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fractint-digest        Thursday, April 5 2001        Volume 01 : Number 548




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

Date: Sun, 01 Apr 2001 00:44:41 +0200
From: Guy Marson <[e-mail]>
Subject: Re: (fractint) Twenty & One

At 19:13 29.03.2001 +0100, you wrote:
>Andrew,
>
>> Thanks for the info. Now how about the Newton-Mandeloid and the General
>> Quartic?
>
>Is this what you wanted for the Newton-Mandeloid?
>
>KRup2000-41{
>;By Rupert Millard
>l=pixel
>a=l*p1
>b=l*p2
>c=l*p3
>;Solve the cubic equation z^3+bz^2+cz+d=0 - I must be mad
>q=(3*b-a^2)/9
>r=(9*a*b-27*c-2*a)/54
>s=(r+sqrt(q^3+r^2))^(1/3)
>t=(r-sqrt(q^3+r^2))^(1/2)
>r1=s+t-a/3
>r2=-(s+t)/2-a/3+(0,0.5)*sqrt(3)*(s-t)
>r3=conj(r2)
>;Then the centroid is the point to iterate
>z=(r1+r2+r3)/3:
>oldz=z
>z=z-(z^3+a*z^2+b*z+c)/(3*z^2+2*a*z+b)
>|oldz-z|>0.0001}
>
>It iterates Newton's method cubic equation with coefficients proportional to
>the coordinates of the pixel (starting at the centroid of the roots of said
>equation.) This formula contains minibrots. For proof try:
>
>temp               {
>  ; By Rupert Millard ([e-mail]) on Mar 29, 2001
>  reset=2001 type=formula formulafile=krup2000.frm
>  formulaname=KRup2000-41 center-mag=-2.02977/-1.38778e-015/7.704635
>  params=0/0/1/0/1/0 float=y maxiter=500 inside=0 symmetry=none
>  cyclerange=0/255 colors=@blues.map
>  }


wouuuuw.. I can't belive it: somebody sending an .frm and a .par!

Thanks a lot.. something to play around, super!

cheers,


Guy




>
>I could make an extended version, for UF as Fractint doesn't have enough
>parameters. This would have a constant amount added on to the multiple of
>the pixel coordinate (it could be stop a coefficient from being varied.)
>Like all my UF formulae you could vary the bailout. It could also be
>quartic. Would that produce cubic minibrots? I'll try and find out. Of
>course, you're all welcome to try to beat me to it. Its a shame that
>Fractint doesn't have the capabilities to handle more than five complex
>parameters.
>
>For the general quartic (nb. Requires patch Fractint 20.0.13 or more
>recent):
>
>QuarticMandelbrot{
>;p1 is multiplier of z^4
>;p2 is multiplier of z^3
>;p3 is multiplier of z^2
>;p4 is multiplier of z
>z=c=pixel:
>z=p1*z*z*z*z+p2*z*z*z+p3*z*z+p4*z+c
>|z|<=128
>}
>
>From,
>
>Rupert
>
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------------------------------

Date: Mon, 2 Apr 2001 00:11:27 +0200
From: "Gerald K. Dobiasovsky" <[e-mail]>
Subject: Re: (fractint) Fractint Development: The Ljapunow Type

Guy Marson wrote:

> Hi fractinters,
>
> Does somebody know the Lyapunow-formula written for the Parser similar to
> the build-in type, or a place (url or so) to find this formula?
>
> Cheers,
>
> Guy

Hi,

Since I have never seen such a beast (although the parser can
be coaxed to do astounding things, as all the formulas by
Sylvie Gallet, Damien Jones, Paul Carlson etc. are proof of),
I feel obliged to post my construct.

A word of caution is in order here.
This thing is not exactly user friendly for a couple of reasons
(some are: the original was written when there existed no if-
statements, the parser supported only much smaller formulas, and *I* know what all those variables
are supposed to achieve - or at least I think I do ;-)).

Some explanations: (Parameter names in the formula comments
                    are written in the form:
                    p# ... real part / imaginary part)

The ab-String is input the same way as in Fractint's Lyapunov
type, converting a's to 1's and b's to 0's, but *without*
dropping the leading a and the trailing b!!!
In fact there's no need to rotate the string at all, it may
have leading b's; the length of the string is input in a
separate variable (abMax).

Scaling Exponent and Scaling Factor are used to bring the
output into the appropriate color range (a bit of fiddling
around is necessary here).

Filter Cycles does the same as Fractint's Lyapunov parameter.

Bailout is used to catch possible overflows of the iteration
function. Fractint is very good at catching those itself (at
first my formula ended in the statement "n == n", letting all pixels iterate maxiter times and
leaving it to Fractint what
happened to those values that grew too big), only it insisted
on painting those pixels with a different color than those with
non-overflowing, but still positive Lyapunov exponents.

Zero Level: Normally all pixels with a positive result are
painted as one color value, those with negative values are
mapped onto the whole color map. Due to small calculation
errors, pixels with results near zero end up "on the wrong
side of the dividing line" (using lyapunov.map and assigning
black as background one sometimes gets black spots in otherwise
yellow areas or yellow "junk" in areas that should be
background). This parameter moves the "dividing line", by
setting it to e.g. -10 all values (-10 < value < 0) will be
painted as background. (Note: This test is done *before* the
value is divided by the number of iterations!)

Divergence Result: This is the value (*not* the color number!)
of background pixels returned to Fractint to map it onto the
loaded color map. Quite a  bit of fiddling is needed here, too,
because every change of the number of iterations needs a
recalibration of this parametrer for getting the same color
output as before (did I point out this formulas not being user
friendly? ;-))

Further notes: One doesn't need to set logmap=1 (as is done
in the accompanying pars), but if one does, maxiter has to
be set to at least 256 or not all colors of the color map can
be reached (=displayed).
Fractint iterates its Lyapunov type differently from these
formula implementations (if one has a string of "aab" then
Fractint iterates its Lyapunov three times for each iteration
set as maxiter - two time because of the two a's, one time for
the lone b; in the formula parser each iteration is *one* loop
using *one* string token, of course).

Well, I hope you will have fun with formulas nevertheless
and I better stop now before this posting grows bigger still.

Regards,

Gerald

- ---------------- cut here, save as .par file ------------------

Lyapunov {;Parser version of Fractint's Lyapunov formula
          ;
  reset=2001 type=formula formulaname=Lyapunov
  corners=0/6/0/4.5
  params=0.66/3/1/0.5/0.35/100/10/1.4/1000000 float=y
  maxiter=1000 inside=zmag outside=255 logmap=yes periodicity=0
  colors=@lyapunov.map
  }

LyapSqrSinR {;Lyapunov-Fractal of "Do-It-Yourself"-Formula
             ;
  reset=2001 type=formula formulaname=LyapSqrSinR
  corners=0.006343064/3.837554/-0.09798406/3.733226
  params=2.5/1.5/3/1/0.5/0.55/10/100/1000000/1.4 float=y
  maxiter=1000 inside=zmag outside=255 logmap=yes periodicity=0
  colors=@lyapunov.map
  }

frm:Lyapunov {;"standard" Lambda-Formula
              ;
   ;abMax = Length of ab-string in the form of: 2^LENGTH - 1
   ;periodicity=no, inside=zmag, outside=ColorNumber
   ;
   ;p1 ... Starting Value / abMax
   ;p2 ... ab-String / Scaling Exponent
   ;p3 ... Scaling Faktor / Filter Cycles
   ;p4 ... Zero Level / Divergence Result
   ;p5 ... Bailout
   ;
   x = real(p1), max = imag(p1), ab = real(p2)
   se = imag(p2), sk = real(p3)
   n = imag(p3), z = imag(p4)
   mxi = n + 1 - maxit
   sum = 0:
     n = n - 1
     ab = 2*ab
     IF (ab > max)
       ab = ab - max
       c = imag(pixel)
     ELSE
       c = real(pixel)
     ENDIF
     IF (n < 0)
       sum = sum + log(abs(c*(1-2*x)))
       IF (n <= mxi && sum < p4)
         z = (sum/n)^se*sk
       ENDIF
     ENDIF
     x = c*x*(1-x)
   p5 >= abs(x)
   }

frm:LyapSqrSinR {;Function a*(sin(x+r))^2
                 ;
   ;ab-String: Swapping of r between two values
   ;abMax = Length of ab-string in the form of: 2^LENGTH - 1
   ;periodicity=no, inside=zmag, outside=ColorNumber
   ;
   ;p1 ... Factor a / Starting Value
   ;p2 ... abMax / ab-String
   ;p3 ... Scaling Exponent / Scaling Faktor
   ;p4 ... Zero Level / Filter Cycles
   ;p5 ... Bailout / Divergence Result
   ;
   a = real(p1), x = imag(p1)
   max = real(p2), ab = imag(p2)
   se = real(p3), sk = imag(p3)
   n = imag(p4), z = imag(p5)
   mxi = n + 1 - maxit
   a2 = 2*a, sum = 0:
     n = n - 1
     ab = 2*ab
     IF (ab > max)
       ab = ab - max
       r = imag(pixel)
     ELSE
       r = real(pixel)
     ENDIF
     xpr = x + r, sxpr = sin(xpr)
     IF (n < 0)
       sum = sum + log(abs(a2*sxpr*cos(xpr)))
       IF (n <= mxi && sum < p4)
         z = (sum/n)^se*sk
       ENDIF
     ENDIF
     x = a*sqr(sxpr)
   p5 >= abs(x)
   }

- ----------------------- end of .par ---------------------------



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

Date: Mon, 02 Apr 2001 15:02:06 -0000
From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) Fractint Development

>From: "Jonathan Osuch" <[e-mail]>
>Reply-To: [e-mail]
>To: <[e-mail]>
>Subject: Re: (fractint) Fractint Development
>Date: Thu, 29 Mar 2001 19:33:11 -0600
>
>I am currently working on the true color support for the DOS version.
>There
>seems to be a problem with the routines that Bert Tyler added.  At any
>rate,
>I'm having difficulty getting the images to appear correctly colored on the
>screen.  I'll let you know when it is fixed.

Hmm... I know those routines were there (there's some debug option that
makes type=test do some truecolour stuff). I always wondered what the deal
was with that...

>The memory limitations stem from two sources.  One is that Fractint is
>compiled in the medium memory model.  This means that memory usable for
>near
>data is limited to 64KB unless some form of swapping is done.  This memory
>includes the stack space, and we are banging up against this limit
>constantly.  And, no it isn't a simple matter to just change the memory
>model.

So, you mean that FractInt can as such only use 64KB of memory?

Are you saying that if you *did* change the memory model this would
magically make everything better? (I must confess to not knowing what a
"memory model" is. I presume it's something to do with the size of the
memory address references or something...)

What's involved in such a change? Is it just a case of going through the
program and changing half a million lines of code on a find-and-replace
basis, or does it require an actaul redesign of the code?

I'd really prefer FractInt to remain a DOS program, or perhaps to have a DOS
*and* a Windows version. (...and a Linux/UNIX version, like they do with
POV-Ray. Hey... isn't that a Stone Soup project too?)

>The other problem is that we do indeed use extended and/or expanded
>memory for options other than just disk video.  Saving the on screen image
>when switching to a menu comes to mind.

If you had more memory to play with, could this be avoided? (I understand
that disk video can use insane quantities of RAM, but keeping a copy of the
video buffer for a normal screen shouldn't be too bad...)

>I'll let all the other developer's respond to your question themselves.

Hmm... they seem rather quiet so far... An the basis that quiet implies
busy, this may well be a good sign 8-)

>Jonathan

Thanks for the information!
Andrew.

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

Date: Mon, 2 Apr 2001 21:47:12 EDT
From: [e-mail]
Subject: (fractint) FOTD  03-04-01  (Many Happy Returns [5])

Classic FOTD -- April 03, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

Today, the FOTD returns after its 1-1/2 week hiatus, with the
first fractal I've calculated in that time.  Of course, this is
the reason I have named it "Many Happy Returns.  The average
rating of 5 reflects my opinion of my first fractal effort in
11 days.

The conditions here at the new Fractal Central auxiliary are
still a bit hectic, but they are becoming more organized every
day.  In fact, the organization is such that I almost know where
everything is located.

Unfortunately, I still lack the time for the long philosophical
discussions that have made the FOTD what it is  :-/  but as
things gradually return to normal in the near future, the FOTD
discussions will become longer and more complex, until hopefully
we finally solve the mystery of the universe.  :-\

Today's image however is no mystery.  It was created by
combining small negative portions of Z^(-1.2) and Z^(-12).  It's
one of those moth-eaten images so full of holes that the holes
are more interesting than the midget at the center.

Since my DSL internet connection is not yet established, the GIF
images are not yet being posted to Usenet, but hopefully Paul
and Scott have posted today's image to their web sites at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and at:

          <http://home.swbell.net/sdboyd56/fotd/>

The fractal weather today was mostly cloudy and a chilly 50F
(10C) -- conditions that combined with a brisk wind to keep the
fractal cats indoors sulking most of the afternoon.  I eased
their distress with a treat of tuna.

I see it's time to do a little more organizing, but I'll return
in another 24 hours with another fractal.  Until then, take
care, and the fractals will keep getting better.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Many_Happy_Returns { ; time=0:29:18.22--SF5 on a p200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+0.02268278481078340/-0.001079531652657\
  37/1.821185e+009/1/-127.5
  params=12/-1.2/1/-12/-1.15/800 float=y maxiter=2500
  inside=0 logmap=380 periodicity=10
  colors=000bmiblhbkgajgaifaieahdagc`fc`eb`da`d``c__\
  b__aZ_`Y__X__XYZWWZVVZUTYTRYSQYROXQMXPLXPKZQJ_QI`Q\
  HaRGbRFcREeSDfSCgSChSBiTAjT9kT8mU7nU6oU5pV4qV3rV3s\
  V5nR7iO8dLA_IBVFDQCEM9DOADQADRACTBCUBCWBBXCBZCB_CB\
  aCAcDAdDAfD9gE9iE9jE8lF8mF8oF8pF9oGAnGBnHCmHDlHElI\
  FkIGkJHjJIiJJiKKhKLgKMgLNfLOfMPeMQdMRdNScNScNRdMQe\
  MPeMOfMOfMNgMMhMLhLKiLKiLJjLIkLHkLGlLGlLHkKHkKkr9h\
  oCflFdiIafL_cOY`RVYUTVXRR_OObMLeKIhHFkFCnD9qA6t83w\
  60yDGqKVjQicTafVViYOl_Hoa8taAqaCoaEmaGjaIhaKfaMcaO\
  aaP_aRXaTVaVTaXQaZOa`MabJadHSt_aeFfhLjjRnmXpt`qqar\
  obsmbskcticugduedvbew`fxZfxXgyVgzThzRhxRewRbvR`uRY\
  tRWsRTqRRpROoRMnRJmRHlREjO8kQAkRClSElUGmVImWKnXMnZ\
  On_Qo`SoaUpcWpdYqe_qfaqhcrierjgskismktnmtootpqpoom\
  nnjmlglkdljakhZjgVieShdPhcMgaJf`GeaDdbAdcBcdBceBcf\
  BcgCchCciCcjCckDclDcmDcnDcoEcpEcqEcrEcsCctEcuGcvIc\
  wKcxMcyOczQczSczUczWczYcz
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================

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

Date: Sun, 1 Apr 2001 13:27:19 +0200
From: Michael Weitzel <[e-mail]>
Subject: Re: (fractint) Fractint Development: The Ljapunow Type

Am Sonntag, den 01. April 2001, um 00:44h schrieb Guy Marson:

> Does somebody know the Lyapunow-formula written for the Parser similar to
> the build-in type, or a place (url or so) to find this formula?

I'm not an expert ... but ...

Ljapunow diagrams are based on simple population models (for yeast for
example) or other oscillating systems. In the beginning (time t=0) of the
experiment you start with x[t] = x[0] individuals.

The number x[t+1] of individuals in generation t+1 is proportional to
the number x[t] in generation t (the generation before) and the food
which is given by the environment (and/or was left over by former
generations) and other environmental parameters - all together expressed
through r:

    x[t+1] ~ x[t]
        x[t+1] ~ r

Fractint uses the "logistic equation" to determine this number:

    x[t+1] = r * x[t] * (1 - x[t])

For the calculation of Ljapunow diagrams the parameter r ist changed
periodically in a predefined way - to A or to B. The sequence of A's
and B's defines the rules of the game: For example ABB results in
...BABBABBABBABBABBA... .

The screen shows an A-B-plane. If the sequence says, that r=B - you have
to set r to the B-coordinate of your current pixel... if it says r=A the
A-coordinate is used.

The formula is iterated a few hundred times ... so that the influence
of the starting value x[0] decreases more and more. Then the calculation
continues another few hundred/thousand times and while iterating the
Ljapunow exponent lambda is calculated (see literature, characterizes
the averange error-growth in the neighborhood of x[0]) using the
simplification that ln(a*b*c) = ln(a)+ln(b)+ln(c) (which protects the
floating point numbers from overflow):

                 1    | En |
 lambda(x[0]) = --- ln|----|
                 n    | E0 |

                                  | En |   | En   | | En-1 |     | E1 |
 with total error amplification : |----| = |------|*|------|*...*|----|
                                  | E0 |   | En-1 | | En-2 |     | E0 |

 | Ea   |                     d f(x[a-1])
 |------| can be expressed as -----------
 | Ea-1 |                       d x[a-1]

                     n                                 n
                 1  ---   |d (r*x[i]*(1-x[i]))|    1  ---
 lambda(x[0]) = --- \   ln|-------------------| = --- \   ln|r*(1-2*x[i])|
                 n  /     |       d x[i]      |    n  /
                    ---                               ---
                    i=0                               i=0

If you use your "natural" screen coordinates (for ex.: x=0...1023, y=0..767)
you probably won't see anything on your screen. You can see Fractint's corner
parameters if you press [Tab].
- --
   Michael                  LDKnet / LDK/LUG / Unix-AG
     *Weitzel* /LinuX --- email: michael(at)ldknet.org

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

Date: Tue, 3 Apr 2001 12:47:55 +0200
From: Michael Weitzel <[e-mail]>
Subject: Re: (fractint) Fractint Development: The Ljapunow Type

Am Montag, den 02. April 2001, um 00:11h schrieb Gerald K. Dobiasovsky:

> > Does somebody know the Lyapunow-formula written for the Parser similar to
> > the build-in type, or a place (url or so) to find this formula?
[your frm + par files]

sorry ... probably a misunderstanding on my side. I thought he was
asking for the algorithm of Fractint's Ljapunows. ;-)

...but together with the description one probably better understands, what's
going on in the formula-file ... sorry again ;*)
- --
   Michael                  LDKnet / LDK/LUG / Unix-AG
     *Weitzel* /LinuX --- email: michael(at)ldknet.org

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

Date: Tue, 3 Apr 2001 22:29:41 +0200
From: "Gerald K. Dobiasovsky" <[e-mail]>
Subject: Re: (fractint) Fractint Development: The Ljapunow Type

Michael Weitzel wrote:


> sorry ... probably a misunderstanding on my side. I thought he was
> asking for the algorithm of Fractint's Ljapunows. ;-)
>
> ...but together with the description one probably better understands, what's
> going on in the formula-file ... sorry again ;*)

No reasons to apologize...

1) Your explanation is a detailed and illuminating one.
2) Maybe I am wrong and he *was* asking for the algorithm?!

Greetings,
Gerald



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

Date: Tue, 03 Apr 2001 16:28:25 -0500
From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Fractint Development: The Ljapunow Type

Michael Weitzel wrote:
>
> sorry ... probably a misunderstanding on my side.
> I thought he was asking for the algorithm of
> Fractint's Ljapunows.   ;-)
>

I personally found your postings on the topic quite interesting, whether
or not the original questions was for FRMs/PARs.  It is always nice to
have an understanding of the details.  Thanks for sharing with all of us
on the List.

Sincerely,
P.N.L.
- --------------------------------------------------------------
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Date: Tue, 03 Apr 2001 16:55:14 -0500
From: "Paul N. Lee" <[e-mail]>
Subject: (fractint) A Fractal Project Completed !!

Greetings,

Philip Northover, the fractal artist known for his "Fractal Alhambra"
website at:

    http://pnorthov.future.easyspace.com/

has recently completed a very lengthy project.  Though Philip has five
online galleries containing over a hundred images, he has also been
working on his private project for approximately two years:

    "A Fractal Interpretation of the King James Version of the Bible"

He kept to a classical fractal style throughout, employing the primary
colours, which he fealt conveyed the biblical simplicity which often
hints at great depths.  Philip wanted an overall feeling of consistency,
unity, order, and purpose to the work, while still reflecting the
essence of each book within the Bible.

I hope everyone has an opportunity to visit his web site to view what
definitely has been a considerable personal project for Philip.


Sincerely,
P.N.L.
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------------------------------

Date: Wed, 04 Apr 2001 01:21:44 +0200
From: Guy Marson <[e-mail]>
Subject: Re: (fractint) Fractint Development: The Ljapunow Type

Hi,


At 12:47 03/04/01 +0200, you wrote:
>Am Montag, den 02. April 2001, um 00:11h schrieb Gerald K. Dobiasovsky:
>
>> > Does somebody know the Lyapunow-formula written for the Parser similar to
>> > the build-in type, or a place (url or so) to find this formula?
>[your frm + par files]
>
>sorry ... probably a misunderstanding on my side. I thought he was
>asking for the algorithm of Fractint's Ljapunows. ;-)
>

It's ok, not being a math, now I understand the Lyapunow-type mutch better!
Having both, the formula and more explanations


Thanks to both of you!

>...but together with the description one probably better understands, what's
>going on in the formula-file ... sorry again ;*)


nix zu entschuldigen, das ist voll in Ordnung so!


>--
>   Michael                  LDKnet / LDK/LUG / Unix-AG
>     *Weitzel* /LinuX --- email: michael(at)ldknet.org
>


cheers,

Guy

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Date: Tue, 3 Apr 2001 22:49:09 EDT
From: [e-mail]
Subject: (fractint) C-FOTD  04-04-01  (A New Midget [6])

Classic FOTD -- April 04, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

I named today's not quite overwhelming fractal "A New Midget".
And it's true -- this particular midget has never before been
seen by the eyes of man, nor by the eyes of woman, who sometimes
can see more than man.

Of course, we always suspected that the midget existed.  We know
that an infinity of midgets exist, of which exactly zero
percent, or more precisely an infinitesimal percent, will ever
be seen.

That's one of the curious things about midgets -- an infinity of
them exist -- and regardless of how many we discover, the number
of undiscovered midgets is never reduced.  Take for example the
parent fractal of today's midget.  The default appearance is a
drab set of concentric circles, with a twisted midget near the
right edge of the screen.  A couple out-zooms will reveal that
the entire fractal appears as a roughly diamond-shaped island in
the middle of an infinite ocean.  The default midget is seen to
be a lake on an island.  This midget has some unusual things
happening in its East Valley area, and today's scene lies deep
in this East Valley area.

Undecided how to rate today's effort, I finally decided on a
slightly above average 6, making the image worth the effort of
downloading it from paul's web site at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

Unfortunately, Scott's FOTD site will be down for a few days.

The fractal weather today was unexpectedly sunny and warm.
Until the middle of the afternoon, the weather experts were
forecasting that chilly clouds and rain would prevail all day.
This caused them to appear a little less than expert, though the
fractal cats had no complaints as they enjoyed the temperature
of 61F (16C).

And after another busy and confusing day, I will now enjoy an
hour or so of relaxation.  I'll return tomorrow around this same
time with another moderately glorious fractal and a few words
about the image.  Until then, take care, and wait with bated,
but not abated, breath.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

A_New_Midget       { ; time=0:25:51.10--SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+1.57276058003352300/+0.186020729751933\
  60/9.061857e+012/1.0002/-154.909/-0.094
  params=-1/-1.5/100/5/-0.93/0 float=y
  maxiter=3000 inside=0 periodicity=10
  colors=000td_sfbrheqjhplkonnnpqmrtjprhopenocmmallZ\
  kjXjiUigShfQgdNfcLeaId`GcZEbYFcUGcRHcNHcKIdHJdDKdA\
  Kd7LcAMbDNaGN`IO_LPZOQYRQYT_cbihlsmupipnfllchj`dgX\
  _eUWcRSaOOZKJXHFVEBTB7R83TA5VC7XE8ZGA`ICbKDdMFfNGh\
  PIjRKlTLnVNpXPrZQt`SuaTt_TtYTtWTtUTtSTsRTsPTsNTsLT\
  sJTsIToDWk8Zh3akHdmLfpOirOkqQjqVjpVipVioUhoUhnUgnU\
  gmTfmTflTelTeeXg__hUciOfjIjkCml6qm0tn3uk5uh8ufAucC\
  uaFrZHoXJlUMiSOfQQcSS`UUYWWVYXS_VPaTMcRJeTJ`VKWXKR\
  YKM_ONaSNcWOd_OfcPhgPikPZnUOqZEtcJjdOaeTSeYJfaAf`B\
  g`Bg`Bg`Ch`Ch`Ch`Di_Di_Di_Ej_Ej_Ej_Fk_Fk_FkZJgYMcX\
  P`XSXWVUVYQUaMUdJTgFSjCRm8Rp5Xf7aY9fOBkFDlEGmDInCL\
  oBNpBQqASr9Vr8Xs7_t7au6dv5fw4ix3kx3ms8nnCnjHneLoaP\
  oXUoTYpObpKfpFjqBoq6sq2wqAniIebQXWYOPeFIcLKbQMaVO`\
  _QZeSYjUXoWWtYI`I5H35E37H68J99MCAOFBQICTLDVOEXRG_U\
  HaXId_JfbKheLkhMmkNonPloQjpSgqTeqVcrW`sYZsZWt`UuaS\
  ucPvdNweLwaMvrZPwYQv`UubX
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================

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Date: Tue, 3 Apr 2001 23:42:13 EDT
From: [e-mail]
Subject: Re: (fractint) A Fractal Project Completed !!

Good Evening,

I am quite confused about the project... are these fractals represent the
books of the Bible, or are the words themselves used in some way or form to
create the fractals? Please respond as soon as possible, thanks, God Bless
Ryan

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Date: Tue, 3 Apr 2001 18:07:08 -1000
From: "David Jones" <[e-mail]>
Subject: (fractint) [fractal-art] Some links to fractal sites

Found these at Netscape's Open Directory Project:

http://dmoz.org/Science/Math/Chaos_and_Fractals/

http://www.3dfractals.com/tetrapics/imageframe.htm

David
[e-mail]


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Date: Tue, 3 Apr 2001 18:07:08 -1000
From: "David Jones" <[e-mail]>
Subject: (fractint) Some links to fractal sites

Found these at Netscape's Open Directory Project:

http://dmoz.org/Science/Math/Chaos_and_Fractals/

http://www.3dfractals.com/tetrapics/imageframe.htm

David
[e-mail]


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

Date: Wed, 04 Apr 2001 10:58:32 -0500
From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) Fractint Development

No one has responded to this in a couple days, so I thought I'd take a
shot at it...

Andrew Coppin wrote:

>> The memory limitations stem from two sources.  One is that Fractint is
>> compiled in the medium memory model.  This means that memory usable for
>> near data is limited to 64KB unless some form of swapping is done.
>
> So, you mean that FractInt can as such only use 64KB of memory?

Sort of.

FractInt was born as an MS-DOS program, and MS-DOS ran on Intel chips.
Intel chips see memory as "segmented" rather than "flat" (as the Motorola
chips (used in Apple machines) do).  Flat memory looks like one huge
"address space".  For any memory location from 0000000 to umpteenzillion,
the memory location just refers to the appropriate point, like milage
along a road.

In segmented memory, a memory location consists of two numbers: a
segment and an offset.  The segment is like a rolling window that jumps
in, IIRC, 256-byte jumps: segment 0 starts at 0, segment 1 starts at 256,
and so on.  And a segment is a 64-k "window".  The offset refers to any
location within that 64-k window.

The Intel chips ran programs in an architecture that had four segments:
a "Code" segment, a "Data" segment, a "Stack" segment and an "Extra"
segment sometimes used as a second, extended Data segment).  Due to the
nature of the C language (a primary development language of the day),
the Stack and Data segments usually had to be identical.  You ended up
with a 64-K window with your data growing from the bottom upwards and
your stack growing from the top downwards.  The space in the middle was
the "heap" and is where you got dynamically allocated memory from.

The "Memory Model" is what various configurations of the segments is
called.  Remember the old .COM programs?  By definition, they always
use the "Tiny" memory model.  All segments are identical, and your
entire program--data and code--must fit in a single 64-K window.

The "Medium" memory model, IIRC, has the stack and data sharing one
64-K segment, while the code lives in its own 64-K segment.

This doesn't mean the program can't access data outside these segments.
It can, but outside memory is "far" in the language of Intel memory
models (opposed to the "near" memory in the data/stack segment).  Because
the data/stack segment is "framed" by the segment pointers of the Intel
architecture, you only need 16 bits (64-K) to address it.  But since "far"
memory is 'somewhere in address space' you need a full address which was,
at the time, 24 bits usually expressed as two 16-bit values with 8 bits of
overlap.  Added together, they form a 24-bit address.

The bottom line is that, in your program, you have a mix of "near" data
and "far" data, and they require different variable types to refer to.

> What's involved in such a change? Is it just a case of going through the
> program and changing half a million lines of code on a find-and-replace
> basis, or does it require an actaul redesign of the code?

I can't speak for the FractInt developers, and I'm not familiar with the
code.  I can guess it lies between those two ideas.  It's not a simple
matter of S&R; I'd guess you want to examine every place you need to change
to see if the change breaks anything.  But it probably does NOT require a
complete redesign.

Ideally you'd like a compiler that let you treat memory as flat and make
all your pointers be the same type.  I have no idea if such exists for
the Intel platforms.

But then *I* think what you *really* want is to get away from MS-DOS.

> I'd really prefer FractInt to remain a DOS program, or perhaps to have
> a DOS *and* a Windows version. (...and a Linux/UNIX version, like they
> do with POV-Ray. Hey... isn't that a Stone Soup project too?)

Don't *think* POV-Ray (great program, BTW) is Stone Soup.  There's actually
a great concept there.  POV-Ray renders to a disk file normally.  The
Windows version just happens to have the extra treat of showing you the
image as it's rendered.  But the heart of POV-Ray is a command line tool
for rendering 3D scenes into an image file of some type.

>> The other problem is that we do indeed use extended and/or expanded
>> memory for options other than just disk video.  Saving the on screen
>> image when switching to a menu comes to mind.
>
> If you had more memory to play with, could this be avoided? (I understand
> that disk video can use insane quantities of RAM, but keeping a copy of
> the video buffer for a normal screen shouldn't be too bad...)

But what I imagine they have to save is the fractal image while the menu
screens are displayed.  That could be considerable.

Anyway, hope this little data dump helped rather than confused...

- --
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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Date: Wed, 4 Apr 2001 17:41:53 -0400
From: "Zorba the Hutt" <[e-mail]>
Subject: Re: (fractint) Fractint Development

>
> Ideally you'd like a compiler that let you treat memory as flat and make
> all your pointers be the same type.  I have no idea if such exists for
> the Intel platforms.
>
> But then *I* think what you *really* want is to get away from MS-DOS.
>

Any 32-bit compiler does this - basically, anything that compiles native
Win95 programs or higher. There *is* a way to use flat memory on MS-DOS, as
I remember - the DOS4GW extension, that everyone who's played games in the
late DOS era will recognize. It was basically a protected-mode flat memory
manager, and you needed a 32-bit compiler to use it, and by golly, it was
worth it.

At least, I think that's what it did. Correct me if I'm wrong ^^;;

- -Zorba


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

Date: Thu, 5 Apr 2001 01:24:33 -0400
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) FOTD 03-04-01 (Many Happy Returns [5])

- ------=_NextPart_001_0000_01C0BD6F.2B90BFE0
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

> Today, the FOTD returns after its 1-1/2 week hiatus, with the
> first fractal I've calculated in that time.  Of course, this is
> the reason I have named it "Many Happy Returns.  The average
> rating of 5 reflects my opinion of my first fractal effort in
> 11 days.
              ^
Error: Unterminated string constant. :-)

> Unfortunately, I still lack the time for the long philosophical
> discussions that have made the FOTD what it is  :-/  but as
> things gradually return to normal in the near future, the FOTD
> discussions will become longer and more complex, until hopefully
> we finally solve the mystery of the universe.  :-\

Hate to tell you this, but it's already been done.
http://www.hep.upenn.edu/~max/toe.html<br clear=3Dall><hr>Get Your Privat=
e, Free E-mail from MSN Hotmail at <a href=3D"http://www.hotmail.com">htt=
p://www.hotmail.com</a>.<br></p>

- ------=_NextPart_001_0000_01C0BD6F.2B90BFE0
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> Today, th=
e FOTD returns after its 1-1/2 week hiatus, with the<BR>> first fracta=
l I've calculated in that time.  Of course, this is<BR>> the reas=
on I have named it "Many Happy Returns.  The average<BR>> rating =
of 5 reflects my opinion of my first fractal effort in<BR>> 11 days.<B=
R>            =
;  ^</DIV> <DIV>Error: Unterminated string constant. :-)</DIV> <DIV>=
<BR>> Unfortunately, I still lack the time for the long philosophical<=
BR>> discussions that have made the FOTD what it is  :-/  bu=
t as<BR>> things gradually return to normal in the near future, the FO=
TD<BR>> discussions will become longer and more complex, until hopeful=
ly<BR>> we finally solve the mystery of the universe.  :-\<BR></D=
IV> <DIV>Hate to tell you this, but it's already been done.</DIV> <DIV><A=
 href=3D"http://www.hep.upenn.edu/~max/toe.html">http://www.hep.upenn.edu=
/~max/toe.html</A></DIV> <DIV><BR> </DIV></BODY></HTML><DIV><BR><br =
clear=3Dall><hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=
=3D"http://www.hotmail.com">http://www.hotmail.com</a>.<br></p></DIV>

- ------=_NextPart_001_0000_01C0BD6F.2B90BFE0--

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End of fractint-digest V1 #548
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