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fractint-digest      Thursday, February 26 1998      Volume 01 : Number 118




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

Date: Tue, 24 Feb 1998 19:20:13 -0500
From: Sylvie Gallet <[e-mail]>
Subject: Re: (fractint) map maker

Hi Bob,

>>  To many really good images become just average due to poor coloring.

  Agreed!  Here is an example that shows the same image with various
palettes: some of the beginners' favorite maps (default, chroma, blues,
volcano, neon) and two of my own maps:

sg_gravijul_15     { ; run this one first
  reset=3D1960 type=3Dformula formulafile=3Dlist_98.frm formulaname=3Dgra=
vijul
  function=3Datanh/tan/atanh passes=3D1
  center-mag=3D-2.22045e-016/2.22045e-016/1.258897
  params=3D0.97/0/0.02/0/3/0 float=3Dy maxiter=3D300 inside=3D0 decomp=3D=
256
  colors=[e-mail] cyclerange=3D0/255
  }
sg_gravijul_15-a   { ; color plug-in: default.map
  colors=[e-mail]
  }

sg_gravijul_15-b   { ; color plug-in: chroma.map
  colors=[e-mail]
  }

sg_gravijul_15-c   { ; color plug-in: chroma.map
  colors=3DUCs<7>ECsCCsCEs<19>CqsCssCsq<19>CsECsCEsE<19>qsqsssssq<19>ssEs=
sCs\
  qC<19>sECsCCqCC<21>ACCCCC<21>sCs<20>ECsCCsCEs<19>CqsCssCsq<9>CsYCCC<21>=
s\
  Cs<11>WCs
  }

sg_gravijul_15-d   { ; color plug-in: neon.map
  colors=3DgEL<8>zKU<30>211000000<14>000010030<29>0z0<30>020000000<14>000=
110\
  330<29>zz0<30>220000000<30>000000200<19>eDK
  }

sg_gravijul_15-e   { ; color plug-in: blues.map
  colors=3D0cz<28>02z00z00y<59>002000000000000<29>00k00m01m<29>0ky0mz1mz<=
30>\
  zzz<46>2zz0zz0yz<15>0dz
  }

sg_gravijul_15-f   { ; color plug-in: volcano.map
  colors=3DzY7<5>zV1zU0zU0zT0<28>z10z00z00y00<30>c00b11a11`22_22<25>FFF00=
0FF\
  F<29>x11z00z10<29>zx0zz0zz1<29>zzxzzzzzz<54>zZ8
  }

sg_gravijul_15-g   { ; color plug-in: volcano.map
  colors=3Dd00<31>FFF000FFF<29>x11z00z10<29>zx0zz0zz1<29>zzxzzzzzz<61>zV1=
zU0\
  zU0zT0<28>z10z00z00y00<27>e00
  }

sg_gravijul_15-h   { ; color plug-in: one of my maps
  colors=3DV_H<5>_dM`eNaeP<26>yyxzzzzzz<27>snRsmPsmOrlMqkM<27>FE2DD2CC1AA=
0AA\
  0AB0<26>OREOSEOTEPUFQVG<29>xxxzzzzzz<29>i_3hZ0gZ0<29>CB0AA0AA0<25>VZG
  }

sg_gravijul_15-i   { ; color plug-in: another one
  colors=3DSSX<16>bckcdldemefmfgmghm<11>ttqvurvuq<45>bK2aJ0`J0<9>NC0LB0KA=
0I9\
  0H80F80E70C60A50<21>AFMAFN9GO9HP<2>AIQAIQBJRCKS<16>UZgVZgW_hX`hYai<14>o=
p\
  pqqqppq<50>33C33C44D<26>PPVPPWQQWQQWRRX
  }

  Cheers,

        - Sylvie


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

Date: Tue, 24 Feb 1998 08:00:00 -0500
From: "DeRobertis" <[e-mail]>
Subject: Re: (fractint) Mac Port of FracInt?

At 11:24 PM -0500 on 2/23/98, Tim Wegner Said...
>DeRobertis wrote:
>
>> I'm interesting in porting FracInt to the mac, but I have no clue about
>> these silly .asm files!
>
>If you start with Xfractint, you won't have any asm to worry about,
>only C. You will only need to port the X user interface to the Mac.
>This shouldn't be too hard.

You know the thing better than me, so could you please give a list of any
files that will need changes?

I may have to ask some questions about XWindows though -- I've never used it.

>
>If you are really serious about this let me know. We can help some,
>even though we don't have macs. A lot of folks have asked about this.

I'm serious about this. I saw the images, and I like them.

As long as it does not take a total rewrite (I don't want to rewrite over 1
meg of source) there will be a Mac version.

>
>
>Tim
>
>
>-
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 -----------------------------------------------
| Leader, The Galactic Battle Project        |
| Coder, The Galactic Battle Project        |
|                        |
| Galactic Battle, a MacOS-based real-time    |
| strategy game in space:            |
|    <http://come.to/gb/>            |
|    <http://www.erols.com/derobert/gb/>    |
|-----------------------------------------------|
| Don't go around saying the world owes you a    |
| living. The world owes you nothing. It was    |
| here first. -- Mark Twain            |
 -----------------------------------------------



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

Date: Tue, 24 Feb 1998 08:00:00 -0500
From: "DeRobertis" <[e-mail]>
Subject: Re: (fractint) Mac Port of FracInt?

At 8:29 PM -0500 on 2/23/98, Peter Gavin Said...
>Someone tell me if I'm wrong, but I believe anything written in asm is also
>in C... ?
>I dunno, I really just glanced through it for a coupla minutes...

Hmmm...okay. I just glanced through and saw a bunch of asm files and said
'ack!'

Anyway, what is <dos.h>? What function does it give that I will need to
locate, write, or work around? What about <Unix.h>?

 -----------------------------------------------
| Leader, The Galactic Battle Project        |
| Coder, The Galactic Battle Project        |
|                        |
| Galactic Battle, a MacOS-based real-time    |
| strategy game in space:            |
|    <http://come.to/gb/>            |
|    <http://www.erols.com/derobert/gb/>    |
|-----------------------------------------------|
| Don't go around saying the world owes you a    |
| living. The world owes you nothing. It was    |
| here first. -- Mark Twain            |
 -----------------------------------------------



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

Date: Tue, 24 Feb 1998 19:40:49 -0500 (EST)
From: Donald Archer <[e-mail]>
Subject: (fractint) palettes

Sylvie,

>>>  Too many really good images become just average due to poor coloring.
>
>  Agreed!  Here is an example that shows the same image with various
>palettes: some of the beginners' favorite maps (default, chroma, blues,
>volcano, neon) and two of my own maps:

This is a splendid dramatic way to make this important point.

Don




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

Date: Mon, 23 Feb 1998 13:56:48 -0500
From: Sylvie Gallet <[e-mail]>
Subject: Re: (fractint) Lee's "Fractal Dimensions": a MUST!!!

Hi Bob,

>> What is the Fractal-Art list?

  See Paul N. Lee's message.  To subscribe, send a message to
[e-mail]
  with "subscribe fractal-art" in the body of the message, no signature.

  Your friend,

        - Sylvie


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

Date: Tue, 24 Feb 1998 19:25:11 -0800
From: Wizzle <[e-mail]>
Subject: Re: (fractint) map maker

A general comment about the maps that are standard with fractint....

Except volcano, several of the jewels maps and the red, green and blue
maps, I have deleted all of the maps that came with Fractint. Even a single
month on this list will give someone a better set of colormaps to work
with.  In addition, there are the excellent maps that Linda Allison
developed which are part of her lessons, either available at one of her
sites or at my mirror at:

http://wizzle.simplenet.com/linda/lindas_lessons.htm

Along with learning from Linda, I've picked up some excellent ideas from
Paul Carlson and Sylvie Gallet which I've incorporated into the set of maps
which can be downloaded from:

http://wizzle.simplenet.com/fractals/wizmaps/wizmaps.htm

along with a discussion fairly similar to Sylvie's.  All in all, I must say
that with such excellent material now available, it might be time to update
the set of maps zipped with Fractint. My suggestion is to provide a set of
representative types:

1.  monochromes....such as the red, blue green maps which come with fractint
2.  stripes....not my favorite...but representative
3.  a black and white and a grey-tone map
4.  several smoothly graduated maps like Linda's or mine or Chessicat's in
varying degrees of color gradation ....I think of them as "long" or "short"
maps....the color steps being either long or short within the map....darn
hard to describe...but easy to supply...the colors are not as important as
the gradations which a student can vary
5.  some two or three color maps like those Paul Carlson uses to such
advantage
6.  2 or 3 maps with large areas of black....which can be so effective
7.  one of Paul's "julia" gradations ....i do like his brightly colored one

I think a more considered set of colormaps would lead the new Fractinter to
better images sooner.

Angela aka wizzle



At 07:20 PM 2/24/98 -0500, you wrote:
>Hi Bob,
>
>>>  To many really good images become just average due to poor coloring.
>
>  Agreed!  Here is an example that shows the same image with various
>palettes: some of the beginners' favorite maps (default, chroma, blues,
>volcano, neon) and two of my own maps:
><<snipped>>
}
>
>  Cheers,
>
>        - Sylvie


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

Date: Tue, 24 Feb 1998 19:36:44 -0800
From: Wizzle <[e-mail]>
Subject: Re: (fractint) map maker

A further comment about map making....

After reading Linda's lesson on using the map maker that comes with
Fractint, the actual steps of making a map were clear to me, even as
challenged as I usually am by standard documentation.  I was making or
adapting maps within a number of hours. What took me far longer was an
understanding of how a "good" map was constructed.

For that understanding, the standard maps bundled with Fractint were a
hinderance rather than a help, except for the jewels maps.  My own
understanding is based on Linda's explanations and was vastly accelerated
by examining the maps Paul Carlson and Sylvie Gallet make. This ain't a
problem with a techno-toys solution, but rather one where the student must
learn the ways and wherefores of one color following another onto the
fractal image.


At 07:25 PM 2/24/98 -0800, you wrote:
>A general comment about the maps that are standard with fractint....


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

Date: Tue, 24 Feb 1998 23:18:38 -0500
From: Atkinson <[e-mail]>
Subject: Re: (fractint) palettes

When I try to run the par file I made with Sylvie's demonstration email, i get
an error.

it says:
'gravijul' entry not found

could someone tell me why it is saying this and how i can fix it?  I get the
impression that the demonstration was posted for my behalf so i would really
like to see it.

I copy-pasted the formula right out of the email and slapped it into a text
file, renamed it syldemo.par and ran fractint (19.6) , hit the @ key and then
hit f6.  I selected syldemo.par and hit the first one  then error

lloyd


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

Date: Wed, 25 Feb 1998 18:50:18 +1300
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) TwinDragon

At 19:18 24/02/98 -0800, Peter Jakubowicz wrote:
>Can somebody pls tell me how I can generate the TwinDragon Julia set cited
>in Knuth , vol. 2, using Fractint, or point me to where it is discussed in
>the docs, if it is?
>Thank you
>
An IFS that does the job is the following:

twindragon {
- -.5 .5 -.5 -.5 0 0 .5
- -.5 .5 -.5 -.5 -1 -1 .5
}

The first transformation is a scaling by a factor of 0.5, followed by a
rotation by 135 degrees. The second transformation does these and also
translates by (-1,-1).

There is a construction that is based on fractional complex numbers in base
i-1 that I'm presntly trying to recast in a form suitable for formula files
a la Kerry Mitchell's Gaussian types. Maybe one day I'll nut it out.

MLO


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

Date: Wed, 25 Feb 1998 18:50:18 +1300
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) TwinDragon

At 19:18 24/02/98 -0800, Peter Jakubowicz wrote:
>Can somebody pls tell me how I can generate the TwinDragon Julia set cited
>in Knuth , vol. 2, using Fractint, or point me to where it is discussed in
>the docs, if it is?
>Thank you
>
An IFS that does the job is the following:

twindragon {
- -.5 .5 -.5 -.5 0 0 .5
- -.5 .5 -.5 -.5 -1 -1 .5
}

The first transformation is a scaling by a factor of 0.5, followed by a
rotation by 135 degrees. The second transformation does these and also
translates by (-1,-1).

There is a construction that is based on fractional complex numbers in base
i-1 that I'm presntly trying to recast in a form suitable for formula files
a la Kerry Mitchell's Gaussian types. Maybe one day I'll nut it out.

MLO


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

Date: Tue, 24 Feb 1998 22:03:48 -0800
From: kathy roth <[e-mail]>
Subject: (fractint) new par

oohhhh...that's pretty

extravaganza       { ; 2-2-98 kathy roth
                     ; frm from Les St.Clair collection
                     ; modified Sylvie Gallet formula
                     ; mod tent_inside.frm  gen'lized by Les St.Clair
  reset=1960 type=formula formulafile=fractint.frm
  formulaname=tent_in_mod function=abs/abs/flip/abs passes=1
  center-mag=1.02487/0.157205/0.4499341 params=0/0/0.033/0 float=y
  inside=zmag logmode=fly invert=1/0/0 decomp=256 periodicity=0
 colors=Hjs<4>y7a<7>fWKcZHb`I<5>WhQ<8>00z<2>000000\
<2>zzW<8>z0z<6>JTw<8>z0\
 0<6>0z0<8>zW0<5>mVpjUyhWy<7>Nhw<6>xkk<8>\
WKG<6>vEP<8>rZM<5>qTjqSorWi<7>zz\
 0<6>Wzt<7>uM7xH0yN5<4>ztRzzWxvV<6>eSNbNM\
ZQM<5>EeL<8>_9z<6>5Yz<8>z5Y<5>nf\
  YllZll_<7>kkk<6>dJz<8>ez0<6>zhQ<8>0zz8rw cyclerange=0/255
  }

star2              { ; 2-2-98 kathy roth
                     ; frm from Les St.Clair collection
                     ; modified Sylvie Gallet formula
                     ; mod tent_inside.frm gen'lzed by Les St.Clair
  reset=1960 type=formula formulafile=fractint.frm
  formulaname=tent_in_mod function=abs/abs/flip/abs passes=1
  center-mag=-0.461469/0.603948/0.04499341 params=0/0/0.033/0 float=y
  inside=zmag logmode=fly decomp=256 periodicity=0
 colors=Hjs<4>y7a<7>fWKcZHb`I<5>WhQ\
<8>00z<2>000000<2>zzW<8>z0z<6>JTw<8>z0\
 0<6>0z0<8>zW0<5>mVpjUyhWy<7>Nhw<6>xkk<8>\
WKG<6>vEP<8>rZM<5>qTjqSorWi<7>zz\
 0<6>Wzt<7>uM7xH0yN5<4>ztRzzWxvV<6>eSNbN\
MZQM<5>EeL<8>_9z<6>5Yz<8>z5Y<5>nf\
  YllZll_<7>kkk<6>dJz<8>ez0<6>zhQ<8>0zz8rw cyclerange=0/255
  }




tent_in_mod { ; Modified Sylvie Gallet formula
              ; Modified tent_inside.frm (generalized by Les St Clair)
              ; use fn1,fn2,fn4=abs & fn3=cabs for default behaviour
              ; set p1=0, p2=0.001 for default behaviour
   IF (p1 || flip(p1))
    r = p1
   ELSE
    r = 1
   ENDIF
   z = 0 :
   l = r+p1
   z = z*z + pixel
   UV = (5,5) - fn1((5,5) - fn2(z))
   r = fn3(UV)
    fn4(l-r) >= p2 && r < 4
  }






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

Date: Wed, 25 Feb 1998 19:23:50 +1300
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) TwinDragon

A second method is via an L-System. This one illustrates the reason for the
twindragon's name, in that it can be constructed by joining two Heighway
dragons end to end.

twindragon {
angle 4
Axiom c13h+c9h
h=hf+af
a=hf-af
f=
}



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Date: Wed, 25 Feb 1998 00:41:24
From: "Lavondyss" <[e-mail]>
Subject: (fractint) fractal prints

I still have an Epson Stylus Color. I printed the fractals at 720 dpi on
matted(coated) and glossy paper. The turned out absolutely gorgeous. I'm
keeping them in plastic sleeves and am making a collection in a binder.
Maybe make a book?...with the fractals' authors' permission of course.

- -Lav




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Date: Wed, 25 Feb 1998 03:54:26 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Arbitrary Precision pisses me off!

>Sorry bout the subject, but it does. I was generating ƒberzoomed M-Sets at
>320x200x256, c. 2,000,000,000 iterations, and suddenly it stopped and no matter
>how long I waited it wouldn't draw another point. I tried again later, and at
>17-decimal arbitrary precision mode, it stopped at the same place. I waited 24
>hours, and it was still at the same point, with the time around 25:32:00. Is
>there something wrong with my computer, (P133), with Windows 95. It does the
>same thing in DOS mode too.

I had this happen also. I reported it, and was told it might be a bug in
the GIF encoder's fault that can cause a restored half-done image to hang.
However, after I pointed out that it happened to a fresh image (not loaded
as a GIF but started fresh), there has been no response. I suspect a
rare(?) arbitrary precision bug causing the occasional hang, unrelated to
GIF encoding/decoding.


- --
    .*.  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: Wed, 25 Feb 1998 04:00:54 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) fractal hardware engine

>Paul,
>
> - Won't the serial port I/O speed become a serious bottleneck? It must be
> - orders of magnitude slower than a PC bus. I wouldn't think all the
> - megahertz in the world would make much difference if your FPU communicated
> - to the CPU/memory at only 57600 baud...
>
>Depends on how much you have to communicate.  If you can simply give the
>DSP a starting point, and have it generate a whole slew of points
>unattended, your communication speed becomes less important.

A couple of FPU registers wouldn't do it... if the DSP came with onboard
memory of some kind (say a 16K buffer) that would suffice.

Also where does it get its code? Same buffer?

>

- --
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 -()  <  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: Wed, 25 Feb 1998 04:31:24 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) TwinDragon

Numbers in base i-1?

And here I thought I'd seen everything.



- --
    .*.  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: Wed, 25 Feb 1998 03:57:39 -0600
From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) palettes

Atkinson wrote:
>
> When I try to run the par file I made with Sylvie's demonstration
> email, i get an error.   it says:   'gravijul' entry not found
>

Here is Mark Christenson's formula:

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


George Martin wrote:
>
> Given p3's use as the bailout, you can enforce your default option by
> adding the following to the initialization section of the formula:
>
>   IF (p3 <= 0)
>     p3 = (4, 0)
>   ENDIF
>

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Date: Wed, 25 Feb 1998 05:33:29 -0500
From: Sylvie Gallet <[e-mail]>
Subject: Re: (fractint) palettes

>> When I try to run the par file I made with Sylvie's demonstration
>> email, i get an error.
>>
>> it says: 'gravijul' entry not found

  Here is the formula:

gravijul { ; r^(-2) Mark Christenson 1/25/98
; defaults: p1 =3D (1,0) p2 =3D (0,0) p3 =3D (4,0)
   z =3D pixel:
   w =3D fn1(z)
   z =3D fn3(p1/fn2(w*w)) + p2
    |z| < p3
  }

  Cheers,

        - Sylvie

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Date: Wed, 25 Feb 1998 10:45:10 -0000
From: Edward Avis <[e-mail]>
Subject: (fractint) ASCII fractals

The real-time Mandelbrot zoomer Xaos can run in curses-based text mode.

- --
Ed Avis
[e-mail]
http://members.tripod.com/~mave/index.html



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Date: Wed, 25 Feb 1998 10:36:27 -0600 (CST)
From: [e-mail]
Subject: Re: (fractint) TwinDragon

On Wed, 25 Feb 1998, Paul Derbyshire wrote:

>
> Numbers in base i-1?
>
> And here I thought I'd seen everything.

Crazy, but true... It explains it in a book called "Fractals, Chaos and
Power Laws", or something with those three words, by an author whose name
I forgot, on one of the pages where it talks about the twindragon,
wherever that may be.  I'ts a sufficiently popular book that you might be
able to find it in a public library... that's where I first found it.

Justin K.

I sense a great disturbance in the Source.


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Date: Wed, 25 Feb 1998 10:47:40 -0700 (MST)
From: Kerry Mitchell <[e-mail]>
Subject: (fractint) Complex bases (was: TwinDragon)

Our base 10 (decimal) number system represents numbers like this:

x = ...p3p2p1p0.n1n2n3n4n5n6...

where the p's are digits on the left side of the decimal point,
representing positive powers of 10 (and 1), and are finite in number.  The
n's represent negative powers of 10 and are infinite.  Essentially, this
is shorthand notation for a power series in the base (10):

x = ... + p3 * 10^3 + p2 * 10^2 + p1 * 10^1 + p0 * 10 ^ 0 + n1 * 10^-1 +
...

There's no real (ha!) reason that the base above can't be complex,
allowing complex numbers to be expressed as power series of complex bases.
The typical bases are 1+i and 1-i; for some reason, 1-i tends to work
"better" than 1+i.  The "digits" in this system are 0 and 1.  I'm not sure
how they would be in a system of base m+ni; in base 3+i, would the digits
be 0,1,2 or 0,1, or...?

There is a fractal connection to complex bases.  I think William Gilbert
did some work on them.  It seems to involve the Gaussian integers (complex
numbers with integer components) that can be expressed in a finite number
of digits with a complex base.  We all know that in decimal (or binary),
most fractions cannot be expressed exactly in a finite number of digits
(say 1/3).  With complex bases, there are integers which can't be
expressed exactly with a finite number of digits, and other integers that
have more than one expression.  I think.

Kerry Mitchell

>On Wed, 25 Feb 1998, Paul Derbyshire wrote:
>
>>
>> Numbers in base i-1?
>>
>> And here I thought I'd seen everything.
>

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


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Date: Wed, 25 Feb 1998 14:21:06 -0500
From: alex dukay <[e-mail]>
Subject: Re: (fractint) TwinDragon

>It explains it in a book called "Fractals, Chaos and Power Laws",

the author is Manfred Schroeder;
publisher W.H. Freeman and Company
41 Madison Ave. NY NY 10010
isbn# 0-7167-2357-3

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Date: Wed, 25 Feb 1998 19:18:19 -0600 (CST)
From: [e-mail] (Paul and/or Joyce Carlson)
Subject: (fractint) Newtons with rings

Here's another of my favorite Newton formulas, this time
rendered using 3D Rings.  The two pars produce very
pretty, almost delicate images.  In both images, a
little Mandy appears to be suspended by chains.

I used passes=t in the pars because there is a lot of
background color (black) at 1000 iterations and there
are no islands of pixels that might be missed.

To change the background color, change color 252.

Paul Carlson

frm:Newt1_Rings_Mset {; Copyright (c) Paul W. Carlson, 1998
    ;****************************************************
    ; Newton's solution of (w*w-1)*(w*w+c)=0
    ; Always use floating point math and outside=summ.
    ;
    ;   real(p1) = a factor controlling the size of the stalks
    ;   imag(p1) = minimum iterations
    ;   real(p2) = number of color ranges
    ;   imag(p2) = number of colors in a range
    ;   real(p3) = value of |w| for bailout
    ;   imag(p3) = iterations count for early exit
    ;
    ; Note that the equation variable is w, not z.  Always
    ; initialize z to zero.
    ;****************************************************
    c = pixel
    sc = sqrt(-c)
    am = c - 1, tam = am + am
    w = sqrt((1 - c) / 6)  ;value where F''(w) = 0
    cr = real(sc), ci = imag(sc)
    z = 0
    bailout = 0
    iter = 0
    t = 0.000001
    stalk_width = real(p1)
    range_num = 0
    num_ranges = real(p2)
    colors_in_range = imag(p2)
    index_factor = (colors_in_range - 1) / stalk_width:
    ;
    w2 = w * w
    w = w - (w2 * w2 + am * w2 - c) / (4 * w2 * w + tam * w)
    ;
    wr = real(w), wi = imag(w)
    dist = abs(wr * wr + wi * wi - 0.25)
    IF (dist < stalk_width && iter > imag(p1))
    z = index_factor * dist + range_num * colors_in_range + 1
    bailout = 1
    ENDIF
    IF (iter > imag(p3))
    IF     (((wr-1) * (wr-1)) < t && (wi * wi) < t)
        z = 252
        bailout = 1
    ELSEIF (((wr+1) * (wr+1)) < t && (wi * wi) < t)
        z = 252
        bailout = 1
    ELSEIF (((wr-cr) * (wr-cr)) < t && ((wi-ci) * (wi-ci)) < t)
        z = 252
        bailout = 1
    ELSEIF (((wr+cr) * (wr+cr)) < t && ((wi+ci) * (wi+ci)) < t)
        z = 252
        bailout = 1
    ENDIF
    ENDIF
    range_num = range_num + 1
    IF (range_num == num_ranges)
        range_num = 0
    ENDIF
    iter = iter + 1
    z = z - iter
    (bailout == 0) && |w| < real(p3)
}

n1rings1       { ; Copyright (c) Paul W. Carlson, 1998
  reset=1960 type=formula formulafile=n1rmset.frm
  formulaname=newt1_rings_mset passes=t
  center-mag=+0.99883132158904500/+0.0483304822356094\
  3/11411.46/1/-2.499
  params=0.1/0/8/30/1e+020/1000
  float=y maxiter=3000 inside=255 outside=summ
  colors=000fOz<28>I0Kz0f<28>O08z88<28>O00zW0<28>c40zz\
  0<28>aG00zR<28>0C40zz<28>0CCGGz<28>00O000<12>000zzz
  }

n1rings2       { ; Copyright (c) Paul W. Carlson, 1998
  reset=1960 type=formula formulafile=n1rmset.frm
  formulaname=newt1_rings_mset passes=t
  center-mag=+1046.85283978193200000/+0.00000000000000\
  000/75.29715/1/90
  params=0.1/0/8/30/1e+020/1000
  float=y maxiter=3000 inside=255 outside=summ
  colors=000fOz<28>I0Kz0f<28>O08z88<28>O00zW0<28>c40zz\
  0<28>aG00zR<28>0C40zz<28>0CCGGz<28>00O000<12>000zzz
  }


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Date: Thu, 26 Feb 1998 22:35:58 +1300
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Complex bases (was: TwinDragon)

At 10:47 25/02/98 -0700, Kerry Mitchell wrote:
>Our base 10 (decimal) number system represents numbers like this:
>
>x = ...p3p2p1p0.n1n2n3n4n5n6...
>
>where the p's are digits on the left side of the decimal point,
>representing positive powers of 10 (and 1), and are finite in number.  The
>n's represent negative powers of 10 and are infinite.  Essentially, this
>is shorthand notation for a power series in the base (10):
>
>x = ... + p3 * 10^3 + p2 * 10^2 + p1 * 10^1 + p0 * 10 ^ 0 + n1 * 10^-1 +
>...
>
>There's no real (ha!) reason that the base above can't be complex,
>allowing complex numbers to be expressed as power series of complex bases.
>The typical bases are 1+i and 1-i; for some reason, 1-i tends to work
>"better" than 1+i.  The "digits" in this system are 0 and 1.  I'm not sure
>how they would be in a system of base m+ni; in base 3+i, would the digits
>be 0,1,2 or 0,1, or...?
>
The set of digits can be any finite set of complex numbers which includes
0. The restriction on the base is that it be larger in magnitude than 1.

Either there exists a number which has two representations in the given
base (as there is in decimal, as Kerry says, where 0.999... = 1.000...) or
there exists numbers which have no representation at all (such as 1/2, in
the case where the base is 3 and the set of digits is {0,2}; this number
base is related to the Cantor dust fractal which can be thought of as the
set of points on the interval [0,1] that can be represented in this base).

>There is a fractal connection to complex bases.  I think William Gilbert
>did some work on them.

The Twindragon is the set of all "fractions" in the number system with base
i-1 and digits 0 and 1. A "fraction" in this case being a complex number of
the form 0.n1n2n3n4n5n6...
One interesting consequence of this is the fact that each possible
selection of the p's gives you a new Twindragon. All these Twindragons -
one for each Gaussian integer - reside on the plane, and their boundaries
mark the points which have more than one representation.
Since any complex number can be represented in this base, the Twindragons
completely cover the complex plane. And since the Twindragons do not
overlap (except at their edges), what we have here is what might as well be
called a "fractile".

Incidentally, since the Twindragon can be constructed as a pair of
Heighway's dragons end-to-end (as I showed in a previous post), this means
that Heighway's dragon is also a fractile. What others are there?

There is no other restriction on the base or the set of digits beyond those
given above. Consider if you will the number system with base -2 and digits
{0, 1, w, w^2}, where w = (-1+i*sqrt(3))/2 = cos(2pi/3)+i*sin(2pi/3).
Numbers of the form a+wb, where a and b are integers, are sometimes called
Eisenstein integers (Eisenstein was Gauss's favourite pupil). (The set of
Eisenstein fractions also forms a fractile, for the same reason that the
Twindragon does).

Morgan



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Date: Thu, 26 Feb 1998 17:23:43 -0500
From: "Peter Gavin" <[e-mail]>
Subject: Re: (fractint) Mac Port of FracInt?

Hi,
dos.h gives you basic dos-specific commands, such as environement variable
handlers.  Maybe you can replace this with mac.h?  I dunno, I don't use macs
:)

Pete


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Date: Thu, 26 Feb 1998 19:10:37 -0500
From: DeRobertis <[e-mail]>
Subject: Re: (fractint) Fractint problem w/ video card

>Justin,
>
> - Well, this is the best argument I've heard yet for producing a Win32
> - version of Fractint.
>
>There's no argument--pretty much everyone agrees that at some point
>FractInt will need a 32-bit (preferably Windows) version.  The biggest
>problem right now is, I presume, the "32-bit" portion of that.  I'd imagine
>a 32-bit DOS version (using DJGPP or something similar) would be the first
>step, and then writing a Windows interface around that.  Which means it's
>still a good ways off.

I've never dealt with porting from a 16-bit system before. What needs to be
converted?

The Macintosh version will need to be 32-bit; there is no such thing as a
16 bit Macintosh.


>Until you start looking at the FractInt code, you don't really get a
>feeling for what a *huge* program it is.

I know what you mean :(



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Date: Thu, 26 Feb 1998 18:52:37 -0500
From: DeRobertis <[e-mail]>
Subject: Re: (fractint) Mac Port of FracInt?

>Peter Gavin wrote:
>>
>> Someone tell me if I'm wrong, but I believe anything written in asm is also
>> in C... ?
>> I dunno, I really just glanced through it for a coupla minutes...
>Yes and no.  Assembler code can be put in a C program, but still is
>assembler code.  And there's a problem.  There are going to be a LOT of
>differences between Mac assembler and Intel assembler just because they
>are different processors with different instruction sets.
>
>A different route to take would be to take the XFractint code with no
>assembler code, replace all the ncurses and X-Windows specific stuff
>with things that work on a Mac, and compile that.  Don't know if it
>would be less or more work, though ;-)

Speedwise, how much of a gain will I get with the asm code over a
good-optimizing compiler?

I guess I'll go with the X-Windows version. Has anyone had experiance with
the IBM/Motorola PowerPC line of microprossesors?



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End of fractint-digest V1 #118
******************************