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fractint-digest       Saturday, January 31 1998       Volume 01 : Number 094




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

Date: Sat, 31 Jan 1998 00:13:31 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) (Fractint) Formula Fricassee

What?! You can assign to "pixel"??


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Paul Derbyshire [e-mail] [e-mail]

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

Date: Fri, 30 Jan 1998 21:42:15 -0800
From: Mark Christenson <[e-mail]>
Subject: Re: (fractint) Re: gravijul formula

At 10:01 PM 1/30/98 -0500, Gedeon wrote:
>...
>Bud...
>Judging from the name you gave to your latest post, you must have quite
>a few pars!!!

Ah, but that's only because you don't know my system!  Like Kathy,
I too am a lazy typist.  I use two alpha characters for the fractal type,
and two alphanumeric chars to enumerate primary images; anything
past the first four characters indicates zooms or variants of the primaries.
For example, the post you referred to was

gj081

which breaks down as
gj = gravijul
08 = primary #8
1 = a zoom, most of one quadrant.

By using alphanumerics for "numbers" (10 numbers + 26 lower case
characters), I get modulo-36 symbols and can encode 36^2 = 1296
items with two characters, versus a rather feeble 100 (using numbers
only).  My highest primary is gj0j (or #19), which is actually misleading
since some of these are related (I'm not too rigorous about enforcing
the system), and others are "branch point" images I've saved for
future investigation.

Since I'm talking about branch points and leverage, this is a good point
to give credit where it's due.  The incredible variety these "roll your own"
formulae exhibit is due to the programmers of and contributors to Fractint.
By writing one simple formula with three embedded functions, the 26
functions available (including ident) create 26^3 = 17576 variations!
Add the six (three complex) variables and multiple coloring schemes,
and we're clearly talking orders of infinity... boggles the mind, no?

Anyway, like I said, most of my pars are a bit rough; but since you
insist, here's one that's *almost* ready for prime time (there are a lot
of nice alternatives among the "outside color" options):

gj0e               { ; "Vine" by Mark "Bud" Christenson 1/25/98
  reset=1930 type=formula formulafile=budz.frm formulaname=gravijul
  function=sin/atanh/exp passes=b
  center-mag=-0.859677/0.701461/1.420455 params=1/0/0/0/4/0 float=y
  inside=111 outside=mult
  colors=0O0<38>0y00z00z01z0<64>jz0jz0kz0kz0mMfmz0<142>zzz
  cyclerange=0/255
  }

Note: there are some minor errors using the "b" option, but it's
entertaining to see drawn and renders twice as fast as any other
method.  I can't guarantee it will work well at less than 640x480.


BTW Les, I really like "Katy Lied" (no lie)!


Aloha, Bud


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

Date: Fri, 30 Jan 1998 22:19:18 -0800
From: Mark Christenson <[e-mail]>
Subject: (fractint) Re: gravijul formula

> gj0e               { ; "Vine" by Mark "Bud" Christenson 1/25/98
> ...
> Note: there are some minor errors using the "b" option, but it's
> entertaining to see drawn and renders twice as fast as any other
> method.

Oops, bad idea; the damage is worse than I thought.  Better go with
passes=t (par below is corrected).

gj0e               { ; "Vine" by Mark "Bud" Christenson 1/25/98
  reset=1930 type=formula formulafile=budz.frm formulaname=gravijul
  function=sin/atanh/exp passes=t
  center-mag=-0.859677/0.701461/1.420455 params=1/0/0/0/4/0 float=y
  inside=111 outside=mult
  colors=0O0<38>0y00z00z01z0<64>jz0jz0kz0kz0mMfmz0<142>zzz
  cyclerange=0/255
  }


Bud


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

Date: Sat, 31 Jan 1998 00:21:45 -0600 (CST)
From: [e-mail] (Paul and/or Joyce Carlson)
Subject: (fractint) A Herman Ring Par

Here's a Herman Ring par that produces a familiar image but
with a nice difference - a very delicate bright image over
a very bold dark "background."  This is a pretty deep zoom
into the ParabolicFixed image that someone posted the par
for, but with a different colormap.  Don't use solid guessing
on this - too much is lost.  Tesseral works well and cuts
down on the time needed to plot the little Mandy (what my
wife calls a baby 'brot) in the center.

Paul Carlson

hring_mandel       { ; Copyright (c) Paul W. Carlson, 1998
  reset=1960 type=formula formulafile=hring.frm
  formulaname=hring_mc passes=t
  center-mag=-1.13968013785657900/+0.00177213235944437/1.3041\
  58e+007/1/127.5
  params=1/0/0/0/0.001/0 float=y
  maxiter=5000 inside=0 outside=real
  colors=000C0C<61>zVzzVzyVy<61>C0C0CC<62>VzzVzzVyy<61>0CC
  }



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

Date: Sat, 31 Jan 1998 01:23:10 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) january wizzle pars

>
>IMHO january was a fantastic month when it came to fractals, pars and
>formulas.  I'm offering this far too long list of pars....made with
>everyone's formulas....which I just loved.  I had a wonderful time with all
>of the formulas posted during the month....

Hey! There aren't any herman rings in there! :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 23:41:52 -0800
From: "Jay Hill" <[e-mail]>
Subject: Re: (fractint) ADDGIFS Program

Hi folks,

Get Paul's program here
http://www.geocities.com/CapeCanaveral/Lab/3825/addgifs.zip

and his par and formula files
http://home.san.rr.com/jayrhill/CARLSON.PAR

and check out the latest adventures of Dr. J
http://home.san.rr.com/jayrhill/FotN/FotNindx.html

Jay

- ----------
> From: Paul and/or Joyce Carlson <[e-mail]>
> To: [e-mail]
> Subject: (fractint) ADDGIFS Program
> Date: Friday, January 30, 1998 5:29 PM
>
> I just uploaded a program I wrote to the alt.binaries.pictures.fractals
> newsgroup.  The program is nice for overlaying fractals, the result
> looking much like some of the PHC fractals created with Fractint.  If
> anyone does not have access to the newsgroup and would like to try the
> program, I'd be glad to email a uuencoded copy to them.  What follows
> is the introductory message that I posted to the newsgroup:
>
> Part (1/1) of this message contains ADDGIS.ZIP in uuencoded
> format.  This will pkunzip into the files ADDGIFS.EXE and
> README.1ST.
>
> ADDGIFS is a combination of three of my prior programs,
> GIFS2PNG, GIFS2JPG and GIFS2BMP into one program with
> a nice, very easy to use interactive interface.  The
> program combines two 256-color GIF files of the same
> resolution and outputs a 24-bit PNG, JPEG or BMP file.
> The GIF files remain unchanged.
>
> The program is FREEWARE.
>
> Enjoy!
> Paul Carlson
> ------------------------------------------------------------------
>                 email   [e-mail]
>
> WWW Fractal Galleries   http://sprott.physics.wisc.edu/carlson.htm
>                         http://fractal.mta.ca/fractals/carlson/
>                         http://www.cnam.fr/fractals/carlson.html
> ------------------------------------------------------------------
>
>
> -
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------------------------------

Date: Sat, 31 Jan 1998 02:45:43 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) ADDGIFS Program

>Get Paul's program here
>http://www.geocities.com/CapeCanaveral/Lab/3825/addgifs.zip

*My* program??...WHAT program???

>and his par and formula files
>http://home.san.rr.com/jayrhill/CARLSON.PAR

Oh, the OTHER Paul. :-)

Could people PLEASE start using last initials or something to distinguish
us? :P A few posts ago Wizzle complimented me on my hring formulas and
Paul Carlson said thanks! :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: Sat, 31 Jan 1998 01:56:43 -0600
From: "Justin A. Kolodziej" <[e-mail]>
Subject: Re: (fractint) How long _is_ the coast of the M-set???

Morgan L. Owens wrote:
>=20
> At 09:44 30/01/98 -0600, Justin A. Kolodziej wrote:
> >Peter Jakubowicz wrote:
> >>
> >> I know the standard answer, that its dimension is 2, ergo it's p=
erimeter is
> >> infinite.
> >>
> >Hmmm, I'm pretty sure someone proved it, but I don't remeber how.
> >
> >My 2.5 yen (or thereabouts),
> >
> How appropriate:
> Mitsuhiro Shishikura. "The boundary of the Mandelbrot set has Hausd=
orff
> dimension two." Complex Analytic Methods in Dynamical Systems. (Rio=
 de
> Janeiro, 1992.) Ast=E9risque No. 222 (1994) 7, 389-405.

I meant proved that the M-set is simply connected, not that the bound=
ary
has dimension 2.  Probably another case of my writing not beig up to
par.  Still, it would be intersting to see how Mr. Shishikura proved
_his_ assertion... =20

- --=20
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: Sat, 31 Jan 1998 00:21:04 -0800
From: kathy roth <[e-mail]>
Subject: (fractint) new pars

So many great pars!  I have to post one more gravijul
one and one from Paul Carlson's Csin_atan_jul which
is in an entirely different mood.

double_spiral      { ; kathy roth 1/30/98
                     ; Paul Carlson's formula
  reset=1960 type=formula formulafile=csin_a~1.frm
  formulaname=CSin_Atan_Julia passes=1
  center-mag=-0.00167584/0.014401/5.745766 params=1/0.5/5/0/50/100
  float=y maxiter=5000 inside=period
  colors=000000000<6>0Gz<6>028000000<6>00z<7>\
000<6>z00<7>000000<6>zG0<7>00\
 0000<6>zW0<7>000000<6>zk0<7>000000\
<6>zz0<7>000000<6>kz0<7>000000<6>Wz0<7\
 >000000<6>0z0<7>000000<6>0zG<7>000000<6>\
0zW<7>000000<6>0zk<7>000000<6>0z\
  z<7>000000<6>0kz<7>000000<6>0Wz<6>048
  }

fleur_de_lys       { ; kathy roth 1/30/98
                     ; Paul Carlson's formula
  reset=1960 type=formula formulafile=csin_a~1.frm
  formulaname=gravijul function=cotan/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
invert=1/0/0
 colors=8CBulX<18>`ym_zn`zk<14>px9113<20>\
UUxWWzXWz<21>yWzzWzzUy<21>z1Xz0W\
 z1U<21>zU1zW0zX0<21>zy0zz0yy2<21>XXxW\
WzUXy<21>1yX0zW0zX<21>0zy0zz2zy<22>\
  yjU<2>vlW
  }


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

Date: Sat, 31 Jan 1998 10:24:05 +1
From: "J.P. Louvet" <[e-mail]>
Subject: (Transmis) Re: (fractint) How long _is_ the coast of the M-set??

From:          Self <louvet>
To:            [e-mail]
Subject:       Re: (fractint) How long _is_ the coast of the M-set???
Reply-to:      [e-mail]
Date:          Fri, 30 Jan 1998 18:54:57 +1

Repost : this message was sent yesterday 01/30, but does not appear in the
bulk of messages received from this list. Can anybody confirm if he has
received the first posting of this message ?

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: Sat, 31 Jan 1998 04:29:57 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (Transmis) Re: (fractint) How long _is_ the coast of the M-set??

>Repost : this message was sent yesterday 01/30, but does not appear in the
>bulk of messages received from this list. Can anybody confirm if he has
>received the first posting of this message ?

I got it.

I had experiences like that too, but they'd all gotten out. It seems the
list occasionally fails to send you your own copy of something, but it
still gets out. (Either that, or it sometimes misses several people, and
sometimes that includes the sender, but I certainly hope not, such an
erratic Mandelbug(qv) would be a pain in the behind to track down!)


Mandelbug: Bug that occurs under deterministic conditions, but with so
many unpredictable factors influencing it, that when it appears might as
well be random. Generally reeealy hard to debug. Name derived from the
chaotic behavior of the Mandelbrot Set with its deterministic
underlying rules. For more details check out the jargon file.


- --
    .*.  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: Sat, 31 Jan 1998 10:38:32 -0800
From: James Polley <[e-mail]>
Subject: (fractint) Dimensionality

Sorry for what is probably an easy question, but I'm a newbie, both here and to
the world of fractals.
What are these 'fractal dimensions' that everybody keeps talking about? eg.
people keep saying that the M-set is 2-dimensional, and I just saw somebody
saying that the Koch snowflake has Fractal Dimension 1.26 or something like that.
What is a fractal dimension? Also, is there a FAQ that answers questions like
these? Or is there any FAQ at all?

Thanks.



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

Date: Sat, 31 Jan 1998 10:06:45 -0800
From: Polley Enterprises <[e-mail]>
Subject: Re: (fractint) Re: Virus

Rich Thomson wrote:

> <snip> The virus companies are aware of all the hoaxes long before most
> people have heard of them.  <more snipping>

>

I wonder why the virus companies are aware of hoaxes long before most
people? Very suggestive, isn't it!




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

Date: Sat, 31 Jan 1998 03:56:33 -0800 (PST)
From: FIRSTNAME LASTNAME <[e-mail]>
Subject: Re: (fractint) A Herman Ring Par

- ---Paul and/or Joyce Carlson <[e-mail]> wrote:
>
> Here's a Herman Ring par that produces a familiar image but
> with a nice difference - a very delicate bright image over
> a very bold dark "background."  This is a pretty deep zoom
> into the ParabolicFixed image that someone posted the par
> for, but with a different colormap.  Don't use solid guessing
> on this - too much is lost.  Tesseral works well and cuts
> down on the time needed to plot the little Mandy (what my
> wife calls a baby 'brot) in the center.
>
> Paul Carlson
>
> hring_mandel       { ; Copyright (c) Paul W. Carlson, 1998
>   reset=1960 type=formula formulafile=hring.frm
>   formulaname=hring_mc passes=t
>   center-mag=-1.13968013785657900/+0.00177213235944437/1.3041\
>   58e+007/1/127.5
>   params=1/0/0/0/0.001/0 float=y
>   maxiter=5000 inside=0 outside=real
>   colors=000C0C<61>zVzzVzyVy<61>C0C0CC<62>VzzVzzVyy<61>0CC
>   }
>
>
>
> -
> ------------------------------------------------------------
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>




I tried it, I couldn't get it to work at all.

once again, how do I grab these postings and use them too.  Your's
came up as an empty file when I did a cut/paste of the PAR section and
saved as a PAR file.

All others I've tried this with do to same thing.


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


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

Date: Sat, 31 Jan 1998 08:17:27 -0800
From: Wizzle <[e-mail]>
Subject: Re: (fractint) january wizzle pars

Paul...

I think I posted several Herman ring formulas just a couple of days
ago......and I'm  sure they will manage to get into the February offering!!!

Angela

At 01:23 AM 1/31/98 -0500, you wrote:
>>
>>IMHO january was a fantastic month when it came to fractals, pars and
>>formulas.  I'm offering this far too long list of pars....made with
>>everyone's formulas....which I just loved.  I had a wonderful time with all
>>of the formulas posted during the month....
>
>Hey! There aren't any herman rings in there! :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]
>
>-
>------------------------------------------------------------
>Thanks for using Fractint, The Fractals and Fractint Discussion List
>Post Message:   [e-mail]
>Get Commands:   [e-mail] "help"
>Administrator:  [e-mail]
>Unsubscribe:    [e-mail] "unsubscribe fractint"
>
>

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

Date: Sat, 31 Jan 1998 08:20:12 -0800
From: Wizzle <[e-mail]>
Subject: Re: (fractint) ADDGIFS Program

Paul D....

I suggest you change your name to "Steve"....that was popular for a while

And what does the addgif program do????  Why do I want it???

Angela

At 02:45 AM 1/31/98 -0500, you wrote:
>
>>Get Paul's program here
>>http://www.geocities.com/CapeCanaveral/Lab/3825/addgifs.zip
>
>*My* program??...WHAT program???
>
>>and his par and formula files
>>http://home.san.rr.com/jayrhill/CARLSON.PAR
>
>Oh, the OTHER Paul. :-)
>
>Could people PLEASE start using last initials or something to distinguish
>us? :P A few posts ago Wizzle complimented me on my hring formulas and
>Paul Carlson said thanks! :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]
>
>-
>------------------------------------------------------------
>Thanks for using Fractint, The Fractals and Fractint Discussion List
>Post Message:   [e-mail]
>Get Commands:   [e-mail] "help"
>Administrator:  [e-mail]
>Unsubscribe:    [e-mail] "unsubscribe fractint"
>
>

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

Date: Sat, 31 Jan 1998 08:57:38 -0800
From: "Jay Hill" <[e-mail]>
Subject: Re: (fractint) Dimensionality

> From: James Polley <[e-mail]>
>
> Sorry for what is probably an easy question, but I'm a newbie, both here and
to
> the world of fractals.
> What are these 'fractal dimensions' that everybody keeps talking about? eg.
> people keep saying that the M-set is 2-dimensional, and I just saw somebody
> saying that the Koch snowflake has Fractal Dimension 1.26 or something like
that.
> What is a fractal dimension? Also, is there a FAQ that answers questions like
> these? Or is there any FAQ at all?

There is always the sci.fractals FAQ to which many of us have contributed. It
is very good.

http://www.mta.ca/~mctaylor/sci.fractals-faq/

and for your question
http://www.mta.ca/~mctaylor/sci.fractals-faq/dimension.html

I will put together a iFAQ, inFrequently Asked Questions collecting some of the

great essays found on this list.

Jay

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Date: Sat, 31 Jan 1998 09:55:40 -0800
From: kathy roth <[e-mail]>
Subject: (fractint) Re:Herman Ring

James McKenzie wrote
>once again, how do I grab these postings and use them too.  Your's
>came up as an empty file when I did a cut/paste of the PAR section and
>saved as a PAR file.

I had had a lot of problems with some of them and I
have saved all of the posts about this in a couple of files.
There have been several sorts of problems, but I think the
Herman ring frm was straightforward.  The best place to get
the Carlson and Skinner pars is from Jay Hill's site that he
listed yesterday or so.  If you want the set of files email
me and I will send it after work tonight.


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Date: Sat, 31 Jan 1998 09:57:24 -0800
From: kathy roth <[e-mail]>
Subject: (fractint) wizzle pars

Hi Wizzle, I really liked your recent group of images,
except I don't have the fomula Ghost_vert_jul,
Range-Y-3_jul, Range-X-1_jul or Crentura_2.




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Date: Sat, 31 Jan 1998 10:40:42 -0800
From: "Jay Hill" <[e-mail]>
Subject: Re: (fractint) wizzle pars

Kathy,
The range formula are Kerry Mitchell's and Crentura is
from the ORGFRM.zip collection on Spanky
http://spanky.triumf.ca/www/spanky.html

Jay


- ----------
> From: kathy roth <[e-mail]>
> To: [e-mail]
> Subject: (fractint) wizzle pars
> Date: Saturday, January 31, 1998 9:57 AM
>
> Hi Wizzle, I really liked your recent group of images,
> except I don't have the fomula Ghost_vert_jul,
> Range-Y-3_jul, Range-X-1_jul or Crentura_2.
>


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Date: Sat, 31 Jan 1998 11:07:29 -0800
From: Wizzle <[e-mail]>
Subject: Re: (fractint) wizzle pars

Kathy writes....

>Hi Wizzle, I really liked your recent group of images,
>except I don't have the fomula Ghost_vert_jul,
>Range-Y-3_jul, Range-X-1_jul or Crentura_2.

Not surprising with the mass of formulas we got in January!!

Here they are

ghost-vert_jul { ; Kerry Mitchell
        ;
        ; colors Julia sets by combining the smoothed iteration
        ; with a background of vertical lines
        ;
        ; use decomp=256
        ; p1 = Julia parameter
        ; real(p2) = bailout
        ; imag(p2) = "ghost" adjustment: set to 0 for only
        ;   background rays, try 2
        ; calculation performed on variable zc, z used for coloring
        ;
        maxr=real(p2), scale=imag(p2)*pi/128
        ol2=1/log(2), fac=log(0.5*log(maxr))
        iter=1, zc=pixel, c=p1
        ;
        ; generate vertical lines
        ;
        xc=(real(scrnmax)-1)/2, x=real(scrnpix)
        t=x/xc*pi, background=cos(t)+flip(sin(t))
        :
        iter=iter+1, zc=sqr(zc)+c
        ;
        ; bailout
        ;   compute smoothed iteration as "angle"
        ;   multiply angle by background to get final z
        ;   set z to background for interior points
        ;   set "iteration done" flag (iter=-1)
        ;
        if ((|zc|>maxr)||(iter==maxit))
          smooth=(iter+ol2*(fac-log(log(cabs(zc)))))*scale
          angle=cos(smooth)+flip(sin(smooth))
          z=background*angle
          if (iter==maxit)
            z=background
            endif
          iter=-1
          endif
        iter>0
        }

range-x-1_jul { ; Kerry Mitchell
        ;
        ; colors Julia set by imaginary part of iterate, only
        ; when real part of iterate falls in certain range;
        ; range specified in terms of c
        ; use decomp=256
        ;
        ; p1 = Julia parameter
        ; real(p2) = bailout (try 4)
        ; imag(p2) = decomposition scale factor (try 16)
        ; real(p3) = center of range (try 1)
        ; imag(p3) = width of range (try 0.1)
        ; center of range is multiplied by real(c)
        ; calculation done on variable zc, z used for coloring
        ;
        zc=pixel, c=p1, maxr=real(p2), scale=imag(p2), iter=1
        angle=0, fac=real(c)
        lo=(real(p3)-imag(p3)/2)*fac, hi=(real(p3)+imag(p3)/2)*fac
        if (hi<lo)
          temp=lo, lo=hi, hi=temp
          end if
        :
        ;
        ; iteration
        ;   if real part of iterate falls into range,
        ;   scale imaginary part into decomp angle
        ;
        iter=iter+1, zc=sqr(zc)+c, r=real(zc)
        if ((r>lo)&&(r<hi))
          angle=scale*imag(zc)
          end if
        ;
        ; bailout--escape and maximum iterations treated the same
        ;   set "iteration done" flag (iter=-1)
        ;   decomposition method will color according to last time
        ;     real part of iterate was within range
        ;   if iterate was never in range, angle was initially set
        ;     to 0, so decomp with use color 0
        ;
        if ((|zc|>maxr)||(iter==maxit))
          iter=-1
          z=cos(angle)+flip(sin(angle))
          end if
        iter>0
        }

range-y-3_jul { ; Kerry Mitchell
        ;
        ; colors Julia set by real part of iterate, only when
        ; imaginary part of iterate falls in certain range;
        ; range specified in terms of c
        ; use decomp=256
        ;
        ; p1 = Julia parameter
        ; real(p2) = bailout (try 4)
        ; imag(p2) = decomposition scale factor (try 16)
        ; real(p3) = center of range (try 1)
        ; imag(p3) = width of range (try 0.1)
        ; center of range is multiplied by imag(sqr(sqr(c)+c)+c)
        ; calculation done on variable zc, z used for coloring
        ;
        zc=pixel, c=p1, maxr=real(p2), scale=imag(p2), iter=1
        angle=0, fac=imag(sqr(sqr(c)+c)+c)
        lo=(real(p3)-imag(p3)/2)*fac, hi=(real(p3)+imag(p3)/2)*fac
        if (hi<lo)
          temp=lo, lo=hi, hi=temp
          end if
        :
        ;
        ; iteration
        ;   if imaginary part of iterate falls into range,
        ;   scale real part into decomp angle
        ;
        iter=iter+1, zc=sqr(zc)+c, r=imag(zc)
        if ((r>lo)&&(r<hi))
          angle=scale*real(zc)
          end if
        ;
        ; bailout--escape and maximum iterations treated the same
        ;   set "iteration done" flag (iter=-1)
        ;   decomposition method will color according to last time
        ;     imaginary part of iterate was within range
        ;   if iterate was never in range, angle was initially set
        ;     to 0, so decomp with use color 0
        ;
        if ((|zc|>maxr)||(iter==maxit))
          iter=-1
          z=cos(angle)+flip(sin(angle))
          end if
        iter>0
        }

Crentura_2 (XAXIS) {
  z = c = pixel - 0.5:
  z = (1/sqr(z)) * z + pixel
  z = fn1(z) * c
  |z| < 4
  ;SOURCE: altura.frm
}

That last frm is from the _c.frm file you can get if you download
orgform.zip.....which I'm trying to explore AND keep up with the formulas
here.

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Date: Sat, 31 Jan 1998 14:50:38 -0800
From: Peter Jakubowicz <[e-mail]>
Subject: Re: (fractint) How long _is_ the coast of the M-set???

>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.

As an article of faith, OK. But it is not something I would have intuited.
Looking at a triangle and transforming it into the Koch curve, or looking
at the Peano curve, it is pretty easy to understand the idea of finite
area/infinite perimeter. But I don't know of a similar way of transforming
a circle into the Mandelbrot set.

Conversely, I do not see how it can be simply connected, although I am well
aware it has been proved. Perhaps Dr. J might be convinced to dilate a bit
upon this some time ? :)

BTW, Feigenbaum_Panorama = kewl (very well worth waiting 15 min for to see
at high rez) although it raises another question: just how _deep_ is the
Mandelbrot set, anyway.


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Date: Sat, 31 Jan 1998 15:35:28 -0600 (CST)
From: [e-mail] (Paul and/or Joyce Carlson)
Subject: Re: (fractint) ADDGIFS Program

Paul D. wrote:

>Could people PLEASE start using last initials or something to distinguish
>us? :P A few posts ago Wizzle complimented me on my hring formulas and
>Paul Carlson said thanks! :P ;-)

I don't remember doing that, but I do get confused sometimes at which Paul
(Paul Derbyshire, Paul Lee or Paul Carlson - any others?) is being
referred to, so I think last initials are a good idea.

Paul C.


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Date: Sat, 31 Jan 1998 13:59:10 -0800
From: "Jay Hill" <[e-mail]>
Subject: Re: (fractint) How long _is_ the coast of the M-set???

Hi Peter,

> From: Peter Jakubowicz <[e-mail]>
> Date: Saturday, January 31, 1998 2:50 PM
>
> >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.
>
> As an article of faith, OK. But it is not something I would have intuited.
> Looking at a triangle and transforming it into the Koch curve, or looking
> at the Peano curve, it is pretty easy to understand the idea of finite
> area/infinite perimeter. But I don't know of a similar way of transforming
> a circle into the Mandelbrot set.

You may have heard of external angles, they have been mentioned on this list.
Examples are 2*pi/3 and 2*pi*2/3, these 'map' to the base of the period 2
circle.  Imagine a very large circle. Now grab it at these two angle points
and pinch it down to the point c=-.75. Now you have two bulges, one to the
left, one to the right.  Now grab in the 2*pi*3/3 or equivalently the 0 angle
point. Push it into the period 1 base, c=+.25.  All periodic sequences here
will end with the period 1 base. Now there are three bulges.

Next, grab these points (ignoring the 2*pi), 1/7, 2/7, 3/7, 4/7, 5/7, 6/7.
These go to the bases of the period 3 components: -.125+-.65i, -1.75.  Now
there are about 9 bulges and depending on how inflated it is, is may be
starting to look like the MSet. The big cardioid is forming. The period 2
circle still bulges out to -1.75.  Keep doing this for higher period angles,
(next is p=4, angles are 1/15, 2/15, etc.) and when we get to infinity, finally

all the bulges are nailed down and we have the Mandelbrot set.

> Conversely, I do not see how it can be simply connected, although I am well
> aware it has been proved. Perhaps Dr. J might be convinced to dilate a bit
> upon this some time ? :)
>
All Dr. J has to say is - well let me quote:
"You humans have it easy getting dressed, just one belt, tie your shoes...
When I get dressed, I have an infinite number of belts, and - and, er things
to fasten down!"

> BTW, Feigenbaum_Panorama = kewl (very well worth waiting 15 min for to see
> at high rez) although it raises another question: just how _deep_ is the
> Mandelbrot set, anyway.

 It goes all the way down...

Jay


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Date: Sat, 31 Jan 1998 17:21:11 -0600 (CST)
From: [e-mail] (Paul and/or Joyce Carlson)
Subject: (fractint) Truncated Stalks Formula

The formula below is a variation on my 3D Stalks rendering
method.  The problem with that method (as well as Pickover's
original epsilon cross method) is that the orbit trap is
unbounded (goes to + and - infinity along both axes) producing
stalks which taper out to just a series of unconnected pixels.
The formula below is my "truncated stalks" rendering method or,
if you prefer, my "cross in a circle" method.

The first par is for a Julia set zoom in which the stalks are converging
to a point.  By truncating the stalks before they reach that point
you can see down into the spiral many levels.  A nice effect, I think.
The second par is for an Mset zoom consisting of many crosses (which is
just what you'd expect with a "cross in a circle" orbit trap).

In both pars, you can try making imag(p2) much larger (this increases
the length of the stalks) to see the effect.

Paul C. (for Carlson)

Truncated_Stalks {; Copyright (c) Paul W. Carlson, 1998
    ;****************************************************
    ; Always use floating point math and outside=summ.
    ;
    ; Parameters:
    ;   p1       = if both real(p1) and imag(p1) equal 0 do Mset,
    ;              otherwise do Julia set
    ;   real(p2) = a factor controlling the width of the stalks
    ;   imag(p2) = a factor controlling the length of the stalks
    ;   real(p3) = number of color ranges
    ;   imag(p3) = number of colors in each color range
    ;
    ; Note that the equation variable is w, not z.  Always
    ; initialize z to zero.
    ;****************************************************
    IF (real(p1) == 0 && imag(p1) == 0)
    w = 0
    c = pixel
    ELSE
    w = pixel
    c = p1
    ENDIF
    z = 0
    bailout = 0
    iter = 0
    range_num = 0
    ;****************************************************
    ; In the accompanying par files, trunspr1 and 2.par,
    ; we have 2 color ranges with 125 colors in each range
    ; for a total of 250 colors. The first range starts at
    ; color 1.  Pixels will use color 0 when |w| < 1000.
    ; Other values can be used here as long as the product
    ; of num_ranges times colors_in_range is less than 255.
    ; Color 0 is reserved for the background color and color
    ; 255 can be used for the inside color.
    ;****************************************************
    num_ranges = real(p3)
    colors_in_range = imag(p3)
    ;****************************************************
    ; Real(p2) controls the width of the stalks.
    ; Imag(p2) controls the length of the stalks.
    ;****************************************************
    stalk_width = real(p2)
    stalk_length = imag(p2)
    index_factor = (colors_in_range - 1) / stalk_width:
    ;****************************************************
    ; The equation being iterated.  Almost any equation
    ; that can be expressed in terms of a complex variable
    ; and a complex constant will work with this method.
    ;****************************************************
    w = c * (1 - w) * (1 + w) / (1 + w * w)
    ;****************************************************
    ; Find which axis the orbit point is closest to.
    ;****************************************************
    IF (abs(real(w)) <= abs(imag(w)))
        min_dist_to_axis = abs(real(w))
    ELSE
        min_dist_to_axis = abs(imag(w))
    ENDIF
    ;****************************************************
    ; If the orbit point is within a stalk width of an axis,
    ; and the value of |w| is less than the stalk length, then
    ; set z to the index into the colormap and set the bailout flag.
    ;****************************************************
    IF (min_dist_to_axis < stalk_width && |w| < stalk_length && iter > 0)
    z = index_factor * min_dist_to_axis + range_num * colors_in_range + 1
    bailout = 1
    ENDIF
    ;****************************************************
    ; Cycle through the range numbers (0 thru num_ranges - 1)
    ; With two color ranges, even iterations use color
    ; range 0, odd iterations use color range 1.
    ;****************************************************
    range_num = range_num + 1
    IF (range_num == num_ranges)
        range_num = 0
    ENDIF
    ;****************************************************
    ; Since we are using outside=summ, we have to subtract
    ; the number of iterations from z.
    ;****************************************************
    iter = iter + 1
    z = z - iter
    ;****************************************************
    ; Finally, we test for bailout
    ;****************************************************
    bailout == 0  && |w| < 1000
}

trunspr1     {; Copyright (c) Paul W. Carlson, 1998
          ; Julia set example
  reset=1960 type=formula formulafile=trunstlk.frm
  formulaname=Truncated_Stalks passes=1
  center-mag=0.498546/0.904963/17.69958/1/20
  params=2.595821505264/0.159242645065/0.05/20/2/125
  float=y maxiter=5000 inside=253 outside=summ
  colors=801sF_<123>C02Mov<123>HKS000<3>000
  }

trunspr2     {; Copyright (c) Paul W. Carlson, 1998
          ; Mset example
  reset=1960 type=formula formulafile=trunstlk.frm
  formulaname=Truncated_Stalks passes=1
  center-mag=+0.78914572989794710/+0.209775364341020\
  20/3108.882/1/7.5
  params=0/0/0.1/0.047/2/125
  float=y maxiter=5000 inside=253 outside=summ
  colors=000zqa<123>WRFz88<123>O00000<3>000
  }



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