how do to this right now.
> Perhaps someone else on the list will pick up the baton.

I now remember how to do this as well.  If l is the natural log of the
magnitude, then the number can be written:

z=exp(l+i*t)

so

z^w=exp(l+i*t)^w=exp((l+i*t)*w)

So this just becomres a case of multiplying the complex exponent w by
the log of z (l+i*t) and then exponentiating.



Ah, this is a great discussion, I'll have to go out and get the latest
fractint copy.

Ocie


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

Date: Tue, 3 Mar 1998 17:15:39 -0800
From: "Jay Hill"<[e-mail]>
Subject: Re: (fractint) gravijul-v3

Hi Ocie,

It is good to see you posting again after so long. Now, about a week ago
we were discussion ASCII Mandelbrot sets and I noted a few sources.
One was you post to sci.fractals in 1993 (or there abouts).  You posted
a new version

ftp://ftp.inria.fr/graphics/aamandel-2.1.shar.gz
Now this, unlike your earlier version does not compile on my compiler -
missing headers etc. So could you install a DOS executable on your web
site?
Since your first version is really portable, you might consider posting it
as well.

>Jay Hill wrote:
>>
>> Hi Ocie,
>>
>> Are you the Ocie Mitchell from Claremont Colleges and Harvey Mudd?
>>
>> Jay Hill
>I sure am.  Actually, I am now an alum.
>Ocie



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

Date: Tue, 3 Mar 1998 17:43:13 -0800 (PST)
From: [e-mail]
Subject: Re: (fractint) gravijul-v3

Jay Hill wrote:
>
>
> Hi Ocie,
>
> It is good to see you posting again after so long. Now, about a week ago
> we were discussion ASCII Mandelbrot sets and I noted a few sources.
> One was you post to sci.fractals in 1993 (or there abouts).  You posted
> a new version
>
> ftp://ftp.inria.fr/graphics/aamandel-2.1.shar.gz
> Now this, unlike your earlier version does not compile on my compiler -
> missing headers etc. So could you install a DOS executable on your web
> site?
> Since your first version is really portable, you might consider posting it
> as well.

My second version had an "interactive" mode which lets the user select
the area to zoom into.  I'll see if I can turn this off gracefully if
there is no curses library.  Don't know about a DOS executable, but I
should be able to at least release sources that will compile under DOS.

Ocie

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

Date: Tue, 03 Mar 1998 19:51:41 -0800
From: Wizzle <[e-mail]>
Subject: Re: (fractint) julias

Jay...

Thanks so much for the explanations and samples!!  I feel like you gave me
a brand new wonderful toy to play with. I'm having such fun finding julias
and minibrots.....I never realized they were there.

One more question.....I figured out that zooming out takes me back to the
mandelbrot set......and when I zoom out from the julia I can see the little
"strings" along the mandelbrot set that contain the julias even at a fairly
low magnification (like looking at a large portion of the "lake").
However, when I start with the mandelbrot set in fractint I never seem to
see those strings no matter how much I zoom in. Why can't I see these
strings when I start with the mandelbrot set and yet I can if I start with
the julia I posted?

Angela

At 05:56 PM 3/2/98 -0800, you wrote:
>
>Wizzle wrote:
>>p.s. I would dearly love to understand why this is a squarish type of
>>julia....if the explanation isn't too terribly mathematical.
>The Julia set image has to have all the features seen around the
>parameter spot in the Mandelbrot set.  So at lower magnification
>in M we have the following (see par). This shows up first twice then
>four times in M when we zoom in. And so it also does as we zoom
>into the Julia. You chose a zoom that shows the four fold and so it
>looks squarish.  Try this par at all zooms into the midget. Then
>press space twice and watch all zooms in the Julia. See the
>same sort of 'stuff'.
>
>Jay
>
><<snipped>>

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

Date: Tue, 03 Mar 1998 21:05:44 -0800
From: dudley brooks <[e-mail]>
Subject: (fractint) video driver question

i hope someone can help me as i have not had fractint for several weeks
now.i had to replace my video card and installed a Diamond Speedstar 64
2000 graphics card.my computer is a ibm clone 486 66 mgz and i have
fractint 19.5.i can only view fractals in the most primitive modes.i
have always used the shift7 1024X780 video mode that works with most
svga.i have no idea where to go from here to get this working.i have
read the fractint documentation on video modes over and over but it is a
little over my head for me to fool with i believe.has anyone had this
problem or can anyone advise me of how to get the sharpest images
possible with this video card?i have had fractint since version 16 and
was one of the programs that amazed me and sparked my interest in the
computer.i am just a lover of fine images and do not really know anyone
else with an interest in fractint like i have.hope someone can help!!!


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

Date: Tue, 3 Mar 1998 20:36:23 -0800
From: "Jay Hill"<[e-mail]>
Subject: Re: (fractint) julias

Angela wrote

Jay wrote:
- ->Try this par at all zooms into the midget. Then
- ->press space twice and watch all zooms in the Julia. See the
- ->same sort of 'stuff'.

- -Jay...
- -Thanks so much for the explanations and samples!!  I feel like you gave
- -me a brand new wonderful toy to play with. I'm having such fun finding
- -julias and minibrots.....I never realized they were there.
There are about 20,000 more posted on my web sites.  Glad you are
having fun.  There is a lot to learn about the old Mandelbrot set. I've
been spending uncounted hours (actually, I think my wife has been
counting the hours) ever since I got my 8086 with CGA in the '80s.  I
used to figure 2 hours to make a nice 320x200 image. It now takes
2 seconds.

- -One more question.....I figured out that zooming out takes me back to the
- -mandelbrot set......and when I zoom out from the julia I can see the
little
- -"strings" along the mandelbrot set that contain the julias even at a
fairly
"strings",  that is an example of the 'stuff' mentioned above.  Stuff in
elephant valley looks like elephants. Stuff in seahorse valley looks
like seahorses. Stuff near the base of the period 3 bud (big one on top)
look like 3 armed galaxies.  Julia sets with parameters set to these
regions will have that look to them.

- -low magnification (like looking at a large portion of the "lake").
- -However, when I start with the mandelbrot set in fractint I never seem to
- -see those strings no matter how much I zoom in. Why can't I see these
- -strings when I start with the mandelbrot set and yet I can if I start with
- -the julia I posted?
And where do we find strings?  Out on the spike, because it is the
mother of all strings.  These start showing up anywhere more
negative than -1.  Near -1.25 they are clumpy and are called scepters.
Your example is out at -1.75 where strings are going strong.

Twiggy strings are found near (-.134, 1) because that filament is
- - you guessed it - twiggy.

Rumor has it that Dr. J is building new wings to his laboratory, new
ones for each of these regions.  Word is that he stepped into
a particularly tangled mess of 'strings, barbed wire and quick sand'.
I'm too busy running tests at work tonight to look after him. He is on
his own.   :-)

Jay



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

Date: Tue, 03 Mar 1998 21:47:13 -0800
From: kathy roth <[e-mail]>
Subject: (fractint) gravijul-v3

um......oh, I do have a life.  Um, I do do something
besides this, really.


newgrav1           { ; 3-2-98 kathy roth
                     ; gravijul-v3 variation by Sylvie Gallet
                  ;on Mark Christenson's gravijul formula
  reset=1960 type=formula formulafile=gravij~3.frm
  formulaname=gravijul-v3 function=cosxx/flip/floor
  center-mag=+0.00024059026236537/+0.00002279441750243/137.0464/1.0397
  params=1.1/3/0.9999999000000001/0/10/0 invert=0.01/0/0 decomp=2048
 colors=000YRD<7>pgTriVulYxn_zpa<4>jdWgaVcZT\
`WSYUR<3>KJNHGMGFL<10>7246027\
 02<20>Q08R09S09T0AU0A<6>`0Da0Db2D\
<14>zVF<10>hAEaI9<6>xTF<8>H3AC09908<6>K\
 BDMDEMFF<2>MMI000<16>C81D92FB3<2>\
LG4OI5QK7<12>vlYxn_yo`zpawn_ukY<16>bVH0\
  00<22>000000223<5>HHNKKQNNTQQXTT_<6>ilploslpr<14>OI5<2>VPB
  }

newgrav2           { ; 3-2-98 kathy roth
                     ; gravijul-v3 variation by Sylvie Gallet
                      ;on Mark Christenson's gravijul formula
                     ; best at least 800x600
  reset=1960 type=formula formulafile=gravij~3.frm
  formulaname=gravijul-v3 function=cosxx/cos/cotan passes=t
  center-mag=-0.00360393/0.00010278/7.524472/1.0397
  params=1.1/3/0.9999999000000001/0/10/0 invert=0.01/0/0 decomp=2048
  colors=000<23>000000223<5>HHNKKQNNTQQXTT_\
<6>ilploslpr<14>OI5<11>pgTriVul\
 Yxn_zpa<4>jdWgaVcZT`WSYUR<3>KJNHGMGFL\
<10>724602702<20>Q08R09S09T0AU0A<6>\
 `0Da0Db2D<14>zVF<10>hAEaI9<6>xTF<8>H3AC09908\
<6>KBDMDEMFF<2>MMI000<16>C81\
  D92FB3<2>LG4OI5QK7<12>vlYxn_yo`zpawn_ukY<16>bVH
  }

newgrav3           { ; 3-2-98 kathy roth
                     ; architect's draft for newgrav2
                     ; gravijul-v3 variation by Sylvie Gallet
                     ; on Mark Christenson's gravijul formula
  reset=1960 type=formula formulafile=gravij~3.frm
  formulaname=gravijul-v3 function=cosxx/cos/cotan passes=t
  center-mag=-0.00360393/0.00010278/7.524472/1.0397
  params=1.1/3/0.9999999000000001/0/10/0 fillcolor=66 invert=0.01/0/0
  decomp=2048
  colors=000<23>000000223<5>HHNKKQNNTQQXTT\
_<6>ilploslpr<14>OI5<11>pgTriVul\
 Yxn_zpa<4>jdWgaVcZT`WSYUR<3>KJNHGMGFL\
<10>724602702<20>Q08R09S09T0AU0A<6>\
 `0Da0Db2D<14>zVF<10>hAEaI9<6>xTF<8>H3A\
C09908<6>KBDMDEMFF<2>MMI000<16>C81\
  D92FB3<2>LG4OI5QK7<12>vlYxn_yo`zpawn_ukY<16>bVH
  }


newgrav4           { ; 3-2-98 kathy roth
                     ; palette by Sylvie Gallet
                     ; gravijul-v3 variation by Sylvie Gallet
                     ; on Mark Christenson's gravijul formula
  reset=1960 type=formula formulafile=gravij~3.frm
  formulaname=gravijul-v3 function=cosxx/cos/flip passes=t
  center-mag=-0.00793577/0.00836294/6.244929/1.0397
  params=1.1/3/0.9999999000000001/0/10/0 invert=0.01/0/0 decomp=2048
colors=000ZdiZdi_eh<15>wwm<15>0mm<7>8eb9da9da\
<12>1VQ0UP1UP<11>GaPHaPIbPK\
 cPKcQLdR<19>bvkcwmbvl<27>4T53S42R20P00P\
10P2<20>AZTAZUD_S<13>st4000kkk00U\
  <13>Ums<5>hrw<4>eoudntcmtblsbksajr<15>\
PYjOXiOXiOXi<4>RYiRYiRYiRYiSZi<24>\
  Zdi
  }

newgrav5           { ; 3-2-98 kathy roth
                     ; gravijul-v3 variation by Sylvie Gallet
                     ; on Mark Christenson's gravijul formula
  reset=1960 type=formula formulafile=gravij~3.frm
  formulaname=gravijul-v2 function=atanh/sqrt/recip passes=t
  center-mag=1.77636e-015/-1.77636e-015/0.09696078
  params=1/0.9/0/0/4/0 float=y maxiter=300 inside=0
decomp=256
colors=000LSXGO`CLd<7>Ums<5>hrwhrwgqv<31>\
OOlNNlOOl<45>wwm<15>0mm<7>8eb9d\
 a9da<12>1VQ0UP1UP<11>GaPHaPIbPKcPKcQLdR\
<19>bvkcwmbvl<30>MS2LR0MS0<36>st4\
  <5>TZQ
  }

newgrav6           { ; 3-2-98 kathy roth
                     ; gravijul-v3 variation by Sylvie Gallet
                     ; on Mark Christenson's gravijul formula
  reset=1960 type=formula formulafile=gravij~3.frm
  formulaname=gravijul-v3 function=cosxx/flip/sinh
  center-mag=+0.00024059026236537/+0.00002279441750243/137.0464/1.0397
  params=1.1/3/0.9999999000000001/0/10/0 invert=0.01/0/0
decomp=2048
colors=000YRD<7>pgTriVulYxn_zpa<4>jdWgaVc\
ZT`WSYUR<3>KJNHGMGFL<10>7246027\
 02<20>Q08R09S09T0AU0A<6>`0Da0Db2D\
<14>zVF<10>hAEaI9<6>xTF<8>H3AC09908<6>K\
 BDMDEMFF<2>MMI000<16>C81D92FB3<2>\
LG4OI5QK7<12>vlYxn_yo`zpawn_ukY<16>bVH0\
  00<22>000000223<5>HHNKKQNNTQQXTT_<6>\
ilploslpr<14>OI5<2>VPB
  }

gravijul-v3 { ; Variation on Mark Christenson's gravijul by Sylvie
Gallet
   z = pixel:
   w = fn1(z)
   z = fn3(fn2(w*w)^p1) + p2
    |z| < p3
  }
 gravijul-v2 { ; Variation on Mark Christenson's gravijul by Sylvie\
Gallet
   z = pixel :
   w = fn1(real(z)) , x = fn3(p1/fn2(w*w))
   w = fn1(imag(z)) , y = fn3(p1/fn2(w*w))
   z = x + flip(y) + p2
    |z| < p3
  }









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

Date: Tue, 03 Mar 1998 22:13:20 -0800
From: kathy roth <[e-mail]>
Subject: (fractint) thank you, thank you etc.

Maybe there should be an award, like  "Fractal of the Year"
or a grammy or a Bammie or something.  I nominate
Mark Christenson for  "gravijul".


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Date: Tue, 03 Mar 1998 23:49:06 -0800
From: Mark Christenson <[e-mail]>
Subject: Re: (fractint) thank you, thank you etc.

comment { commentary and pars by Bud 3/3/98

At 10:13 PM 3/3/98 -0800, Kathy wrote:
>Maybe there should be an award, like  "Fractal of the Year"
>or a grammy or a Bammie or something.  I nominate
>Mark Christenson for  "gravijul".

Thanks for the praise, but the year is *very* young.  And the
competition is stiff.  One of the great things about this list is the
way it enables collaboration and cross-fertilization at light speed;
I know it has made *me* a better fractal artist.  I haven't had time
to explore Sylvie's gravijul-v3 yet; and while v2 seems a bit less
fertile than the original, its potential for unusual structures
(especially periodic "tiles") is really stunning.

Here's another v2; it's basically "Internal Reflections" on steriods,
with a precious metal finish.  This color map (called "sil&gold") and
the one I used for "I.R." (called "circus") are two of my new faves
for decomposition images (I'm also on a decomp jag, as you may
have noticed).  Hard to believe I got along for 10 years with only one
option, color=iter (it was all I ever built into my programs).
Note: Both images/maps are also great for color cycling!


Bud

}

gjv2-04b           { ; gjv2-04a in silver & gold, (c)  Bud 3/2/98 - cycle
me, please!
                     ; frm gjv2 by Sylvie Gallet
  reset=1930 type=formula formulafile=filist.frm
  formulaname=gravijul-v2 function=sin/log/acosh passes=t
  center-mag=0/0.78/0.426 params=0/1.2/0/0/20/0 float=y
  maxiter=300 inside=0 decomp=256
  colors=200<30>z00<30>200000111<30>sss<30>222000012<30>0kz<30>022000211<3\
  0>zsX<31>000 cyclerange=0/255
  }

frm:gravijul-v2 { ; Variation on Mark Christenson's gravijul by Sylvie Gallet
   z = pixel :
   w = fn1(real(z)) , x = fn3(p1/fn2(w*w))
   w = fn1(imag(z)) , y = fn3(p1/fn2(w*w))
   z = x + flip(y) + p2
    |z| < p3
  }



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

Date: Tue, 03 Mar 1998 23:58:14 -0800
From: Mark Christenson <[e-mail]>
Subject: Re: (fractint) thank you, thank you etc.

I wrote:
> Here's another v2; it's basically "Internal Reflections" on

*steroids*, not steriods.

I'm careless, not illiterate.


Bud



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Date: Wed, 04 Mar 1998 00:12:20 -0800
From: Mark Christenson <[e-mail]>
Subject: (fractint) Re: complex powers

Ocie -

Thanks for the run-down.  Guess I gotta shake out the cobwebs.
It all made sense, but things like coordinate system conversions
and identities are quite foreign now, having not been used since
college (cripes, 1979?!?).  I'm pretty certain I couldn't do integration
by parts or substitution to save my life.

Bud


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Date: Wed, 04 Mar 1998 07:50:52 -0800
From: Wizzle <[e-mail]>
Subject: (fractint) minibrot question

How come if I start with the julia formula I can't find any mini-brots no
matter how much I zoom.......if I start with a mandelbrot with "stuff"
(those strings....which I still don't know where they come from).....I
don't have any trouble finding lots of minibrots among the julias on the
"stuff".

Where did the mandelbrot with "stuff" come from to begin with? And how do
the coordinates work? Is the middle of my screen ground zero in the
mandlebrot? Up and to the right is plus.....down and to the left is minus?

Can I input coordinates somewhere?

Angela aka wizzle



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Date: Wed, 04 Mar 1998 07:56:29 -0800
From: Wizzle <[e-mail]>
Subject: Re: (fractint) thank you, thank you etc.

Bud writes....

>Here's another v2; it's basically "Internal Reflections" on steriods,
>with a precious metal finish.  This color map (called "sil&gold") and
>the one I used for "I.R." (called "circus") are two of my new faves
>for decomposition images (I'm also on a decomp jag, as you may
>have noticed).  Hard to believe I got along for 10 years with only one
>option, color=iter (it was all I ever built into my programs).
>Note: Both images/maps are also great for color cycling!
>
>
>Bud
>


Bud....the sil&gold map is truly excellent and I love what it did to your
image.  I thought the original lovely in a "painterly" sort of way. This
new variation has such a different feel....much more 3 dimensional.

I've had a wonderful time with all the gravijul variations. For some
reason, crosses and mandalas keep coming up for me.....must be a "sign"
that I need to update my gallery for Easter/Vernal Equinox. Thanks you so
much Buc and Sylvie.

Angela aka wizzle

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Date: Wed, 04 Mar 1998 16:17:33 -0800
From: Daniel Sadoc <[e-mail]>
Subject: (fractint) Feigenbaum number

This is a multi-part message in MIME format.

- --------------45B3F0F2189
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit

Hi!

        As I had an expecial interest in the Bifurcation Fractal and the Bifurcation Lambda, I got contact with the Feigenbaum number, which is good covered at the address below:

        http://www.stud.ntnu.no/~berland/math/feigenbaum/index.html

        Some days ago, however, I've found a little and "simple" program that calculates the Feigenbaum number.  Although I've understood how the Feigenbaum number is calculated based on the Bifurcation Fractal design,  I've passed many days trying to compreend how this program works, but I couldn't...

        So, I would like to ask if someone can help me to understand the logic of this code that I've attached to this message.

Thanks in advance,
Daniel Sadoc

- --------------45B3F0F2189
Content-Type: text/plain; charset=us-ascii; name="FEIGENBM.PAS"
Content-Transfer-Encoding: 7bit
Content-Disposition: inline; filename="FEIGENBM.PAS"

{$N+}
program feigenbm;

uses CRT;

var
   x,lambda,f,step_size,old_x,test,lambda_1,lambda_2,delta,
   init_step,old_lambda,new_step,old_step: extended;

   i,iterations: longint;

   j,sign: integer;

begin
        ClrScr;
        lambda := 3.0;
    Writeln('n          Lambda                 Delta');
    init_step := 1;
    for j:=1 to 19 do
    begin
             if j mod 2 = 0 then
                sign := -1
             else
        sign := 1;
             GotoXY(0,15+j);
             init_step := init_step/4.67;
             step_size := init_step;
             iterations := 2;
             for i:=1 to j-1 do
                      iterations := iterations*2;

             old_x := 0.5;
             lambda := lambda + step_size;
             repeat
        x := old_x;
        for i:=0 to iterations-1 do
                    x := lambda*x*(1-x);  { x := x * r * (1-x) }
                test := (x - old_x)*sign;
                if test < 0 then
                begin
             lambda := lambda - step_size;
                     step_size := step_size/2;
                end;
                old_lambda := lambda;
                lambda := lambda + step_size;
                GotoXY(1,j+3);
        write(j:2,'   ',lambda:20:18,'   ');
             until old_lambda >= lambda;
             if j > 2 then
         begin
        delta := (lambda_1 - lambda_2)/(lambda - lambda_1);
        write(delta:20:18);
             end;
             lambda_2 := lambda_1;
             lambda_1 := lambda;
    end;
end.

- --------------45B3F0F2189--



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

Date: Wed, 04 Mar 1998 16:16:03 -0800
From: Daniel Sadoc <[e-mail]>
Subject: (fractint) New WinFract User

Hi!

        I've bought the book Fractals for Windows (from Wegner, Peterson, Tyler and Branderhorst), here where I live, in Brazil, and since than I'm very interested in fractals.  I've just got some experience with the WinFract, which I really appreciated.

        I've been reading some very interesting messages from this mail-list, and now I have a question, which I've sent in the following e-mail.

        I expect that I can contribute to the growing of this list.

Sincerily Yours,
Daniel Sadoc



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

Date: Wed, 04 Mar 1998 16:25:09 -0800
From: Daniel Sadoc <[e-mail]>
Subject: (fractint) Especial

Hi!
    I'm sorry by the English faults! I've just seen I had written "expecial", in the last e-mail, when I was trying to say "special"...

    Although the English errors, I hope everyboy had understood my question...

Waiting for reply,
Daniel Sadoc


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

Date: Wed, 4 Mar 1998 12:52:13 -0700
From: "Peter Gavin" <[e-mail]>
Subject: (fractint) Date: Wed, 4 Mar 1998 14:52:02 -0500

I've been totally unable to get diskvideo to work in batch mode, short of
making another fractint.cfg containing only the diskvideo mode I want.
Could someone tell me how I can continue an image I started in regulr
1024x768 graphics mode in 1024x768 diskvideo mode, without modifying my
sstools.ini and fractint.cfg?

Thanks,
Pete



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

Date: Wed, 4 Mar 1998 12:28:41 -0800
From: "Jay Hill" <[e-mail]>
Subject: Re: (fractint) minibrot question

Hi wizzle,

The Mandelbrot set is a Map of the Julia sets for the iteration
equation, any iteration equation. It is showing us the convergence or
divergence results we shall see (an image of results vs. c)  if we
make a Julia set. The Julia set image shows us the
convergence or divergence using different initial z0 values.

If we want to see midgets in the Mandelbrot map, we must use
z0 = a critical point. That is why we use z0=0 for the classic MSet.
Given that we use z0=critical point, we will see some midgets
(depending on the iteration formula).  In the classic MSet, all the
midgets are connected by smaller midgets and other 'points'.

These are the filaments. The pretty stuff we see are there because
there are midgets all lined up in some organized pattern. Now the
Julia set explicitly avoids the critical points (except for a few samples
in the z0 plain that happen to be critical points). So you don't see
midgets.  If c (the parameter for the Julia set) is in a solid part of
the corresponding Mandelbrot map, we shall see solid parts (non-
divergent) in the Julia set. Why?  Because where that z0=critical
point is, there at least, the iteration does not diverge. (It is in a solid
part of the MSet and so it must be a solid part of JSet. It is after all
the one point belonging to both.)  If this point is well inside a solid
component of the MSet, like in a bud, then for some region around
it in the JSet we shall see it is solid (non-divergent).

If the point is not in or next to a MSet component, the point diverges
and none of the JSet has a chance of converging. The JSet has no
solid parts.

If you put c in the 'center' of a midget's cardioid, there will be a
circular solid spot in the center of the Julia (at the critical point).
If c is in a bud center, there will be several solid parts in JSet
corresponding in a sense to the period of the orbits.

Hope this helps,

Jay
PS more below...

- ----------
> From: Wizzle <[e-mail]>
> To: [e-mail]
> Subject: (fractint) minibrot question
> Date: Wednesday, March 04, 1998 7:50 AM
>
> How come if I start with the julia formula I can't find any mini-brots no
> matter how much I zoom.......if I start with a mandelbrot with "stuff"
> (those strings....which I still don't know where they come from).....I
> don't have any trouble finding lots of minibrots among the julias on the
> "stuff".

see above

>
> Where did the mandelbrot with "stuff" come from to begin with? And how do
> the coordinates work?

The coordinates are the complex number plain. If there is a rotation or
skewing then it gets messed up (but prettier for an image).

> Is the middle of my screen ground zero in the
> mandlebrot?

Press 'z' and 'F6' to see the coordinates of the screen center.


>Up and to the right is plus.....down and to the left is minus?

Yes.

> Can I input coordinates somewhere?

Yes. In the 'z' F6 screen you can change center and zoom, etc.
>
> Angela aka wizzle


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

Date: Wed, 04 Mar 1998 13:34:12 -0800
From: kathy roth <[e-mail]>
Subject: (fractint) Especial

Your English is fine! Much better than my Portuguese.


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Date: Wed, 4 Mar 1998 18:06:58 -0500
From: Sylvie Gallet <[e-mail]>
Subject: (fractint) (Fwd) Fix needed for F-tint 20

This is a MIME-encapsulated message

- --d1dea504-b3b2-11d1-a106-00805feaacd2
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable
Content-Disposition: inline

Hi Tim,

>> Can anyone else duplicate this problem? With Bob's permission I am =

>> posting some mail he sent me privately.
<snipped>
>> I discovered that when I had somewhere around 150 formulas, the
>> formula names listed on the selection menu would run up against each
>> other like this: formula1formula2formula3 etc.

  You can duplicate it with the formula file attached.  Just change the
name of the first formula.

  The bug appears when the formula name has 4, 5, 7, 9, 12, 15 chars.  In=

all of these cases, (mumber of chars + 1) * number of colums =3D 78 or 80=
=2E

  Cheers,

        - Sylvie

- --d1dea504-b3b2-11d1-a106-00805feaacd2
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- --d1dea504-b3b2-11d1-a106-00805feaacd2--

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Date: Wed, 04 Mar 1998 00:18:24 -0300
From: "Alexandre de C. Borges" <[e-mail]>
Subject: (fractint) Fractais in Brazil

>Hi!
>
>        I've bought the book Fractals for Windows (from Wegner, Peterson,
Tyler and Branderhorst), here where I live, in Brazil, and since than I'm
very interested in fractals.  I've just got some experience with the
WinFract, which I really appreciated.
>
>        I've been reading some very interesting messages from this
mail-list, and now I have a question, which I've sent in the following e-mail.
>
>        I expect that I can contribute to the growing of this list.
>
>Sincerily Yours,
>Daniel Sadoc


Hello!!!

Brazil ???

Eh um prazer ver alguem da terra brazilis aqui na lista :-)


Eu tambem sou do Brazil companheiro

Opa, opa...os americanso nao devem estar entendendo nada do que escrevi
aqui...

ja fui,

abracos




       _/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
      _/    Alexandre de C. Borges      _/
     _/      [e-mail]      _/
    _/       [e-mail]     _/
   _/          ICQ UIN: 3236595      _/
  _/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/

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End of fractint-digest V1 #121
******************************