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fractint-digest        Tuesday, January 6 1998        Volume 01 : Number 063




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

Date: Tue, 06 Jan 1998 11:03:03 -0800
From: Mark Christenson <[e-mail]>
Subject: Re: (fractint) Computer (as) Artist

At 09:54 AM 1/6/98 -0800, I wrote:
>...
>Similar efforts to optimize computing for specific
>tasks have proven successful to various degrees...

Oh, I forgot another obvious example, in light of recent developments:
music!  I think if we were to ask someone in *that* field, we might get
more optimistic and perhaps helpful input.


Bud


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Date: Tue, 6 Jan 1998 19:00:02 -0000
From: Edward Avis <[e-mail]>
Subject: (fractint) RE: fractint-digest V1 #62

>It is provable that the problem-solving ability, meaning the ability to
answer a given question, of any computer is equivalent to that of >what is
called a Turing machine. It is fairly easy to also prove that there are
problems which, despite having quite definite solutions, >cannot be solved
by a Turing machine and thus any computer. This, and related discoveries of
early-twentieth-century mathematics like >Godel's theorem, are probably
what your son is referring to... Note that from a scientific standpoint,
the term "computer" as used here >includes a computer like the human
brain.

No, it doesn't.  The human brain is not a Turing machine in any shape or
form, and does not work algorithmically.  Hence there are propositions
(Godel's theorem being the first example) which we humans can see as
"obvious" (or least mathematicians can!), but are provably impossible for a
computer to "understand".
- --
Ed Avis
[e-mail]
http://members.tripod.com/~mave/index.html


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

Date: Tue, 6 Jan 1998 19:04:01 -0000
From: Edward Avis <[e-mail]>
Subject: (fractint) RE: fractint-digest V1 #62

>Back in the "(fractint) text editor" there was various discussion on how
to rid text files of the dreaded accented 'a'.
Could I suggest that people put their pars into zip files, then post them
UUEncoded?

Many people may think this is heresy, but I think it would be preferable to
having half of the list devoted to how mailers manage to mangle text
messages.

It might even be possible for the mail server to automatically gather up
all the par files and put them into a "best of fractint-digest" collection
on a web page.
- --
Ed Avis
[e-mail]
http://members.tripod.com/~mave/index.html


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

Date: Tue, 6 Jan 1998 14:24:07 -0500 (EST)
From: Ian Kaplan <[e-mail]>
Subject: Re: (fractint) RE: fractint-digest V1 #62

[snip stuff I wrote]

> what your son is referring to... Note that from a scientific standpoint,
> the term "computer" as used here >includes a computer like the human
> brain.
>

Ed wrote:

> No, it doesn't.  The human brain is not a Turing machine in any shape or
> form, and does not work algorithmically.  Hence there are propositions
> (Godel's theorem being the first example) which we humans can see as
> "obvious" (or least mathematicians can!), but are provably impossible for a
> computer to "understand".
> --
> Ed Avis

   er... not sure I know what you mean by "see as 'obvious'" or
"'understand'" here. I don't know how to discuss what a computer does or
does not "understand". A computer, however, can certainly re-create the
proof of Godel's theorem by following the same logical steps.

   To clarify my previous statement, which is admittedly controversial as
stated: From the standpoint of theoretical computer-science modeling of
computing, no aspect of the human brain which has been found
scientifically describable, appears to be exempt from the models of
automata theory which leads to the proofs about Turing machines. This
does not suggest that we understand processes of thought or that emergent
properties cannot exist; but assuming that all functions of the brain do
in fact ultimately depend on the physical nature of the brain, all
its low-level physical or chemical processes can indeed be modeled as
automata, and the proofs do thus apply.

   It is entirely possible to disagree with this statement on religious
or mystical grounds and I freely accept that our scientific knowledge of
the brain is as yet quite insufficient to describe it fully; however, to
the extent to which we can describe it, this appears quite clear.


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Date: Tue, 06 Jan 1998 12:27:42 -0700
From: Rich Thomson <[e-mail]>
Subject: Re: (fractint) RE: fractint-digest V1 #62

In article <c=GB%a=TMAILUK%p=DCNET%l=[e-mail]> ,
    Edward Avis <[e-mail]>  writes:
> Could I suggest that people put their pars into zip files, then post them
> UUEncoded?

This is going to cause more problems than it solves.

It requires attachments, which have already been voted down.
It adds two extra layers of encoding, making two extra places where
    things can go wrong (zip + uue)
Uuencode is less portable than base64 encoding, upon which MIME is
    based.
Since uuencode (and base64) expands source material by 1/3rd, its not
    clear that anything would be gained by taking a text file and
    compressing it and then expanding it again.
All PAR/FRM/IFS/etc. files are text files -- treating them as binary
    attachments makes them unavailable to text search engines that
    search through the list archives.

In summary... just deal with the plain text files.  There will always
be problems with embedded text files, all of which are solved by the
use of MIME (an existing standard).  However, until the majority of
people (or at least the ones who complain about MIME) get MIME
compliant software, I don't see MIME approaches being accepted.
- --
  ``Between stimulus and response is the will to choose.''  -- Steven Covey
 =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
     3D Paint: The Power to Create in 3D;        Rich Thomson
     email me for more info                [e-mail]

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

Date: Tue, 06 Jan 1998 23:40:25 -0800
From: cindy mitchell <[e-mail]>
Subject: Re: (fractint) Lost messages

Hi,
You can pick up messages you have missed at
ftp://ftp.xmission.com/pub/lists/fractint/archive/
   Cindy

http://www.geocities.com/Paris/Rue/3542/
http://www.tou.com/host/fractallady/




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

Date: Tue, 06 Jan 1998 14:43:34 -0600
From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) terrible oversight

Jack Valero wrote:
>
> Yep. That was the start. So how would you judge my predictions?
>

Pretty darn accurate.  How are you with Stocks and the Lottery??

>
> I went on to set up my But is it Art page and Name the Artist
> pages but the responses to them have been pretty minimal. Not
> enough interest I suppose... sigh. I think they will be the
> last of my group experiments. Too bad really because I have some
> interesting questions I would like to have explored that would
> help us determine just what "fractal art" might or could be. But
> without a large enough participation sample there is no useful
> information, just data.
>

I found that section of your website interesting.  The easist images to
recognize were from Earl Hinrichs (almost instantly) and Linda Allison.

But this was a "trick" question:  twelve images shown, nine artists
listed in the side bar, two listed in the fine print (at the bottom),
and one unlisted unknown.  Not exactly a one for one match.

P.N.L.

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

Date: Tue, 6 Jan 1998 16:24:04 -0500
From: Sylvie Gallet <[e-mail]>
Subject: (fractint) Yet another formula from Paul Carlson

Hi All,

  Paul still gets his messages to this list bounced back, so he asked me =
to
post this mew formula.  He gets all the messages posted there so, feel fr=
ee
to comment!

        - Sylvie

- ---------------------------------------------------------
Here is a formula and PAR file that demonstrates how the
parametric form of an equation of a curve can be used as
an orbit trap.
 =

Astroid_Mset  {; Copyright (c) Paul W. Carlson, 1997
    ;****************************************************
    ; Always use floating point math and outside=3Dsumm.
    ;
    ; Parameters:
    ;   real(p1) =3D a factor controlling the width of the curves
    ;   imag(p1) =3D radius of the astroid
    ;   real(p2) =3D number of color ranges
    ;   imag(p2) =3D number of colors in each color range
    ;
    ; Note that the equation variable is w, not z.  Always
    ; initialize z to zero.
    ;****************************************************
    w =3D 0
    c =3D pixel
    z =3D 0
    bailout =3D 0
    iter =3D 0
    range_num =3D 0
    i =3D (0,1)
    r =3D imag(p1)
    ;****************************************************
    ; In the accompanying par file, astmset.par,
    ; we have 8 color ranges with 30 colors in each range
    ; for a total of 240 colors. The first range starts at
    ; color 1.  Pixels will use color 0 when |w| < 10000.
    ; 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 =3D real(p2)
    colors_in_range =3D imag(p2)
    ;****************************************************
    ; Real(p1) controls the width of the curves.
    ; These values will usually be in the range 0.001 to 0.1
    ;****************************************************
    width =3D real(p1)
    index_factor =3D (colors_in_range - 1) / 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.
    ; This example uses the standard Mandelbrot set equation.
    ;****************************************************
    w =3D w * w + c
    ;****************************************************
    ; The orbit trap curve.  This example uses an "astroid"
    ; curve (which has absolutely nothing to do with huge
    ; rocks in outer space).  Any two-dimensional curve can
    ; be used which can be expressed in parametric form in
    ; terms of the angle from the origin.
    ;****************************************************
    ang =3D atan(imag(w) / real(w))
    astroid =3D r * (cos(ang)^3 + i * sin(ang)^3)
    ;****************************************************
    ; If the orbit point is within some distance of the curve,
    ; set z to the index into the colormap and set the bailout
    ; flag.  Note: the way we use the "distance" here has
    ; the effect of turning the curves inside-out in the image.
    ;****************************************************
    distance =3D abs(|w| - |astroid|)
    IF (distance < width && iter > 1)
        z =3D index_factor * distance + range_num * colors_in_range + 1
        bailout =3D 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 =3D range_num + 1
    IF (range_num =3D=3D num_ranges)
        range_num =3D 0
    ENDIF
    ;****************************************************
    ; Since we are using outside=3Dsumm, we have to subtract
    ; the number of iterations from z.
    ;****************************************************
    iter =3D iter + 1
    z =3D z - iter
    ;****************************************************
    ; Finally, we test for bailout
    ;****************************************************
    bailout =3D=3D 0  && |w| < 1000
}


astmset            { ; Copyright (c) Paul W. Carlson, 1997
  reset=3D1960 type=3Dformula formulafile=3Drast.frm
  formulaname=3DAstroid_Mset passes=3Dt
  center-mag=3D+0.36126226339583390/+0.09037301461753901/5.967617e+008
  params=3D0.016/0.3/8/30
  float=3Dy maxiter=3D3000 inside=3D253 outside=3Dsumm
  colors=3D000fOz<28>I0Kz0f<28>O08z88<28>O00zW0<28>c40zz0<28>aG00z\
  R<28>0C40zz<28>0CCGGz<28>00O000<10>000z88000000
  }




  =



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

Date: Tue, 06 Jan 1998 14:35:24 -0700
From: Rich Thomson <[e-mail]>
Subject: Re: (fractint) Yet another formula from Paul Carlson

In article <[e-mail]> ,
    Sylvie Gallet <[e-mail]>  writes:
> Paul still gets his messages to this list bounced back, so he asked me to
> post this mew formula.

I keep seeing this problem about Paul getting his messages bounced
back.  I haven't seen what address he's posting to -- he should post to
[e-mail], NOT [e-mail] since
lists.xmission.com now handles all list traffic for xmission and list
mail sent to any other machine will bounce.

If Paul is using that address, but still having problems with the
messages being bounced, he should forward one of the bounced messages
WITH ALL HEADERS INTACT to Tim Wegner <[e-mail]>, list
administrator.

With a sample bounce, Tim can work with the folks at xmission to sort
out the problem.
- --
  ``Between stimulus and response is the will to choose.''  -- Steven Covey
 =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
     3D Paint: The Power to Create in 3D;        Rich Thomson
     email me for more info                [e-mail]

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

Date: Tue, 6 Jan 1998 16:35:13 -0500
From: George Martin <[e-mail]>
Subject: Re: (fractint) Happy New Year!

Beth,

   I'm sorry you're having so much trouble recreating the images posted
here as parameter entries. One side effect of the center of gravity of
Fractint discussion moving from the CompuServe forum to this message list
is that a majority of new images are now posted as part of messages rather
than in the traditional .par and related files. Getting from a message to
an image drawing on your screen does take a fair amount of knowledge of how
Fractint works. I'll try a step by step explanation of how to do it; I hope
it solves your problems for you. If not, let me know, and we'll keep at it.

   First, make sure you have the most recent version of Fractint, currently
19.6. Each new release incorporates new features, and many current postings
will only work with the latest version.

   Second, a word about directories. Unless you give instructions to
Fractint to the contrary (via special command line options or in a file
called "sstools.ini"), Fractint will look for all relevant files in the
same directory where Fractint.exe is located. Starting off, it is probably
easiest simply to use the one directory. As you get more familiar with the
program, you will learn how to create separate subdirectories for the
various kinds of files, and how to tell Fractint where those subdirectories
are.

   Finally, the information which Fractint uses to draw an image is
contained in entries with the form:

Name  {; comments
  various commands
}

The relevant entries are

   1. Parameter entries. These are entries with commands such as type=xxx
colors=lots_of_Martian, etc. Usually, the first command is "reset=####",
where the #### is the version of fractint which was in use when the entry
was created. Don't worry about that; if a version earlier than 19.6 was
used, the current version will still draw the image.

      Parameter entries contain all the information needed for fractint to
draw an image, unless "type=formula", in which case fractint will need to
find the formula. The name of the formula is identified in the entry with
the command "formulaname=xxx". There is also usually a command in the
parameter entry "formulafile=xxx.frm", but this is not important, because
Fractint is quite clever in searching for and finding formulas. More about
that later. "type=ifs" and "type=lsystem" also require fractint to find the
relevant ifs or lsystem entries, but postings with these commands are
reletively rare, so I wouldn't worry about that now.

     Parameter entries should be copied to a file with the extension
".par". You can use any name you want for the file, such as 1998msg.par.
Just copy the text of the message to the .par file, and then edit it to
delete everything except the parameter entry or entries contained in the
message (in each case beginning with the name of the entry and ending with
the "}"). The .par file should be in your Fractint directory, as I
discussed above, unless you have explicitly specified a different
directory. Don't delete the original message if there are formulas in the
message! Those entries will be copied to a separate file.

   Occasionally, problems are caused by the email software which people use
to post these entries. Take a look at each entry; there should be no blank
lines, and for the long commands such as colors=, the last character of the
intermediate lines should be a "\".

   2. Formula entries.  When the parameter entry is "type=formula",
fractint must find the named formula in order to draw the image. A formula
has the same overall structure as a parameter entry, i.e.

Name {; comments
  various calculation instructions
}

and are pretty easy to identify; they have assignment instructions such as
z=pixel or c=sin(pixel); a ":" will appear somewhere in the formula; and in
some you will see flow control instructions such as IF (x==y) etc.

   Formulas need to be copied to a file with the extension ".frm". Any name
is OK, such as "1998msg.frm". The file should be in your fractint directory
as discussed above unless you have explicitly specified a different
directory as a command line option or in sstools.ini. Edit the file to
delete everything except the formula entry or entries. If an entry name is
preceded with "frm:", delete the "frm:". This is a feature which permits
the formula to be included in a .par file, but it is a good habit, I think,
to get the formulas into files with the .frm extension. That way they will
be available for general use and not just the initial drawing of the
related parameter entry.


   3. Ifs and Lsystem entries. The general format is the same, but the
information in these entries looks quite a bit different. They should be
copied to files with extensions ".ifs" and ".L" respectively, and any
preceding "ifs:" or "lsys:" edited out.


Now, to run the parameter entry.

   1. Go to your fractint directory and start Fractint.
   2. Select your video mode.
   3. Hit Shift-2 (the "@" key). This will probably bring up a list of
parameter entries in the default .par file "fractint.par".
   4. Hit F6. This exits fractint.par and shows you a list of .par files in
the default directory. Presumably, your 1998msg.par will be one of them.
Put the cursor on it, and hit <CR>. This will show you a list of the
parameter entries in that .par file.
   5. Move the cursor to the entry you want to draw, and hit <CR>.
   6. The image should start drawing. Enjoy.
   7. You can zoom, change parameters, and do anything else that fractint
permits you to do with an image. Important commands to do these things are
Page-UP (for zooming), and "x", "y", and "z" for changing various options.
You can save the image by hitting "s". You  can create your own parameter
entry by hitting "b" and entering the requested information.


Finally, if you want to draw your own image using a formula, hit "t" from
any image screen or the main menu, select type "formula", and hit F6 to get
out of the default fractint.frm list of formulas to see a list of .frm
files. Select the file you are interested in, hit <CR>, and select the
formula you want to draw. Before drawing the formula, Fractint will show
you the formula text and provide space for entering user specified
variables (p1, p2, and p3) and user specified functions (fn1, fn2, fn3, and
fn4), if any. You can change your selections at any time the image is
drawing by hitting "z".

   That's a long message! Let me know how you make out.

George Martin


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

Date: Tue, 06 Jan 1998 17:50:40 -0500
From: Dick Amerman <[e-mail]>
Subject: Re: (fractint) Happy New Year!

B Michie wrote:

> Dick, you write about separating the pars and the frms, and putting them
> into appropriate directories. Please can you answer my question? ....

Beth:

Mark and George answered your question quite well.  There is one concept that
may not have come through clearly:

A named par file consists of parameter sets for a number of named Fractint
images.  During December, 1997, for example, there were a whole bunch of sets
of image parameters that were included in messages from the various subscribers
to this list.  I selected and copied them all, one by one, into a single par
file that I just called Dec97.par.  George described how to use <2> or <@> and
<F6> to get to the par file, then arrow up or down to the image you want.

Essentially the same scheme applies to formula files.  A named frm file may
contain many individually named formulas.  I placed last month's formulas, for
the most part, in Dec97.frm, for example.  In a couple cases the message
contained a full file of formulas that I saved under the name used by the
sender.  Again, George described how to start with <t> to get to any individual
formula file you want.

Of course, if you want to generate a particular image, the formula called for
by that image must be present somewhere in the Fractint directory.

Since you are new to Fractint, maybe you are not aware that par and frm files
are ASCII text files.  You can examine how they are put together by using a
text editor or your word processor in .txt mode -- just open the name.par or
name.frm as you would any other document and look it over.  In fact, you can
use your editor to make changes directly in the par parameters or in the frm
files -- and that is what you have to do if the color  or other parameters are
garbled as George mentioned.

I think your best bet might be to play around some more with the 'standard'
formula and parameter files that come along with Fractint and not worry about
downloading and implementing the ones in these messages until you have the
'standards' mastered.

Dick




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Date: Wed, 07 Jan 1998 00:13:25 +0100
From: Andrew Fraser <[e-mail]>
Subject: (fractint) 3d curses

Help!
I've been enjoying generating lots of the wonderful fractals posted on
the list, especially the fantastic 3Dballs series with variations. This
all came to an abrupt end when I downloaded somebody's files infected
with the dreaded "=3D" disease. Full of confidence, I found and replaced
all of these, and now none of the ball fractals work either! Guess I
must have stripped out too many 3D's.
Can any kind soul send me directly all the ball-related par and frm
files. Thanks.
Andrew


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Date: Tue, 6 Jan 1998 23:12:54 -0000
From: Peter Moreland <[e-mail]>
Subject: Re: (fractint) Yet another formula from Paul Carlson

- -----Original Message-----
From: Rich Thomson <[e-mail]>
To: [e-mail] <[e-mail]>
Date: 06 January 1998 21:37
Subject: Re: (fractint) Yet another formula from Paul Carlson


<snip
>I keep seeing this problem about Paul getting his messages bounced
>back.  I haven't seen what address he's posting to -- he should post to
>[e-mail], NOT [e-mail] since
>lists.xmission.com now handles all list traffic for xmission and list
>mail sent to any other machine will bounce.
<snip>

I found the opposite I had problems with "[e-mail]" when
I changed to straight "[e-mail]" things worked fine...

Peter


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

Date: Tue, 6 Jan 1998 18:08:19 -0500
From: "Jason Hine" <[e-mail]>
Subject: Re: (fractint) Computer (as) Artist

Ian pointed out:
>   Note also that the determination of what problems are and are not
>solvable is often a tricky task that people spend whole careers on...


This question is one I have wondered if fractals might be a good application for
(what a horrible sentence that was, eh?)... E.F. Schumaker (a philosopher)
points out that there are basically two types of problems, convergent and
divergent.  For a convergent problem, many starting solutions can be refined
into a single, optimum solution.  I think the evolution of the bicycle is the
example he gives for this... a divergent problem, on the other hand, has two (or
more?) optimum solutions, and which solution is the right one becomes a matter
of intrinsic or personal values. Ask any statistician and she will tell you that
values are too flighty to be modelled - enter fractals.  Or at least, that's the
idea.

Asleep yet?  :)   Jason


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Date: Tue, 6 Jan 1998 18:43:00 -0500
From: "Jason Hine" <[e-mail]>
Subject: Re: (fractint) RE: fractint-digest V1 #62

I plan to take this thread a little more off-topic, so if the philosophy of the
mind doesn't interest you, I suggest skipping this message...

[snipped most of this off-topic (?) stuff]

Ian logicsticizes:
>properties cannot exist; but assuming that all functions of the brain do
>in fact ultimately depend on the physical nature of the brain, all
>its low-level physical or chemical processes can indeed be modeled as
>automata, and the proofs do thus apply.

>
>   It is entirely possible to disagree with this statement on religious
>or mystical grounds and I freely accept that our scientific knowledge of
>the brain is as yet quite insufficient to describe it fully; however, to

Here's my hunch: recent progress in the field of quantum physics has revealed
that information can travel faster than the speed of light between two particles
that once interacted.  This phenomenon has been experimentally proven (1).  What
if our brains make use of this phenomenon, and are able to receive information
in a similar manner?  The experiment in which information was shown to travel
faster than light doesn't dare to suggest a *medium* for the transfer, but what
if our brains can access this medium?  If this could be proven, it might shed
light on all manner of 'otherworldly' phenomena (I'm especially interested in
the contagiousness of yawns... :)  To be sure, I'm below novice status when it
comes to these topics, but what I've read doesn't seem to negate the
possibility.  And of course, fractals will come into play at some point...

Put that in your snipe and poke it!  Wonder, Jason

(1) "Quantum Mechanics: Teleportation Beams Up a Photon's State", Science 1997
December 12.  Sorry, my footnoting's a bit rusty....


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Date: Tue, 6 Jan 1998 16:50:05 -0700 (MST)
From: Kerry Mitchell <[e-mail]>
Subject: (fractint) Updated web site (repost)

With the message about using [e-mail] instead of
fractint@xmission, it occurred to me that my last post may not have gone
out.  Just in case it didn't, here I go again:  over the holidays, I made
some new stuff and put it up on my page:

http://www.primenet.com/~lkmitch/

Have a look!

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



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Date: Tue, 6 Jan 1998 19:05:47 -0500
From: Lee Skinner <[e-mail]>
Subject: (fractint) Yet another f

Paul,

>>Here is a formula and PAR file that demonstrates how the parametric for=
m
of an equation of a curve can be used as an orbit trap.

Astroid_Mset  {; Copyright (c) Paul W. Carlson, 1997<<

Fantastic!!  Thanks for sharing all of this wealth of wonderful formulas
and images that you've created!  They have all been stunning and absolute=
ly
beautiful.

Lee

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Date: Wed, 07 Jan 1998 01:17:08 +0100
From: [e-mail] (Guy Marson)
Subject: Re: (fractint) Lost messages

Bonjour Jean-Pierre,

Je pourrais vous passer les email's si vous ne les avez pas d=E9ja eu..?



>Hi all and happy new year,
>
>The workstation where my mailbox is lodged was down for several days.=20
>Therefore majordomo has suppressed my name from the list of subscribers.=20
>All the messages posted between 12/22 and 01/05 where lost. Can somebody=20
>forward me these messages (one of you only !) ?
>Thank you.
>
>Jean-Pierre louvet : [e-mail]
>Fractal album :
>http://graffiti.cribx1.u-bordeaux.fr/MAPBX/louvet/jpl0.html
>
>-
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>


Fungi for fun =3D FunGUY... @:-]

(Guy Marson, 45b, rue de Bettembourg, L-5810 Hesperange)
(Tel./Fax : [phone])  e-mail: [e-mail]


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Date: Tue, 06 Jan 1998 19:47:02 -0800
From: Peter Jakubowicz <[e-mail]>
Subject: (fractint) Vector pars

Cool formulas, Paul. Do you have any pars you might post? Pardon mind


The_Nose           {
  reset=1960 type=formula formulafile=vector.frm formulaname=Vector1M
  center-mag=-0.630895/0.171354/16.19516 params=0/0/0/0/128/512
  float=y maxiter=1500 inside=bof61
  colors=000ET7<5>8G47E36C3492371241120000<9>BBUCCWDDZEE`FFc<4>KKnKKpLLq<3\
  >NNwNNxOOxOOy<2>OOzPPzOOzOOz<3>NNxNNwNNu<2>LLqKKpKKnJJl<6>CCWBBUAAR99O<7\
  >000<7>OJ4RL5UN5WP6ZR6<3>hZ8j`9la9ncApdA<3>uiBwjBxjBxkCylC<2>zlCzmCzlCzl\
  CzlC<2>xjBwjBuiB<2>qeApdAncAla9<6>WP6UN5RL5OJ4<6>320300<8>U55W66Z66`77c7\
  7<4>nAApAAqAA<3>wBBxBBxCCyCC<5>zCCzCCyCCxCCxBB<4>qAApAAnAAl99<6>W66U55R5\
  5O44<7>000<7>9J4AL5BN5CP6DR6<4>I`9Ja9KcAKdALeA<2>NiBNjBNjBOkC<3>OlCPmCOl\
  COlCOlC<5>MhBMgBLeA<2>Ja9I`9HZ8GX8FV7
  }

Domino             {
  reset=1960 type=formula formulafile=vector.frm formulaname=Vector1M
  center-mag=-0.64823164078975020/+0.15992038613467530/865.1313/1/90
  params=0/0/0/0/4/400 float=y maxiter=1500 inside=bof61
  colors=000yCC<5>zCCzCCyCCxCCxBB<4>qAApAAnAAl99<6>W66U55R55O44<7>000<7>9J\
  4AL5BN5CP6DR6<4>I`9Ja9KcAKdALeA<2>NiBNjBNjBOkC<3>OlCPmCOlCOlCOlC<5>MhBMg\
  BLeA<2>Ja9I`9HZ8GX8<7>8G47E36C3492371241120000<9>BBUCCWDDZEE`FFc<4>KKnKK\
  pLLq<3>NNwNNxOOxOOy<2>OOzPPzOOzOOz<3>NNxNNwNNu<2>LLqKKpKKnJJl<6>CCWBBUAA\
  R99O<7>000<7>OJ4RL5UN5WP6ZR6<3>hZ8j`9la9ncApdA<3>uiBwjBxjBxkCylC<2>zlCzm\
  CzlCzlCzlC<2>xjBwjBuiB<2>qeApdAncAla9<6>WP6UN5RL5OJ4<6>320300<8>U55W66Z6\
  6`77c77<4>nAApAAqAA<3>wBBxBBxCC
  }

The Grin           {
  reset=1960 type=formula formulafile=vector.frm formulaname=Vector2M
  center-mag=-0.44474231273223350/+0.00415666005338331/5.456301e+009
  params=0/0/0/0/2/400 float=y maxiter=256 outside=atan
  colors=000LG4<2>UN5WP6ZR6`T7cV7<2>j`9la9ncApdAqeA<2>uiBwjBxjBxkCylC<2>zl\
  CzmCzlCzlCzlC<2>xjBwjBuiB<2>qeApdAncAla9<6>WP6UN5RL5OJ4<6>320300<8>U55W6\
  6Z66`77c77<4>nAApAAqAA<3>wBBxBBxCCyCC<5>zCCzCCyCCxCCxBB<4>qAApAAnAAl99<6\
  >W66U55R55O44<7>000<7>9J4AL5BN5CP6DR6<4>I`9Ja9KcAKdALeA<2>NiBNjBNjBOkC<3\
  >OlCPmCOlCOlCOlC<5>MhBMgBLeA<2>Ja9I`9HZ8GX8<7>8G47E36C3492371241120000<9\
  >BBUCCWDDZEE`FFc<4>KKnKKpLLq<3>NNwNNxOOxOOy<2>OOzPPzOOzOOz<3>NNxNNwNNu<2\
  >LLqKKpKKnJJl<6>CCWBBUAAR99O<7>000<5>IE3
  }

Require Paul Derbyshire's formulas,

Vector1M { ; 2D Mandelbrot set from vector valued function.
           ; p3 bailout.
  z=0, w=0, c=pixel:
  z2=sqr(z)
  w2=sqr(w)
  z=z2+w2+c
  w=c*z2*w2+1,
  |z2+w2|<=p3
}

Vector2M { ; 2D Mandelbrot set from vector valued function.
           ; p3 bailout.
  z=0, w=0, c=pixel:
  z2=sqr(z)
  w2=sqr(w)
  z=z2+2*w*z+w2+c
  w=z*Z2+w*w2+w2*z2+c,
  |z2+w2|<=p3
}




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Date: Tue, 06 Jan 1998 18:16:31 -0800
From: Wizzle <[e-mail]>
Subject: Re: (fractint) Computer (as) Artist

It wasn't the turing machine proof......I know about that one (ex hubby got
phd in computer science and tried to explain that to me).....son says this
is a recent proof from a mathematician....if there is interest I will get
the name of the guy...I know my son's name already.


At 01:03 PM 1/6/98 -0500, you wrote:
>> At 07:40 AM 1/6/98 -0800, Angela wrote:
>
>> >...my
>> >computer scientist son was babbling about a mathematical proof that
>> >computers are limited....can't remember quite how...but we were discussing
>> >the fractal art conundrum.
>
>   It is provable that the problem-solving ability, meaning the ability
>to answer a given question, of any computer is equivalent to that of what
>is called a Turing machine. It is fairly easy to also prove that there
>are problems which, despite having quite definite solutions, cannot be
>solved by a Turing machine and thus any computer. This, and related
>discoveries of early-twentieth-century mathematics like Godel's theorem,
>are probably what your son is referring to... Note that from a scientific
>standpoint, the term "computer" as used here includes a computer like the
>human brain.
>   Note also that the determination of what problems are and are not
>solvable is often a tricky task that people spend whole careers on...
>
>
>-
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>

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End of fractint-digest V1 #63
*****************************