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fractint-digest        Friday, January 30 1998        Volume 01 : Number 092




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

Date: Thu, 29 Jan 1998 22:29:56 -0800
From: "Jay Hill" <[e-mail]>
Subject: (fractint) F.O.T.N. (Fractal of the Night) 30 Jan 1998 (Fractint Virus)

F.O.T.N. (Fractal of the Night) 30 Jan 1998 (Fractint Virus)


I just found out why Dr. J has been mostly unavailable for comment
since the FractoBowl. He has come down with some kind of fractal
flu.  Dr. J., it would seem has caught a bad case of something, which
especially in fractal space, can result in quarantine.  Positive ID of
the cause was just announced. He has the dreaded and feared Fractint
Virus. This virus can result in previously well connected fractals
becoming Fatou dust in hours. See Figure 1.

http://home.san.rr.com/jayrhill/FotN/FotN30.html
Figure 1. Dr. J has the dreaded and feared Fractint Virus.

Please, if you know of a cure for this illness, let us know immediately.
Dr. J does not have much time.

Stay healthy,
Jay



frm:FGZ-Mand { ; (c) Jay Hill, 1998
IF( |p3| == 0)
p3 = 16
ENDIF
c=pixel, z=sqrt(-c), bailout = real(p3):
z1=z*z + c;
z = p1*z1*z1/(z1 + p2) + c;
|z| <= bailout
}

FractintVirus { ; (c) Jay Hill, 1998
reset=1960 type=formula formulafile=fgz.frm formulaname=fgz-mand
center-mag=-0.12717649272918370/+0.00083633064855477/9263.533/1/90
params=100/0/3/0/0/0 float=y maxiter=54 inside=bof61 outside=0
colors=AAA000000000U00000<25>000UKAw\
cFwcA<6>cA0<3>RA0cA0KA0mA0KA0UA0KA0c\
A0KA0cA0KA0mA0KA0JA0JA0UB0LC0<9>VM0m\
N0XO0<4>aT0cU0cU0<10>`R0wK0_Q0<158>2\
20111000000
}

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

Date: Fri, 30 Jan 1998 20:47:37 +1300
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) 2(-dimensionally) Dumb ??

At 11:41 29/01/98 -0800, Jay Hill wrote:
>Hi Paul,
>
>You wrote:
>>Peter Jakubowicz wrote
>> >2)How long is the coast of the Mandelbrot set?
>>=20
>> Infinite. (In fact it has dimension 2, which you can feel is true if you
>> look at a deephorse or zoom about four full zooms around the point where
>> the usual golden ratio Siegel disk Julia is found.)
>
>I agree, the usual answer to the question - what is the dimension of the
>MSet...
>is 2.
>
Mitsuhiro Shishikura. "The boundary of the Mandelbrot set has Hausdorff
dimension two." Complex Analytic Methods in Dynamical Systems. (Rio de
Janeiro, 1992.) Ast=E9risque No. 222 (1994) 7, 389-405.=20

>
>How ever the question here is a little different. It is perhaps not well=20
>stated mathematically.  The dimension of the coast of the=20
>'contiguous' Mandelbrot set (the cardioid and attached buds, skipping the=
=20
>filaments and midgets) is not dimension 2.=20
>
But what do you mean by "contiguous", then? The M-set is simply connected,
which would make the entire boundary (midgets and filaments both) a simple
closed curve. There are other characterisations of "connectedness" for
which the connectedness of the M-set is not known (exercises for the
reader), but I'm not sure if they apply in this case. If they do, I would
be happy to be enlightened.

Anyway, how much of those filaments are no more than really really really
tiny M-sets? Whatever that means mathematically.

Morgan L. Owens



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

Date: Fri, 30 Jan 1998 09:49:20 +0100
From: Peter Otterstaetter <[e-mail]>
Subject: (fractint) Hermann Ring formula

Paul Derbyshire wrote:

> FixedPoint         {
>   reset=1960 type=formula formulafile=hring.frm formulaname=HRing_J

please, can anyone tell me where I can find the Hermann Ring formula?
May be I lost some posting.
TIA
Peter

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Date: Fri, 30 Jan 1998 04:34:41 -0500
From: George Martin <[e-mail]>
Subject: (fractint) Hermann Ring formula

Peter,

Here is the whole series:

HRing_J {; This thing is capable of generating Herman rings for alpha
         ; equal to exp(2*pi*i*a), a irrational.
         ; p1: alpha. p2: c. p3: Orbit trap radius about 0, reciprocal is
         ; used for infinity.
         ; Use outside=real, logmap=0, periodicity=0.
  z=pixel, a=p1, c=p2, r=real(p3), rr=1/r, iter=0, done=0:
  z2=sqr(z)
  z=a*z2*(z-c)/(1-c*z)
  iter=iter+1
  IF(lastsqr<r || lastsqr>rr)
    color=iter
    IF(color<1)
      color=1
    ELSEIF(color>127)
      color=127
    ENDIF
    IF(lastsqr<r)
      color=color+127
    ENDIF
    z=color-iter-7
    done=1
  ENDIF
  done==0
  ;SOURCE: 98msg.frm
}


HRing_J2 {; This thing is capable of generating Herman rings for alpha
          ; equal to exp(2*pi*i*a), a irrational.
          ; p1: alpha. p2: c. p3: Orbit trap radius about 0, reciprocal is
          ; used for infinity.
          ; Color variant: stretches to maxiter.
          ; Use outside=real, logmap=0, periodicity=0.
  z=pixel, a=p1, c=p2, r=real(p3), rr=1/r, iter=0, done=0:
  z2=sqr(z)
  z=a*z2*(z-c)/(1-c*z)
  iter=iter+1
  IF(lastsqr<r || lastsqr>rr)
    color=(iter/maxit)*127
    IF(color<1)
      color=1
    ELSEIF(color>127)
      color=127
    ENDIF
    IF(lastsqr<r)
      color=color+127
    ENDIF
    z=color-iter-7
    done=1
  ENDIF
  done==0
  ;SOURCE: 98msg.frm
}


HRing_Ma {; Mandelbrot set slice, alpha varies, c fixed.
          ; p2: c. p3: Orbit trap radius about 0, reciprocal is
          ; used for infinity.
          ; Use outside=real, logmap=0, periodicity=0.
  a=pixel, c=p2, r=real(p3), rr=1/r, iter=0, done=0, flag=0, m=maxit
  z=(3+sqr(c)+sqrt(9-10*sqr(c)+sqr(sqr(c))))/(4*c)
  IF(real(c)*real(c)-imag(c)*imag(c)-5>=0)
    flag=1-flag
  ENDIF
  IF(imag(c)<0)
    flag=1-flag
  ENDIF
  IF(flag==1)
    z=(3+sqr(c)-sqrt(9-10*sqr(c)+sqr(sqr(c))))/(4*c)
  ENDIF
  :
  z2=sqr(z)
  z=a*z2*(z-c)/(1-c*z)
  iter=iter+1
  IF(lastsqr<r || lastsqr>rr)
    color=(iter/maxit)*127
    IF(color<1)
      color=1
    ELSEIF(color>127)
      color=127
    ENDIF
    IF(lastsqr<r)
      color=color+127
    ENDIF
    z=color-iter-7
    done=1
  ENDIF
  done==0
  ;SOURCE: 98msg.frm
}


HRing_Mc {; Mandelbrot set slice, c varies, alpha fixed.
          ; p1: alpha. p3: Orbit trap radius about 0, reciprocal is
          ; used for infinity.
          ; Use outside=real, logmap=0, periodicity=0.
  a=p1, c=pixel, r=real(p3), rr=1/r, iter=0, done=0, flag=0, m=maxit
  z=(3+sqr(c)+sqrt(9-10*sqr(c)+sqr(sqr(c))))/(4*c)
  IF(real(c)*real(c)-imag(c)*imag(c)-5>=0)
    flag=1-flag
  ENDIF
  IF(imag(c)<0)
    flag=1-flag
  ENDIF
  IF(flag==1)
    z=(3+sqr(c)-sqrt(9-10*sqr(c)+sqr(sqr(c))))/(4*c)
  ENDIF
  :
  z2=sqr(z)
  z=a*z2*(z-c)/(1-c*z)
  iter=iter+1
  IF(lastsqr<r || lastsqr>rr)
    color=(iter/maxit)*127
    IF(color<1)
      color=1
    ELSEIF(color>127)
      color=127
    ENDIF
    IF(lastsqr<r)
      color=color+127
    ENDIF
    z=color-iter-7
    done=1
  ENDIF
  done==0
  ;SOURCE: 98msg.frm
}

Regards,

George Martin

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

Date: Fri, 30 Jan 1998 03:17:01 -0800 (PST)
From: FIRSTNAME LASTNAME <[e-mail]>
Subject: Re: (fractint) Another formula

- ---Paul and/or Joyce Carlson <[e-mail]> wrote:
>
> This formula and par produce a very colorful spiral.
> Since much of the logic in this formula is the same
> as that in other formulas I've posted, I've eliminated
> most of the comments that have appeared in the other
> formulas.
>
> Paul Carlson
>
> CSin_Atan_Julia {; Copyright (c) Paul W. Carlson, 1998
>     ;****************************************************
>     ; Always use floating point math and outside=summ.
>     ;
>     ; Parameters:
>     ;   p1       = Julia set coordinates
>     ;   real(p2) = maximum value of abs(real(w))
>     ;   real(p3) = number of color ranges
>     ;   imag(p3) = number of colors in each color range
>     ;****************************************************
>     prev_w = pixel
>     c = p1
>     z = 0
>     bailout = 0
>     iter = 0
>     range_num = 0
>     max_real = real(p2)
>     num_ranges = real(p3)
>     colors_in_range = imag(p3):
>     ;****************************************************
>     w = c * sin(prev_w)
>     ;****************************************************
>     IF (abs(real(w)) > max_real)
>     delta_i = imag(w) - imag(prev_w)
>     delta_r = real(w) - real(prev_w)
>     angle = abs(atan(delta_i / delta_r))
>     bailout = 1
>     range_index = 2 * colors_in_range * angle / pi
>     z = range_index + range_num * colors_in_range + 1
>     ENDIF
>     prev_w = w
>     range_num = range_num + 1
>     IF (range_num == num_ranges)
>         range_num = 0
>     ENDIF
>     iter = iter + 1
>     z = z - iter
>     bailout == 0
> }
>
> c_sin_atan_jul     { ; Copyright (c) Paul W. Carlson, 1998
>   reset=1960 type=formula formulafile=csinatan.frm
>   formulaname=csin_atan_julia passes=1
>   corners=0.50200688/0.62208688/0.481622813/0.571682813
>   params=1/0.1/1.35/0/8/30
>   float=y maxiter=5000 inside=253 outside=summ
>   colors=000fOz<28>I0Kz0f<28>O08z88<28>O00zW0<28>c40zz0<28>aG0\
>   0zR<28>0C40zz<28>0CCGGz<28>00O000<13>000
>   }
>
>
>
> -
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>


Umm....

Exactly how do I place these FRM & PAR files into FRACTINT to use
them?  I'm not new to FRACTINT but I am new to the idea of grabbing
stuff off the list and slapping it into my copy of FRACTINT.  Also if
the par calls for a color scheme I don't have how do I tell it to use
another one.




THANX


James R. McKenzie

_________________________________________________________
DO YOU YAHOO!?
Get your free @yahoo.com address at http://mail.yahoo.com


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

Date: Fri, 30 Jan 1998 07:47:27 -0800
From: Peter Jakubowicz <[e-mail]>
Subject: (fractint) How long _is_ the coast of the M-set???

OK.  How can the M-set be infinitely fuzzy, have an infinite perimeter,
_and_ be simply connected at the same time? If you can measure its area,
then why is the perimeter infinite. I was thinking there must be some way
of closing in on the perimeter; that it must approach a limit, the way the
area does.

I know the standard answer, that its dimension is 2, ergo it's perimeter is
infinite. But is it not something like the behavior of matter? At the
subatomic level things are really weird, unmeasurable, but not so at the
quotidian level; for example, I'm 5'11'', and I exist whether someone is
holding a yardstick to me or not. Similarly, when you look at the M-set
close up, zoom in on it, it gets weird; but from a distance it looks like
an island, connected. Maybe I just don't know enough math??? This M-set
connectedness problem has been nagging at me for a while.

Well, I guess that's enough obfuscating,

Peter


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

Date: Fri, 30 Jan 1998 07:55:41 -0500
From: Lee Skinner <[e-mail]>
Subject: (fractint) Re: Steven vs

Hi Steve,

  I really enjoyed your "The Seven Highly Effective Habits of Creating
Fractals".  (Now reading "The Joy of Fractals".)

Lee

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

Date: Fri, 30 Jan 1998 13:44:59 +0100
From: Peter Otterstaetter <[e-mail]>
Subject: (fractint) Herman Rings

George Martin wrote:
> Here is the whole series:
Thank you very much!

Peter

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

Date: Fri, 30 Jan 1998 09:05:48 -0500
From: George Martin <[e-mail]>
Subject: Re: (fractint) Another formula

James,

You wrote asking how to get from a message to an image, and how to change
colors.

1. Add the image entry to a DOS text file with the extension .par and the
formula to one with an extension .frm, and make sure those files are in the
directories where your other .par and .frm files are located, respectively.
This takes a bit of work, but in the long run is best. A short cut is to
add the letters "frm:" in front of the formula (sometimes this is already
done in the message). Then you can simply add the whole message to a .par
file, but be cautioned that the formula will only be available for drawing
the image. You won't be able to access it otherwise. If you add the formula
to a .frm file, don't forget to delete the "frm:" identifier.

   I gather from your message that you know how to navigate Fractint to
draw the image at this point.

2. If a .par entry calls for a .map file you don't have, fractint will
automatically use the default .map file (appropriately named default.map).
To change the color palette, hit "C" and then "L". This will bring up a
list of the .map files in your default .map directory. Selecting one will
apply that .map file to you image.

   You can cycle colors of the current palette by hitting "+" or "-".

   You can edit the current palette by hitting "e" and then "<CR>". See the
Fractint documentation for how to manipulate the palette.

   <ESC> gets you out of the color mode and back to the regular image.

   You can save the current palette as a .map file by hitting "C" and then
"S".

George Martin

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

Date: Fri, 30 Jan 1998 09:44:19 -0600
From: "Justin A. Kolodziej" <[e-mail]>
Subject: Re: (fractint) How long _is_ the coast of the M-set???

Peter Jakubowicz wrote:
>
> OK.  How can the M-set be infinitely fuzzy, have an infinite perimeter,
> _and_ be simply connected at the same time? If you can measure its area,
> then why is the perimeter infinite. I was thinking there must be some way
> of closing in on the perimeter; that it must approach a limit, the way the
> area does.

This may come as a shock, but the Koch snowflake is the same way.  Its
perimeter is infinite because each stap in its construction multiplies
the perimeter by 4/3, yet it has less area than a circle circumscribed
about it!  And its fractal dimension is only 1.26 or something low like
that.

About it and the M-set being "infinitely fuzzy,"  that's probably a
different matter.  If you mean the little arms and spirals that contain
the minibrots, then, no, I admit the Koch snowflake doesn't have those.
But you don't even need the dimension of the boundary to reach 2 to get
an infinite perimeter.

> I know the standard answer, that its dimension is 2, ergo it's perimeter is
> infinite. But is it not something like the behavior of matter? At the
> subatomic level things are really weird, unmeasurable, but not so at the
> quotidian level; for example, I'm 5'11'', and I exist whether someone is
> holding a yardstick to me or not. Similarly, when you look at the M-set
> close up, zoom in on it, it gets weird; but from a distance it looks like
> an island, connected. Maybe I just don't know enough math??? This M-set
> connectedness problem has been nagging at me for a while.
>
Hmmm, I'm pretty sure someone proved it, but I don't remeber how.  What
I do remember is that in the excellent book "The Beauty of Fractals"
there was a description of one way to prove it.  The way described was
to make a model by pinching points on a unit circle together, prove that
the model was connected, then prove that the model was equivalent th the
M-set, and voila!  I don't know if it was actually done like that,
though.
My 2.5 yen (or thereabouts),
- --
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: Fri, 30 Jan 1998 08:11:53 -0800
From: kathy roth <[e-mail]>
Subject: (fractint) gravijul

Hey , have a look at these two.  I would
have thought they were from one of the
if....else formulas.

pretzel_logic      { ; formula by Mark "Bud" Christenson
                     ; palette from Les St.Clair
  reset=1960 type=formula formulafile=gravijul.frm
  formulaname=gravijul function=cotanh/atanh/atan passes=t
  center-mag=-4.44089e-015/2.66454e-015/0.4137324
  params=1/0/0/0/2.95/0 float=y inside=111 outside=atan
colors=GBRHCS<11>X`tZcwZcw<10>imvW0B<5>`0D\
a0Db2D<14>zVF<14>b2Da0D`0D<18>\
 I06I06H07<20>00K<22>zpa<13>RK7OI5NH6<12>D\
5IC4JD6LE8NGAQjnv<3>nru<2>gkldh\
  ibef_bdY_a<12>000<18>f`V<9>JCM<9>zzc<9>F05\
<12>R0AS0AU0AV0A
  }

where_did_all_the_spirals_go      { ; formula by Mark "Bud" Christenson
                     ; palette from Les St.Clair
  reset=1960 type=formula formulafile=gravijul.frm
  formulaname=gravijul function=cotanh/atanh/atan passes=t
  center-mag=-4.44089e-015/2.66454e-015/0.4137324
  params=1/0.1/0/0/2.95/0 float=y inside=111 outside=atan
 colors=GBRHCS<11>X`tZcwZcw<10>imvW0B<5>`0Da\
0Db2D<14>zVF<14>b2Da0D`0D<18>\
 I06I06H07<20>00K<22>zpa<13>RK7OI5NH6<12>D5IC\
4JD6LE8NGAQjnv<3>nru<2>gkldh\
  ibef_bdY_a<12>000<18>f`V<9>JCM<9>zzc<9\
>F05<12>R0AS0AU0AV0A
  }






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

Date: Fri, 30 Jan 1998 18:54:55 +1
From: "J.P. Louvet" <[e-mail]>
Subject: Re: (fractint) How long _is_ the coast of the M-set???

le 30 Jan 98 a 7:47, Peter Jakubowicz ecrivait (Peter Jakubowicz wrote) :

>  If you can measure its area,
> then why is the perimeter infinite. I was thinking there must be some way

There is a simple way to show that a curve may have an infinite length but
encloses a finite area.
Start with an equilateral triangle and its circumcircle. Then transform
the triangle to have a Koch snowflake : the Koch curve has an infinite
length but it is surrounded by the circle. Therefore, the area enclosed is
limited.

Or look at an island : do you accept, as stated by Mandelbrot that the
length of its coat is infinite ? But the area of the island is limited.

Jean-Pierre louvet : [e-mail]
Fractal album :
http://graffiti.cribx1.u-bordeaux.fr/MAPBX/louvet/jpl0.html

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

Date: Fri, 30 Jan 1998 13:28:26 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) a`a`a`a`a`a`

>
>Whaaaaaat are these horrible little a`a`a`s doing on my par screen. They
>don't appear in the file itself, so  I can't even delete them. They are
>completely preventing me from doing the herman rings, and a number of other
>par files I cut and pasted the same day. Any clues please?
>Beth

Whaaat?
MY HERMAN RING PAR HAS GLITCHES??
I didn't use any funky encoding or attachments or anything!
What the hell???


- --
    .*.  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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------------------------------

Date: Fri, 30 Jan 1998 10:50:44 -0800
From: Mark Christenson <[e-mail]>
Subject: (fractint) gravijul

At 08:11 AM 1/30/98 -0800, Kathy Roth wrote:
>Hey , have a look at these two.  I would
>have thought they were from one of the
>if....else formulas.
>...

Very cool!  I especially liked "where...".  I haven't played with
the imaginary variables yet (or p2, for that matter); hard to believe
such a small tweak could fragment the fractal in that manner!
It reminds me of some of Don Archer's fragtals.  From your first
batch, my fave was "Please!"

Here's one more of mine, in a style very different from my usual MO.

gj081              { ; "Parasols", Mark "Bud" Christenson 1/25/98
  reset=1930 type=formula formulafile=budz.frm formulaname=gravijul
  function=tanh/atanh/asin passes=t
  center-mag=1.18968/0.963934/1.804124 params=1/0/0/0/4/0 float=y
  inside=bof60 outside=imag
  colors=000SS_<3>cTgfUjhUkjUl<2>tYo<12>zz0<5>ct0_s0Ys3<11>7on5nr3nv0mz1kz\
  3hz<12>TDwVAvX9r<11>p15r00v00z00<30>YVVXXXXWX<29>y2yz0zz1y<23>zlEznCznC<\
  35>zn1zm0zm0zl0zl0<43>zU0zzz
  }

Aloha, Bud


P.S.: Kathy, please don't credit my formula in the *first* comment
 field.  The artist should get primary credit!  :o)


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Date: Fri, 30 Jan 1998 13:54:07 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) 2(-dimensionally) Dumb ??

>But what do you mean by "contiguous", then? The M-set is simply connected,
>which would make the entire boundary (midgets and filaments both) a simple
>closed curve.

Simple closed curve?? I think not... it has infinitely many points of
self-contact. (Filament necked down points, filament branch points, cusps
and component roots...) The boundary of a connected *open* set is a simple
closed curve. The M-set is a connected *closed* set.

>Anyway, how much of those filaments are no more than really really really
>tiny M-sets? Whatever that means mathematically.

The filaments include mini Mandelbrots but also various points of
accumulation of the M-set that are not in any mini Mandelbrot (either
inside or on the boundary of one of its disks or cardioids that is).
The preperiodic Misiurewicz points are some (but not all) of these points of
accumulation (for example the "band merging" point where the sequence of
front buds ends and the spike begins, is not a Misiurewicz point).

- --
    .*.  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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Date: Fri, 30 Jan 1998 11:02:13 -0800
From: "Jay Hill"<[e-mail]>
Subject: Re: (fractint) a`a`a`a`a`a`

>>Whaaaaaat are these horrible little a`a`a`s doing on my par screen. They
>>don't appear in the file itself, so  I can't even delete them. They are
>>completely preventing me from doing the herman rings, and a
>>number of other par files I cut and pasted the same day. Any clues
>>please?
>>Beth
>Whaaat?
>MY HERMAN RING PAR HAS GLITCHES??
>I didn't use any funky encoding or attachments or anything!
>What the hell???

This has been discussed at length here. The problem is in the servers
and emailers. Most of us get the postings just fine. You can edit these
'special' space characters out using PFE

http://www.lancs.ac.uk/people/cpaap/pfe

We can give you some special help on these files (the =3D problem
and the aaaaa problem) if you specify exactly which post gave you
trouble. I can email you a good copy or put one on my web site.
Unfortunately, the official archive suffers from these problems so
there is no relief there.

An example of the help available is
http://home.san.rr.com/jayrhill/CARLSON.PAR
which I placed there and maintain because Paul Carlson was not
able to post except indirectly. All of his fine formula were messed
up in the archive.  Several subscribers were having great difficulty.

Jay



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Date: Fri, 30 Jan 1998 14:03:18 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) How long _is_ the coast of the M-set???

An infinite perimeter can easily enclose a finite area. Take a triangle.
(Equilateral). Perimeter is 3, area is 1 (using custom units here). Add a
one-third scale triangle at the center of each side: area is now 1/3 greater
than what it was, and boundary is 4/3 what it was. Repeat adding ever smaller
triangles to the center of each side, and the perimeter keeps going by 4/3
while the area keeps adding a smaller and smaller amount. The perimeter
tends to infinity, the area to a finite amount.


- --
    .*.  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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------------------------------

Date: Fri, 30 Jan 1998 14:11:04 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) a`a`a`a`a`a`

>This has been discussed at length here. The problem is in the servers
>and emailers. Most of us get the postings just fine. You can edit these
>'special' space characters out using PFE

Yeah, but I'm using the same mailer that never gave me any trouble before,
i.e. never encoded my PARs or anything... why would it suddenly start now?


- --
    .*.  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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------------------------------

Date: Fri, 30 Jan 1998 11:16:51 -0800
From: "Jay Hill"<[e-mail]>
Subject: Re: (fractint) 2(-dimensionally) Dumb ??

>But what do you mean by "contiguous", then? The M-set is simply connected,
>which would make the entire boundary (midgets and filaments both) a simple
>closed curve.

contiguous - adj
1. in physical contact; touching along all or most of one side.
2. near, next, or adjacent

In this case, since the first derivative of the separation distance between
a bud and its parent is zero while at the Feigenbaum points it is very
different, I would call contiguous the attached buds and parent cardioid.
One can change c smoothly along the real line for example and get a
progression of periodic orbits. When you get to the Feigenbuam point at



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Date: Fri, 30 Jan 1998 14:20:54 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: (fractint) Apology re: encrypted PAR

I apologise for the encoding on the second posting of hring.par. I can
only surmise that some clueless moron in the admin here at freenet has
decided to change the settings on the mail software we use to encode
outgoing mail. I have informed them that their change is far from
transparent and is actually causing at least 2 freenet users problems,
hopefully, they will do away with this ill-conceived and
poorly-thought-out change very soon. I'll keep you posted...
 Until then, since us lowly users on freenet don't have access to change
the mail settings, such as encoding, I'm afraid I either won't be able to
post PARs, if you won't accept encoded ones, or else I will have to post
encoded PARs and you will have to decode them. In that case I would love
it if someone could please take any encoded pars I post, fix them in PFE
and repost them for others' benefit. If there are any volunteers
(obviously, you need to not be on freenet), then thanks... if not, then I
guess I'll just wait until freenet fixes this. If they ever do. If they
don't, I might unsubscribe this list here and subscribe from my Hotmail
address. (grr, what a mess of inconvenience...clueless admins...)

- --
    .*.  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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------------------------------

Date: Fri, 30 Jan 1998 14:24:05 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) 2(-dimensionally) Dumb ??

Someone wrote:

>In this case, since the first derivative of the separation distance between
>a bud and its parent is zero while at the Feigenbaum points it is very
>different, I would call contiguous the attached buds and parent cardioid.
>One can change c smoothly along the real line for example and get a
>progression of periodic orbits. When you get to the Feigenbuam point at

"When you get to the Feigenbaum point at"??? When you get to the
Feigenbaum poiont at WHAT???


Let me guess: some glitch cut off the end of your message? :P


- --
    .*.  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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------------------------------

Date: Fri, 30 Jan 1998 11:45:51 -0800
From: Mark Christenson <[e-mail]>
Subject: (fractint) gravijul

Kathy:
>From your first batch, my fave was "Please!"...

Wait!  How could I forget "field_of_attraction"?  Another artifact...
Does anyone know why/how boundary tracing sometimes
produces these things?  BTW, would you prefer (as does mr. lebow)
that we not Capitalize your Name?

And Gedeon, I haven't forgotten about you.  My favorite from
your offerings was gp-gj09-05.  Similar comments (coolness
and fragmentation) apply to it as well as to k/Kathy's "where..."


Aloha, Bud


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

Date: Fri, 30 Jan 1998 19:04:38 -0000
From: "Bagpuss" <[e-mail]>
Subject: Re: (fractint) a`a`a`a`a`a`

>>Whaaaaaat are these horrible little a`a`a`s doing on my
par screen. They
>>don't appear in the file itself, so  I can't even delete
them. They are
>>completely preventing me from doing the herman rings, and
a number of other
>>par files I cut and pasted the same day. Any clues please?
>>Beth
>
>Whaaat?
>MY HERMAN RING PAR HAS GLITCHES??
>I didn't use any funky encoding or attachments or anything!
>What the hell???
These a' things seem to be produced by notepad sometimes...
Apparently it has to do with the fact that notepad saves
spaces as a different ascii number than Dos programs.

I usually get around this problem by saving the par with
notepad, and then loading it into DOS edit and doing a
search and replace replacing the a' thingys with spaces

    Hope this helps
            Stephen

Visit my fractal page
http://ireland.iol.ie/~bagpuss



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

Date: Fri, 30 Jan 1998 15:42:21 -0500
From: "aardvarko" <[e-mail]>
Subject: (fractint) (Fractint) Formula Fricassee

Can someone help me out with my formula? This:

TEST4 {
  z= Pixel, z=Sqr(z)
x=real(z), y=imag(z), tst=p1+4, t=1+pixel
IF (whitesq)
   y=Pixel-x/z
   x=Pixel-y/z
   x=abs(x)+fn1(y)
   y=abs(y)+fn1(x)
   Pixel=fn2(x*y)
   Pixel=fn1(Pixel)
ELSE
   y=Pixel-x/z
   x=Pixel-y/z
   x=abs(x)+fn1(y)
   y=abs(y)+fn1(x)
   Pixel=fn2(x*y)
ENDIF
:
}

just produces a blue screen. And, yes, I realize that I have some unused
vars. Same with this variant:

TEST4 {
  z= Pixel, z=Sqr(z)
x=real(z), y=imag(z), tst=p1+4, t=1+pixel
   y=Pixel-x/z
   x=Pixel-y/z
   x=abs(x)+fn1(y)
   y=abs(y)+fn1(x)
   Pixel=fn2(x*y)
IF (whitesq)
   Pixel=fn1(Pixel)
ELSE
ENDIF
:
}


However, this:

TEST3 {
  z= Pixel, z=Sqr(z)
  tst=p1+4, t=1+pixel, x=real(z), y=imag(z)
y=Pixel-x/z
x=Pixel-y/z
x=abs(x)+fn1(y)
y=abs(y)+fn1(x)
Pixel=fn2(x*y)
Pixel=fn1(Pixel)
}

and this:

TEST2

  z= Pixel, z=Sqr(z)
  tst=p1+4, t=1+pixel, x=real(z), y=imag(z)
y=Pixel-x/z
x=Pixel-y/z
x=abs(x)+fn1(y)
y=abs(y)+fn1(x)
Pixel=fn2(x*y)

}

function perfectly. Whaddid I do wrong?

<signature="begin">
|thank you for reading my message
|                            __    __  o
|putt putt...               /  \/\/  \/
|                           \__/\/\__/\o
|. . . . . . . . . . . . . . /\ . ./\ rdv
|                    __              __
|  ___ ____ ________/ /  _____ _____/ /_____
| / _ `/ _ `/ __/ _  / |/ / _ `/ __/  '_/ _ \
| \_,_/\_,_/_/  \_,_/|___/\_,_/_/ /_/\_\\___/
|               aka Turret
|BobCode: K l E m6 C B-x O L S+++ T A H b8 D2
|http://www.geocities.com/SiliconValley/Lab/2672/index.html
<signature="none">




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

Date: Fri, 30 Jan 1998 12:43:14 -0800
From: "Jay Hill"<[e-mail]>
Subject: (fractint) How long is the coast of the Mandelbrot set?

Peter Jakubowicz wrote
>>>2)How long is the coast of the Mandelbrot set?

Jay Hill wrote:
>>How ever the question here is a little different. It is perhaps not well
>>stated mathematically.  The dimension of the coast of the
>>'contiguous' Mandelbrot set (the cardioid and attached buds, skipping the
>>filaments and midgets) is not dimension 2.

Paul Derbyshire wrote:
>But what do you mean by "contiguous", then? The M-set is simply connected,
>which would make the entire boundary (midgets and filaments both) a simple
>closed curve.

contiguous - adj
1. in physical contact; touching along all or most of one side.
2. near, next, or adjacent

Since the cardioids and buds are often referred to as the lake, I
took the original question about the coast to be the lakes'
boundaries - an interesting question as I shall show.

In this case, since the first derivative of the separation distance
between a bud and its parent is zero while at the Feigenbaum
points it is very different, I would call "contiguous" the attached buds
and parent cardioid.  The derivative I'm refering to is with respect
to the tangent direction.  One can change c, in the Mandelbrot
iteration formula, smoothly along the real line, for example, and
get a progression of periodic orbits. When you get to the
Feigenbaum point at

- -1.401155189092050600523826787893861292226308...

we see a change in the pattern.  The orbit is chaotic. We have
entered the 'chaos zone' - dee-dee dee-dee dee-dee.
Oopps sorry Rod Sterling.   See Jim Muth's Fractal-Art list
F.O.T.D., 27-01 (String of Bays) post or use the par below.
http://home.att.net/~Paul.N.Lee/FotD/FotD.html
In the center, we see a tower showing the row of ever small buds
approaching the Feigenbaum point. Their size approaches a
geometric progression with the Feigenbaum constant
4.6692016091029906718532038204662... as the size ratio. They
look the same size because of the logarithmic transformation. Now
look at the other two 'towers', each representing the same thing,
namely the spike beyond the Feigenbaum point.  We see a row
of midgets which all look the same size.  They are not really,
since there is a logarithmic transformation involved. But it does
show that near the Feigenbaum point the fraction of the real
line inside midgets approaches a constant. And, I claim, that
constant is not unity. There is a zon-zero portion which is chaotic
or pre-periodic.  Several years ago, I calculated this fraction. I'm
trying to locate my post to sci.fractals. The fraction of the real line
from -2 to .25 that was periodic was about 82%, as I recall.

It therefore, is of interest to some, to separate the midgets from the
rest.  For example, I have calculated a lower bound of the area of
the interior of the MSet, that being the part contained within the
"contiguous" midgets.  See this URL and references there.

http://www.geocities.com/CapeCanaveral/Lab/3825/Period-Area-16.html

Since there is a non-zero portion of the real line not contained in
any midgets, there may well be a non-zero portion of the MSet
area remaining uncounted in the 'interior' calculations.  This is,
as I understand it, still an open question.

As for the perimeter or dimension of the "contiguous" part of the
Mandelbrot set, I have estimated that also. It comes as a by
product of the area calculation. For each bud, calculate the radius
and sort these. Now make a running perimeter sum vs. radius.
The result gives a measure of the perimeter dimension.  I get
a value close to 1.250 +- 0.003.

 period   'radius'   perimeter
 1      0.61237244  4.00000000
 2      0.25000000  5.57079633
 3      0.09452154  6.16469318
...
60      0.00029358 26.25024235


Jay

PS Sorry about the partial post. I hit some alt key while typing
and suddenly found my article had escaped!

frm:MandelbrotPanorama { ; Jay Hill, 1998
              ; Panorama Mandelbrot set
  z = 0, c = exp(flip(pixel))+p2:
    z = z*z + c
    |z| < 4
}


Panorama_Fiegenbaum { ; (c) Jay Hill, 1998
                      ; Panorama view from Fiegenbaum point
           ; -1.401155189092050600523826787893861292226308
  reset=1960 type=formula formulaname=MandelbrotPanorama
  center-mag=0/-3.27483/0.2449042 symmetry=yaxis
  params=0/0/-1.4011551890920506005/0 passes=1
  float=y maxiter=25600 inside=0 outside=summ periodicity=0
  colors=000<7>00z<6>ccc<8>w0w<6>hhh<8\
  >z00<6>mmm<2>qg`seWtcRvaMw_IyYDzW8<6\
  >jjj<8>zz0<6>mmm<8>0w0<6>mmm<8>0zz<6\
  >rrr<56>00z00z00y<81>001000000000
  }




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

End of fractint-digest V1 #92
*****************************