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fractint-digest         Wednesday, May 5 1999         Volume 01 : Number 386




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

Date: Fri, 30 Apr 1999 19:44:51 GMT
From: "Jack Baker" <[e-mail]>
Subject: Re: (fractint) Running under windows98

It enables the system to use software that actively seeks a 3D accelerator
(ie:MS Motocross Madness), without an added card.  Graphics and other FPU
functions are greatly enhanced.

- -Jack

- ----Original Message Follows----
From: "Adam Leggett" <[e-mail]>
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Subject: Re: (fractint) Running under windows98
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 > 3D-Now! makes the system think that it has a 3D accelerator card
(Voodoo2,
 > etc), when in fact it does not.  Therefore, the system will run software
 > that REQUIRES an accelerator card. Basically, AMD finally did something
 > right.  Yes, the 350MHz processor would be the slowest that I would go
with
 > on K6-2s, though.  My advice, wait for the K6-3s to become available.

Sorry, I have no idea what you mean by making the system think it has an
accelerator card, care to elaborate?

Thanks
adam


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

Date: Fri, 30 Apr 1999 19:47:21 GMT
From: "Jack Baker" <[e-mail]>
Subject: Re: (fractint) Running under windows98

It is not possible - according to the physics of CPU architecture - to get a
80486 processor to run at 1GHz.

- -Jack

Adam,

  - I'm sure a 1 GHz 486 would waste most of what I see these days.

Er, not quite. If you're comparing FPU speeds, it's not even a close
match--a 350MHz P-II will run rings around the hypothetical 1GHz 486 at FPU
ops, because the 486 FPU just isn't that fast. That's why when Quake came
out, it required an FPU--the FPU multiply on the Pentium is a lot faster
than the integer multiply.

Damien M. Jones   \\
[e-mail]  \\  Fractalus Galleries & Info:
                     \\  http://www.fractalus.com/

Please do not post my e-mail address on a web site or
in a newsgroup.  Thank you.

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Date: Fri, 30 Apr 1999 19:49:20 GMT
From: "Jack Baker" <[e-mail]>
Subject: Re: (fractint) Running under windows98

Not to seem argumentative, but if it is able to run consequtive processes,
does that not effectively increase the overall speed of the FPU?

- -Jack

Ken,

  - How is the floating point performance on the K6 II or the K7?

K6-2: approximately half an equivalently-clocked P-II. The FPU on the K6-2
isn't significantly faster than the FPU on the original K6.

K7: according to the spec this FPU can manage an add, a multiply, and a
move all in the same cycle. If this bears out, it will actually be higher
performance than the P-II.

  - I had a K6-166 and swapped it out for a Pentium MMX 233.  I got more
  - than a 2x increase in floating point performance just by going to an
  - Intel chip.

Right. The ratio of Pentium:K6 FPU performance is something like 2.3 or
2.4, last time I ran those benchmarks.

Damien M. Jones   \\
[e-mail]  \\  Fractalus Galleries & Info:
                     \\  http://www.fractalus.com/

Please do not post my e-mail address on a web site or
in a newsgroup.  Thank you.

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

Date: Fri, 30 Apr 1999 19:56:08 GMT
From: "Jack Baker" <[e-mail]>
Subject: Re: (fractint) Running under windows98

Oops- I mean concurrently, not consequtively.....Jack :)
Not to seem argumentative, but if it is able to run consequtive processes,
does that not effectively increase the overall speed of the FPU?

- -Jack

Ken,

  - How is the floating point performance on the K6 II or the K7?

K6-2: approximately half an equivalently-clocked P-II. The FPU on the K6-2
isn't significantly faster than the FPU on the original K6.

K7: according to the spec this FPU can manage an add, a multiply, and a
move all in the same cycle. If this bears out, it will actually be higher
performance than the P-II.

  - I had a K6-166 and swapped it out for a Pentium MMX 233.  I got more
  - than a 2x increase in floating point performance just by going to an
  - Intel chip.

Right. The ratio of Pentium:K6 FPU performance is something like 2.3 or
2.4, last time I ran those benchmarks.

Damien M. Jones   \\
[e-mail]  \\  Fractalus Galleries & Info:
                     \\  http://www.fractalus.com/

Please do not post my e-mail address on a web site or
in a newsgroup.  Thank you.

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

Date: Fri, 30 Apr 1999 15:17:00 -0500
From: "Damien M. Jones" <[e-mail]>
Subject: Re: (fractint) Running under windows98

Jack,

As I said, the K7 supposedly can perform simultaneous FPU ops; until I've
personally seen one run, I won't say. I saw specs that said the K6-2 was
supposed to have an optimized FPU, but in practice it doesn't. Ditto for
Cyrix.

If you read what I wrote, I said the K7, if it performs as the specs
indicate, will be a serious competitor for the P-III in the FPU department.
(It is unquestionably competent in the integer department.) The K6-2 is
*not* a good FPU substitute for a Pentium or Pentium-II.

Keep in mind all this is fairly academic for the current version of
FractInt, which is not Pentium-optimized. I am sure future versions will be
better optimized, but if FractInt is all you are running, the difference is
not *as* great as it could be.

Damien M. Jones   \\
[e-mail]  \\  Fractalus Galleries & Info:
                    \\  http://www.fractalus.com/

Please do not post my e-mail address on a web site or
in a newsgroup.  Thank you.

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

Date: Fri, 30 Apr 1999 20:37:54 GMT
From: "Jack Baker" <[e-mail]>
Subject: Re: (fractint) Running under windows98

From my experience, other than the networking problems with AMD processors,
they are excellent CPUs.  While they are not quite as fast as Intel's on
most applications, on some applications I have seen them be faster.  But,
personally, I am an Intel person.  All but one of my machines at home have
Intel processors, and I will not buy anything else for the office.  The one
machine at home that is not Intel is an AMD K6/266.  (a pretty quick little
machine, but the Intel Pentium 133 that I have is just as fast).  Of course,
as I said, the AMDs do not like being networked.  Something to do with FPU
on the K6, and God only knows on the K6-2.

- -Jack

Hopefully the K7 will live up to predictions.  They are definitely giving
Intel a run for the money in the sales department right now though.  I guess
when you do not want to make a 60% profit, you can sell your processors for
less money!


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

Date: Sat, 1 May 1999 02:24:11 -0400
From: "Eric Litwak" <[e-mail]>
Subject: RE: (fractint) Running under windows98

The preliminary data on the K-7 SEEMS to indicate it will run faster than a
P-III. There are still some chipset issues to be worked out (the K-7
requires a new chipset to support it) but if it even comes close to the
expected performance I will go with it.

> I guess when you do not want to make a 60% profit, you can sell your
processors for
> less money!

Amen! Isn't competition a wonderful thing? BTW, I have my K-6 networked
right now and it works fine. It did take a few days for it to become happy
with the network (now I know why, Thanks!) but the bugs are finally gone.


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

Date: Sat, 1 May 1999 10:29:54 -0500
From: "Adam Leggett" <[e-mail]>
Subject: Re: (fractint) Running under windows98

I still don't get it.  Do you mean that AMD has a 3DNow optimized, software
rendering Direct3D driver, or what?  3DNow doesn't actually give you
hardware 3D acceleration; in fact the only point on the rendering pipeline
(whether OpenGL or D3D) that it really helps with is transforms (which most
of the consumer 3D accelerators up until now don't handle).  I believe the
M$ OpenGL DDK has 3DNow acceleration for transforms, which helps speed
things up a bit whether you have hardware acceleration or not, but the
software GL driver still returns a nonaccelerated pixel format through WGL.
If Direct3D always says you have acceleration if you have 3DNow, that's a
bug..

If Motocross Madness will not run unless D3D returns an accelerated mode,
that's also a bug

Adam

> It enables the system to use software that actively seeks a 3D accelerator
> (ie:MS Motocross Madness), without an added card.  Graphics and other FPU
> functions are greatly enhanced.
>
> -Jack
>
>  > 3D-Now! makes the system think that it has a 3D accelerator card
> (Voodoo2,
>  > etc), when in fact it does not.  Therefore, the system will run
software
>  > that REQUIRES an accelerator card. Basically, AMD finally did something
>  > right.  Yes, the 350MHz processor would be the slowest that I would go
> with
>  > on K6-2s, though.  My advice, wait for the K6-3s to become available.
>
> Sorry, I have no idea what you mean by making the system think it has an
> accelerator card, care to elaborate?
>
> Thanks
>


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

Date: Sat, 1 May 1999 10:43:30 -0600
From: "Tim Wegner" <[e-mail]>
Subject: Re: (fractint) Running under windows98

The AMD/ 3D now thread seems to have drifted away from the list
topic (fractals/fractint).

Tim


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Date: Sat, 1 May 1999 14:55:30 EDT
From: [e-mail]
Subject: (fractint) Fractint Formula Question

My math is mediocre and I'm hoping the more accomplished of you out there can
answer what is probably a simple question.

How would you express the equation for the Julia type fractals in terms of a
Fractint formula FRM file?

Thanks!
Bill

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Date: Sat, 1 May 1999 16:15:57 EDT
From: [e-mail]
Subject: Re: (fractint) Fractint Formula Question

Hi Bill,

> How would you express the equation for the Julia type fractals in terms of
a
>  Fractint formula FRM file?

Here's the formula for the Mandelbrot equation Julia sets.

Julia {
    c = p1  ; the Julia set coordinates
    b = 4    ; bailout value
    z = pixel
    :
    z = z * z + c
    |z| < b
}

Paul Carlson

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Date: Sat, 01 May 1999 22:50:50 -0400
From: Tom Conally <[e-mail]>
Subject: (fractint) new page

Hi Folks
I am rather redfaced. I have been trying to post to the list for two days
and non of my posts have come up. I was getting other posts so I did a "who
fractint" command and immediately got a "This is a private list, you are
not a subscriber". I see said the blind man. I had changed my reply address
to a net forwarder as I anticipate changing my ISP sometime soon. I guess
the joke's on me.
Well, I have put up a new page that shows an original fractal and the
result of my post processing. I thought it would be interesting to show
both versions. Take a look and let me know what you think.
http://members.tripod.com/afractal/beforeafter.html

Tom Conally
In every boomerang there is a perfect throw.
Your life, Grasshopper, is to practice  till you find that throw
and become one with that boomerang!
__________________________________________
Boomerangs        http://www.angelfire.com/nc/conally
Paradise             http://www.netpath.net/~conally/
Fractal Images   http://members.tripod.com/afractal
Teddybear's picnic http://members.tripod.com/afractal/picnic/teddybear.html


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Date: Sat, 01 May 1999 23:28:21 -0400
From: Paul DeCelle <[e-mail]>
Subject: Re: (fractint) new page

Looks good, Tom--

PSP is my post-processor of choice, too.  I mainly use it for
anti-aliasing and special effects like drop shadows, but the hot wax
filter is pretty cool, too.

Regards, Paul

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Date: Sun, 2 May 1999 08:46:59 EDT
From: [e-mail]
Subject: Re: (fractint) Fractint Formula Question

In a message dated 5/1/99 4:21:21 PM Eastern Daylight Time, [e-mail]
writes:

<< Here's the formula for the Mandelbrot equation Julia sets.

 Julia {
     c = p1  ; the Julia set coordinates
     b = 4    ; bailout value
     z = pixel
     :
     z = z * z + c
     |z| < b
 }

 Paul Carlson
  >>
Thanks Paul!  It was the c=p1 part that I wasn't understanding properly.  It
makes sense to me now.

Bill

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Date: Sun, 02 May 1999 10:01:27 -0500
From: Barry Spreen <[e-mail]>
Subject: RE: (fractint) Running under windows98

At 08:30 AM 4/30/99 -0400, Eric Litwak wrote:
>I have to respectfully disagree with Adam. I have a clone I built myself;
>AMD K-6 233, 64Mb, Creative Voodoo Banshee, and other than an occasional
>lockup (caused by a cheesy motherboard) fractint and other programs run
>great.
>
>Right click on the shortcut and go to properties. Under the memory tab set
>initial environment to 512. This should clear up your errors. All other
>settings are auto. If that doesn't work, try 1024.

Eric,

I have tried both 512 and 1024 on Initial Environment, and the problem
persists. The screen goes blank for a second - A message is displayed,
upper left, but too fast to read - then the desktop reappears.



Best,
Barry
mailto:[e-mail]

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Date: Sun, 2 May 1999 17:57:16 -0400
From: "Phil DiGiorgi" <[e-mail]>
Subject: Re: (fractint) Running under windows98

> I have tried both 512 and 1024 on Initial Environment, and the problem
> persists. The screen goes blank for a second - A message is displayed,
> upper left, but too fast to read - then the desktop reappears.
>

Hi Barry,

Did you try starting a full-screen DOS session under windows first, then
running fractint from there?   What happens then?   Also, look in your
'sstools.ini' and see what the "video=" line is set to.   Try commenting it
out (put a ; in front of it) or set it to a lo-res mode like "video=F3" and
see what happens.

As to running Fractint in real-mode DOS (no windows running), check that you
are not loading the real-mode compression drivers 'drvspace.bin' or
'dblspace.bin'.   These are hidden files that are sometimes placed in your
root directory and are loaded before windows boots, then unloaded and replaced
by the windows 32-bit drivers if needed.   If either of these files is in your
'C:\' directory, move them somewhere else, then boot up into dos and see if
fractint will run.

Hope this helps,

Phil D.


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Date: Mon, 3 May 1999 09:13:36 +0200
From: "Randall Britten" <[e-mail]>
Subject: (fractint) XFractint on Solaris 2.6.1

Has anyone got xfractint running on Solaris 2.6.1 (SunOS 5.6)?

The instructions in the make file don't work

The furtherest I have got is that everything compiles, but during linking
(with gcc) I get:

Undefined                       first referenced
 symbol                             in file
_fmemmove                           bigflt.o
_fmemset                            bigflt.o
_fmemcpy                            bigflt.o

- -------------------------
Randall Britten




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Date: Mon, 03 May 1999 01:26:38 -0600
From: Phil McRevis <[e-mail]>
Subject: Re: (fractint) XFractint on Solaris 2.6.1

In article <000301be9534$76e41650$[e-mail]>,
    "Randall Britten" <[e-mail]>  writes:

> Has anyone got xfractint running on Solaris 2.6.1 (SunOS 5.6)?

I've not had any problems on Solaris; I think you just need the right
defines.  I compile with XFRACT, NOBSTRING and BIG_ANSI_C all defined
and then it works OK.  If that doesn't fix it for you, mail me your
makefile and I'll see if I can spot the problem.
- --
<http://www.xmission.com/~legalize/>    Legalize Adulthood!
    ``Ain't it funny that they all fire the pistol,
      at the wrong end of the race?''--PDBT
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Date: Mon, 3 May 1999 11:08:11 +0200
From: "Randall Britten" <[e-mail]>
Subject: RE: (fractint) XFractint on Solaris 2.6.1

Thanks, that solved it.  I was missing BIG_ANSI_C.



- -----Original Message-----
From:    [e-mail]
[mailto:[e-mail]] On Behalf Of Phil McRevis
Sent:    Monday 03 May 1999 09:27
To:    [e-mail]
Subject:    Re: (fractint) XFractint on Solaris 2.6.1


In article <000301be9534$76e41650$[e-mail]>,
    "Randall Britten" <[e-mail]>  writes:

> Has anyone got xfractint running on Solaris 2.6.1 (SunOS 5.6)?

I've not had any problems on Solaris; I think you just need the right
defines.  I compile with XFRACT, NOBSTRING and BIG_ANSI_C all defined
and then it works OK.  If that doesn't fix it for you, mail me your
makefile and I'll see if I can spot the problem.
- --
<http://www.xmission.com/~legalize/>    Legalize Adulthood!
    ``Ain't it funny that they all fire the pistol,
      at the wrong end of the race?''--PDBT
[e-mail]    <http://www.eden.com/~thewho>

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

Date: Tue, 4 May 1999 09:55:03 +0200
From: "Randall Britten" <[e-mail]>
Subject: (fractint) Orbits configuration

Is there a way to configure how many points of an orbit are shown (i.e. in
orbits mode (pressing o) if I only wanted to see the first three points of
the orbit, how could this be done) ?

Secondly, is there a way to see the scale of the orbits screen (i.e. xy
coordinates of corners) ?

Thirdly, during picture generation (if one presses o), the orbits are on the
actual fractal, but is there a way to have the orbits on the actual fractal
in ordinary orbits mode?

Thanks in advance.

- -------------------------
Randall Britten




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Date: Tue, 4 May 1999 16:15:17 +0200
From: "Randall Britten" <[e-mail]>
Subject: (fractint) JuliaSaver

Here is a really cool screen saver, analogous to the space bar feature of
Fractint where one scrolls through various julia's corresponding to points
in Mandelbrot.

http://www.fractalus.com/juliasaver/

Tips: Animation: "Cardioid II"
Color: neon.map (from the fractint distribution).

- -------------------------
Randall Britten




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Date: Tue, 04 May 1999 11:35:40 -0600
From: Phil McRevis <[e-mail]>
Subject: Re: (fractint) Orbits configuration

In article <002401be9603$6bfd6730$[e-mail]>,
    "Randall Britten" <[e-mail]>  writes:

> Is there a way to configure how many points of an orbit are shown (i.e. in
> orbits mode (pressing o) if I only wanted to see the first three points of
> the orbit, how could this be done) ?

Have you tried setting maximum number of iterations to three?  Then
the "orbit" will consist of at most three points.

> Secondly, is there a way to see the scale of the orbits screen (i.e. xy
> coordinates of corners) ?

The help file says:

    <<> or <,>  Zoom orbits image smaller
    <>> or <.>  Zoom orbits image larger
    <z>         Restore default zoom.

Did you try these?

> Thirdly, during picture generation (if one presses o), the orbits are on the
> actual fractal, but is there a way to have the orbits on the actual fractal
> in ordinary orbits mode?

I'm not sure what you're asking here...
- --
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Date: Tue, 4 May 1999 23:20:49 -0400
From: Lee Skinner <[e-mail]>
Subject: (fractint) Two Pars

Here are a couple of pretty pars:

frm: rsp_a304 { ; 3/99     R Parracho
  c=3Dz=3Dpixel:
  oz=3Dz, z=3Dz*z+c,test=3D|z|/|oz|
  |test|<1 || |test|>2
}

6a304003           { ;                                       t=3D  0:05:5=
4.17
                     ; on a P233 at 1600x1200  May 04, 1999  12:22:46
                     ; Image Copyright 1999 by Lee H. Skinner ver=3D1961
                     ;  Version 1961 Patchlevel 71
  reset=3D1961 type=3Dformula formulafile=3Dfractint.frm
  formulaname=3Drsp_a304 passes=3D1
  center-mag=3D-0.330647/0.653639/16.56586/1/-29.999 float=3Dy
  maxiter=3D1024 inside=3D0 outside=3Datan periodicity=3D0
  colors=3D0008MS<3>88E85B717<3>Z54e63l72s81zA0<11>R50O40L40<3>920<8>UXAW=
`BZ\
  cD<3>hrI<3>UnXRm_NlcJkgFfpAaz<2>`Lz<6>nfUpiPrmL<2>xv6zz1zzC<2>zzz<3>jqd=
f\
  o_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriA=
t\
  m9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6<13>J52G42D32<3>000000<2>903C04D05<3=
2\
  >r2qs2rt2t<3>z3z<3>X7`Q8UI9NAAG<2>0Qc<3>5Xc6Zc7`c8bcAdc<2>LhfOigQih<11>=
m\
  ttouuqvv<3>zzz<3>rwzovzhsw<4>8_d<2>8QV sound=3Dbeep/pc
  }

6a304005           { ;                                       t=3D  0:04:0=
8.85
                     ; on a P233 at 1600x1200  May 04, 1999  12:22:46
                     ; Image Copyright 1999 by Lee H. Skinner ver=3D1961
                     ;  Version 1961 Patchlevel 71
  reset=3D1961 type=3Dformula formulafile=3Dfractint.frm
  formulaname=3Drsp_a304 passes=3D1
  center-mag=3D-0.38969609952775690/+0.64719029552820840/192.6263/1/-30
  float=3Dy maxiter=3D1024 inside=3D0 outside=3Datan periodicity=3D0
  colors=3D000uxxwyyzzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<2>717<3>Z54e6=
3l7\
  2s81zA0<11>R50O40L40<3>920<8>UXAW`BZcD<3>hrI<3>UnXRm_NlcJkgFfpAaz<2>`Lz=
<\
  6>nfUpiPrmL<2>xv6zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00=
<\
  3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6=
<\
  13>J52G42D32<3>000000<2>903C04D05<32>r2qs2rt2t<3>z3z<3>X7`Q8UI9NAAG<2>0=
Q\
  c<3>5Xc6Zc7`c8bcAdc<2>LhfOigQih<14>sww sound=3Dbeep/pc
  }

Lee

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Date: Wed, 5 May 1999 10:26:50 +0200
From: "Randall Britten" <[e-mail]>
Subject: RE: (fractint) Orbits configuration

> > Is there a way to configure how many points of an orbit are  shown (i.e.
in
> > orbits mode (pressing o) if I only wanted to see the first three points
of
> > the orbit, how could this be done) ?
>
> Have you tried setting maximum number of iterations to three?  Then
> the "orbit" will consist of at most three points.

Thanks for this tip, it helps control the orbits, but now the source fractal
has low resolution.  What is needed is the facility to specify lower
iterations for the orbits than for the source fractal.

> > Secondly, is there a way to see the scale of the orbits  screen (i.e. xy
> > coordinates of corners) ?
>
> The help file says:
>
>     <<> or <,>  Zoom orbits image smaller
>     <>> or <.>  Zoom orbits image larger
>     <z>         Restore default zoom.
>
> Did you try these?

Yes, I know about those, but I want to have more exact information on the
scale of the orbits window as in the exact xy coordinates of the corners.

> > Thirdly, during picture generation (if one presses o), the  orbits are
on the
> > actual fractal, but is there a way to have the orbits on  the actual
fractal
> > in ordinary orbits mode?
>
> I'm not sure what you're asking here...

It relates to question 2.  Especially in the Julia set, which is in the
"dynamic plane" it would be nice to be able to follow the orbits relative to
the actual julia set.  But since orbits and the actual fractal are in
separate windows, it is hard track where the one is relative to the other.
During picture generation, orbits appear in the same window as the fractal,
and it would be nice to be able to do this with manual orbits explore mode.
I tried using view windows and setting the view window of the main fractal
to the size of the whole screen, hoping that the orbits window would
overlap, but it is too clever, and the orbits window became small again.



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

Date: Wed, 5 May 1999 10:28:15 -0300
From: "Ricardo M. Forno" <[e-mail]>
Subject: RE: (fractint) Two Pars

I see you use reset=1961 in your pars. Is there a fractint version after
19.6? Where can I get it?

- ----------
De: Lee Skinner <[e-mail]>
A: [e-mail]
Asunto: (fractint) Two Pars
Fecha: MiΘrcoles 5 de Mayo de 1999 12:20 AM

Here are a couple of pretty pars:

frm: rsp_a304 { ; 3/99     R Parracho
  c=z=pixel:
  oz=z, z=z*z+c,test=|z|/|oz|
  |test|<1 || |test|>2
}

6a304003           { ;                                       t=  0:05:54.17
                     ; on a P233 at 1600x1200  May 04, 1999  12:22:46
                     ; Image Copyright 1999 by Lee H. Skinner ver=1961
                     ;  Version 1961 Patchlevel 71
  reset=1961 type=formula formulafile=fractint.frm
  formulaname=rsp_a304 passes=1
  center-mag=-0.330647/0.653639/16.56586/1/-29.999 float=y
  maxiter=1024 inside=0 outside=atan periodicity=0
  colors=0008MS<3>88E85B717<3>Z54e63l72s81zA0<11>R50O40L40<3>920<8>UXAW`BZ\
  cD<3>hrI<3>UnXRm_NlcJkgFfpAaz<2>`Lz<6>nfUpiPrmL<2>xv6zz1zzC<2>zzz<3>jqdf\
  o_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAt\
  m9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6<13>J52G42D32<3>000000<2>903C04D05<32\
  >r2qs2rt2t<3>z3z<3>X7`Q8UI9NAAG<2>0Qc<3>5Xc6Zc7`c8bcAdc<2>LhfOigQih<11>m\
  ttouuqvv<3>zzz<3>rwzovzhsw<4>8_d<2>8QV sound=beep/pc
  }

6a304005           { ;                                       t=  0:04:08.85
                     ; on a P233 at 1600x1200  May 04, 1999  12:22:46
                     ; Image Copyright 1999 by Lee H. Skinner ver=1961
                     ;  Version 1961 Patchlevel 71
  reset=1961 type=formula formulafile=fractint.frm
  formulaname=rsp_a304 passes=1
  center-mag=-0.38969609952775690/+0.64719029552820840/192.6263/1/-30
  float=y maxiter=1024 inside=0 outside=atan periodicity=0
  colors=000uxxwyyzzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<2>717<3>Z54e63l7\
  2s81zA0<11>R50O40L40<3>920<8>UXAW`BZcD<3>hrI<3>UnXRm_NlcJkgFfpAaz<2>`Lz<\
  6>nfUpiPrmL<2>xv6zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<\
  3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6<\
  13>J52G42D32<3>000000<2>903C04D05<32>r2qs2rt2t<3>z3z<3>X7`Q8UI9NAAG<2>0Q\
  c<3>5Xc6Zc7`c8bcAdc<2>LhfOigQih<14>sww sound=beep/pc
  }

Lee

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

Date: Wed, 5 May 1999 15:14:40 GMT
From: "Andrew Coppin" <[e-mail]>
Subject: (fractint) Purely mathematical

I have a question: For those of you who can't remember, the formulas
for the "Barnsley Julia" fractals are:

BJ1: If real(Z) >= 0
  Then Z=(Z-1)*C
  Else Z=Z(Z+1)*C

BJ2: If real(Z)*imag(C) + real(C)*imag(Z) >= 0
  Then Z=(Z-1)*C
  Else Z=(Z+1)*C

BJ3: Re(Z) >= 0
  Then Z=(real(Z)^2 - imag(Z)^2 - 1) + (2*real(Z)*imag(Z))i
  Else Z=(real(Z)^2 - imag(Z)^2 - 1 + real(C)*real(Z)) +
(2*real(Z)*imag(Z) + imag(C)*real(Z)))i.

My question is this: Where on earth did M. Barnsley *get* these from?

Julia #3 is the only one which looks remotely recognisible (and
indeed its graphical form is more "Juliaish"). That first term looks
a bit like real(Z)^2 - imag(Z)^2, which is the result of real(Z^2).
But the rest? What is the mathematical reasons behind it? I know a
lot of people out there simply type formulas into FractInt and get
pretty pictures, but I can't imagine someone like Barnsley inventing
them out of thin air. What's the background? And how do you work out
the derrivatives of functions like that?!?!

P. S. I too would like to know out to super-impose orbits over the
fractal and not a seperate window. FractInt does it while rendering,
but not it seems once it's finnished...

P. P. S. I'm talking to you Tim: So you can't generalise Complex
Numbers into a 4D field... But *can* you generalise them into a 3D
set without loosing any field properties? Just how complicated is the
proof of there being no 4D fields (i.e. would someone like me
understand it)?

- ---------------------------------
Nam et ipsa scientia potestus est!
(Sir Francis Bacon)
Andrew Orphi Coppin
DMU MK.

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End of fractint-digest V1 #386
******************************