ftp.xmission.com/2014.06.ftp.xmission.com.tar/ftp.xmission.com/pub/lists/fractint/archive/fractint.200104

Internet Message Format | 2001-04-30 | 296KB

From: "Gerald K. Dobiasovsky" <[e-mail]>
Subject: Re: (fractint) Fractint Development: The Ljapunow Type
Date: 02 Apr 2001 00:11:27 +0200

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

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

>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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-------------------------------------------------------------------------------

From: [e-mail]
Subject: (fractint) FOTD  03-04-01  (Many Happy Returns [5])
Date: 02 Apr 2001 21:47:12 EDT


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

From: Michael Weitzel <[e-mail]>
Subject: Re: (fractint) Fractint Development: The Ljapunow Type
Date: 01 Apr 2001 13:27:19 +0200

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

From: Michael Weitzel <[e-mail]>
Subject: Re: (fractint) Fractint Development: The Ljapunow Type
Date: 03 Apr 2001 12:47:55 +0200

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

From: "Gerald K. Dobiasovsky" <[e-mail]>
Subject: Re: (fractint) Fractint Development: The Ljapunow Type
Date: 03 Apr 2001 22:29:41 +0200


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

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

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.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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

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

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.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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

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

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

From: [e-mail]
Subject: (fractint) C-FOTD  04-04-01  (A New Midget [6])
Date: 03 Apr 2001 22:49:09 EDT


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

From: [e-mail]
Subject: Re: (fractint) A Fractal Project Completed !!
Date: 03 Apr 2001 23:42:13 EDT

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

From: "David Jones" <[e-mail]>
Subject: (fractint) [fractal-art] Some links to fractal sites
Date: 03 Apr 2001 18:07:08 -1000

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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From: "David Jones" <[e-mail]>
Subject: (fractint) Some links to fractal sites
Date: 03 Apr 2001 18:07:08 -1000

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

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

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

From: "Zorba the Hutt" <[e-mail]>
Subject: Re: (fractint) Fractint Development
Date: 04 Apr 2001 17:41:53 -0400


>
> 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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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) FOTD 03-04-01 (Many Happy Returns [5])
Date: 05 Apr 2001 01:24:33 -0400


------=_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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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Fractint Development
Date: 05 Apr 2001 01:37:30 -0400


------=_NextPart_001_0001_01C0BD70.FB2274A0
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

You can also use djgpp and cwsdpmi to get 32-bit flat memory programs for=
 MS-DOS. If you use Allegro as an API to mouse/low-level keyboard/graphic=
s/etc. stuff, as an added bonus it is easily ported to Windows and Linux,=
 since Allegro has been ported to these and gcc (of which djgpp is a port=
) exists for Linux and has at least 2 Windows ports.<br clear=3Dall><hr>G=
et Your Private, Free E-mail from MSN Hotmail at <a href=3D"http://www.ho=
tmail.com">http://www.hotmail.com</a>.<br></p>

------=_NextPart_001_0001_01C0BD70.FB2274A0
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>You can also u=
se djgpp and cwsdpmi to get 32-bit flat memory programs for MS-DOS. If yo=
u use Allegro as an API to mouse/low-level keyboard/graphics/etc. stuff, =
as an added bonus it is easily ported to Windows and Linux, since Allegro=
 has been ported to these and gcc (of which djgpp is a port) exists for L=
inux and has at least 2 Windows ports.</DIV></BODY></HTML><DIV><BR><br cl=
ear=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_0001_01C0BD70.FB2274A0--

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

From: [e-mail]
Subject: (fractint) Re: FOTD 03-04-01 (Many Happy Returns [5])
Date: 05 Apr 2001 07:25:18 EDT

I wrote:

>>          <snip>       .....the FOTD discussions will become
>>longer and more complex, until hopefully we finally solve the
>>mystery of the universe.  :-\

Multiple Bogeys replied:

>Hate to tell you this, but it's already been done.

Aw shucks, I missed it!   ;-(

FOTD in one hour.

Jim M.

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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  05-04-01  (Specular Reflection [6])
Date: 05 Apr 2001 08:31:11 -0400 (EDT)


Classic FOTD -- April 05, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Once again, due to unavoidable things that had to be done, the
FOTD is late.  This will continue to happen occasionally until
things are totally back into the familiar routine here at the
new Fractal Central auxiliary.

Despite the rush, I managed to find a fractal midget worthy of a
rating of 6.  I named the picture "Specular Reflection" when I
had the impression of a brilliant light reflecting from a
metallic surface around the edges of the midget.

The formula behind the image is another of my whimsical ones --
-(Z^(-1.25))+Z^(1.25)+(1/C).  The 6-1/2 minute render time of
the parameter file is just slow enough to make a download of the
GIF image worth the effort.  That image will soon be available
on Paul's web site at:

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

Scott once again has his site up and running.  The GIF image
will also soon be available there at:

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

The fractal weather today was sunny and mild, with a temperature
of 59F (15C), which the fractal cats found ideal.  They spent
nearly the entire afternoon sunning themselves in the yard and
thinking of what trouble to get into.

I lack the time today to reveal the one true mystery of the
universe, but I must warn about all those false mysteries of the
universe out there.  Don't be deceived by these imitations, wait
for the real thing to be revealed.  ;-)

Until the real thing is revealed, and even after the revelation,
I'll continue with the 4-year-old FOTD, which has no end in
sight.  The next one will appear in about 15 hours.  I'll see
you then.


Jim Muth
[e-mail]


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

SpecularReflection { ; time=0:06:30.52--SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.466396676467665/+1.55164254988776/1.\
  393514e+012/1/-50.009/0.012 params=-1/-1.25/1/1.25\
  /0/0 float=y maxiter=1400 inside=0
  logmap=125 periodicity=10
  colors=000B8ZB7`C6cD5fE3iF3lG2oH1pE0oC2mB3jA5f87c7\
  8_6AW5BT9DUCHXHKYKN`RRaYYdddfiiinnnssswwwzzzzzzzzz\
  tttlllddiYYhRRdKKcEE`98ZE3XK1WR5TY9QdDPlIMtNKzTIzY\
  HzZGz`Ez`EzaDzaCzcCzcBzdAzdAzf9zf9zhAyiAtiAokAnlAk\
  lAhnAdoBaoB`qBYsBWsBTtBQuBPuBToDWiEYcG`YHcTIfPJiJM\
  lENoAPs6Qu2Ry0T1d03`17X39U5CQ7EM9IJBMGEPCHTAJW7MZ3\
  Pa2RotPosNnqMnoKnoJlnIllH1oR0oR0oQ0oQ0oP0oP0oN0oN0\
  oN0nM0nK0lK0lJ1lI2lI3kI3kH5iH6iG8iE9hEAhDBfDCfCEfB\
  GdBHdAIcAKc9Mc8Na8Pa7Q`7T`6U`5WZ5XZ3YY3`Y3aY2cX2dX\
  10U60U50U51U52U53U53U55U56U57U38U38U39U3AU3BU3CU3D\
  U3EU3GU3HU3IU3IU3JU3KU3MU3NU2PU2QU2RU2TU2UU2UU2WU2\
  XU1YU1ZU1`U1aU1cU1dW1fX1j`NqZInYDhYUhZck`miawiczid\
  sifnihihidhk`hlXhnThoPhqKfsHftDfuAfw7fy39z0Gz0Mz0T\
  z0Zz0RzPTzNTzNTzMTzMUzKUzKUzJUzJWzIWzIWzHWzHXzHXzG\
  XzGXzEYzEYzDYzDYzCZzCZzBZzBZzBZzA`zA`z9`z9`z8az8az\
  7az7az6cz6cz6cz5cz5dz3dz3
  }

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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  06-04-01  (Rainy Evening [6])
Date: 05 Apr 2001 20:29:11 -0400 (EDT)


Classic FOTD -- April 06, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Things were really hopping today here at Fractal Central II.  My
efficiency was at its maximum however, and I finished the day's
jobs in near record time.  This burst of efficiency gave me more
time than expected to search the world of numbers for a fractal
worthy of being christened FOTD for April 6.  The world I chose
to search is the one created by the whimsical formula
0.3(Z^2)-7.5(Z^(-0.1))+(1/C).  I was not disappointed with what
I found there.

Today's fractal is named "Rainy Evening", a name that was
inspired by the cusps surrounding the midget, which remind me of
the pattern seen around street lights when viewed in the evening
through water droplets on one's eyeglasses.

After some indecision, I rated the picture, which is just
slightly above average, at a 6.  A year or two ago I might have
rated it a 7 or 8, but my opinion of what constitutes an
'average' FOTD image seems to be growing ever more strict, and
if the present trend continues, I'll have a hard time producing
even an average FOTD.

The parent fractal of today's image is a grossly mis-shapen
Mandeloid, so twisted and torn that it is barely recognizable.
At the southwest corner of the figure lies a Mandel-bud with a
filament that extends in a disjointed manner into the Seahorse
Valley area of a satellite midget.  Since filaments usually join
midgets in the East Valley area, this unusual junction appeared
a likely place to start the day's search.  The result speaks for
itself, figuratively speaking of course.

The result of all this effort may be seen by running the
attached parameter file and waiting 5 minutes, or by giving Paul
and Scott a chance to post the GIF file of the image to their
web sites, and downloading it from there.

The URL of Paul's web site is:

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

And Scott's is:

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

The weather today turned out to be the finest of the young
Spring season, with bright sun, light winds, and a temperature
of 64F (18C), which kept the fractal cats outdoors for several
happy hours.

The fine weather also stirred my philosophical muse, once again
raising unanswerable questions about the nature of reality.
Every time I discuss this tired, worn-out, but ever-fascinating
topic I seem to get into trouble.  So stay in touch.  I might be
in more trouble in a few days' time.

But for now it's time to shutter down the fractal shoppe and
call it an evening. . . . OK, so it's an evening!  Until next
time, take care, and the more one wonders about what's real, the
less one knows for sure.


Jim Muth
[e-mail]


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

Rainy_Evening      { ; time=0:05:15.04--SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.12191239695861750/-0.037765464265300\
  23/3.704671e+008/1/30 params=1/2/-25/-0.1/-0.7/0
  float=y maxiter=1200 inside=0
  logmap=91 periodicity=10
  colors=000000G1AJ1JQ1SV3a`3je3ql3zxIpzXdvYllYr`_xQ\
  _zF`z4`z6Vz7Pz9JxADrA9mDAoFApICrJCsMDuODvQFxSFyQDv\
  QCsQApPAoP9lP7iO6fO6dO4aM3_M1XM1VL9YLF_LL`LScLYdJc\
  fJjiJpjJvlJzm0Tz0Pz3Mz9IzGFzOAxT7v`4sg0pm0ou0lz0iz\
  0g0zT0zI9z77v66s66o64l44g43d41a31Y30V30Q10O10L10L0\
  0J00J0P66P9CQCGQFMQIQSLXSO`SQdTTjTXoT_uVayVdzVgzVj\
  z_lzamzdmvgopjpjmpdpr_ssTvsOyuIzvCzv6zx0zy0zy0zz0x\
  z0pz4iz9`zFTzJMzOFzS7zX6z`4yd4si3lm1fr1_v0Tz0Mz0Gz\
  FYpVmYizFfzGczG`zGYzGVzGSzGPzIMzIJzIGzIDzICzIFzGIv\
  GLsGOoGQlGTgGXdG_`GaYGdTGgQGjMGmJGpFGrCGoAJm9Mj7Pi\
  6Sf4Td3Xa1_`0aY0dX0fV1cT4aS7`SA_QDYPGVOJTOLSMOQLQP\
  JTMJXLI_JGaIFdGFfF4pP0z_0zi0zg0zf4zdAzcFzcLzaQz`Xz\
  _azYfzYczX`zXYzXVzXSzXPzVMzVJzVGzVDzVAzVDzSGzQJzOM\
  zMPzJSzIVzFYzD`zCcz9fz7iz4lz3oz0rz0uz0czXfzOizGlz7\
  oz0lz0jz0iz0gz0fz0dz0cz0az0`z0_z0Yz0Xz0zz0yz0vz0sz\
  0pz0mz0iz0dz0az0Yz0GzADz4
  }

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

From: "Multiple Bogeys" <[e-mail]>
Subject: (fractint) Oh no! Something is *very* wrong with the FOTD!
Date: 05 Apr 2001 22:43:55 -0400


------=_NextPart_001_0001_01C0BE21.E5AD1E20
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

...the last four have all been grossly underrated. ;-) Keep up the good w=
ork!<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>

------=_NextPart_001_0001_01C0BE21.E5AD1E20
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>...the last fo=
ur have all been grossly underrated. ;-) Keep up the good work!</DIV></BO=
DY></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_0001_01C0BE21.E5AD1E20--

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

From: Lee Skinner <[e-mail]>
Subject: (fractint) C-FOTD  06-04-01  (Rainy Evening [6])
Date: 06 Apr 2001 10:07:07 -0500

Jim Muth wrote:

>> At the southwest corner of the figure lies a Mandel-bud with a filamen=
t
that extends in a disjointed manner into the Seahorse Valley area of a
satellite midget.  Since filaments usually join midgets in the East Valle=
y
area, this unusual junction ... <<

Very unusual indeed!!!   I don't think I've ever seen such a junction!

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

From: [e-mail]
Subject: (fractint) C-FOTD  07-04-01  {Fractal Dimples [6])
Date: 06 Apr 2001 22:49:09 EDT


Classic FOTD -- April 07, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Another unexpectedly busy day kept the fractals at bay, but I
still managed to scrounge up today's slightly striking image.  I
first found it, then went off to do other things while the
image rendered.  When I returned and saw the screen, I thought
of dimples.  The name "Fractal Dimples" came naturally.

The image is yet another 6-rated one found in haste.
Unfortunately, the haste vanishes when the parameter file starts
running, since this one takes over 1-1/2 hours to render.

The formula that drew the image, 0.5(Z^2)+Z^(-2)+(1/C), is once
again one that I pecked out at random.  Since the parameter file
is quite slow, my advice is to give Paul and Scott an hour or so
to render and post the GIF image to their Web sites, and
download it from there.  The URL of Paul's site is:

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

Scott's site is at:

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

The fractal weather today was mostly cloudy with light rain and
a temperature of 55F (13C).  The cats disapproved vigorously by
staying indoors and sulking most of the afternoon.

There was no time for philosophy today.  Perhaps it will appear
tomorrow.  But even if the philosophy is absent, a new and
unique fractal will appear in the next FOTD.  Until then, take
care, and wait until you see that fractal!


Jim Muth
[e-mail]


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

Fractal_Dimples    { ; time=1:33:02.89--SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-13.91207242091377000/+18.4986369015475\
  7000/11315.38/1/165 params=0.5/2/1/-2/0/0 float=y
  maxiter=25000 inside=0 logmap=420 periodicity=0
  colors=000e8me7me7mf7nf7nf6nf6of6of6og4nf5of6of7of\
  8of9ofAofBofCoeDpeEpeFpeGpeHpeIpeJpeKpdLqdMqdNqdOq\
  dPqdQqdRqdSqcTrcUrcVrcWrcXrcYrcZrc_rb`sbasbbsbcsbd\
  sbesbfsbgsahtaitajtaktaltamtantaou`pv`qv`rv`sv`tw`\
  uw`vw`wxayy`xz`wz`wz_vz_uy_uxZtwZsuZssYrqYqoYqlXpk\
  XpjXoiWniWnhWmgVlfVleVkdUjcUjcUibThaTh`Tg_TgZSfYSe\
  XSeXRdWRcVRcUQbTQaSQaRP`RP_QP_POZOOZNOYMNXLNXKNWKM\
  VJMVIMUHLTGLTFLSELSEKUFJVFIXFHYFGZFF`FFaFEbFDdFCeF\
  BfGAhG9iG9jG8lG7mG6nG5pG4qG3sF4rG5qG6pG7oG7nG8mG9l\
  GAkGAjGBiGChGDgGDfGEeGFdGGcGHbGHaGI`GJ_GKZGKYGLXGM\
  WGNUGNSGQQGSOGUNGUMGULGUKJUHIUDIU6IU3HU3HU3HU3HU3G\
  U3GU3GU3GU3FU3FU3FU3FU3EU3EU3EU3EV3DW3DX3DY3DZ3C_3\
  C`3Ca3Cb3Bc3Bd3Be3Bf3Ag3Ah3Ai3Aj59k59l59m37n48o59p\
  5Aq6Br5Cs5Ct6Du6Ev7Fw8Gx8Hy9HzDIzEJzFKzFLzGMzGMzHN\
  zIOzJPzKQzKRzLRzMSzMTzNUzNVzOWzPWzPXzQYzQZzR_zT`zV\
  azXbzZcz`ezbfzdgzfhzhizjj
  }

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

From: jerome schatten <[e-mail]>
Subject: Re: (fractint) C-FOTD  07-04-01  {Fractal Dimples [6])
Date: 07 Apr 2001 23:20:01 -0700

[e-mail] wrote:

[...]
.  When I returned and saw the screen, I thought
> of dimples.  The name "Fractal Dimples" came naturally.
>

A beauty... but perhaps "Fractal Pimples" ?

jerome

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

From: [e-mail]
Subject: (fractint) C-FOTD  08-04-01  (A Midget Eruption [6])
Date: 08 Apr 2001 07:55:48 EDT


Classic FOTD -- April 08, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Yes, yes, I realize that the FOTD is once again late.  It's late
because I spent most of my spare time today organizing the new
Fractal Central auxiliary HQ, leaving me little time for fun
with fractals.  But by entering values at random and searching
aimlessly, I managed to find a fractal worthy of being declared
today's FOTD.

I named the fractal image "A Midget Eruption".  The reason is
most likely that I was impressed by the eruption of unusual
features in the elements surrounding the ever-present midget at
the center.

The overall pattern resembles the typical Julia pattern that
characterizes midgets found in the East Valley area of larger
midgets, but today's midget has far more intricate detail than
most.  I have rated the picture a 6, the fourth or fifth 6
rating in a row.  It's really quite an interesting scene.  Maybe
if I had more time to appreciate it, I would have rated it
higher.

The parameter file renders in under 9 minutes, slow enough to
make a download of the GIF image worth the effort.  That image
will be available in an hour or so at:

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

and at:

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

The fractal weather today was unpleasant -- cloudy and chilly,
with just enough light rain to keep the fractal cats confined to
the indoors.  Afternoon temperatures in the 50's F (lower teens
Celsius) did not help.

And now it's late, or more accurately, early, and I've got a lot
of organizing to do.  So until the next FOTD, take care, and all
rushes eventually come to an end.


Jim Muth
[e-mail]


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

A_Midget_Eruption  { ; time=0:08:46.12--SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.127297927751329/-0.054242224379125/1\
  .173881e+007/1/167.499 params=1/1.9/-25/-0.1/-0.7/0
  float=y maxiter=1500 inside=0
  logmap=156 periodicity=10
  colors=000VM_XL_ZN`aQ`cU`eY`h``jcalfaojaqnasramiYh\
  aVcUSYLOTDLO5INFOMPTLPZLPWJPTHSIGQJGOKGMLFLMFJNFHO\
  EGPEEQECRDBSD9TD7UC6VC4WC2XC1YH3VL5SP6PT8MXAJ`BGdD\
  DhFAlG7pI4tJ1qU3nc4lm5`oJPpWDri1sv1mq1gm1bi1Xe1SaG\
  NTUIKhDBv82105EAEQJMbSVn`bzijsVfmHbg3Ze9ZdFZbKZaQZ\
  _VZZ`ZXeZWkZVpZYiX_cVaYUcRSeLQgFPeGOdHNcIMbJLaKK`L\
  J_MIZNHYOGXPFWQEVRDUSCTTCRUIQUNPUSNUYMUbLUgJUmIUrH\
  UwMSsRRpVQm_PidOfhNcPbBScCUcDXdDZdE`eFceFefGgfGjfH\
  lgIogIqhJshKviKxiLziLxyTtvUqsUnpVknVhkWehWbeX_cXW`\
  YTYYQVZNTZKQ_HN_EK`BI`AH_9HZ8HZ8HY7HY6HX5HW5HW4HV3\
  HV2HU2HU5GS8GQBGPEGNHGLKFKNFIQFHTFFWFDZECaEAdE8gE7\
  jE5mE4jF6gG8eG9bHB`ICYIEWJFTKHRKIQMJQOJPPJPRJOTKOU\
  KOWKNYKNZLM`LMbLMcLJZNHVPFQRDMTBIVAOZ9Ta9YdBZbC_aD\
  ``E`_FaZGbYHbXKcYMcZOcZRd_Td_Vd`Yea_eaaebdfbfgchhd\
  kidmjeokeplaqmZrmWsmStmPumMvmIwmFwmCwm8wm5wm2wm6wm\
  AwmEwmIwmMwmPwmTwmXwm`wmd
  }

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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  09-04-01  (Mandelbrot Mayhem [5])
Date: 09 Apr 2001 00:42:15 -0400 (EDT)


Classic FOTD -- April 09, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

With today's 5-rated fractal image we break away from the string
of FOTD's that have been rated a 6.  Unfortunately, the break
is in the less desirable direction, but then one can't have
everything.

We also break away from the world of the MandelbrotMix4 formula
into the world of the MandelbrotBC formula to explore the more
remote parts of the fractal created by the very simple formula,
Z^(sqrt2)+C.

The scene I found is one of the most disorderly of all time,
with bits and pieces of fractal stuff scattered around the
midget in total disarray, showing no signs at all of an orderly
arrangement.  The unusually chaotic image is well worth the name
I gave it -- "Mandelbrot Mayhem".

At just under 13 minutes, the parameter file tries one's
patience.  Relief for the impatient is available on the Web at:

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

and at:

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

where the GIF file of the image will soon be posted.

The fractal weather today started cloudy and chilly, but turned
sunny and milder at midday.  The bright sun and afternoon
temperature of 63F (17C) then lured the fractal cats into the
yard, where they sampled the new grass.

It's now time to shut down the shoppe and call it a night.
Until tomorrow around this same time, take care, and one of
these days someone will find the ultimate fractal -- but will
they recognize it?.


Jim Muth
[e-mail]


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

Mandelbrot_Mayhem  { ; time=0:12:54.45--SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotBC passes=1
  center-mag=+0.45672737879421720/+0.492387056367433\
  40/1550.388/1/92.5 params=1.414213562373/0/11/0
  float=y maxiter=6000 inside=0 logmap=128
  symmetry=none periodicity=10
  colors=000W`eYei`jmbnqidizMauMUpNQlNMgOJcOF_OCZNDY\
  MDXLDWKDWJDVIDUHETGETFESEERDEQCEQBERAIR9LS9OS8RS8U\
  T7XT7_T6bU6eU5hU5kS9lRCmPFnOIoMMpLPpJSqIVrGZsFatDd\
  uCguQaacXJpS0mQ3jP6gO9dNBaMEZLHXKJUJMRIPOHRLGUIFXG\
  EZKG`NIbQJdULfXNh_OjbQlfSniTplVroWtnXomXklYgkYcjY_\
  iZWiZShZOg_Kf_Ge_Cd`8c`4c`0fbAhdKjfTfKsiNlkQfnS_pV\
  UrYNu_HwbAyd4w_5uV5sR5qM5oI5mK9kLDiMHgNKbLIZKGVJEQ\
  ICMGAIF8DE69D45C26D56E86EA7FD7GF7GI7HK8IN8IP8JS8JU\
  9KV9KVALVALVAMVBMWBNWCNWCOWCOWHTZLY`PbbTfdRegPdjNc\
  mLcpJbsHavFaxHgoJmfKsYGj_Db`AVd7Mg4Ei16k28l2Am2Cn2\
  Eo2Gp2Iq2Kr2Ms2Ot2Qu3Sv4Uw5Ww5Yw6_w7aw8cw8ew9gwAiw\
  BkwBmwCovDpuDqtErsErrFpqFnoFmoGknGjoGipHiqHirHirIi\
  qIiqIiqIiqIiqIiqIiqNjqIiqIiqJiqJiqJiqJiqJiqJipJipJ\
  ipJipKipKipKipKipKipKipKipKipKipKipLjoLjoLjoLjoLjo\
  LjoLjoLjoLjoMjoMjoMjoMjoMjoMjnMjnMjnMjnNjnNjnNjnNj\
  nNjnNjnNjnNjnNjnCilDjmDjm
  }

frm:MandelbrotBC = { ; Z = Z^E + C
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<100
}

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


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

From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) C-FOTD  09-04-01  (Mandelbrot Mayhem [5])
Date: 09 Apr 2001 10:38:14 -0500

Jim Muth wrote:

> ...and one of these days someone will find the ultimate fractal -- but
> will they recognize it?.

Why should there *be* an ultimate fractal?  Seems kind of limiting...

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

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

From: [e-mail]
Subject: (fractint) C-FOTD  10-04-01  (A Naming Problem [4])
Date: 10 Apr 2001 07:58:03 EDT


Classic FOTD -- April 10, 2001 (Rating 4)

Fractal visionaries and enthusiasts:

Another very busy day at Fractal Central left insufficient time
for a proper fractal search, so I turned to a strange image I
found a week or so ago.  Being only a backup, the image comes
down another notch on my scale of fractal worth, rating only a
4 on the scale.  I named the picture "A Naming Problem" because
of the complexity of the Mandeloid that fills the frame.

It's hard enough to identify the various features of the classic
Mandelbrot set by colloquial names.  Imagine the problem if such
a naming system were applied to the many parts of the Mandel-
thing in today's image.

To make matters even more difficult, the image has a strange
kind of symmetry.  The Y-axis symmetry of the Mandel-shaped
feature is obvious, but there are bits of foreground debris
scattered throughout the picture, which have no symmetry
whatsoever.  I suspect that this unusual symmetrical-
unsymmetrical character is caused by the two different exponents
of the formula, one of which is positive, the other negative.

But I'm not positive.

Regardless, the parameter file renders in about 9 minutes, and
the GIF file of the image will soon be available on the Web at:

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

and at:

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

The fractal weather today here at Fractal Central started with a
light thunder-shower, turned unusually sunny and warm, then
ended with a heavy thunder-storm.  The fractal cats approved of
the 90F (32C) temperature by basking all afternoon in the shade
of the holly trees, but they disapproved of the noise of the
evening storm.

As for me -- I worked all day.  And tomorrow will likely be just
as busy, but I'll still manage to find at least one fractal.
Until then, take care, and see you in 16 hours.


Jim Muth
[e-mail]


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

A_Naming_Problem  { ; time=0:08:53.78--SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=0.0881747/0.0124835/0.4235847/1/-90
  params=-0.075/2/10/-2.25/-0.88/1000000000 float=y
  maxiter=3000 inside=0 logmap=7 periodicity=10
  colors=000fQLeQLeQLeQMePMePMePMePMdPMdONdONdONdONd\
  ONdNOcNOcNOcNOcMOcMOcMPcMPbMPbLPbLPbLPbLQbLQbKQaKQ\
  aKQaKRaKRaJRaJRaJR`JR`IS`IS`IS`IS`IS`HT_HT_HT_HT_H\
  T_GT_GU_GUZGUZGUZFUZFUZFVZFVZEVYEVYEVYEWYEWYDWYDWY\
  DWXDWXDXXCXXCXXCXXCXWBWXCXXCXXCXXCXXDXXDXXDXXDXXDX\
  XEXXEXXEXXEXXFYXFYXFYXFYXFYXGYXGYXGYXGYYGYYHYYHYYH\
  YYHZYIZYIZYIZYIZYIZYJZYJZYJZYJZYJZYKZYKZYK_YK_YL_Y\
  L_YL_ZL_ZL_ZM_ZM_ZM_ZM_ZN_ZN_ZN_ZN`ZN`ZO`ZO`ZO`ZO`\
  ZO`ZP`ZP`ZP`ZP`ZQ`ZQ`_Qa_Qa_Qa_Ra_Ra_Ra_Ra_Ra_Sa_S\
  a_Sa_Sa_Ta_Tb_Tb_Tb_Tb_Ub_Ub_Ub_Ub_Vb`Vb`Vb`Vb`Vb`\
  Wc`Wc`Wc`Wc`Wc`Xc`Xc`Xc`Xc`Yc`Yc`Yc`Yc`Yc`Zd`Zd`Zd\
  `ZdaZda_da_da_da_da`da`da`da`da`eaaeaaeaaeaaeabeab\
  eabeabeabeaceaceacebcfbcfbdfbdfbdfbdfbefbefbefbefb\
  efbffbffbfgbfgbfgbggbggbggbggbhgbhgchgchgchgcigcig\
  cihcihcjhcjhcjhcjhcjhckhckhckhckhckhclhclicliclicm\
  idmidmidmidmidnidnidnidni
  }

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

From: Guy Marson <[e-mail]>
Subject: (fractint) a little tease
Date: 11 Apr 2001 10:41:45 +0200

Hi Fractinters,

1) run this .par with its original values..

2) reload the 'first1.gif' and set REAL(P4) to 35 .. (Z-screen)

3) set REAL(P5) to 0.1'500'000'002 (zero point 1500000002 :-)


4) now reload the 'second1.gif' and set REAL(P4) to 30 .. (Z-screen)

5) set REAL(P5) to 0.1500000001 ..

If you wanna experiment with the text, set IMAG(P4) to e.g. 0.14

Thanks to Sylvie Gallet, Jim Muth and Jan Marten van der Walk for their
fantastic pattern!

*************************
par and frm's:
*************************

first1              { ; Version 2001 Patchlevel 6
  reset=2001 type=formula formulafile=lakerise.frm
  formulaname=lakerise function=recip/ident passes=1
  center-mag=+19.06420449201231000/+0.00105725129748224/6.787838e+007/0.93\
  15/90 savename=first1
  params=95158716/1/0.015/0.51/2.55e-009/-1.25e-008/85/0.15/0.15/1
  float=y maxiter=6000 inside=0 logmap=46 periodicity=0
  colors=00082A<3>819818818907<3>H46J46L55<2>T85V94YB4_C3bD3<3>lI2nJ1pK1rM\
  0<6>v`4vb5wd5wf6xi6<2>xm8xn9yn9<3>yrCysDytEyuE<17>zwczwdzwfzwh<3>zwmzvoz\
  vpzvrzvszuu<104>P77P77P77<6>M33M33M22<3>K000CP<3>0BO0BO0BO<4>0AL0AL0AK<3\
  >0AK0AK0AK<12>46G46G46F56F55F55F<3>64D64D74D<3>73D73C73C73B73A73A72A
  }

second1             { ; Version 2001 Patchlevel 6
  reset=2001 type=formula formulafile=e-viva-c.frm
  formulaname=e-viva-c function=recip/ident passes=1 savename=second1
  center-mag=+19.06442878086688000/+0.00068889924650949/6.303265e+007/1/47\
  .499 params=95180095/1/0.1/0.4/-2.56e-008/3.32e-008/90/0.15/0.15/1
  float=y maxiter=6000 inside=0 logmap=55 periodicity=0
  colors=00082A<3>819818818907<3>H36J46L55<5>_C3bD3eE3<3>nJ1pK1rM0<6>v`4vb\
  5wd5wf6xi6<2>xm8xn9yn9<3>yrCysDytEyuE<17>zwczwdzwfzwh<3>zwmzvozvpzvrzvsz\
  uu<96>SAASAAR99<5>P77P77P77<4>N44N44M33<3>L11L11K000CP<3>0BO0BO0BO<4>0AL\
  0AL0AK<3>0AK0AK0AK<12>46G46G46F56F55F55F<3>64D64D74D<6>73C72B72B82A
  }

frm:lakerise   { ; lake-transformation = Sylvie Gallet, Jan 16, 2000
; requires: float=on, Fractint 20.0.6, periodicity=0' and 'passes=1'
; real part of p1: diameter of text bailout
; imag part of p1: position of text bailout (x and y)
; real part of p2: merging of text (position)
; imag part of p2: merging of text (position)
; real part of p3: x-position of text bailout versus background
; imag part of p3: y-position of text bailout versus background
; real part of p4: 0 = lake transform disabled
;                  any value between 0 and 100: water level in % of
;                  the screen height (0 = bottom, 100 = top)
; Try fn1=recip, fn2=ident: If (A=B*C) then text=invisible, else=visible!
; imag part of p4: A (position of text & picture bailout)
; real part of p5: B (position of text bailout)
; imag part of p5: C (position of picture bailout)
; to position text into the picture, try e.g.: A=0.18, B=0.18005, C=1
; finaly set B to the best value found by 'try and error'
pp_p3 = (0.2,300) ;  0.2=amplitude  and  300=frequency of the lake

; Lake transformation
; -------------------

if (real(p4) > 0 && real(p4) <= 100)
  level = real(p4) / 100            ; water level
  ampl = real(pp_p3)                ; amplitude of the wave
  freq = imag(pp_p3)                ; frequency
  angle = real(rotskew * pi / 180)
  exp_irot = exp(-flip(angle))
  h = 1 / real(magxmag)
  w = h / 0.75 * imag(magxmag)
  tanskew = tan(imag(rotskew * pi / 180))
  u = 2 * w * exp_irot
  v = 2 * h * (tanskew + flip(1)) * exp_irot
  z3rd = center + (-w-h*tanskew - flip(h)) * exp_irot
  z = pixel - z3rd
  b = imag(conj(u)*z) / imag(conj(u)*v)
  if (b <= level)
    dy = level - b
    z = z + 2*dy * (1+ampl*sin(freq*dy^0.2)) * v
  endif

 pixel = z + z3rd

endif

  z=(sinh(sinh(sinh(pixel-p3)-real(p1))-p2))/imag(p1)
    x=real(z), y=imag(z)
;Text = generated with FRACTEXT.EXE from J.M.v.d. WALK
  chrI1 = x>-0.51186&&x<-0.49236
  chrS2 = abs(cabs(z+(0.43498,-0.70762))-0.03262)<0.00975&&(x<=-0.434\
  98||y>0.70762)||(abs(cabs(z+(0.43498,-0.64238))-0.03262)<0.00975&&(\
  x>-0.43498||y<0.64238))
  chrF4 = x<-0.28311||(y<0.68475&&y>0.66525)||y>0.7305&&x>-0.30261&&x\
  <-0.22311
  xCR=2*x
  chrR5 = y<0.68475&&y>0.66525||y>0.7305||x<-0.18861&&x>-0.20811&&x<-\
  0.15861||(abs(cabs(z+(0.15861,-0.70762))-0.03262)<0.00975&&x>=-0.15\
  861)||(y<0.675&&y<-xCR+0.36753&&y>-xCR+0.32393)
  xCA=3*x
  chrA6 = y>xCA+0.84203||y>-xCA+0.5963||(y<0.66&&y>0.6405)&&y<xCA+0.9\
  037&&y<-xCA+0.65797
  xCC=1*x
  chrC7 = abs(cabs(z+(-0.10932,-0.675))-0.06525)<0.00975&&(x<0.10932|\
  |y>xCC+0.56568||y<-xCC+0.78432)
  chrT8 = y>0.7305&&x>0.17736&&x<0.27186||(x>0.21486&&x<0.23436)
  chrI9 = x>0.28686&&x<0.30636
  xCN=2.5*x
  chrN10 = x>0.32136&&x<0.34086||(x>0.38136&&x<0.40236)||(y>-xCN+1.55\
  339&&y<-xCN+1.60589)
  chrT11 = y>0.7305&&x>0.41736&&x<0.51186||(x>0.45486&&x<0.47436)
  test1 = chrI1||chrS2||chrF4||chrR5||chrA6||chrC7||chrT8||chrI9||chr\
  N10||chrT11&&y>0.6&&y<0.75
  chrS12 = abs(cabs(z+(0.64457,-0.4936))-0.0286)<0.0078&&(x<=-0.64457\
  ||y>0.4936)||(abs(cabs(z+(0.64457,-0.4364))-0.0286)<0.0078&&(x>-0.6\
  4457||y<0.4364))
  chrI13 = x>-0.59517&&x<-0.57957
  chrN14 = x>-0.56657&&x<-0.55097||(x>-0.51457&&x<-0.49776)||(y>-xCN-\
  0.88641&&y<-xCN-0.84441)
  xCK=1.5*x
  chrK15 = x<-0.46916||(y<xCK+1.17048&&y>xCK+1.14236)||(y>-xCK-0.2404\
  8&&y<-xCK-0.21236&&y<xCK+1.17048)&&x>-0.48476
  chrI16 = x>-0.39524&&x<-0.37964
  chrN17 = x>-0.36664&&x<-0.35104||(x>-0.31464&&x<-0.29784)||(y>-xCN-\
  0.38659&&y<-xCN-0.34459)
  chrG18 = abs(cabs(z+(0.21984,-0.465))-0.0572)<0.0078&&(x<-0.21984||\
  y<0.4728||y>0.4806)||(x>-0.21984&&x<=-0.17044&&y<0.4728&&y>0.4572)
  chrO20 = abs(cabs(z+(0.01184,-0.465))-0.0572)<0.0078
  chrR21 = y<0.4728&&y>0.4572||y>0.5144||x<0.08176&&x>0.06616&&x<0.10\
  776||(abs(cabs(z+(-0.10776,-0.4936))-0.0286)<0.0078&&x>=0.10776)||(\
  y<0.465&&y<-xCR+0.68833&&y>-xCR+0.65345)
  chrR23 = y<0.4728&&y>0.4572||y>0.5144||x<0.23776&&x>0.22216&&x<0.26\
  376||(abs(cabs(z+(-0.26376,-0.4936))-0.0286)<0.0078&&x>=0.26376)||(\
  y<0.465&&y<-xCR+1.00033&&y>-xCR+0.96545)
  chrI24 = x>0.31316&&x<0.32876
  chrS25 = abs(cabs(z+(-0.37816,-0.4936))-0.0286)<0.0078&&(x<=0.37816\
  ||y>0.4936)||(abs(cabs(z+(-0.37816,-0.4364))-0.0286)<0.0078&&(x>0.3\
  7816||y<0.4364))
  chrI26 = x>0.42756&&x<0.44316
  chrN27 = x>0.45616&&x<0.47176||(x>0.50816&&x<0.52497)||(y>-xCN+1.67\
  041&&y<-xCN+1.71241)
  chrG28 = abs(cabs(z+(-0.60297,-0.465))-0.0572)<0.0078&&(x<0.60297||\
  y<0.4728||y>0.4806)||(x>0.60297&&x<=0.65237&&y<0.4728&&y>0.4572)
  test2 = chrS12||chrI13||chrN14||chrK15||chrI16||chrN17||chrG18||chr\
  O20||chrR21||chrR23||chrI24||chrS25||chrI26||chrN27||chrG28&&y>0.4&\
  &y<0.53
  test=test1||test2
  test0=test0&&whitesq
  test0=((test0||test)==0)
  f1=fn1(imag(p5))*fn2(imag(p4))*pixel
  f2=real(p5)*pixel
  pixel=(test==0)*f1+test*f2
  p_p1=(1,-9999), p_p2=(1.3,2), p_p3=(-0.5,0)
  ; Import of formula 'mmix3' from file MMIX4-3.FRM from Jim Muth
  ;p_p1=(1,-9999), p_p2=(1.3,2), p_p3=(-0.5,0)
  a=real(p_p1), b=imag(p_p1), d=real(p_p2), f=imag(p_p2),
  g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
  k=real(p_p3)+1, l=imag(p_p3)+100, c=fn1(pixel):
  z=k*((a*(z^b))+(d*(z^f)))+c,
  |z| < l
  }

;******************************************************************


frm:e-viva-c   { ; lake-transformation = Sylvie Gallet, Jan 16, 2000
; requires: float=on, Fractint 20.0.6, periodicity=0' and 'passes=1'
; real part of p1: diameter of text bailout
; imag part of p1: position of text bailout (x and y)
; real part of p2: merging of text (position)
; imag part of p2: merging of text (position)
; real part of p3: x-position of text bailout versus background
; imag part of p3: y-position of text bailout versus background
; real part of p4: 0 = lake transform disabled
;                  any value between 0 and 100: water level in % of
;                  the screen height (0 = bottom, 100 = top)
; Try fn1=recip, fn2=ident: If (A=B*C) then text=invisible, else=visible!
; imag part of p4: A (position of text & picture bailout)
; real part of p5: B (position of text bailout)
; imag part of p5: C (position of picture bailout)
; to position text into the picture, try e.g.: A=0.18, B=0.18005, C=1
; finaly set B to the best value found by 'try and error'
pp_p3 = (0.2,300) ;  0.2=amplitude  and  300=frequency of the lake

; Lake transformation
; -------------------

if (real(p4) > 0 && real(p4) <= 100)
  level = real(p4) / 100            ; water level
  ampl = real(pp_p3)                ; amplitude of the wave
  freq = imag(pp_p3)                ; frequency
  angle = real(rotskew * pi / 180)
  exp_irot = exp(-flip(angle))
  h = 1 / real(magxmag)
  w = h / 0.75 * imag(magxmag)
  tanskew = tan(imag(rotskew * pi / 180))
  u = 2 * w * exp_irot
  v = 2 * h * (tanskew + flip(1)) * exp_irot
  z3rd = center + (-w-h*tanskew - flip(h)) * exp_irot
  z = pixel - z3rd
  b = imag(conj(u)*z) / imag(conj(u)*v)
  if (b <= level)
    dy = level - b
    z = z + 2*dy * (1+ampl*sin(freq*dy^0.2)) * v
  endif

 pixel = z + z3rd

endif

  z=(sinh(sinh(sinh(pixel-p3)-real(p1))-p2))/imag(p1)
    x=real(z), y=imag(z)
;Text = generated with FRACTEXT.EXE from J.M.v.d. WALK
  chrE1 = x<-0.54802||y<0.6195||(y<0.68475&&y>0.66525)||y>0.7305&&x>-\
  0.56752&&x<-0.48802
  xCV=3.5*x
  chrV3 = y>-xCV-0.64308&&y<-xCV-0.5721||y<xCV+1.84308&&y>xCV+1.7721
  chrI4 = x>-0.27703&&x<-0.25753
  chrV5 = y>-xCV-0.09885&&y<-xCV-0.02787||y<xCV+1.29885&&y>xCV+1.2278\
  7
  xCA=3*x
  chrA6 = y>xCA+0.90293||y>-xCA+0.5354||(y<0.66&&y>0.6405)&&y<xCA+0.9\
  646&&y<-xCA+0.59707
  chrF8 = x<0.10852||(y<0.68475&&y>0.66525)||y>0.7305&&x>0.08902&&x<0\
  .16852
  chrO9 = abs(cabs(z+(-0.25852,-0.675))-0.06525)<0.00975
  chrT10 = y>0.7305&&x>0.34852&&x<0.44302||(x>0.38602&&x<0.40552)
  chrD11 = x<0.47752||y<0.6195||y>0.7305&&x>0.45802&&x<0.49252||(abs(\
  cabs(z+(-0.49252,-0.675))-0.06525)<0.00975&&x>=0.49252)
  test1 = chrE1||chrV3||chrI4||chrV5||chrA6||chrF8||chrO9||chrT10||ch\
  rD11&&y>0.6&&y<0.75
  chrE12 = x<-0.6137||y<0.4156||(y<0.4728&&y>0.4572)||y>0.5144&&x>-0.\
  6293&&x<-0.5617
  chrV14 = y>-xCV-1.16296&&y<-xCV-1.10617||y<xCV+1.96296&&y>xCV+1.906\
  17
  chrI15 = x>-0.38019&&x<-0.36459
  chrV16 = y>-xCV-0.70057&&y<-xCV-0.64379||y<xCV+1.50057&&y>xCV+1.443\
  79
  chrA17 = y>xCA+1.09492||y>-xCA-0.08425||(y<0.452&&y>0.4364)&&y<xCA+\
  1.14425&&y<-xCA-0.03492
  chrF19 = x<-0.05137||(y<0.4728&&y>0.4572)||y>0.5144&&x>-0.06697&&x<\
  0.00063
  xCR=2*x
  chrR20 = y<0.4728&&y>0.4572||y>0.5144||x<0.02923&&x>0.01363&&x<0.05\
  523||(abs(cabs(z+(-0.05523,-0.4936))-0.0286)<0.0078&&x>=0.05523)||(\
  y<0.465&&y<-xCR+0.58326&&y>-xCR+0.54837)
  chrA21 = y>xCA+0.03678||y>-xCA+0.97388||(y<0.452&&y>0.4364)&&y<xCA+\
  0.08612&&y<-xCA+1.02322
  xCC=1*x
  chrC22 = abs(cabs(z+(-0.28574,-0.465))-0.0572)<0.0078&&(x<0.28574||\
  y>xCC+0.17926||y<-xCC+0.75074)
  chrT23 = y>0.5144&&x>0.3447&&x<0.4253||(x>0.3772&&x<0.3928)
  chrI24 = x>0.4383&&x<0.4539
  xCN=2.5*x
  chrN25 = x>0.4669&&x<0.4825||(x>0.5189&&x<0.5357)||(y>-xCN+1.69725&\
  &y<-xCN+1.73926)
  chrT26 = y>0.5144&&x>0.5487&&x<0.6293||(x>0.5812&&x<0.5968)
  test2 = chrE12||chrV14||chrI15||chrV16||chrA17||chrF19||chrR20||chr\
  A21||chrC22||chrT23||chrI24||chrN25||chrT26&&y>0.4&&y<0.53
  test=test1||test2
  test0=test0&&whitesq
  test0=((test0||test)==0)
  f1=fn1(imag(p5))*fn2(imag(p4))*pixel
  f2=real(p5)*pixel
  pixel=(test==0)*f1+test*f2
  p_p1=(1,-9999), p_p2=(1.3,2), p_p3=(-0.5,0)
  ; Import of formula 'mmix3' from file MMIX4-3.FRM from Jim Muth
  ;p_p1=(1,-9999), p_p2=(1.3,2), p_p3=(-0.5,0)
  a=real(p_p1), b=imag(p_p1), d=real(p_p2), f=imag(p_p2),
  g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
  k=real(p_p3)+1, l=imag(p_p3)+100, c=fn1(pixel):
  z=k*((a*(z^b))+(d*(z^f)))+c,
  |z| < l
  }

********************

cheers,

Guy

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

From: [e-mail]
Subject: (fractint) C-FOTD  11-04-01  (Veiled Objects [7])
Date: 11 Apr 2001 08:21:31 EDT


Classic FOTD -- April 11, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

Today's FOTD is late again . . . no surprise in that.  I'm still
busy.  But I have finally managed to find an image that rates
above a 6.  True, at a rating of 7, it's only a single step
above 6, but it's a start.

I named the image "Veiled Objects" when I noticed that the
smaller features seem to be draped over the larger objects like
a gossamer veil.  To create the image I unpacked number 6 in my
series of 12 MandNewt formulae.  This formula is a random
variation of the Ikenaga function, and the Ikenaga function is a
minor mystery.

The image takes 8-1/2 minutes to render at a low-resolution SF5,
but the highest resolution available is needed to do it justice.
The image may be seen by running the parameter file at the
resolution of your choice, or by downloading the GIF file from:

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

or from:

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

once it has been posted.

The fractal weather today was cloudy but dry, with a temperature
of 68F (20C).  The fractal cats approved of the conditions.

That's it for today.  I've got a busy day ahead of me, and it's
time to get to work.  Until next time, take care, and hug at
least one fractal every day.


Jim Muth
[e-mail]


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

Veiled_Objects     { ; time=0:08:38.44--SF5 on a P200
  reset=2001 type=formula formulafile=mandnewt.frm
  formulaname=MandNewt06 passes=1
  center-mag=0.277319/-1.04425/35.70909/1/82.499
  params=-2.37/2.17/-1.56/-1.05/3.29/-3.17 float=y
  maxiter=254 inside=bof60 logmap=yes periodicity=0
  colors=000jwpjwqjwqhuogsmfqlepjdniclgajf`id_gcZeaY\
  c`XbZV`YUZWTXVSWTRUSQSQOQPNPNMNMLLKKJJJIHHGGGEEFCD\
  EBBD9AC78945B67D78F8AH9BJACLBENCFODGQEISFJUGKWHMYI\
  N_JO`KQbLRdMSfNUhOVjPWlQYmRZoS_qTasUbuVcwWexXfxYgr\
  ZdkZadZ_XZXQZVJZSAYRCZQDaNFeKGhHIlEInBJoCKoCKoCLoC\
  LoCMoCMoCNoCNoDOoDOoDPoDQoDQoDRoDRoDSoESoEToEToEUo\
  EUoEVoEWoEWoFXoFXoFYoFYoFZoFZoF_oF_oF`mG`lH`kIajIa\
  hJagKafLbeLbdMbbNbaOc`Oc_PcYQcXRdWRdVSdUTdSUeRUeQV\
  ePWdMYeOWeQVeRTeTSeUQeWPeXOeZMe_LeaJebIedHeeFegEeh\
  CejBekAdj9dj9cj9cj8cj8bj8bi8bi7ai7ai7ai7`i6`i6`h6_\
  h6_h5_h5Zh5Zh4Yh4Yg4Yg4Xg3Xg3Xg3Wg3Wg2Wf2Vf2Vf2Vf1\
  Uf1Uf1Uf1Te3Td4Td5Tc6Tc7Tb8Tb9TaBSaCS`DS`ES_FS_GSZ\
  HSZJSYKSYLRXMRXNRWORWPRVQRUSRUTRTURTVQSWQSXQRYQR_Q\
  Q`QQaQPbQPcQOdPOePNgPNhPMiPMjPLkPLlPKmPKnRMmTNmUOm\
  WQmXRlZSl`UlaVlcWkdYkfZkh_kiajkbjlcjnejpfiqgisiitj\
  ivkhxmhxnhxohkunkunkvojvp
  }

frm:MandNewt06 {; Jim Muth
z=c=(pixel*p1):
a=z^3+(c-p2)*z-c
b=p3*z^2+c-1
z=z-1*a/b
0.000000000000000000000000000001 <= |a|
}

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

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

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) C-FOTD 11-04-01 (Veiled Objects [7])
Date: 11 Apr 2001 13:28:18 -0000

>From: [e-mail]
>Subject: (fractint) C-FOTD  11-04-01  (Veiled Objects [7])
>Date: Wed, 11 Apr 2001 08:21:31 EDT
>
>Classic FOTD -- April 11, 2001 (Rating 7)
>
>This formula is a random
>variation of the Ikenaga function, and the Ikenaga function is a
>minor mystery.

What the heck is the Ikenaga function?!?!

_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.


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Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"


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

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) Fractint Development
Date: 11 Apr 2001 13:35:54 -0000

>From: Programmer Dude <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>Subject: Re: (fractint) Fractint Development
>Date: Wed, 04 Apr 2001 10:58:32 -0500
>
>No one has responded to this in a couple days, so I thought I'd take a
>shot at it...

Thanks.

>Andrew Coppin wrote:
>
> > 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.

So it's an address space thing? What you're saying is that for certain
address ranges you can miss out a couple of the MSBits? (Hence presumably
smaller/faster code?)

> > 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.

Can't you just treat everything as "far"?

>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.

Yeah, POV-Ray = utterly cool program!
Actually, the DOS and Amiga verisons show you previouse too (unless you turn
it off).

> >> 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...

Hmm... I remember back on the old 6502 processor found in the legendary C64
there was a "zero page" addressing mode, which only required an 8-bit
address instead of the usuall "absolute addressing" which required a 16-bit
address. I think you're saying the Intel CPU has a "base-offset" register or
something that lets you use shorter addresses (and limits your address
space). Close?

Thanks.
Andrew.

PS. I am now in possetion of the fractint source code. I'll spend some time
failing to understand it later...

_________________________________________________________________________
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-------------------------------------------------------------------------------

From: [e-mail]
Subject: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
Date: 11 Apr 2001 09:54:18 EDT

Andrew Coppin asked:

>What the heck is the Ikenaga function?!?!

That's the minor mystery!  The function is mentioned in the fractint.frm
file,
but no one seems to know where the function came from or whether it has
any use other than creating fractals.  There is an Ikenaga page on the 'net,
but the owner of that page denies being the function's originator.

Jim M.

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From: [e-mail]
Subject: (fractint) Re: C-FOTD  09-04-01  (Mandelbrot Mayhem [5])
Date: 11 Apr 2001 10:03:34 EDT

The Programmer Dude wondered:

>Why should there *be* an ultimate fractal?  Seems kind of limiting...

There is no 'ultimate' fractal.  I intended the statement to be taken
ironically.

Jim M.

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

From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) Fractint Development
Date: 11 Apr 2001 10:13:07 -0500

Andrew Coppin wrote:

>> 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).
>>
>> The "Memory Model" is what various configurations of the segments is
>> called.
>>
>> The "Medium" memory model, IIRC, has the stack and data sharing one
>> 64K segment, while the code lives in its own 64K 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...
>
> So it's an address space thing? What you're saying is that for certain
> address ranges you can miss out a couple of the MSBits? (Hence presumably
> smaller/faster code?)

You can miss out on eight of them, yes.

>> Ideally you'd like a compiler that let you treat memory as flat and make
>> all your pointers be the same type.
>
> Can't you just treat everything as "far"?

Yes, and I'm sure this is what the developers would like to do.  It does
require a re-write, since it was NOT done this way originally.  Remember
the age of FractInt; back then speed was an issue (well, it still is),
and universal far addressing was often significantly slower depending on
the compiler, compiler libraries and how you went about it.  As has been
mentioned, even back then, there were MS-DOS "extenders" that could
present a flat address space to the system, but your compiler needed to
know about it to use it.

> Hmm... I remember back on the old 6502 processor found in the legendary C64
> there was a "zero page" addressing mode, which only required an 8-bit
> address instead of the usuall "absolute addressing" which required a 16-bit
> address. I think you're saying the Intel CPU has a "base-offset" register or
> something that lets you use shorter addresses (and limits your address
> space). Close?

Yes.  In fact, it has four (mentioned in the first paragraph above).  It
allows you to use 16-bit addresses with the tradeoff that you only get a
64K address space.  Unlike the 6502, your "segment" can start at any 256
byte boundary in the total address space.

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

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

From: Lee Skinner <[e-mail]>
Subject: (fractint) C-FOTD  11-04-01  (Veiled Objects [7])
Date: 11 Apr 2001 13:10:58 -0400

>> I named the image "Veiled Objects" when I noticed that the smaller
features seem to be draped over the larger objects like a gossamer veil. =
<<

It reminds me of a spacecraft orbiting around a planet.

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

From: [e-mail]
Subject: (fractint) C-FOTD  12-04-01  {Blueberries [5])
Date: 12 Apr 2001 08:31:49 EDT


Classic FOTD -- April 12, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

With today's fractal, which pictures a midget in the land of
Z^sqrt2+C, we slip back to a rating of 5.  This perfectly
average picture features a perfectly normal, though fractured,
midget that exists in a remote valley of its parent fractal.

I visit the Z^sqrt2 figure frequently because in this figure the
midgets are relatively easy to find compared to the midgets in
other figures with exponents of Z between 1 and 2.  Since 1.4142
is the square root of 2, the midgets in the Z^1.4142 figure
reveal their hiding places by being surrounded with the same
two-way symmetry that reveals midgets in the classic Z^2+C
figure.  But in the Z^1.4142 figure the midgets lie far deeper
and farther apart.

I named the image "Blueberries" when I noticed the berry-like
depressions surrounding the barely visible midget at the center.
There are roughly 9 berries in the outer ring and roughly 13
berries in the smaller inner ring, which is not at all
surprising, since 13/9 equals roughly 1.4142.

The parameter file takes over 23 minutes to render on a 200mhz
Pentium machine.  It will run faster on a faster machine, but
not so fast as to make a download of the GIF image file
superfluous.  That image file may be found on the Web at:

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

and at:

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

The fractal weather today featured a steady rain from dawn to
dusk.  The temperature of 52F (11C) combined with the rain to
keep the cats snug indoors in their beds.

Once again we come to the end of the FOTD.  It was a relatively
brief one because I'm still busy.  But eventually I'll catch up,
and then, anything could happen.  Until next time, take care,
and help preserve fractals from extinction.


Jim Muth
[e-mail]


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

Blueberries        { ; time=0:23:16.75--SF5 on a P200
  reset=2001 type=formula formulafile=branchct.frm
  formulaname=MandelbrotBC passes=1
  center-mag=-1.04105767849226400/-1.142969742678717\
  00/1.290666e+007/1/90 params=1.414213562373/0/100/0
  float=y maxiter=2800 inside=0
  logmap=569 periodicity=10
  colors=000GU0GU0ET0CQ0AO08M06K04I02G00D00D00B00900\
  60050020020000000000000000000000000000000000000000\
  0000000200200400400400600620640840860A80A80AA0CC0C\
  E0CE0EG0EH0GH2GJ2GL2HL4HN4HP6JR6JR8LT8LVALVANXCNZC\
  NZEP`EPbEPbCRdCRdATdATd8Vd8Vd6Vd6Xd4Xd4Ze2Ze2Ze0`e\
  0`e0be0be0be0de0de0eg0eg0gg0gg0gg0ig0ig0kg0kg0kg0m\
  i0mi0oi0oi0oi0qi0qi0si0si0uk0si0sg0qg0qe0oe0od0ob0\
  mb0m`4k`6kZAiZCiXGiVHgVLgTNeTReRTeRXdP`dNbbNebLg`L\
  k`Jm`HqZHsZGvXGxXEzVEzVCzVAzTAzT8zR8zR6zN4zR6zV8zX\
  8z`AzbAzeCzgCzkEzmEzqGzsGzvHxxHvzJuzJszLszLozNmzNk\
  zNizNgvNeuPdsPbqP`mPZkPXiPVgRTdRRbRP`RNZRNZTLXRJXR\
  JXPHVPGYNG`NEcNEfLCiLAfJAcJ8_J6WI6SJ4PK4ML2JM0GN0D\
  O0AP0AQ0AR0AS0AT0AU0AV0AW0CX0EY0GZ0G_0E`0Ga0Gb0Gc0\
  Gd0He0Hf0Hg0Hh0Ji0Jj0Jk2Jl2Lm4Ln6Lo8Lp8NqANrCNsENt\
  EPuGPvHPwJPxJRyLRzNRzPRzPTzRTzTTzVTzVVzXVzZVz`Vz`V\
  zbTzdTzdTzeTzeTzgTzgRziRz
  }

frm:MandelbrotBC = { ; Z = Z^E + C
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<100
}

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

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

From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
Date: 12 Apr 2001 19:54:54 -0500

> That's the minor mystery!  The function is mentioned in the fractint.frm
> file, but no one seems to know where the function came from or whether it
has
> any use other than creating fractals.

From the ikenaga.frm file that came with FRAC'Cetera volume 2 issue 7 (Jon
Horner's publication):

  IKENAGA - Formula originally discovered by Bruce Ikenaga, at Western
Reserve
  University, Indiana.  Documented in Dewdney's `Armchair Universe".

          The Ikenaga set is:    Z(n+1) =Z(n)^3 + (C-1) * Z(n) - C
          where:                      Z(n) = x + yi and C = a + bi

Jonathan



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

From: Bill Jemison <[e-mail]>
Subject: (fractint) Jonathan - puzzling par
Date: 12 Apr 2001 23:15:35 -0400

Jonathan,

I can't get the following par to generate at any higher res that SF5
(640x480x256).

Is this a bug? or is something going on that I am missing?

***************************************************

billtest           {
                     ;  Version 2001 Patchlevel 6
  reset=3D2001 type=3Dlorenz passes=3Dd
  center-mag=3D+0.00000000000000000/+15.00000000000000000/1.333333/1.3333=

  params=3D0.02/5/15/1 float=3Dy maxiter=3D1000 fillcolor=3D0 inside=3D0
  outside=3D0 cyclerange=3D1/1 sound=3Dbeep/fm orbitdelay=3D1000 showorbi=
t=3Dyes
  colors=3D000pdQ0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKK=
KOO\
  O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>z=
V\
  V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S=
0\
  S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSK=
K\
  S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<=
3\
  >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88=
G\
  8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFB=
G\
  GBFGBDGBCG000<6>000
  }

****************************************************

Bill

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

From: [e-mail]
Subject: (fractint) C-FOTD  13-04-01  (Squirt [6])
Date: 12 Apr 2001 23:42:46 EDT


Classic FOTD -- April 13, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

It's been another very busy day here at Fractal Central, but not
so busy that I needed to forego my daily fractal search.  It was
however too busy for the enlightening philosophy that you've all
been waiting for.  But there's a long future ahead, and the
philosophy will come at the proper time.  (I don't want to solve
the riddle of the universe too soon -- that would take all the
fun out of it.)

Today's fractal is named "Squirt".  I gave it this name because
the image pictures another midget in the Z^(sqrt2)+C Mandeloid,
and the Fractint abbreviation for 'square root' is 'sqrt', and
if the letters u and i are added to the middle of 'sqrt', the
word becomes 'squirt'.  Another reason is that I often pronounce
'square root' as 'squirt'.

The image, which vaguely resembles an octopus or starfish, is a
bit above average, just enough to deserve the rating of 6 that I
gave it.  These 'squirt' midgets are becoming more interesting
as I develop the knack of finding them.  And the Z^(sqrt2)+C
figure, unlike the familiar Z^2+C figure, is infinite in its
surface extent.

The attached parameter file takes 29 minutes to render on an
aging Pentium running at 200mhz.  Newer and faster machines will
render the image in far less time.  Older, slower ones will take
far longer.

Regardless, the GIF file of the image will soon be posted to:

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

and to:

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

The fractal weather today was partly cloudy with an afternoon
temperature of 66F (19C).  These conditions must have suited the
dynamic duo of cats perfectly, since they spent the entire
afternoon basking in the on-again off-again sunshine.  As for
me, I spent the afternoon trying to work my way through the
backlog, having only minor success.

Well, I see it's now time to shut down the fractal place and
call it a night.  Until next time, when I'll return with more
goodies, take care and be ever vigilant for that once-in-a-
lifetime fractal.


Jim Muth
[e-mail]


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

Squirt             { ; time=0:29:41.84--SF5 on a P200
  reset=2001 type=formula formulafile=branchct.frm
  formulaname=MandelbrotBC passes=1
  center-mag=-0.91532246418772030/+0.387841135413711\
  50/2.102521e+012/1/90 params=1.414213562373/0/120/0
  float=y maxiter=2800 inside=0 logmap=890
  mathtolerance=/1 periodicity=10
  colors=000IgmEzwEzwEzwGzxGzxGzxGzzGzzHzzHzzHzzHzzJ\
  zzJzzJzzJzzKzzJzzJxzJwzJtxJrwJouJlrJkqJhoJfnJckJbi\
  J_hJXeJVcHSbHQ`HNYHKXHJVHGSBEQ8BPBAN77K24J02HH0EH0\
  DH0BH0AJ0BK0BM2DN5DP7EQAESDETGGVHGXKHYNH_QH`TJbVJc\
  YKe`KfcKheMihMkkNlnNloNlnNlnMklMkkMkkKiiKiiJihJihH\
  hfHheHheGfcGfcEfbEfbEe`Ge`Hc_Jc_KcYMbYNbXPbXQ`XS`V\
  T`VV_TX_TY_S_YS`YS`YQbXQcXPeXPfVNhVNiVMkTMlTMnTKoS\
  KqSJrSJtQHuQHwQHwPKuPMuPPuNQtNTtNVtNYrM_rMbrMcqMfq\
  KhqKkoKloJooJqnJtnJunHxlHzlHzlHzlJznJznKxoKwoMtqMr\
  qNqrNorNlrPktPitQhuQeuScwSbwT`xTYxTXxVVzVTzXQzXPzY\
  NzYMz_MzYKzXKzXJzVJzVHzTHzTGxSGxQExQExPDzUDzZPzcUz\
  UPzUEzK8zJ8xJ7tH7qH5lG5iG4eE4bD2_D2YB1YB1XA0_A0`80\
  c50i80iB0fE0cH1`K1YM2XP4TS4QV5NY5K`7Hc4Hb7G`AG_BEY\
  EEYHDXJDVMDTPBSQBSTAQVAPY8N`8Mb8Me7Kh7Ji5Hl5Hn5Go4\
  Eq4Dr4Br4At48u47u45w44x42z42z21z20z20z20z20z20z20z\
  20z20z20z10z20z40z40z50z7
  }

frm:MandelbrotBC = { ; Z = Z^E + C
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<100
}

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

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

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Fractint Development
Date: 13 Apr 2001 03:57:28 -0400


------=_NextPart_001_0000_01C0C3CD.DC545440
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

> Can't you just treat everything as "far"?

Sure, which solves problems of total available memory. But you still get =
problems trying to maintain any contiguous data structure (e.g. array) sp=
anning more than 64kb. With flat memory this is as easy as smaller data s=
tructures.<br clear=3Dall><hr>Get Your Private, Free E-mail from MSN Hotm=
ail at <a href=3D"http://www.hotmail.com">http://www.hotmail.com</a>.<br>=
</p>

------=_NextPart_001_0000_01C0C3CD.DC545440
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> Can't you=
 just treat everything as "far"?<BR></DIV> <DIV>Sure, which solves proble=
ms of total available memory. But you still get problems trying to mainta=
in any contiguous data structure (e.g. array) spanning more than 64kb. Wi=
th flat memory this is as easy as smaller data structures.</DIV> <DIV>&nb=
sp;</DIV> <DIV> </DIV></BODY></HTML><DIV><BR><br clear=3Dall><hr>Get=
 Your Private, Free E-mail from MSN Hotmail at <a href=3D"http://www.hotm=
ail.com">http://www.hotmail.com</a>.<br></p></DIV>

------=_NextPart_001_0000_01C0C3CD.DC545440--

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

From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) Jonathan - puzzling par
Date: 13 Apr 2001 07:56:34 -0500

Bill,

> I can't get the following par to generate at any higher res that SF5
> (640x480x256).

> Is this a bug? or is something going on that I am missing?

Here is an excerpt from lorenz.c:

>>
/* BAD_PIXEL is used to cutoff orbits that are diverging. It might be better
to test the actual floating point orbit values, but this seems safe for now.
A higher value cannot be used - to test, turn off math coprocessor and
use +2.24 for type ICONS. If BAD_PIXEL is set to 20000, this will abort
Fractint with a math error. Note that this approach precludes zooming in
very
far to an orbit type. */

#define BAD_PIXEL  10000L    /* pixels can't get this big */
<<

Setting BAD_PIXEL to 20000 does let your par generate.  I suspect that upon
further zooming in, the same thing will happen.  IMO, this qualifies as a
bug.  Although I'm not sure what we would gain by being able to zoom into
these types.  Tim may have more insight into what the problem is.

Jonathan



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From: DeBow Freed <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
Date: 13 Apr 2001 11:28:54 -0500

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
Thanks to Jonathan!
<p>A Bruce Ikenaga currently on the Math Faculty at Millersberg, PA last
year denied any knowledge or authorship of the IF's. I was unable to locate
any other "Ikenaga" in the US, Europe or Japan using various Mathematical
Society Membership Records available at this January's Joint Math Meeting
in New Orleans.
<p>Are their <u>two</u> Bruce Ikenaga's, both teaching math at US universities?
Maybe this is akin to expressing surprise that there are 2 John Smith's
selling pork bellies in Chicago, but I don't know common the name Ikenaga
is, nor the joint probability of first name Bruce and being a practicing
Math academic.
<p>Perhaps the "Veiled Object" is really just Ikenaga.
<br>
<p>Freed
<br>
<br>
<p>Jonathan Osuch wrote:
<blockquote TYPE=CITE>> That's the minor mystery!  The function is
mentioned in the fractint.frm
<br>> file, but no one seems to know where the function came from or whether
it
<br>has
<br>> any use other than creating fractals.
<p>>From the ikenaga.frm file that came with FRAC'Cetera volume 2 issue
7 (Jon
<br>Horner's publication):
<p>  IKENAGA - Formula originally discovered by Bruce Ikenaga, at
Western
<br>Reserve
<br>  University, Indiana.  Documented in Dewdney's `Armchair
Universe".
<p>          The Ikenaga set
is:    Z(n+1) =Z(n)^3 + (C-1) * Z(n) - C
<br>          where:
Z(n) = x + yi and C = a + bi
<p>Jonathan
<p>--------------------------------------------------------------
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From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
Date: 13 Apr 2001 11:38:14 -0500

DeBow Freed wrote:
>
> Are their two Bruce Ikenaga's, both teaching math
> at US universities?

No, it is the same person.  All details may be found at his home page
and the associated web pages (see the page on Biographical Information):

       http://www.millersv.edu/~bikenaga/

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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From: DeBow Freed <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
Date: 13 Apr 2001 12:07:16 -0500

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
Thanks Paul.
<p>Ikenaga's response to my query last year (and I believe his homepage
also lists) one fairly lengthy Adobe-ized set of "classnotes" concerning
Fractals which he (Ikenaga) stated were "trivial".
<p>He also said he had, indeed, heard of a program called "Fractint", which
he liked, and perhaps would take a look at some of last year's pod of Ikenaga-based
FOTD's from Jim (which I forwarded to him) and some the Discussion Group
pages. Subsequently, <i>no mas </i>was ever heard from Dr. Ikenaga<i>.</i>
<p>He twice denied any recollection of having produced anything substantive.
<br>Perhaps we should let him in on the secret.
<p>DeBow
<p>"Paul N. Lee" wrote:
<blockquote TYPE=CITE>DeBow Freed wrote:
<br>>
<br>> Are their two Bruce Ikenaga's, both teaching math
<br>> at US universities?
<p>No, it is the same person.  All details may be found at his home
page
<br>and the associated web pages (see the page on Biographical Information):
<p>       <a href="http://www.millersv.edu/~bikenaga/">http://www.millersv.edu/~bikenaga/</a>
<p>Sincerely,
<br>P.N.L.
<br>--------------------------------------------------------------
<br><a href="http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go">http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go</a>
<p>--------------------------------------------------------------
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-------------------------------------------------------------------------------

From: Bill Jemison <[e-mail]>
Subject: (fractint) Jonathan - puzzling par
Date: 13 Apr 2001 13:07:04 -0400

Thanks Jonathan (although I don't have a clue as to what you are talking =

about <g>) As you may have surmised, my reason for zooming into this =

type fractal is strictly for sound-generation purposes.
  =

************************

> I can't get the following par to generate at any higher res that SF5
> (640x480x256).

> Is this a bug? or is something going on that I am missing?

Here is an excerpt from lorenz.c:

>>
/* BAD_PIXEL is used to cutoff orbits that are diverging. It might be =

better
to test the actual floating point orbit values, but this seems safe for =

now. A higher value cannot be used - to test, turn off math coprocessor a=
nd
use +2.24 for type ICONS. If BAD_PIXEL is set to 20000, this will abort
Fractint with a math error. Note that this approach precludes zooming in
very far to an orbit type. */

#define BAD_PIXEL  10000L    /* pixels can't get this big */
<<

Setting BAD_PIXEL to 20000 does let your par generate.  I suspect that up=
on
further zooming in, the same thing will happen.  IMO, this qualifies as a=

bug.  Although I'm not sure what we would gain by being able to zoom into=

these types.  Tim may have more insight into what the problem is.

Jonathan



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From: DeBow Freed <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
Date: 13 Apr 2001 12:20:48 -0500

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
To all-
<p>Before I disseminate more misinformation than usual, Dr. Ik's "classnotes"
[his phrase] on "Self-SimilarFractals" are available at the homepage address
provided by PNL in the form of a <u>Mathematica 2.1 Notebook</u> [<b>not
Adobe</b>, as I previously stated], which I did not have the ability to
convert to legible text at the time.
<p>When I heard nothing further from Dr. Ikenaga, I (obviously mistakenly)
assumed he knew his own work better than I ever would, gave up the search
for archaic versions of Mathematica software with which to translate his
2.1 Notebook, and took the man at his word.
<p>Funny, wonder what the real genesis of the functionals was.
<p>Freed
<br>
<p>DeBow Freed wrote:
<blockquote TYPE=CITE>Thanks Paul.
<p>Ikenaga's response to my query last year (and I believe his homepage
also lists) one fairly lengthy Adobe-ized set of "classnotes" concerning
Fractals which he (Ikenaga) stated were "trivial".
<p>He also said he had, indeed, heard of a program called "Fractint", which
he liked, and perhaps would take a look at some of last year's pod of Ikenaga-based
FOTD's from Jim (which I forwarded to him) and some the Discussion Group
pages. Subsequently, <i>no mas </i>was ever heard from Dr. Ikenaga<i>.</i>
<p>He twice denied any recollection of having produced anything substantive.
<br>Perhaps we should let him in on the secret.
<p>DeBow
<p>"Paul N. Lee" wrote:
<blockquote TYPE=CITE>DeBow Freed wrote:
<br>>
<br>> Are their two Bruce Ikenaga's, both teaching math
<br>> at US universities?
<p>No, it is the same person.  All details may be found at his home
page
<br>and the associated web pages (see the page on Biographical Information):
<p>       <a href="http://www.millersv.edu/~bikenaga/">http://www.millersv.edu/~bikenaga/</a>
<p>Sincerely,
<br>P.N.L.
<br>--------------------------------------------------------------
<br><a href="http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go">http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go</a>
<p>--------------------------------------------------------------
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-------------------------------------------------------------------------------

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
Date: 13 Apr 2001 19:40:42 -0000

>From: "Jonathan Osuch" <[e-mail]>
>Reply-To: [e-mail]
>To: <[e-mail]>
>Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
>Date: Thu, 12 Apr 2001 19:54:54 -0500
>
>           The Ikenaga set is:    Z(n+1) =Z(n)^3 + (C-1) * Z(n) - C
>           where:                      Z(n) = x + yi and C = a + bi
>
>Jonathan

Now *that* was what I was asking!

Thanks.
Andrew.

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

From: DeBow Freed <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
Date: 13 Apr 2001 15:35:36 -0500

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
Fellow Fractaliers:
<p>FYI, what follows is a <u>direct quote</u> from Dr. Ikenaga's response
to the second of a total of 4 messages I sent to him in September of last
year attempting to inquire about "Ikenaga functions" in general, and the
publication called "<i><u>Self Similar Fractals</u></i>" listed in his
own Bibliograhy on his own Homepage in specific (addresss provided in PNL's
earlier note):
<p><b>"Dear Dr. Freed-</b>
<p> <b>  "I wish I could be of help, but I have no idea what
you're</b>
<br><b>  talking about </b>[<i>?????? </i>- DBF]<b>. If someone named
something after me,</b>
<br><b>  they certainly never told me about it. :-)</b><b></b>
<p><b>    "And I've never written articles about fractals
</b><i>[??????-
</i>DBF<i>]</i><b>. Do you</b>
<br><b>  have references for them?</b>
<p><b>     "Also, are you sure that whoever is doing
this </b><i>[Jim Muth</i><b>-</b>DBF]<b> got the name right?</b>
<p><b>     "(Thanks for mentioning fractint. I always
enjoyed that program,</b>
<br><b>  but I'd thought they stopped developing it. Maybe I should
go look</b>
<br><b>  again.)</b>
<p><b>  Bruce"</b>
<p>    After 2 more similarly confusing attempts to gain
further information regarding the functions themselves or Dr. Ikenaga's
publication entitled "Self-Similar Fractals" which was at that time also
referenced in his own Homepage, I gave up further efforts at deciphering
Dr. Ikenaga's courteous but paradoxical responses.
<p>DeBow Freed (a/k/a DBF)
<p>  -----
<br>  Bruce Ikenaga
[e-mail]
<br>  Dept. of Math, P.O. Box 1002,    :::::::::::::::::::
<br>  Millersville University,
<br>  Millersville, PA 17551-0302
<p>Andrew Coppin wrote:
<blockquote TYPE=CITE>>From: "Jonathan Osuch" <[e-mail]>
<br>>Reply-To: [e-mail]
<br>>To: <[e-mail]>
<br>>Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
<br>>Date: Thu, 12 Apr 2001 19:54:54 -0500
<br>>
<br>>           The Ikenaga
set is:    Z(n+1) =Z(n)^3 + (C-1) * Z(n) - C
<br>>           where:
Z(n) = x + yi and C = a + bi
<br>>
<br>>Jonathan
<p>Now *that* was what I was asking!
<p>Thanks.
<br>Andrew.
<p>_________________________________________________________________________
<br>Get Your Private, Free E-mail from MSN Hotmail at <a href="http://www.hotmail.com">http://www.hotmail.com</a>.
<p>--------------------------------------------------------------
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-------------------------------------------------------------------------------

From: [e-mail]
Subject: (fractint) C-FOTD  14-04-01  (Squirt II [5])
Date: 13 Apr 2001 22:18:35 EDT


Classic FOTD -- April 14, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

Another busy and somewhat frustrating day has ended, to be
replaced by a busy and equally frustrating evening.  But at
least the fractals were working right.

Today's FOTD might have been named "Son of the Squirt", or
"Return of the Squirt", or "Curse of the Squirt", or even "The
Squirt Rises Again".  All these names might have happened, but
they did not.  Instead I named today's image "Squirt II".

I gave the fractal this unassuming name because it comes from
the same Mandeloid as yesterday's image, though from a far
different layer of the hyper-dimensional corkscrew caused by the
multi-valued nature of the complex log function.

The image, a picture of a rather gaudily colored midget in a
valley of the Z^(sqrt2)+C figure, is as unassuming as its name.
Because of several flaws, I could rate the image no higher than
an average 5, but it's still an interesting view of things that
exist in the unexplored depths of the Squirt fractal.

The parameter file takes over 24 minutes to run on a 200mhz
Pentium.  All but the most hardy fractaliers will choose to
download the GIF image file from Paul's web site at:

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

or from Scott's site at:

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

The fractal weather today started with a steady rain.  But by
11am the rain ended and the sky cleared, leading to a sunny
afternoon with a temperature of 77F (25C).  The fractal cats
found the conditions ideal, and showed their approval by
spending the entire afternoon relaxing outdoors.

My day was far from ideal, though the day's fractal partly made
up for all the other things that went wrong.  I'll try to have a
better day tomorrow, when I'll also return with the next FOTD.
Until then, take care, and perhaps I'll soon tackle the remote
parts of the Zexpe (Z^2.71828...) fractal.


Jim Muth
[e-mail]


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

Squirt_II          { ; time=0:24:48.96--SF5 on a P200
  reset=2001 type=formula formulafile=branchct.frm
  formulaname=MandelbrotBC passes=1
  center-mag=-0.72227094168292330/+0.175944088697707\
  90/1.898783e+007/1/-15 params=1.414213562373/0/33/0
  float=y maxiter=4200 inside=0
  logmap=630 periodicity=10
  colors=000huIdsI`nGXjGUfFQbFM`EIXEESC9OC5KB3IB5K98\
  M89N8CO7EQ5GR5IS4KU3MX3OY1QZ0S`0Va0Xb0Zd0`e0bh0di0\
  fj0hl0jm0ln0np0pq0lm0hi8deI`bRXZ`SViORsKOzOSwRXqV`\
  mYdh`hddlZfnVjsQmwMpzGtzCwz7yz3wz5uz7tz8szBqzCnyEm\
  xGlwIjtJisMhqNenOdmRbjSaiU`hXYeYXdZVbaU`bSZdRYeSXd\
  SVbSUbSSaSRaSQ`SO`SNZSMZSKYSJYSIXSGXSFVSEVSCUSBUS9\
  SS8SS7RS5RS4QS3QS1OS0OS0NS0NS0MS0MS0KS0KS0JS0IS0GR\
  0GR0FR0ER0CR0BR09Q09Q08Q07Q05Q04Q03O03O01O00O00O00\
  O00O00R00S01U03V35X57Y89ZBB`EEaGFdJIeMKfOMhROiUQjX\
  SlZUmaXndYqf`sibtldunfwqhytjzwlzynzzpzymzwjztizqfz\
  nezlbziazfZzdYzaVzZSzXRzUOzRNzOKyMJuJGtGFtECtB9s88\
  s55s34q01q00q00q00n00m00l00j00h00f00e00d11a31`41Z5\
  3Y75X78U8BS9ERBGQCJNEMMFOKFRJGUGIXFJZEKaCMdBMf9Ni9\
  Nl9Nn8Nq8Nt8Nw7Ny7Oz7Qz7Rz5Sz5Uz5Vz4Xz4Yz4Zz3`z3az\
  3bz3dz1ez1fz1fz0fz0fz0fz0fz0fz0fz0fz0fz1fz3fz4fz5f\
  z4fz4fz3fz3fz3fz3fz3fz3fz
  }

frm:MandelbrotBC = { ; Z = Z^E + C
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<100
}

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

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

From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
Date: 14 Apr 2001 16:11:17 +1200

At 05:20 14/04/2001, you wrote:
>To all-
>
>Before I disseminate more misinformation than usual, Dr. Ik's "classnotes"
>[his phrase] on "Self-SimilarFractals" are available at the homepage
>address provided by PNL in the form of a Mathematica 2.1 Notebook [not
>Adobe, as I previously stated], which I did not have the ability to
>convert to legible text at the time.

Most of them are Postscript documents, there's only the occasional
Mathematica file there (and of course "Fractals.ma" is one of them).

>When I heard nothing further from Dr. Ikenaga, I (obviously mistakenly)
>assumed he knew his own work better than I ever would, gave up the search
>for archaic versions of Mathematica software with which to translate his
>2.1 Notebook, and took the man at his word.

Not that an "archaic version" would have been needed - all subsequent
versions of Mathematica are capable of reading and converting pre v.3
notebooks, as can the downloadable MathReader software.

>Funny, wonder what the real genesis of the functionals was.

Before learning of the Dewedney reference I did a wee bit of a search -
"Ikenaga" seemed fairly common, and I came up with a topologist in named
Shogo Ikenaga. That looked promising, but I can't read Japanese. There was
also a roboticist, who may have been another Bruce - I forget, but that
didn't look very likely.

Morgan L. Owens.
"Most of the pages found were about Fractint's Ikenaga function."


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

From: [e-mail]
Subject: (fractint) C-FOTD  15-04-01  (Deep in Hyperspace [7])
Date: 14 Apr 2001 21:04:51 EDT


Classic FOTD -- April 15, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

I love vast open spaces filled with tiny distant objects, and
today's image fits that description perfectly.  I named the
picture "Deep in Hyperspace", though the scene pictured exists
obviously in everyday 3-dimensional space.  It still rates a
7 however.

The image is one that cries out for truecolor, but that feature
is not yet available, at least in Fractint.  If and when it does
become available, I'll probably re-render this image as well as
a batch of earlier images which suffer from the unavoidable
bands.  Normally, I am not bothered by bands, especially the
equal-iteration bands that make a fractal a classic fractal, but
occasionally, as in today's image, I would like to have perfect
smoothness.

I first thought of a name like "Flying Spectacles" for today's
FOTD, but that name has no class whatsoever.  Then I pictured
myself in the vicinity of a very hot star deep in a cloud of
dust.  The bits and pieces floating in the foreground could only
be protoplanets, so I decided on the name "Stellar Nursery".
But that name has nothing to do with fractals.  After a few more
minutes thought, I arrived at the present name, which conveys
the surreal feeling of the image quite well.

The formula that created the image is number 8 in my series of
12 MandNewt formulae, which are based loosely on the Ikenaga
function, the function with apparently no author to claim it.
The parameter file renders in 9 minutes, making a download of
the GIF file of the image more efficient.  The download may be
found on the W.W.Web at:

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

and at:

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

The fractal weather today was once again ideal, with sunny skies
and a temperature of 70F (21C).  The fractal cats however spent
little time in the yard due to noisy sidewalk repair work at the
house next door.

I'm leaving now, but I shall return in 24 hours, more or less.
The backlog of work is finally beginning to shrink, so the
enlightening philosophy can't be too far off.  Until tomorrow,
take care, and don't get lost in hyperspace.


Jim Muth
[e-mail]


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

Deep_in_Hyperspace { ; time=0:08:56.89--SF5 on a P200
  reset=2001 type=formula formulafile=mandnewt.frm
  formulaname=MandNewt08 passes=1
  center-mag=0.0465338/0.0891693/27.49057/1/-82.5
  params=2.945/-3.071/3.082/1.704/-3.535/2.935
  float=y maxiter=250 inside=bof60
  logmap=yes periodicity=0
  colors=000zzzy_zx`zw`zv`zu_ztZzsYzrXzqWzpVzoUynTxm\
  SwlRvkQujPtiOshNrgMqfLpeKodJncImbHlaGk`Fj_EiZDhYCg\
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  UJIVMIVOIVPIUQIURITTITUISVISWIRYIRZIQ_IQ`IPaIPcIOd\
  IOeINfINhIMiIMjILkIJmJKlI
  }

frm:MandNewt08 {; Jim Muth
z=c=(pixel*p1):
a=z^p2+(c-1)*z-c
b=p3*z^2+c-1
z=z-1*a/b
0.000000000000000000000000000001 <= |a|
}

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

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

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) C-FOTD  15-04-01  (Deep in Hyperspace [7])
Date: 14 Apr 2001 23:00:30 -0500

[e-mail] wrote:
>
> The bits and pieces floating in the foreground.....
> .....  The download may be found on the W.W.Web at:
>      <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
> and at:
>      <http://home.swbell.net/sdboyd56/fotd/>

I have noticed over the past week or so, that the images created from
Scott's running the "X" version of FractInt does not reproduce the level
of detail with which is found in the DOS version.

I usually compare the images and there was a considerable difference
between several of them, especially on FOTD 13-04-01 "Squirt" (that is
until Scott copied over the one from my site).  But the latest image,
FOTD 15-04-01 "Deep in Hyperspace" will show some of what I am talking
about.

My question is this, why is there so much variance between the two
versions of FractInt all of a sudden??  I don't believe it was this much
of a problem several months ago.


Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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

From: [e-mail]
Subject: (fractint) C-FOTD  16-04-00  (Remotely Mandeloid [3])
Date: 16 Apr 2001 08:59:28 EDT


Classic FOTD --  April 16, 2001 (Rating 3)

Fractal visionaries and enthusiasts:

A very busy easter Sunday left little time for fractal activity.
I found time only for a quick trip to the classic Mandelbrot
set, where, not surprisingly, I found a midget.

The midget is located on the north shore of the bud located
around -1.31, in a spiral in the third valley of a sub-radical
-- a very remote location -- which is the reason I named the
image "Remotely Mandeloid".

Since I put next to no effort into the image, settling on the
first FOTD candidate that appeared, I can rate it at only a 3.
But even at a 3, it's still a midget in the M-set, almost
certainly one never before seen.

The area of the midget is one of near chaos, though a broad
color palette reveals the familiar pattern seen in the shallow
parts of valley spirals.  With a render time of over 13 minutes
on an old Pentium machine, the parameter file tries ones'
patience.  A faster way of satisfying curiosity is to download
the GIF image from Paul's web site at:

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

or from Scott's site at:

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

And this time both sites will display the same rendered image.

The fractal weather today was very pleasant most of the day,
with clear skies and a temperature of 68F (20C), which lured the
cats into the yard.  Late in the afternoon however, clouds moved
in and a chilly rain set in, cutting the cats' outdoor
activities short.

I've been thinking much philosophy lately.  I simply have no
time to write it.  But eventually the wisdom or nonsense
(depending on one's view of my ideas), will appear.  So stay
posted for more than I've had to say lately.  (We really need to
wake up that sleeping philofractal list.)

For now it's 8:30am and back to work time.  The next FOTD, a
return to the MandelbrotMix4 formula, will appear in around 16
hours.  Until then, take care, and from simple complex numbers
mighty fractals come.


Jim Muth
[e-mail]


START 20.0 PARAMETER FILE==================================

Remotely_Mandeloid { ; time=0:13:39.72--SF5 on a p200
  reset=2001 type=mandel passes=1
  center-mag=-1.31202873989414700/+0.067685741726728\
  05/5.82079e+010/1/-52.492/-0.004 params=0/0 float=y
  maxiter=100000 bailout=25 inside=0 logmap=-11450
  symmetry=none periodicity=10
  colors=000UUgUUgUUhUUiUUjUUkUUlUUmUUnVUoTUpRVqPXrO\
  YsM_tK`tIbsHcsIeoIflIgiIifIjcJk`JlYJnVJoSJpPJqMMrO\
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  Aoz9qz8sz7tzRuzQuzPuzPuzO
  }

END 20.0 PARAMETER FILE====================================

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

From: [e-mail]
Subject: (fractint) C-FOTD  17-04-01  (Fractal Celebration [5])
Date: 16 Apr 2001 22:07:42 EDT


Classic FOTD -- April 17, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

Today was a day of playing catch-up here at Fractal Central.
Luckily, the work actually is catching up, and though the end is
not quite in sight, it is lurking just around the next corner.

While catching up, I somehow managed to find time for one
fractal.  That image is the one that appears as today's FOTD.
It's only a 5-rated image, but still worth the effort of
downloading the GIF file from:

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

or from:

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

The iterated formula combines 15 parts of Z^(-1.1) with 1.5
parts of Z^(-13), and then adds 1/C.  I named the image "Fractal
Celebration" mostly in memory of my recent enjoyment of the
festivities of the religious season.

The fractal weather today featured cold 48F (9C) air and
occasional rain.  The cats tried to go outdoors, but when they
saw the conditions, their noses were back inside before their
tails were out.

And now it's time to quickly shutter down the fractal shoppe and
call it a night.  But I'll return in approximately 24 hours with
more fractal things.  Until then, take care, and if fractals had
never been discovered, I would still have faith in them.


Jim Muth
[e-mail]


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

FractalCelebration { ; time=0:13:04.22--SF5 on a p200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+3.22981160230094/+1.682986998869586/3.\
  658132e+008/1/-147.5 params=15/-1.1/1.5/-13/0/300
  float=y maxiter=1200 inside=0
  logmap=172 periodicity=10
  colors=000QX`PY_PYYPYXPYVVXT`XSdVSjVQoTPuTPySOzSMz\
  SMzPPxMSrLTmIXgFYaD`XAaS7dM6fL3iA0jF0m00o00r00s03v\
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  0z61zMFzaSzrdzzczzczzazxazvazs`zp`zm`zlazlczlczldz\
  ldzlfzlfzldziczgazdazc`z`
  }

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

From: [e-mail]
Subject: (fractint) C-FOTD  18-04-01  (Fractured Fractal [6])
Date: 17 Apr 2001 23:10:15 EDT


Classic FOTD -- April 18, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

For today's fractal wonder, we turn once again to the
MandelbrotBC formula, which works wonders with Mandeloids of
fractional orders.  I'll be using this formula often in the days
to come, but unfortunately I have lost track of the formula's
author.  I believe the author is Andrew Coppin, though I'm not
sure.  Perhaps the author will claim his authorship.

I noticed a flurry of mail on the fractal-art list when I opened
my virtual mailbox this afternoon.  The flap appears to be about
another case of fractal thievery.  It appears that someone was
caught with someone else's fractals on their web page, and might
be making money from fractals that are not theirs.

Of all the things I have to worry about, copyright infringement
is pretty far down the list.  Maybe my lack of concern is
because I feel that my fractals are not worth stealing.  After
all, they're only one-layered 256-color images of midgets, in a
world of more colors than the eye can distinguish, and multiple
layers piled on top of one another.

Actually, I simply accept that my images and discussion might be
stolen.  If they are stolen and used for profit, and I don't
know about it, I'll have nothing to get upset about.  I have no
time to worry about all the things that might be happening that
I don't know about.  If I find out about blatant profiteering
from my work, then I'll know what to do and who to do it to.

The mere act of posting something on the internet makes it
available to anyone in the world with an online computer.  And
it's nearly impossible to prevent thievery.  It's the artistic
quandary.  We want as many as possible to admire our work, yet
we don't want the admirers to admire it so much that they steal
it and make more money from our work than we make ourselves.

While I'm trying to think of a solution to this unsolvable
problem, I'll draw attention to today's FOTD, which I have named
"Fractured Fractal", and which I have rated a respectable 6.
The name arises from the fractured nature of the elements
surrounding the mis-shapen midget.

The iterated expression behind the image is Z^(2.05)+C.  I have
used the MandelbrotBC formula to draw a remote part of the
infinite fractal created by this expression, a part that is
quite chaotic and filled with almost-but-not-quite perfect
midgets.

The attached parameter file is slow -- 20 minutes slow.  A
download of the GIF image file is fast.  I leave it up to the
reader to decide which way to go.  If they decide to take the
download, the image file will be posted shortly to:

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

and to:

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

The fractal weather today was partly cloudy breezy and chilly,
with a sunshine shower of small hail just before sunset.  The
temperature of 46F (8C) permitted the fractal cats only 15
minutes out of doors, leaving them testy.

Well, I see it's time to shut down.  I'm just starting to get
things back into their familiar state of dis-organization, and I
want to do a bit more of my style of organizing before I totally
run out of steam.  Until tomorrow, take care, and exist in peace.


Jim Muth
[e-mail]


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

Fractured_Fractal  { ; time=0:20:05.34--SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotBC passes=1
  center-mag=+1.35355495637857600/-0.015397043802760\
  70/475604.2/1/-52.499 params=2.05/0/56/0 float=y
  maxiter=5000 inside=0 logmap=295 periodicity=10
  colors=000olLQfJPdJPcIOaIM`GL_GJYFIXFIVDGTDFSCDQCC\
  PAAOAAM99L97J76I74G63F64D33D63D73DA3DC3DF1DG1DJ1DL\
  1DO1DP1DS0DT0DX0DY0D`0Da0Dd0Df0Di0Dj0Dm0Do0Dr0Ds0D\
  v0Dx0Dz0Fz0Dz0Dy0Cx0Cu0As0Ap09o09l09i07g07d06c06`0\
  4_04X04V03S03P01O01L00J00G00F00C009007004003000000\
  0000000000000000100410630960A70D90GC0ID0LF0MG0PJ0S\
  L0TM0XP0YQ0`S0cV1dX1gY1i_1lY1mV1oT7rQFsOMvMTxJ`zId\
  zFizDmzArz9vz6vz4vz7rz9ozAvzCzzDzzFzzGzxIzvJzuMzsO\
  zrPvpQyoSzlTzjVziXzgYzf`zdavccoadg_f`YgXXiYVj_Tl`S\
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  fIafGadFadDadAcc9cc7ca6ca3ca1c`0c`0c_0c_0c_0cY0cY0\
  cX0dY0c_0c_0c`0ca0aa0ac0ac0ad0af0`f0`g0`g0`i0_j0_j\
  0_l0_l0_m0Yo0Yo0Yp0Yp0Yr0Xs0as0fu0jv0ov0sx1xx1zy1z\
  z3zz3zz3zz3zz4zz4zz4zz6zz6zz6zz7zz7zz7zz7zz7zz9zzA\
  zzAzzCzzDzzDzzFzzFzzGzzIz
  }

frm:MandelbrotBC = { ; formula written by ? ?
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<100
}

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

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

From: "Paul N. Lee" <[e-mail]>
Subject: (fractint) Re: C-FOTD  18-04-01  (Fractured Fractal [6])
Date: 18 Apr 2001 00:08:41 -0500

[e-mail] wrote:
>
> ....we turn once again to the MandelbrotBC formula....
> ....but unfortunately I have lost track of the formula's
> author.  I believe the author is Andrew Coppin, though
> I'm not sure.

Yes, it was Andrew that first started the conversation on "Branch Cuts"
back on April 07, 2000.  Within about three to four days, he was able to
come up with the following, as quoted from his email:

_______________________________________________________________________


I now have two working formulas:

---BEGIN
MandelbrotBC = { ; Z = Z^E + C
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<4
}

JuliaBC = { ; Z = Z^E + C
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  C=p3
  Z=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<4
}
---END

Plug these into the evolver, with real(p1) changing from 2 to 3 along
the X axis and real(p2) changine from -6 to +6 along the Y axis and you
have a real treat of an image (depending on the other parameters; I used
p3=-1).  Now, if I can just remember how to do that IsMand() stuff...


_______________________________________________________________________


Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6])
Date: 18 Apr 2001 17:56:35 -0000

Thankyou paul. Yes, it was indeed I who thought of it, and [eventually] came
up with the .frm text. It seems only fair to mention that I had help from
others on this list thought... (Wish I could remember whom, but I definitly
had help!)

Thanks.
Andrew


>From: "Paul N. Lee" <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>CC: [e-mail]
>Subject: (fractint) Re: C-FOTD  18-04-01  (Fractured Fractal [6])
>Date: Wed, 18 Apr 2001 00:08:41 -0500
>
>[e-mail] wrote:
> >
> > ....we turn once again to the MandelbrotBC formula....
> > ....but unfortunately I have lost track of the formula's
> > author.  I believe the author is Andrew Coppin, though
> > I'm not sure.
>
>Yes, it was Andrew that first started the conversation on "Branch Cuts"
>back on April 07, 2000.  Within about three to four days, he was able to
>come up with the following, as quoted from his email:
>
>_______________________________________________________________________
>
>
>I now have two working formulas:
>
>---BEGIN
>MandelbrotBC = { ; Z = Z^E + C
>   e=p1
>   p=real(p2)+PI
>   q=2*PI*trunc(p/(2*PI))
>   r=real(p2)-q
>   Z=C=Pixel:
>     Z=log(Z)
>     IF(imag(Z)>r)
>       Z=Z+flip(2*PI)
>     ENDIF
>     Z=exp(e*(Z+flip(q)))+C
>   |Z|<4
>}
>
>JuliaBC = { ; Z = Z^E + C
>   e=p1
>   p=real(p2)+PI
>   q=2*PI*trunc(p/(2*PI))
>   r=real(p2)-q
>   C=p3
>   Z=Pixel:
>     Z=log(Z)
>     IF(imag(Z)>r)
>       Z=Z+flip(2*PI)
>     ENDIF
>     Z=exp(e*(Z+flip(q)))+C
>   |Z|<4
>}
>---END
>
>Plug these into the evolver, with real(p1) changing from 2 to 3 along
>the X axis and real(p2) changine from -6 to +6 along the Y axis and you
>have a real treat of an image (depending on the other parameters; I used
>p3=-1).  Now, if I can just remember how to do that IsMand() stuff...
>
>
>_______________________________________________________________________
>
>
>Sincerely,
>P.N.L.
>--------------------------------------------------------------
>http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go
>
>--------------------------------------------------------------
>Thanks for using Fractint, The Fractals and Fractint Discussion List
>Post Message:   [e-mail]
>Get Commands:   [e-mail] "help"
>Administrator:  [e-mail]
>Unsubscribe:    [e-mail] "unsubscribe fractint"

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From: "Zorba the Hutt" <[e-mail]>
Subject: (fractint) The specter of schoolwork, and really really big fractals
Date: 18 Apr 2001 16:33:04 -0400


Finally I managed to beat down the looming demon of Far Too Much Homework
That You've Been Putting Off, You Slacker, And Why Are We Paying For You To
Go To College Anyway If All You Do Is Play Computer Games? I Mean, It's Not
Like The Ones You Play Are Educational Or Anything, and managed to eke out
some time for myself, which I spent updating my Really Big Fractals page.
Today (this week? this month? this year?), I provide for you all those
Fractal-Swarm-inspired images that Sylvie Gallet posted a while back. Yes,
all of them. All 9. Done in beautiful 1600x1280, and do they ever look good.

And, sigh, I really should have asked *before* this, but if I ask, wait for
an answer, and *then* post 'em, I'll never get around to it. Sylvie, do you
mind if I put those up? They're all credited to you and everything :) I just
wanted to provide them for people who might not have the CPU power (or
desire) to render them on their own. If you say you do mind, I'll take 'em
off immediately, or if there's modifications you want me to make or
anything.

Anyway, the website is http://www.geocities.com/zorbathut - may you find a
new desktop wallpaper . . .

-Zorba


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From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) The specter of schoolwork, and really really big fractals
Date: 18 Apr 2001 15:53:44 -0500

Zorba the Hutt wrote:

> ...which I spent updating my Really Big Fractals page.

Cool!  Wonderful!!  Delightful!!!

Thanks!

p.s.
Unexpected Fractal's link is ge-broken.  ;-(

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

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

From: Sylvie Gallet <[e-mail]>
Subject: (fractint) The specter of schoolwork, and really really big
Date: 18 Apr 2001 17:43:56 -0400

Hi Zorba,

>> And, sigh, I really should have asked *before* this, but if I ask, wai=
t
>> for an answer, and *then* post 'em, I'll never get around to it. Sylvi=
e,
>> do you mind if I put those up? They're all credited to you and
>> everything :) I just wanted to provide them for people who might not
>> have the CPU power (or desire) to render them on their own. If you say=

>> you do mind, I'll take 'em off immediately, or if there's modification=
s
>> you want me to make or anything.

  I am not favorable to making high resolution images available on the we=
b,
and I would definitely have preferred you to ask before doing it.  Since =
I
have a slow internet connection, I haven't downloaded any of them, but th=
e
size of some of the PNGs make me think that anti-aliasing made some of th=
em
lose their particular texture (at least two of them: 18 and 27).
  I'll make an exception and let you keep them but please, change the
copyright notice so that it makes clear people are not allowed to print
them, put them on a web site, etc.

  Best regards,

        - Sylvie

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

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6])
Date: 19 Apr 2001 00:16:05 -0500

Andrew Coppin wrote:
>
> Thankyou paul.

Just thought credit should be mentioned where due.    :-)

>
> It seems only fair to mention that I had
> help from others on this list thought...
> (Wish I could remember whom, but I definitly
> had help!)

You first started discussing the "Branch Cuts" on Fri, 07 Apr 2000.  And
some of the individuals involved with that topic on the List were as
follows:

    Barry N. Merenoff (Collin Merenoff)
    Morgan L. Owens
    Tim Wegner
    Jim Muth
    Kenneth Childress
    Damien M. Jones

This went on until Tue, 18 Apr 2000.  I am sure that the archives will
show the details of who did what.

P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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From: [e-mail]
Subject: (fractint) C-FOTD  19-04-01  (Pi in the Sky [6])
Date: 19 Apr 2001 10:51:09 EDT


Classic FOTD -- April 19, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

It's 9:30am and the FOTD is once again late.  But what's new
about that?  I offer excuse number three -- that things were too
busy here at Fractal Central Auxiliary to get the discussion
written at the regular time.  Maybe I need to get a day or two
ahead in my FOTD's.  That way I won't be late every time I have
a busy day.  Of course, the problem with this solution is that
I have little time to get ahead.

Today's image is a picture of a midget in the Z^(pi)+C fractal,
as rendered by Andrew's MandelbrotBC formula.  After a moment's
consideration, I rated the image a 6 and named it "Pi in the
Sky".  At 4-1/2 minutes on an aging Pentium, it's not too
difficult an image to render from the parameter file.

But for those who would rather not render, the GIF image is, or
soon will be, posted to the WWW at Paul Lee's site at:

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

and at Scott's site at:

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

The intrepid fractal cats had a rough day, as very un-springlike
cold enveloped the area.  The temperature of 42F (5.5C) was
entirely too chilly for their sensitive ears, forcing them to
sulk indoors all afternoon, while blaming me for the outside
conditions.  I finally eased their moodiness by treating them to
a meal of tuna fish.

When I checked my virtual mailbox first thing this morning, I
found a very long letter telling me how to get rich quick.  The
letter is one of those pyramid chain letters with a MLM twist,
which claims one can get rich by sending money to other people.
Having my name and address so widespread on the net, I have been
receiving different versions of this same letter for years.  I
usually delete it at once, but for some strange reason I decided
this morning to skim through it.

The letter begins by telling me that it is the letter I've been
hearing about so much in the news lately.  Now, I keep up pretty
well with the news, but I have no recollection of ever hearing
or reading about such a letter.  I suppose that a reader who
might take the letter seriously is supposed to think that the
letter was indeed in the news, but that he missed it.

Basically, the letter claims that one can become wealthy by
doing nothing but sending money to others and having them send
money back to you.  If this were true, everyone on earth should
be a USA-style millionaire by this time, though I have no idea
where the extra money could come from or how inflation could be
kept under control once everyone was rich.  (Of course, we could
blame the inflation on the political party in power.)

In my experience, one gets rich by starting out doing work for
others and receiving money from them in return, not by starting
by sending money to others.  In all my years of earning money
working at real jobs, I have never started on a job by sending
money to someone else in return for the privilege of working on
their job.  But apparently, from the frequency with which I
receive this same letter, many are still out there who fail to
understand this simple fact of life.

Well, I seem to have gotten off the fractal topic.  My intent
was to discuss the current state of the Fractint program and the
possibilities for its future development.  This will be my topic
when the next FOTD appears in only 12 hours or so.

It's now time to start the day's rush.  Until next time, take
care, and I'm sorry Jonathan Roarke.


Jim Muth
[e-mail]


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

Pi_in_the_Sky      { ; time=0:04:37.66--SF5 on a p200
  reset=2001 type=formula formulafile=branchct.frm
  formulaname=MandelbrotBC passes=1
  center-mag=-0.9197872859930445/-0.1300422309794571\
  /5.421884e+007/1/-25 params=3.14159265358979/0/32/0
  float=y maxiter=2400 inside=0
  logmap=103 periodicity=10
  colors=000zszzszztzzuzzvyzwvzxszyqzynyzkyziszfnyej\
  sceob_j_XeZRaYNXXIQSDKQ8EN37K03J2DO3KS4UY6aa8geAog\
  BvkDznHwjKsfOocSj_XfX_bUcYQgUMjQJaSISVHKXHIZFH_FFa\
  EEbEDeDBfD8gD7iB6kB4mA3nA2oA8q8Fq7Kr7Rr6Xr6Yn7Yj8Z\
  fAZbA_ZB_VDaRDaNEbJFbHFfJHiMImOJoRJsSKvVMzYMz_NzbO\
  zcOziUwmZqqckuifyn_zsVzyQzzayjmmSybBwbDvbEubHsbIrb\
  JqbM72u60w60yD0zI3zN7zSBzZFzcJziNznRzsUzuYwuaqueju\
  icukZsg_sc_s__rXarUarQaqMbqIbqFboBco7co3co0ccBXUMO\
  JXI8fA0o36n4Dn6Jm6Qm7Xm7So6Qq4Ns3Ju2Hv0Ey0Bz07z04z\
  02z00z00z02v03q04k36f47a78X8ARBBMDDHFEBHF6JH0KI0NI\
  0OH0NH0MH0KH0JF3IF6HF8FFBEEEDEHBEJAEM8DO7DR6DU4DX4\
  DY0vZ2r_0oa0mb0ic0fe0cf0_g0Yi0Vj0Rk0Om0Mn0Io0Fq00r\
  z0sw0us0vn0wj2ye3za4zX4zS6zN7zJ8zEAzABz4Dz00zv0zk2\
  za4zR7zHAz6vzMqzJmzHgzEczBZz8rz0vz0yz0zz0vz0qz6kzB\
  fzIbzNYzSSzZNzcJziEzo8zu3zz0zz4zzAzzFzyJzwOzuUzsYz\
  qbzogzmmzkqzivzgzzezzzzzz
  }


frm:MandelbrotBC  { ; Formula by Andrew Coppin
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<100
}

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

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

From: [e-mail]
Subject: (fractint) C-FOTD  19-04-01  (Pi in the Sky [6])
Date: 19 Apr 2001 10:51:09 EDT


Classic FOTD -- April 19, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

It's 9:30am and the FOTD is once again late.  But what's new
about that?  I offer excuse number three -- that things were too
busy here at Fractal Central Auxiliary to get the discussion
written at the regular time.  Maybe I need to get a day or two
ahead in my FOTD's.  That way I won't be late every time I have
a busy day.  Of course, the problem with this solution is that
I have little time to get ahead.

Today's image is a picture of a midget in the Z^(pi)+C fractal,
as rendered by Andrew's MandelbrotBC formula.  After a moment's
consideration, I rated the image a 6 and named it "Pi in the
Sky".  At 4-1/2 minutes on an aging Pentium, it's not too
difficult an image to render from the parameter file.

But for those who would rather not render, the GIF image is, or
soon will be, posted to the WWW at Paul Lee's site at:

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

and at Scott's site at:

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

The intrepid fractal cats had a rough day, as very un-springlike
cold enveloped the area.  The temperature of 42F (5.5C) was
entirely too chilly for their sensitive ears, forcing them to
sulk indoors all afternoon, while blaming me for the outside
conditions.  I finally eased their moodiness by treating them to
a meal of tuna fish.

When I checked my virtual mailbox first thing this morning, I
found a very long letter telling me how to get rich quick.  The
letter is one of those pyramid chain letters with a MLM twist,
which claims one can get rich by sending money to other people.
Having my name and address so widespread on the net, I have been
receiving different versions of this same letter for years.  I
usually delete it at once, but for some strange reason I decided
this morning to skim through it.

The letter begins by telling me that it is the letter I've been
hearing about so much in the news lately.  Now, I keep up pretty
well with the news, but I have no recollection of ever hearing
or reading about such a letter.  I suppose that a reader who
might take the letter seriously is supposed to think that the
letter was indeed in the news, but that he missed it.

Basically, the letter claims that one can become wealthy by
doing nothing but sending money to others and having them send
money back to you.  If this were true, everyone on earth should
be a USA-style millionaire by this time, though I have no idea
where the extra money could come from or how inflation could be
kept under control once everyone was rich.  (Of course, we could
blame the inflation on the political party in power.)

In my experience, one gets rich by starting out doing work for
others and receiving money from them in return, not by starting
by sending money to others.  In all my years of earning money
working at real jobs, I have never started on a job by sending
money to someone else in return for the privilege of working on
their job.  But apparently, from the frequency with which I
receive this same letter, many are still out there who fail to
understand this simple fact of life.

Well, I seem to have gotten off the fractal topic.  My intent
was to discuss the current state of the Fractint program and the
possibilities for its future development.  This will be my topic
when the next FOTD appears in only 12 hours or so.

It's now time to start the day's rush.  Until next time, take
care, and I'm sorry Jonathan Roarke.


Jim Muth
[e-mail]


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

Pi_in_the_Sky      { ; time=0:04:37.66--SF5 on a p200
  reset=2001 type=formula formulafile=branchct.frm
  formulaname=MandelbrotBC passes=1
  center-mag=-0.9197872859930445/-0.1300422309794571\
  /5.421884e+007/1/-25 params=3.14159265358979/0/32/0
  float=y maxiter=2400 inside=0
  logmap=103 periodicity=10
  colors=000zszzszztzzuzzvyzwvzxszyqzynyzkyziszfnyej\
  sceob_j_XeZRaYNXXIQSDKQ8EN37K03J2DO3KS4UY6aa8geAog\
  BvkDznHwjKsfOocSj_XfX_bUcYQgUMjQJaSISVHKXHIZFH_FFa\
  EEbEDeDBfD8gD7iB6kB4mA3nA2oA8q8Fq7Kr7Rr6Xr6Yn7Yj8Z\
  fAZbA_ZB_VDaRDaNEbJFbHFfJHiMImOJoRJsSKvVMzYMz_NzbO\
  zcOziUwmZqqckuifyn_zsVzyQzzayjmmSybBwbDvbEubHsbIrb\
  JqbM72u60w60yD0zI3zN7zSBzZFzcJziNznRzsUzuYwuaqueju\
  icukZsg_sc_s__rXarUarQaqMbqIbqFboBco7co3co0ccBXUMO\
  JXI8fA0o36n4Dn6Jm6Qm7Xm7So6Qq4Ns3Ju2Hv0Ey0Bz07z04z\
  02z00z00z02v03q04k36f47a78X8ARBBMDDHFEBHF6JH0KI0NI\
  0OH0NH0MH0KH0JF3IF6HF8FFBEEEDEHBEJAEM8DO7DR6DU4DX4\
  DY0vZ2r_0oa0mb0ic0fe0cf0_g0Yi0Vj0Rk0Om0Mn0Io0Fq00r\
  z0sw0us0vn0wj2ye3za4zX4zS6zN7zJ8zEAzABz4Dz00zv0zk2\
  za4zR7zHAz6vzMqzJmzHgzEczBZz8rz0vz0yz0zz0vz0qz6kzB\
  fzIbzNYzSSzZNzcJziEzo8zu3zz0zz4zzAzzFzyJzwOzuUzsYz\
  qbzogzmmzkqzivzgzzezzzzzz
  }


frm:MandelbrotBC  { ; Formula by Andrew Coppin
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<100
}

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

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

From: Sylvie Gallet <[e-mail]>
Subject: (fractint) The specter of schoolwork, and really really big
Date: 19 Apr 2001 18:22:45 -0400

Hi Zorba,

  All of the images are different from their Fractint version, and in lot=
s
of them, UF replaced the nice texture with banding so, I'd like you to
remove them or redo them with Fractint (maybe in a standard 1600x1200
format).

  Cheers,

        - Sylvie

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

From: "Zorba the Hutt" <[e-mail]>
Subject: Re: (fractint) The specter of schoolwork, and really really big  fractals
Date: 19 Apr 2001 21:30:27 -0400


Done. I don't know why they're different - I remember I checked some of
them, and they were the same, or at least I thought they were. Perhaps it's
a fractint difference also. Anyway, they're gone now - really sorry about
the annoyance ^^;;

-Zorba

----- Original Message -----
Sent: Thursday, April 19, 2001 6:22 PM
fractals


Hi Zorba,

  All of the images are different from their Fractint version, and in lots
of them, UF replaced the nice texture with banding so, I'd like you to
remove them or redo them with Fractint (maybe in a standard 1600x1200
format).

  Cheers,

        - Sylvie

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

From: [e-mail]
Subject: (fractint) C-FOTD  20-04-01  (Fairy Gardens [6])
Date: 19 Apr 2001 22:35:37 EDT


Classic FOTD -- April 20, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Do fairies, elves, gnomes, sylphs, etc. exist?  Of course they
do.  Every culture on earth is rich with stories and legends of
fairies.  But since fairies, just like dragons, do indeed exist,
are they then real?  The answer to that question depends on the
meaning one gives to the word 'real'.  Not yet being in my deep
philosophical mode, I'll not at this time state my opinion of
the meaning of the word 'real', but if fairies do not dwell in
the intricacies of the garden-like scene of today's fractal,
what then does?

The formula that drew the image, TowerMinExp04a, is one I rarely
use.  It is but one in a remote series of 26 such formulae,
which pile up the exponents of Z into exponent towers.  The four
functions in today's formula merely add variety.

I named the image "Fairy Garden" when a lawn fairy flew past the
window while I was trying to think of a name.  The image is a
bit too busy and fragmented for a very high rating, but the 6,
which is a little above average, is satisfactory.  As long as my
FOTD's rate above a 5, I'm satisfied with them.

I'll not divulge at this time whether I believe in magical
things such as fairies, and yes even dragons.  I will state
however that I believe in some things that many consider weird
or downright kooky.  My beliefs are not limited by the
discoveries of science, nor by common sense or reason, though I
certainly do occasionally use these attributes.

The parameter file of today's image, which is attached to the
bottom of this letter, renders in 2-1/2 minutes.  For extra
convenience, the GIF image file is or soon will be posted to the
W.W.Web at the URL:

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

and at:

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

I read recently that the venerable Fractint fractal generating
program is over the hill, on its last lap, abandoned by all but
a few backward fractalists in favor of more advanced fractal
generating programs with glittery advanced features such as
true-color, multiple layers, transforms, etc.

Well, one would never guess it here at Fractal Central, where
the old warhorse program continues to do what it was designed to
do -- find fractals.  It's not that I have no other programs --
three other fractal generating programs are on my drive.  But I
rarely use them.  Other than true-color, which is Fractint's
greatest lack, I feel that the other features of the state-of-
the-art programs are leading us from the basic idea of fractals.
We are drifting from a "look what I found" attitude to a "look
Ma, I'm an artist" attitude.  When the fractalist does more work
on an image than the numbers, perhaps the resulting image should
be called something like computer art, rather than fractal art.

I guess I have never been able to make the switch from admiring
the things the numbers have done to admiring the things I have
done.  Maybe my reluctance to embrace the newer programs is due
to the fact that I had been working with graphic programs such
as Photoshop long before the same image manipulating features
appeared included in fractal programs, and I therefore failed to
be impressed with such features.  (Of course, the features are
far less expensive when part of the actual fractal program.)

I also find myself amused at the extreme concern on the fractal-
art list about copyright infringement.  Fractals are fun --
they're philosophical, mystical and scientific at the same time.
They're not a means of becoming wealthy.  Do we really think
that someone is going to steal our fractals and get rich from
our efforts?  If anyone were planning to do this, they certainly
would not post their stolen goods on the Web for the whole world
to see.

I started the FOTD almost exactly 4 years ago for the fun of it.
I continue the FOTD 4 years later for the fun of it.  If it were
not fun, I would have grown bored with the effort years ago and
stopped posting.  But I have no intention of ending the FOTD in
the foreseeable future, because I know that finding fractals
will be as much fun in 2005 as it is in 2001 and was in 1997.

The fractal weather today was a big improvement over yesterday.
A warm sun brought the temperature up to 61F (16C), and brought
out the fractal cats into the yard for an afternoon's romp in
the new grass.

The rush is easing somewhat, but there's still lots to be done.
Between other stuff I'll find time for another FOTD in 24 hours.
Until then, take care, and watch out for the fairies as you
trim your newly greened lawn.


Jim Muth
[e-mail]


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

Fairy_Gardens      { ; time=0:02:30.77--SF5 on a P200
  reset=2001 type=formula formulafile=tower.frm
  formulaname=TowerMinExp04a function=sqrt/sinh/acos\
  h/tanh passes=1 center-mag=1.39458/-1.16573e-015/3\
  .617023/1.0776/90 params=3.91/0/3.75/0/-3.215/0
  float=y maxiter=250 inside=bof60
  logmap=yes periodicity=10
  colors=000zzzVLRD9Q00N00P00R00T01V13X34Y46_67a89c9\
  AeBCfCDhEFjFGlHInJJoKLqMMsNOuPPwQQxPPuOOrNNoMMlLLj\
  KKgJJdIIaII_HHXGGUFFREEODDMCCJBBGAADAAB7A95A82A70A\
  50A40A30900A20B40C50D70E90FA0GC0HE1IF2JH3KJ4LK5MM6\
  NO7OP8PR9QTARUBSWCTYDTZJWYPYYV`Y`bXfeXkgXheWecVcbU\
  ``UY_TWYSTXRQVROUQLSPIQPGPODNNAMM8KM5JL2IK0IK1KO2N\
  S3QW4T_5Wb6Zf7aj8dn7fp8gq8fq8dq8bq9_q9Xq9Vq9TqARqA\
  PqAMqAKqBIqBGqBEqBBqC9qC7qC5qD1sC3qC5pC7oC9nCBmCCl\
  CEkCGjCIhCKgCLfCNeCPdCRcCTbDT`CUaBVaAWaAXa9Ya8Za8Z\
  a7_b6`b5ab5bb4cb3db3db2ec1fc0gc0hc0ic0jc0jc0eb0`a0\
  X`0S_0N_0JZ0EY09X07X05X26Y36Y47Z67Z77_88_A8`B9`C9`\
  E9aFAaGAbHBbJBcKBcLCcNCdODdPDeRDeSEfTEfTEfTEfTFcTF\
  `TFYTFVTFSTEPTEMTEJTDGTDETDFUCFTCGSCGQBGPBHOBHNBHP\
  AHQAHR9HS9HT9HU8HW8HX8HY7HZ7H_7H`6Ha6Hc6Hd5He5Hf5H\
  g4Hh4Hi4Hh1Kg0Mh0Ng0Og0Pg0Qg3Rg5Sg7TgAUgCUfEVfGWfJ\
  XfLYfNZfQ_fS`fU`eWagXVjYT
  }

frm:TowerMinExp04a {; Jim Muth
z=pixel, c=p2+(p3*pixel):
z=z^fn1(z^fn2(-z^fn3(z^fn4(-z+p1))))+c,
|z| <= 100
}

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

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

From: erdal mazlum <[e-mail]>
Subject: Re: (fractint) C-FOTD  19-04-01  (Pi in the Sky [6])
Date: 19 Apr 2001 22:28:51 -0700 (PDT)

hi jim,

your comment about the letter is pretty cool, and FOTD
ofcourse... have a nice day!

erdal.

--- [e-mail] wrote:
>
> Classic FOTD -- April 19, 2001 (Rating 6)
>
> Fractal visionaries and enthusiasts:
>
> It's 9:30am and the FOTD is once again late.  But
> what's new
> about that?  I offer excuse number three -- that
> things were too
> busy here at Fractal Central Auxiliary to get the
> discussion
> written at the regular time.  Maybe I need to get a
> day or two
> ahead in my FOTD's.  That way I won't be late every
> time I have
> a busy day.  Of course, the problem with this
> solution is that
> I have little time to get ahead.
>
> Today's image is a picture of a midget in the
> Z^(pi)+C fractal,
> as rendered by Andrew's MandelbrotBC formula.  After
> a moment's
> consideration, I rated the image a 6 and named it
> "Pi in the
> Sky".  At 4-1/2 minutes on an aging Pentium, it's
> not too
> difficult an image to render from the parameter
> file.
>
> But for those who would rather not render, the GIF
> image is, or
> soon will be, posted to the WWW at Paul Lee's site
> at:
>
>
> <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
>
> and at Scott's site at:
>
>           <http://home.swbell.net/sdboyd56/fotd/>
>
> The intrepid fractal cats had a rough day, as very
> un-springlike
> cold enveloped the area.  The temperature of 42F
> (5.5C) was
> entirely too chilly for their sensitive ears,
> forcing them to
> sulk indoors all afternoon, while blaming me for the
> outside
> conditions.  I finally eased their moodiness by
> treating them to
> a meal of tuna fish.
>
> When I checked my virtual mailbox first thing this
> morning, I
> found a very long letter telling me how to get rich
> quick.  The
> letter is one of those pyramid chain letters with a
> MLM twist,
> which claims one can get rich by sending money to
> other people.
> Having my name and address so widespread on the net,
> I have been
> receiving different versions of this same letter for
> years.  I
> usually delete it at once, but for some strange
> reason I decided
> this morning to skim through it.
>
> The letter begins by telling me that it is the
> letter I've been
> hearing about so much in the news lately.  Now, I
> keep up pretty
> well with the news, but I have no recollection of
> ever hearing
> or reading about such a letter.  I suppose that a
> reader who
> might take the letter seriously is supposed to think
> that the
> letter was indeed in the news, but that he missed
> it.
>
> Basically, the letter claims that one can become
> wealthy by
> doing nothing but sending money to others and having
> them send
> money back to you.  If this were true, everyone on
> earth should
> be a USA-style millionaire by this time, though I
> have no idea
> where the extra money could come from or how
> inflation could be
> kept under control once everyone was rich.  (Of
> course, we could
> blame the inflation on the political party in
> power.)
>
> In my experience, one gets rich by starting out
> doing work for
> others and receiving money from them in return, not
> by starting
> by sending money to others.  In all my years of
> earning money
> working at real jobs, I have never started on a job
> by sending
> money to someone else in return for the privilege of
> working on
> their job.  But apparently, from the frequency with
> which I
> receive this same letter, many are still out there
> who fail to
> understand this simple fact of life.
>
> Well, I seem to have gotten off the fractal topic.
> My intent
> was to discuss the current state of the Fractint
> program and the
> possibilities for its future development.  This will
> be my topic
> when the next FOTD appears in only 12 hours or so.
>
> It's now time to start the day's rush.  Until next
> time, take
> care, and I'm sorry Jonathan Roarke.
>
>
> Jim Muth
> [e-mail]
>
>
> START 20.0 PAR-FORMULA
> FILE================================
>
> Pi_in_the_Sky      { ; time=0:04:37.66--SF5 on a
> p200
>   reset=2001 type=formula formulafile=branchct.frm
>   formulaname=MandelbrotBC passes=1
>
> center-mag=-0.9197872859930445/-0.1300422309794571\
>   /5.421884e+007/1/-25
> params=3.14159265358979/0/32/0
>   float=y maxiter=2400 inside=0
>   logmap=103 periodicity=10
>
> colors=000zszzszztzzuzzvyzwvzxszyqzynyzkyziszfnyej\
>
> sceob_j_XeZRaYNXXIQSDKQ8EN37K03J2DO3KS4UY6aa8geAog\
>
> BvkDznHwjKsfOocSj_XfX_bUcYQgUMjQJaSISVHKXHIZFH_FFa\
>
> EEbEDeDBfD8gD7iB6kB4mA3nA2oA8q8Fq7Kr7Rr6Xr6Yn7Yj8Z\
>
> fAZbA_ZB_VDaRDaNEbJFbHFfJHiMImOJoRJsSKvVMzYMz_NzbO\
>
> zcOziUwmZqqckuifyn_zsVzyQzzayjmmSybBwbDvbEubHsbIrb\
>
> JqbM72u60w60yD0zI3zN7zSBzZFzcJziNznRzsUzuYwuaqueju\
>
> icukZsg_sc_s__rXarUarQaqMbqIbqFboBco7co3co0ccBXUMO\
>
> JXI8fA0o36n4Dn6Jm6Qm7Xm7So6Qq4Ns3Ju2Hv0Ey0Bz07z04z\
>
> 02z00z00z02v03q04k36f47a78X8ARBBMDDHFEBHF6JH0KI0NI\
>
> 0OH0NH0MH0KH0JF3IF6HF8FFBEEEDEHBEJAEM8DO7DR6DU4DX4\
>
> DY0vZ2r_0oa0mb0ic0fe0cf0_g0Yi0Vj0Rk0Om0Mn0Io0Fq00r\
>
> z0sw0us0vn0wj2ye3za4zX4zS6zN7zJ8zEAzABz4Dz00zv0zk2\
>
> za4zR7zHAz6vzMqzJmzHgzEczBZz8rz0vz0yz0zz0vz0qz6kzB\
>
> fzIbzNYzSSzZNzcJziEzo8zu3zz0zz4zzAzzFzyJzwOzuUzsYz\
>   qbzogzmmzkqzivzgzzezzzzzz
>   }
>
>
> frm:MandelbrotBC  { ; Formula by Andrew Coppin
>   e=p1
>   p=real(p2)+PI
>   q=2*PI*trunc(p/(2*PI))
>   r=real(p2)-q
>   Z=C=Pixel:
>     Z=log(Z)
>     IF(imag(Z)>r)
>       Z=Z+flip(2*PI)
>     ENDIF
>     Z=exp(e*(Z+flip(q)))+C
>   |Z|<100
> }
>
> END 20.0 PAR-FORMULA
> FILE==================================
>
>
> Thanks for using Fractint, The Fractals and Fractint
> Discussion List
> Post Message:   [e-mail]
> Get Commands:   [e-mail] "help"
> Administrator:  [e-mail]
>
=== message truncated ===


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

From: [e-mail]
Subject: (fractint) C-FOTD  21-04-01  (Oriental Lanterns [7])
Date: 20 Apr 2001 22:24:43 EDT


Classic FOTD -- April 21, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

The day grew far busier far sooner than I had expected, and then
the fairies returned to their fairy nests.  Nothing remained for
me to do but tackle the work, finish it as quickly as possible,
and see what kind of a fractal I could scrounge up from the
depths of infinity.

I did my scrounging in the fractal created by the unassuming
formula 1.25Z^(-20)+15Z^(-1.23)+(1/C), which consists of an
eastward-facing Mandeloid with many spurious bays and valleys.
The scene of today's midget is at the tip of the stem shooting
out from a rudimentary bud on the unusually smooth north shore
of the largest bay.

I named the final picture "Oriental Lanterns" when I noticed
that the orangish square features vaguely resemble those festive
decorative lanterns.  Because of the unusually brilliant color
palette, I rated the image at a 7.  Whether I'll still rate it a
7 next week at this time remains to be seen.

The attached parameter file renders in just over 4 minutes on a
somewhat tired old Pentium 200mhz machine.  It will render
significantly faster on a fresh young PentiumIV machine.  For
those who fail to enjoy the effort of running parameter files,
the finished GIF image file is available on the Web at:

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

and at:

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

The fractal weather today turned cloudy, but the temperature
reached 69F (20.5C), allowing the fractal cats a good
afternoon's romp in the balmy outdoors.  When a neighborhood
stray intruded, the dynamic duo almost got into a fight with the
intruder, but common sense prevailed, and the duo managed to
stay out of trouble all afternoon.

My urge to philosophize is rising, but so is the pile of work to
be done.  And only two days ago I thought the rush was near an
end.  One of these weeks I'll manage to get caught up, but this
week isn't the one.  So until next time, which will come in 24
hours plus or minus 2 hours, take care, and relish your
fractals, but don't add onions, or you'll be in a pickle.


Jim Muth
[e-mail]


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

Oriental_Lanterns  { ; time=0:04:20.78--SF5 on a p200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.381370015722773/+0.65420816277382/6.\
  862245e+007/1/112.5 params=1.25/-20/15/-1.23/0/800
  float=y maxiter=1300 inside=0
  logmap=54 periodicity=10
  colors=00010010010010010S100100100100100100C0EH0SE\
  0e90g40j10m00p04r0Cu0Mx0Uz0ez0mz0xz0zz0zz0zz0pz0bz\
  4SzEHzM4zY0zg0zr0zz0zz0zu0ze0u00190K00100000000000\
  0000000600E40PP0Y_0ej0mu0up0zm0zj0ze0zb4z_CzYKz_Hz\
  _Ez_Cz_9z_6z_4z_1z_0z_0z_0z_0z_0z_0z_0rb0gb0_b1Pe6\
  EeC6eH0eM0gS0gY0gb0gg0jj0mm0pp0pr0rr0uu0xx0xz0zz0z\
  z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz6pgSbMjP4zC0z00z10z\
  40z60z90zC0zE0zH0zK0zM0xP0uS0rU0pY0m_0jb0ge0eg0bj0\
  _m0Yp0Ur0Su0Px0Px0Uz0_z0bz1gz9mzHpzMuzUzzbzzjzzrzz\
  zzzzzzzzzzzzzzzzzzzzzzzrzzrzzrzzrrxrjpr_jrSerU_rYU\
  r_PrbKreErg9rj4rm0rp0rr0ru0ru0rm0re0r_0rS0rM0rE0u9\
  0z10z00mS0ju0jz0mz0mz0pz0pz0rz4rz9uzEuzKuzPxzUxz_z\
  zezzjzzpzzuzzzzzzzzzzzzzzzzzzzxzzxzzzzuzzuzzxzzzzz\
  zzxzzuzzpzzjzzgzzbzz_zzgzzmzzrzuzzbzzMzz4zz0zz0zz0\
  zz0zz0zz0rz9jzMbz_UzmUzpYzpYzrYzu_zu_zx_zxbzzbzzez\
  zezzgzzjzzmzzpzzrzzrzzrzz
  }

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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  22-04-01  (Minibrot with Aura [7])
Date: 21 Apr 2001 22:18:20 -0400 (EDT)


Classic FOTD -- April 22, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

The hazy blue glow surrounding today's tiny Minibrot reminds me
of the mystical aura that is sometimes claimed to surround the
human body, and is said to be especially brilliant around the
heads of saints and holy people.  This resemblance inspired the
name "Minibrot with Aura".  Since I'm not yet in my mystical or
philosophical mode, I'll not speculate as to whether such an
ethereal glow actually exists around the human body, and can
actually be seen by those with extrasensory vision, but if no
such thing exists, a lot of hallucinating people or liars are
out there.

One needs no psychic ability to see the aura in today's image.
It was produced by the formula Z^(-1.5)+0.0001*(Z^(-150))+(1/C).
The sickle-shaped elements are typical features in the images
that result when different portions of high and low powers of Z
are combined.

After much indecision, I settled on a rating of 7 for today's
image, with its soft colors and sharp contrasts.  The parameter
file renders in a little over 10 minutes on a tired but still
functional Pentium 200mhz machine.  The GIF image file downloads
in a fraction of that time.  For those who choose the download,
the file may be found on the Web, posted to Paul's site at:

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

and to Scott's site at:

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

But give Paul and Scott an hour or so to post the image.

The fractal weather today here at Fractal Central was sunny in
the morning and much warmer, but it became cloudy in the
afternoon, with a few drops of rain.  The temperature of 75F
(24C) had the fractal cats in the yard most all day, twitching
their ears whenever a drop of rain hit them.

As for me, I see that it's time to shut down the fractal shoppe
and call it a night.  If I can find a trashy enough old sci-fi
movie to watch, the day will be complete.  If not, I'll watch a
Dr. Who show.  Until tomorrow or Monday morning, take care, and
just because you can't see something doesn't mean that it's not
there.


Jim Muth
[e-mail]


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

Minibrot_with_Aura { ; time=0:10:18.08--SF5 on a p200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+3.22503694025169900/+0.092233759045437\
  49/3.857046e+010/1/64.992/-0.026
  params=1/-1.5/0.0001/-150/0/300 float=y
  maxiter=1500 inside=0 logmap=-220 periodicity=10
  colors=000A0FA0FA0FA0FA0FA1FA2FA3EA4EA5DA6DA7CA8CA\
  9BAAAABEACAAD6AE2AF3AI4AL5AN6AQ7AT8AV9PYAU`BUbCceD\
  hhEmjFq`poZlnYilXekVfiUghTigSkiRmjRokRqlRsmRunRwoR\
  yqRzrRzsRzqRzoRzmRzmRzmUznXzo_zpbzqdzJH8JRCGaFCmJ9\
  vMCsPEqSHnVJlXMi_OgbRddTbgW_jYYldWbjUToSJuQ9zO0zM4\
  vL7rKAnIEjHHfGKbEO_DRXCUUAYR9`O8cL6gI5jF4mC3pF7oHA\
  oKEoMHnPKnROnURmWVmZYm``mYZkWYjUXhRWgPVeNUdLTbIRaG\
  Q_EPZBOX9NW7MU5LT7OS9RSAURCXRE_RFbQHeQJhQKkPMnPOqP\
  PtORwOSzOUzNVzNWzNYzMZzM_zMazLbzLczL`zRYzXVzaSzgPz\
  lMzrJzwNzsQzpTzlWziZzfazbdz_gzXjzTmzQpzNozQnzSmzUm\
  zXlzZkz`jzcjzeizghzjgzlgznfzqezsezubzs`zqZzoXznVzl\
  TzjRziPzgNzeLzcJzbHz`FzZDzYEz_FzaGzcHzdIzfJzhKzjLz\
  kMzmNzoOzqOzrRzqUzqWzqZzq`zqczqezphzpjzpmzpozprzpt\
  zpIzXWzSizOwzKszNozPkzShzUdzW`zZYz`UzbQzeNzgJzjFzl\
  Czn8zq4zs1zu5zr8zoCzmFzjJzgMzeQzbTz_XzY_zVczSfzQhz\
  RjzTkzUmzWozXpzZrz_sz`6ze
  }

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

From: [e-mail]
Subject: (fractint) C-FOTD  23-04-01  (Swirls [4])
Date: 23 Apr 2001 10:36:06 EDT


Classic FOTD -- April 23, 2001 (Rating 4)

Fractal visionaries and enthusiasts:

Today's fractal rates a 4, though I feel that it has a higher
rating in it, which I could develop if I had time to tweak the
colors some more.  But the FOTD is already as late as it has
ever been and I've got a busy day ahead of me, so the image,
which I have named "Swirls", will have to stand as it is.

The parameter file renders in 2 minutes, making running it as
convenient as downloading the completed GIF image.  Those who
would rather download the image will find the file at:

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

and at:

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

allowing Paul and Scott time to post the file of course.

The fractal weather today, (Sunday the 22nd), was like
mid-summer, with hot sun and a temperature of 86F (30C), which
lured not only the fractal cats, but me also, into the outdoors.
This explains today's lateness.

That's it for today.  Until next time, take care, and be happy.


Jim Muth
[e-mail]


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

Swirls             { ; time=0:01:50.78--SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+4.830750037059846/-2.891827230043619/1\
  126735/1/-35 params=0.01/-100/100/-1.1/-0.95/300
  float=y maxiter=400 inside=0
  logmap=16 periodicity=10
  colors=0000DR7Mc8FQ6GQAHTEIVIJYMJ_QKbULdXLf`MidNkh\
  OnlOppPstQuwQwuNrtLmsJhqHdpF_oDVmBRl9Mk7Hj5Di4Gh4J\
  h4Mg4Pg3Rf3Uf3Xe3_e2ad2dd2gc2jc2lbBhbJdbRaaZYafVan\
  RavO_oLZhIXaFWWCXXGXXJXYMYYPYYTYZWZZZZ_aZ_e__h_`k_\
  `n_`qijirtass`sr`tq`tp`up_uo_un_vm_vl_wlZwkZxjZxiZ\
  xiZtfXpdVlbTh_RdYQ`WOXTMTRKPPJLMHHKFDID9GCbg5dd6fa\
  7gZ7iW8jU8lR9mO9oLApJArGBsDBuACv8CpEEjJGdOIZTJUYLO\
  bNIgOClQ6qS1vT3uR4uQ5uP6tN8tM9tLAsJBsIDsHErFFrEGrD\
  JsCLsBNsAPs9Rs9Ts8Wt7Yt6_t6at5ct4et3gt3bp8YmDUmHPm\
  MLmRGmVCm_7md3mh6mg9mgCmfFmfImeLmeOmeRmdUndXoc_pcb\
  qc`rcZrcfr`mrYgsUbtRXuOSvLMwIHxFByC6z91z64z86z98zB\
  BzCDzEFzFIzHKzIMzKPzLRzNTzOWzQYzR_zTazUYzPUzKTzLTz\
  LTzMTzMTzNTzNTzNTzOTzOTzPTzPTzPTzQTzQTzRTzRTzRTzST\
  zSTzTTzTTzTUzUUzUVzUVzUVzUWzUWzUWzVXzVXzVXzVYzVYzV\
  YzVWzUVzTUzSSzSRzRQzQOzQNzPMzOKzOJzNIzMHzLFzLEzKDz\
  JBzJAzI9zH9zs9zv9zx9zz8zr
  }

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

From: [e-mail]
Subject: (fractint) C-FOTD  24-04-01  (Windmills of Chaos [6])
Date: 23 Apr 2001 21:52:34 EDT


Classic FOTD -- April 24, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

What kind of fractal does the formula Z^0+C or 1+C create?  It
creates no fractal at all, just an empty circle.  What type of
fractal then does Z^(0.05)+C create?  In this case the empty
circle is lopsided, with no evidence of the typical fractal
chaos.  But take Z^2, subtract Z^0.05 from it, and then add C,
and an interesting fractal does appear.

I'll not try to describe the indescribable figure, but the
oversized thing can be seen by entering the parameters
-1, 0.05, 1, 2, 0, 0 into the M-Mix4 formula and letting it
iterate.  Today's midget lies in a prominent valley on the north
side of this fractal.

I named the image "Windmills of Chaos" when I noticed that the
four open spirals toward the corners vaguely resemble windmill
blades.  And of course the chaos is there as always, lying in
vaguely organized form all through the picture.

With a render time of just under 5 minutes, running the
parameter file is a bit annoying.  A better choice is to give
Paul and Scott a chance to post the GIF file of the image to
their web sites at:

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

and at:

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

and download the image from there.

The fractal weather today was very summer-like.  In fact the
temperature of 90F (32C) felt a bit too warm.  The fractal cats
enjoyed the warmth however, as they stretched to their full
cat-lengths on the porch most of the afternoon.

As for me, I'm about finished for the day.  It's been another
busy one, but I'll be here again tomorrow, with more fractal
goodies.  Until then, take care, and be at ease.


Jim Muth
[e-mail]


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

Windmills_of_Chaos { ; time=0:04:45.45--SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.64915135165492830/-0.619948053295606\
  6/1320520/1/-134.999 params=-1/0.05/1/2/0/0 float=y
  maxiter=500 inside=0 logmap=78 periodicity=10
  colors=000d1gd1ge2hf3ig4jh5ki6li7lh8if8dd8`b9W`9SZ\
  ANXAJVAETBARB5PB1V9F_7Td9fi6tjNokSklXgk_`hZZdXV`UR\
  WQMSNIOJEJG9FC5B91CB2CC2DD3DE3EF3EG4FH4FJ5GK5GL5HM\
  6HN6KO7PP7UQ7ZOAcNChLEmPHrUJvZLzaNwZOrUPmPQhNRcPSa\
  QSXTYTWbPZgKalGdqCgvDhsDhpDimDijDigEjdEjaEkZEkWEmT\
  FrQFwNFzKFwHFsFHoMIkSJjZKidLhkMgqNgwPisQjoRlkSmhUo\
  dVp`WrXXsUVoXTkZSgaQccO_fNWhLSkJOmIKpGGrECuD9wCCuC\
  EtBHrBJqBMpAOnARmATl9Wj9Yi9_hI`PO`9QbFSdLUeRVgWXia\
  Zjg`lmamrdkpfjohimjgllfjneimbol`tkZyi_uh`qg`mfajeb\
  fcbbbc_acW`dS_ePYeLXfHWgEVgAUh6Th3WaCZWL`PTcJafCjh\
  6rf8seAsdCscEsaGs`Is_KsZMsXOsWQsVSsUTsXVpZWm`YjbZh\
  d_efabhb`jcYleVnfSpgQriNtjKvkIicUXWeKOpQJhWFaaBVf7\
  Od8Rb8T`9VZ9XXA_VAaTAcRBePBhNCjLClKCnIFhHHcGKZFMTE\
  PODRJCUDBW8AY3FZ2J_2N`2Ra2Vb2Zc1be1fg1ji1nk1jm8goE\
  dqKarQZsWWtaTugQvmNwsKxyNyuPzqRznTzjVzfXzc_z`azXcz\
  TezPgzLizIdzG_zFqzKpzKpzK
  }

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

From: "Edward Barton" <[e-mail]>
Subject: Re: (fractint) C-FOTD
Date: 24 Apr 2001 11:34:08 +0200

Jim Muth,
Throughout the short time I have been part of this discussion list, I have
noticed that in your FOTDs, you continually state that a faster rendering
speeds are to be searched for, even if that means getting a new computer.
I don't mean to sound like I am criticising you, but I ask you to remember
what the waiting time was when fractals were discovered, as well as the
quality of the resulting image, and remember that the more interesting
fractal images are those which are hidden deep inside the pattern of a
fractal, and so take significantly longer to render.

Edward Barton

BTW: Despite the tradition of waiting for a week for a fractal, I do so wish
that I didn't have to.  I use my Pentium 133 for other things as well, and
during the rendering, I can do nothing.
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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) Re: C-FOTD
Date: 24 Apr 2001 09:31:04 -0400 (EDT)

At 11:34 AM 4/24/01 +0200, you wrote:

>Jim Muth,
>Throughout the short time I have been part of this discussion list, I have
>noticed that in your FOTDs, you continually state that a faster rendering
>speeds are to be searched for, even if that means getting a new computer.

When one is working with fractals, it is obvious that CPU speed is
important.  I do not need to state the fact.  When I do state it, I am
merely repeating the obvious.  I have no memory of stating that one
should go out and spend money they cannot afford on a new computer, though
I suppose it could be implied in my words.

>I don't mean to sound like I am criticising you,

Your post reads more like a letter of frustration than one of criticism.

>but I ask you to remember
>what the waiting time was when fractals were discovered, as well as the
>quality of the resulting image,

I was there, and I remember well the overnight waits to see a fractal
that we now see in a few minutes.

>and remember that the more interesting
>fractal images are those which are hidden deep inside the pattern of a
>fractal, and so take significantly longer to render.

True!  This is where I search for my FOTD's.


>Edward Barton
>
>BTW: Despite the tradition of waiting for a week for a fractal, I do so wish
>that I didn't have to.  I use my Pentium 133 for other things as well, and
>during the rendering, I can do nothing.

Yes, sometimes the wait does become annoying.

FOTD coming in 15 hours.

Jim Muth


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

From: O Bd <[e-mail]>
Subject: (fractint) Targa Output
Date: 24 Apr 2001 13:39:04 -0400 (EDT)

Hi! I've been trying to get a Targa output file but the file seems to be
created in the wrong format. Instead of an image I get one that's sort of
looking like a slinky!!!

Is there a way to fix this?

Or am I using the wrong version? Im using 19.2

Any help will be appreciated.

Thanks

O Bd.

The No.1 Utah Jazz fan in England


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

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Targa Output
Date: 24 Apr 2001 14:16:26 -0500

O Bd wrote:
>
> Hi! I've been trying to get a Targa output
> file but the file seems to be created in
> the wrong format.  Instead of an image I get
> one that's sort of looking like a slinky!!!
> Is there a way to fix this?

Are you trying to do 3-D transforms??  And are you doing any Overlays??
Have you set any of the Light Source Parameters??

>
> Or am I using the wrong version?  Im using 19.2

The most current version being developed is 20.1.07 and may be acquired
from the Development Team's web site:

     http://www.fractint.org/

But the latest released version of Fractint is 20.0 and is available
from the Spanky Fractal Database location:

     http://spanky.triumf.ca/www/fractint/fractint.html

>
> Any help will be appreciated.

What program are you using to open the Targa file that was created??


Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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

From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) Targa Output
Date: 24 Apr 2001 20:07:33 -0500

> But the latest released version of Fractint is 20.0 and is available
> from the Spanky Fractal Database location:

I believe you will find that the Targa output was broken in version 20.0.
It's been fixed in the developer's version.

Jonathan



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

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Targa Output
Date: 24 Apr 2001 23:11:51 -0500

Jonathan Osuch wrote:
>
> I believe you will find that the Targa
> output was broken in version 20.0.
> It's been fixed in the developer's version.
>

Yes, I knew some Patches had been applied, just did not go through all
of the notes to see exactly what version/release/mod-level the repairs
were made at.

Hopefully "O Bd" will choose to upgrade from the 19.2 level that is
being used by him/her, and use the 20.1.07 level.  And maybe do some
further testing for you guys within the area of Targa files.

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6])
Date: 25 Apr 2001 11:51:43 -0000

>From: "Paul N. Lee" <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6])
>Date: Thu, 19 Apr 2001 00:16:05 -0500
>
>Andrew Coppin wrote:
> >
> > Thankyou paul.
>
>Just thought credit should be mentioned where due.    :-)
>
> >
> > It seems only fair to mention that I had
> > help from others on this list thought...
> > (Wish I could remember whom, but I definitly
> > had help!)
>
>You first started discussing the "Branch Cuts" on Fri, 07 Apr 2000.  And
>some of the individuals involved with that topic on the List were as
>follows:
>
>     Barry N. Merenoff (Collin Merenoff)
>     Morgan L. Owens
>     Tim Wegner
>     Jim Muth
>     Kenneth Childress
>     Damien M. Jones
>
>This went on until Tue, 18 Apr 2000.  I am sure that the archives will
>show the details of who did what.

Just spend an hour trolling through the FractInt archives. Gee! I really
must do this more often!!!

The archives show that Morgan provided his usuall deep insights, and Jim
produced a couple of top-notch FotDs with the resulting formula, but the
formula itself basically came from Mr. Merenoff (with a type-error
correction form Kenneth).

Basically, I posted a formula that was partially broken, thus:
>From: "Andrew Coppin" <[e-mail]>
>Subject: (fractint) Branch Cuts
>Date: 10 Apr 2000 10:22:48 GMT
>
>So log(Z) is a cork screw, and you have to take a 360 degree slice of >it.
>Hmmm... This formula (I think) varies the slice taken, but only by >another
>360 degrees. If k is below -3 then you get what the formula parser
> >normally does. If you now raise k, you get a nice branch cut shift...
>until you >reach +3, and thereafter there is no further change. Any ideas
>how to >correct this?
>
>--BEGIN
>comment
>{
>  Andrew Orphi Coppin, 10 May 2000AD
>}
>
>BrotBC = { ; Z^2.5 + C
>           ; real(p1) = phase shift.
>
>  p = real(p1)
>  Z = C = Pixel:
>    Z = log(Z)
>    IF(imag(Z) > p) Z = Z + flip(2*PI) ENDIF
>    Z = exp(2.5*Z) + C
>  |Z| < 4
>}
>--END
Later that day, the following message appeared:
>From: Barry N Merenoff <[e-mail]>
>Subject: (fractint) Branch Cuts
>Date: 10 Apr 2000 08:31:09 -0400
>
>Andrew, try this:
>
>p=3Dreal(p1)+PI
>q=3D2*PI*floor(p/(2*PI))
>r=3Dreal(p1)-q
>Z=3DC=3DPixel:
>Z=3Dlog(Z)
>IF(imag(Z)>p) Z=3DZ+flip(2*PI) ENDIF
>Z=3Dexp(2.5*(Z+flip(q)))+C
>|Z|<4
>}
>
>Note: I don't know if Fractint has a floor function, but it should >have
>something equivalent to it.
>
>Sincerely,
>        Collin Merenoff
As said, the formula was corrected (the "IF(imag(Z)>p)" should actually be
"IF(imag(z)>r)"). And then I posted the message Paul quoted, which is
basically the same but with different variable names. (But still, Jim posted
half a dozen FotDs with my name on 'em. And why not? I *thought* of it!)

Interestingly, the archive also shows that this is the thread that
eventually lead to the addition of extra .FRM parameters in a developer's
patch (can't remember which number tho).

Also during this period there was some cool descussion on why the Mandelbrot
set pops up everywhere. And I asked if fractint's parser could have an arg()
function added. (It never happened!) There was some talk from Tim about
making movable branch-cuts an integral feature of fractint (which also never
happened).

Thanks.
Andrew.

PS. Hey Morgan... What the hell _are_ "sheets in the Riemann surface"?

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

From: [e-mail]
Subject: (fractint) C-FOTD  25-04-01  (OOOF! [3])
Date: 25 Apr 2001 09:20:35 EDT


Classic FOTD -- April 25, 2001 (Rating 3)

Fractal visionaries and enthusiasts:

Yes, I'm late again today with the FOTD.  It's getting to be a
habit.  My excuse is the same old one which needs no repetition.

Today's fractal image, which looks like a rotten melon with a
face drawn on it, being squashed, fairly cries "OOOF!".  So this
is what I named it.  Normally, I avoid images that resemble
funny faces, but today's picture is so ridiculous that I had no
choice but to declare it FOTD for April 25.  I displayed my
disgust with comedy fractals by rating the image a lowly 3.

The formula behind the image is Z^2+C -- the Mandelbrot formula.
The mouth of the squashed melon-head is actually a Mandel-midget
on the tip of the longest northwest filament shooting out from
the fifth bud along the negative tail of the M-set.  The midget
is so distorted because it has been sliced in a different
direction through the 4-dimensional Julibrot, which is the
assemblage of all Julia sets and all perturbed Mandelbrot sets.

Though the Mandelbrot formula drew the image, the image is not
part of any Mandelbrot set.  Nor is it part of any Julia set.
It is kind of a hybrid, with both Mandelbrot and Julia
characteristics, and a few entirely new characteristics, such as
the stretching effect, thrown in for extra measure.

I seem to have forgotten the Julibrot and the fourth dimension
since becoming involved with the M-Mix4 formula and its
limitless variety of midgets.  But perhaps it's time to get back
to basics as well as the unknown, and nothing is more unknown
than the fourth dimension.

Since the FOTD is so,late, the parameter file is the fastest in
many months, rendering in less than a minute on a 200mhz
Pentium.  It will take longer than that to reach the GIF image,
which is posted to:

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

and to:

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

The fractal weather was very warm again today.  The cats,
comfort seekers that they are, took full advantage of the 86F
(30C) temperature, by spending the entire afternoon lounging in
the yard.

That's it for today.  It's time to rev up the fractal shoppe and
get busy with other things.  Until next time, take care, and
life is never so good that it can't get better.


Jim Muth
[e-mail]


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

OOOF               { ; time=0:00:54.58--SF5 on a p200
  reset=2001 type=formula formulafile=multirot.frm
  formulaname=multirot-xz-yw passes=b
  center-mag=-0.00000000002107355/-0.000000000029447\
  31/8.638531e+009/14.687/-180/35.229
  params=45/45/-1.4041038040019/0.00422258114480\
  08/-1.4041038040019/0.0042225811448008 float=y
  maxiter=600 inside=255 logmap=147 periodicity=10
  colors=000Eg`JgbOgdSgfXgh`gjeglignfijckg`ldYnaVpYS\
  qVPsSMtPVrJbpD_rFXsGUtIRvJOwLMxMKpQIiTGaXFV_DNbBGf\
  98i81lYQN`UQbYTdaWgdZihakldmogelgZjgShgLfgEdg7bg0`\
  gFcMTf091V74X67Z5A`4Db3Gd2Jf1MgJaYDaP7aG1a7TF6UO9U\
  WBUdEUlGUtIQjTM`bIRmFIwNLqVNlbQfjSaqUXpSVpRTpPRpOP\
  pNOjLLeJI`HFWFCQD9LB6G93B7195Y9ak8Vj7Pj6Ji6DiCKcHQ\
  YNWTSaNXgIfbVoYgxUskdr_nrcgkfaeiW_lPUoJOrDIu7CkCQa\
  GcbLebQfcVhcZidckdhlemneqofiofaogUogMogFoaLmWQkRVj\
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  ZPM9ZEAaFAcFBeGBgGCfEDeDEeBFdAGd8Hc7Ic6HZ7HV7GR76h\
  l4ilGcdRYYaSQlMJwHCgQL000
  }

frm:multirot-XZ-YW {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p2, c=e*imag(pixel)+p3:
z=sqr(z)+c,
|z| <= 36  }

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

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

From: [e-mail]
Subject: (fractint) C-FOTD  26-04-01  (Baubles [6])
Date: 26 Apr 2001 00:40:06 EDT


Classic FOTD -- April 26, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Today's fractal formula takes Z^(-11.5), adds 4 times as much
Z^(-1.15), then adds the reciprocal of C.  Adding 1/C instead of
the usual C turns a fractal inside-out.  The Mandelbrot set,
instead of appearing as a lake in an infinite continent, appears
as an island in an infinite lake.

But fractals created by negative powers of Z normally appear as
islands in infinite lakes, so turning these fractals inside-out
changes them into lakes surrounded by infinite continents.
Combining two different negative powers of Z in an inside-out
fractal and initializing Z to a critical value produces a
fractal with quadratic midgets.  This is the type of fractal
that is the parent of today's scene.

This parent fractal is a huge thing filled with circular
features resembling zippers, with a size exceeding even the full
outzoom capability of the Fractint program.  Today's midget lies
in an area rich with these zipper-circles.

I named the image "Baubles".  The name came to mind after I
spent 1/2 hour with the image on the screen, doing other tasks
and thinking of nothing better.  I rated the image an above-
average 6.

The parameter file renders in under 6 minutes, which is slow
enough to make a download of the GIF image file the better
choice.  That download will ba available within the hour at:

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

and at:

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

The fractal weather today here at Fractal central was cloudy and
much cooler than yesterday.  The temperature of 52F (11C) was
just cool enough to keep the fractal cats confined to their
windows, where they sit to watch the outside when they can't
actually be out there.

It's now time to call it a night. . . It's a night! . . . Until
next time, which, within an accuracy of 67 percent, will arrive
in 24 hours, take care, and life as well as cats are better with
fractals.


Jim Muth
[e-mail]


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

Baubles            { ; time=0:05:53.56--SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=456.568/-70.8747/1.353355/1/132.499
  params=1/-11.5/4/-1.15/0/300 float=y maxiter=1200
  inside=0 logmap=55 periodicity=0
  colors=00020K30N60S80V90YA0bD0eE0kG0oH0tN6vSCwYHyb\
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  KjzJjzHkzEmzDmzAoz9oz6pz5
  }

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

From: "Paul N. Lee" <[e-mail]>
Subject: (fractint) Web Based Archives
Date: 26 Apr 2001 14:31:24 -0500

Greetings,

This information is for those that do not know how to use the Usenet
Newsgroups or may have problems using them.  Since some of the other web
based Usenet Newsgroup Archives are either no longer available or not
functioning (such as NailNews), another one has become available:  ETIN
Technologies

Chronologically relevant searching of messages.  Browsing of text and
binary newsgroups.  Posting available.  Free, Public, Complete, and
Anonymous.

Text messages are archived and retained permanently.  Binaries are
retained 10 to 20 days.

Here are the direct URLs for fractal related NGs:

A.B.P.F.
    http://www.etin.com/?folder=alt%2Ebinaries%2Epictures%2Efractals
A.F.P.
    http://www.etin.com/?folder=alt%2Efractals%2Epictures
A.F.
    http://www.etin.com/?folder=alt%2Efractals
S.F.
    http://www.etin.com/?folder=sci%2Efractals
A.B.F-A.
    (this one is not available)


Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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

From: "Rupert Millard" <[e-mail]>
Subject: (fractint) Sinusoidal gradient maker
Date: 27 Apr 2001 07:40:42 -0000

Hello everybody!

It seems that Polynomial gradient maker was a bit boring for you colourful
lot - So I've made Sinusoidal gradient maker.

This program is the same as polynomial gradient maker, except that it puts
sine waves in the red, green and blue channels, instead of polynomials.

You can see the page and donwload the program at:
http://www.geocities.com/kangarupert/sinu_grad_maker.html

From,

Rupert
_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.


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

From: "Thierry B." <[e-mail]>
Subject: Re: (fractint) Sinusoidal gradient maker
Date: 27 Apr 2001 08:03:58 +0000

Rupert Millard wrote:
>
>
> This program is the same as polynomial gradient maker, except that it puts
> sine waves in the red, green and blue channels, instead of polynomials.
>
> You can see the page and donwload the program at:
> http://www.geocities.com/kangarupert/sinu_grad_maker.html
>

    Same thing, but in fortran with a web interface
    http://la.buvette.org/fractales/palette.html

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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  27-04-01  (Object Around Midget [5])
Date: 27 Apr 2001 08:29:52 -0400 (EDT)


Classic FOTD -- April 27, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

As I pondered today's image, I was reminded of nothing in
particular.  The decorations around the midget do resemble
several computer animations I have seen.  And they sometimes
impressed me as the tentacles of some fantastic monster lurking
on the sea floor.  But all these impressions are so vague that I
named the image with the very simple and non-descriptive name,
"Object Around Midget".

The MandelbrotBC formula is responsible for the image, which is
part of the infinite Z^(sqrt2)+C fractal.  This fractal is my
most frequently explored with an exponent of Z between 1 and 2
because in this fractal the midgets are easier to find than in
most fractals lying in this exponent range.

Confining explorations to the fractal created by only one
exponent between 1 and 2 is not limiting, since when drawn by
the MandelbrotBC formula, the fractal is infinite in surface
extent as well as depth and variety.

On my 200mhz Pentium the image takes almost 3/4 of an hour to
render.  It will therefore be an hour or so before it is
available on the Web at:

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

and at:

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

The fractal weather today (actually yesterday, April 26) was
just about average for this location at this time of year, with
warm sun and a temperature of 65F (18C).  These conditions had
the fractal cats in the yard most of the afternoon, acting like
kittens.  Such behavior is most undignified for cats of their
venerable age of 9 years.

As for me, it's past 8:15am, and I've got a busy day before me.
So until next time, take care, and enjoy the flowers of Spring
of the leaves of Autumn.


Jim Muth
[e-mail]


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

ObjectAroundMidget { ; time=0:43:53.22--SF5 on a P200
  reset=2001 type=formula formulafile=branchct.frm
  formulaname=MandelbrotBC passes=1 center-mag=-0.15\
  578257934389980/+1.535940899307265/4.223478e+008/1\
  /12.5 params=1.414213562373/0/0/0 float=y
  maxiter=6000 inside=0 logmap=-1150 periodicity=10
  colors=000SaZOfUHiRDnM8qJ2vE0yB0x80rZ0mU0hP0cM1`H4\
  YE8ZADd6Hi2Mp0Pt0Op0Ml0Ki0Jf0Ha0GZ0EW0DS0BP0MfOXvn\
  RkiK`dEP`AEX44S00O00K00J00H00G00E04D08B1DA2G82K74P\
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  4KRARUEXXKc`PicWpf`vdkzcvzazz`zzXzzWzzSzzRzzOzzMxz\
  KuxHqvGnsDkqBhnAflRWhhKdnAhu0ky0nx0ix0fx4ax7ZxBUxG\
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  4sp1xp0zp0zp0zzK`zOZzRZzUXzXXz`WzcWxfUviUslUppSnsS\
  kvRhyRfzPczPazPazUZzSXzRWzPSzORzMPzMOzKKzJJyHHyGGy\
  GRlJ``MiOPsBSz0Wz0Zp6hWMpBcx0uz0qz0py0nx2mu4msAmnG\
  mkMmhRmdXmacmXhmUnmRumOymKcmnJmzMmzOmzPmzSmzUmzWmz\
  Zmz`mzamzdnzfqzhuzixz0zD0zE4zGBzHJzHRzJZzKfzMnzMqz\
  PuzSxzUzzXzzZzzazzcXz0az0dz0hz0kz0nz0qz0uz0xz0sz0n\
  z0iz0dz0az0Xz0Sz0Oz0Jz0Gz0Bz07z02z00z01zG1zX2zn2zz\
  1zv0zl0zc0zW0zM0zD0z40z00z06z2Bz6Hz8OzBUzEazHhzKnz\
  OuzRzzUzzX7z0Bz4hziczfZza
  }

frm:MandelbrotBC   { ; Inspired by Andrew Coppin
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<100
}

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


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

From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6])
Date: 28 Apr 2001 17:07:15 +1200

At 23:51 25/04/2001, Andrew Coppin wrote:

>PS. Hey Morgan... What the hell _are_ "sheets in the Riemann surface"?

One of the hassles involved with many functions is that they are many-
valued (and hence, strictly speaking, not functions at all). Even the
humble square root is guilty of this - z^(1/2) usually has two values.
And as for log(z), or arcsin(z)...

What would be nice is if there were some way of turning these many-
valued functions into single-valued functions. Bermhard Riemann came up
with a geometrical stunt that did just this by replacing the complex
plane with a suitable generalisation (mathematicians just loooove to
generalise things).

His idea was to separate each value of the function by placing it on a
separate "sheet", which on its own looks like an entire complex plane.
For example, if the values of z^(1/2) for a given z were a_z and -a_z,
then a_z would go on one sheet and -a_z would go on another. Then you
could take one sheet and say that the values on it are _the_ values of
the function. To drop down into real arithmetic for a second, this is
analogous to saying that _the_ values of the square root function are
the nonnegative ones.

A function may require more than one sheet. The log(z) function, as
immortalised in the MandelbrotBC formula, has an infinite number of
sheets, since log(z) usually produces an infinite number of values for a
given z (if w is one such value, then so are w+2pi, w+4pi, w+6pi...,
among others).

But of course there is more to it than just slapping down extra layers
on the complex plane like tracing paper. For a start, there are often
points where the sheets merge (such as the point z=0 for the function
z^(1/2)). Also significant is the question of where the function moves
from one sheet to another. After all, if this is supposed to be a nice
continuous function, you don't want to introduce a nasty discontinuous
artefact by suddenly jumping from one sheet to another.

So you want to stitch all these sheets together in some way into a
single continuous surface, and it is exactly this that Riemann
described.

Let's take the log function as an example, mainly because that way the
MandelbrotBC formula is available to play with. The log function goes
blecchh at z=0, so we'll stick with nonzero complex numbers. As I said,
if log(z)=w, then log(z)=w+2npi, for any integer n. So w and w+2pi,
w+4pi, w-2pi, w-4pi, w+158pi, ... are all on separate sheets (which we
can index by n, if we are so inclined). The surface is sort of helical.
We start on the ground floor (n=0), and we can walk around the origin
until we've made a complete circle, whereupon we find ourselves on the
first floor (n=1). Another complete circle and we're on the second floor
(n=2). Going the other way from the ground floor we find ourselves on
the first basement level (n=-1), then the second basement (n=-2), and so
on in that direction.

But where precisely do we change floors? What the Riemann surface shows
is that such a question is more a matter of convention than anything to
do with the property of the log() function itself. We could draw a line
out along the positive real axis (on each sheet) and say "Here is where
we change sheets", but we could just as easily draw it along the negative
real axis, or either imaginary axis or anything in between. Wherever you
place it, you can extract a sheet out of the surface that covers the
entire complex plane (except of course for the origin) by cutting along
your chosen axis on any sheet and an adjacent sheet.

It should be pretty obvious that these lines I've been talking about are
the branch cuts. Conventionally, the log() function is cut along the
negative real axis. So is the square root function, for that matter,
while the arctangent function is cut along the negative imaginary axis
starting at 0-i and extending downwards towards -infinity.

To provide a bit of a summary, I'll describe the Riemann surface of the
z^(1/2) function. Since this function is at most two-valued (the only
exception being of course z=0, which has one value), the Riemann surface
is made by stitching two sheets together. Laying them atop each other,
we see that they have to actually meet at z=0 (because they have the
same value there). Now, what do the two values of z^(1/2) have in
common? They're negations of each other, of course, which on the complex
plane is equivalent to rotation about the origin of 180 degrees (or
more appropriately, pi radians). So if we were to start at one value and
walk around the origin and arrive back at our starting point, we'd
find ourselves on the other sheet. Another walk around and we really
will be back where we started. We can manage this by cutting the sheets
as follows. Starting at the origin, we cut a slit out to infinity
(conventionally as I mentioned above), join the lower edge of the lower
sheet to the upper edge of the upper sheet, and the upper edge of the
lower sheet to the lower edge of the upper sheet. Don't worry if this
violates your three-dimensional imagery - it's not a stunt that can be
pulled off in 3D without the optical illusion of the two sheets
apparently interpenetrating. And there's the surface. The (illusory)
crossover line along the axis can be waved and wiggled about all over
the complex plane - as long as one end remains rooted at the origin -
and every such wave and wiggle can be used to define a branch cut for
separating the surface back into sheets again.

Its precisely the positioning of the branch cut for the log() function
that is explored by the MandelbrotBC formula. If you build an animation
where you steadily increase the branch cut parameter, you can almost see
the spiral staircase effect as you climb higher and higher.

See also:http://library.wolfram.com/examples/riemannsurface/

Morgan L. Owens
"I _had_ to ask..."


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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  28-04-01  (Semi-Chaos [4])
Date: 28 Apr 2001 08:39:43 -0400 (EDT)


Classic FOTD -- April 28, 2001 (Rating 4)

Fractal visionaries and enthusiasts:

Today's image is of a type that I rather enjoy exploring --
chaotic, yet filled with just enough patches of order and
theme-sections to make it interesting.  I named the image
"Semi-Chaos" mostly as a description.

The midget in today's image is of the order 1.618..., and, for a
change, is not at the dead center of the frame.  Actually, the
midget is an added attraction, the main interest lying in the
fragmentary elements scattered throughout the scene.

Since I find only minor artistic merit in the image, and only a
modicum of math interest, I could rate it no higher than a 4.
But it's still worth a look, if only to see what a Z^1.618+C
Mandeloid midget looks like.

The MandelbrotBC formula, which is rather a committee project,
once again did the work of rendering the image.  The render was
completed in 13-1/2 minutes on a 200mhz Pentium.

The GIF image, already rendered, will soon be available on the
Web at:

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

and at:

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

The all-important fractal weather was quite pleasant today.  The
cats approved of the warm sunshine and temperature of 77F (25C),
and showed their approval by sleeping on the porch most of the
afternoon.

While searching this evening for today's fractal, my mind
drifted into heavy philosophical speculation, and I pondered
about gravity and dark matter.  The problem is that the outer
parts of the galaxies are rotating too fast to be caused by the
gravity created by the visible matter of the galaxies.  To
account for this discrepancy, astronomers have hypothesized that
the galaxies are filled with large amounts of undetectable
material they have named dark matter, and this unseen material
is causing the excess gravitational acceleration.  But this
explanation is not satisfactory, since if the matter cannot be
detected, it will be most difficult if not impossible to confirm
its existence.

There may be another possible way of accounting for the excess
rotational velocity, and this is to assume that, like so many
other natural phenomena, the Newtonian law of gravity is valid
only within a limited range, which includes our scale of
experience in everyday life, as well as the solar system.  But
perhaps, beyond this scale, gravity is quantized, and there is a
minimum possible gravitational acceleration.

If this is the case, then the outer parts of the galaxies would
be subject to this minimum acceleration, which, being greater
than the Newtonian laws of gravity would produce, would cause
the excess velocities observed in the outer parts of the
galaxies.  I'll not speculate on how this might affect the
ultimate fate of the universe.

Since this alternate explanation is so obvious, it must have
already been thought of by many astronomers, and probably
discarded because it contains a fatal flaw.  But it did supply
me an hour or so of diversion while working on a dull routine
job.  Perhaps I'll continue this line of speculation on the
philofractal list in the next FOTD.

I now see that it's post time, so until tomorrow, take care, and
could the big bang turn into a big bust?


Jim Muth
[e-mail]


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

Semi-Chaos         { ; time=0:13:37.34--SF5 on a P200
  reset=2001 type=formula formulafile=semikaos.par
  formulaname=MandelbrotBC passes=1
  center-mag=-0.501937/-0.59952/582.5136/1/49.999
  params=1.618034/0/122/0 float=y maxiter=30000
  inside=0 logmap=145 periodicity=10
  colors=00050U4DU2DU0FU0FU00U05U0AU0Fc5KmCPpKVnR_kY\
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  u`9qY7pS5lP4kM2gH0eD0bA0`70Y20W00S00P00R00R00R00R0\
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  00S00S00S00S00S20S20S20S22S42S42V44V44V44V55V55V55\
  V57V77V77V79V79V99V9AV9AV9AW44V57V79V9AV9CSADSCFSD\
  HSDISFKRHNRHPRIRRKSRMVPMWPNYPP_PR`PRbNSeNVgNYiN`kN\
  dlMgnMipMkqMls_qseuu`quYnuWguN`wP`wP_wP_wR_wRYyRYy\
  SYySWySWyVWzVVzVVzWVzWSzWSzYSzYRzYRz_Rz_Pz_Pz`Pz`P\
  z`NzbNzbNzbMzdMzdMzdKzeKzeKzeIzgIzgIzgHziHziHziFzk\
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  sHzuIyuKuuMqwNpwPlwRiySeyVbyW`zYYz_Vz`Rz_Kz`MzbNzb\
  PzdRzeSzeVzgVziWziYzk_zk`zlbzndzndzpezqgzqizskzslz\
  unzwnzwpzyqzzszzuzzwzzwzzszzpzzlzzkzzizzgzzgzzgzzg\
  zzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzzgzz\
  gzzgzzgzzgzzgzzgzzgzzgzzg
  }

frm:MandelbrotBC   { ; Formula by Andrew Coppin
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<100
}

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


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

From: Jim Muth <[e-mail]>
Subject: (fractint) Re: C-FOTD 18-04-01
Date: 28 Apr 2001 08:45:26 -0400 (EDT)

At 05:07 PM 4/28/01 +1200, Morgan Owens wrote:
>At 23:51 25/04/2001, Andrew Coppin wrote:
>
>>PS. Hey Morgan... What the hell _are_ "sheets in the Riemann surface"?

<long reply from Morgan explaining branch cuts snipped>

Great explanation Morgan!  This is the first time I've actually
understood exactly what the branch-cut discontinuities are.

Jim M.


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

From: DeBow Freed <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6])
Date: 28 Apr 2001 08:17:02 -0500

Cheers to Morgan from the peanut gallery, too.

"Morgan L. Owens" wrote:

> At 23:51 25/04/2001, Andrew Coppin wrote:
>
> >PS. Hey Morgan... What the hell _are_ "sheets in the Riemann surface"?
>
> One of the hassles involved with many functions is that they are many-
> valued (and hence, strictly speaking, not functions at all). Even the
> humble square root is guilty of this - z^(1/2) usually has two values.
> And as for log(z), or arcsin(z)...
>
> What would be nice is if there were some way of turning these many-
> valued functions into single-valued functions. Bermhard Riemann came up
> with a geometrical stunt that did just this by replacing the complex
> plane with a suitable generalisation (mathematicians just loooove to
> generalise things).
>
> His idea was to separate each value of the function by placing it on a
> separate "sheet", which on its own looks like an entire complex plane.
> For example, if the values of z^(1/2) for a given z were a_z and -a_z,
> then a_z would go on one sheet and -a_z would go on another. Then you
> could take one sheet and say that the values on it are _the_ values of
> the function. To drop down into real arithmetic for a second, this is
> analogous to saying that _the_ values of the square root function are
> the nonnegative ones.
>
> A function may require more than one sheet. The log(z) function, as
> immortalised in the MandelbrotBC formula, has an infinite number of
> sheets, since log(z) usually produces an infinite number of values for a
> given z (if w is one such value, then so are w+2pi, w+4pi, w+6pi...,
> among others).
>
> But of course there is more to it than just slapping down extra layers
> on the complex plane like tracing paper. For a start, there are often
> points where the sheets merge (such as the point z=0 for the function
> z^(1/2)). Also significant is the question of where the function moves
> from one sheet to another. After all, if this is supposed to be a nice
> continuous function, you don't want to introduce a nasty discontinuous
> artefact by suddenly jumping from one sheet to another.
>
> So you want to stitch all these sheets together in some way into a
> single continuous surface, and it is exactly this that Riemann
> described.
>
> Let's take the log function as an example, mainly because that way the
> MandelbrotBC formula is available to play with. The log function goes
> blecchh at z=0, so we'll stick with nonzero complex numbers. As I said,
> if log(z)=w, then log(z)=w+2npi, for any integer n. So w and w+2pi,
> w+4pi, w-2pi, w-4pi, w+158pi, ... are all on separate sheets (which we
> can index by n, if we are so inclined). The surface is sort of helical.
> We start on the ground floor (n=0), and we can walk around the origin
> until we've made a complete circle, whereupon we find ourselves on the
> first floor (n=1). Another complete circle and we're on the second floor
> (n=2). Going the other way from the ground floor we find ourselves on
> the first basement level (n=-1), then the second basement (n=-2), and so
> on in that direction.
>
> But where precisely do we change floors? What the Riemann surface shows
> is that such a question is more a matter of convention than anything to
> do with the property of the log() function itself. We could draw a line
> out along the positive real axis (on each sheet) and say "Here is where
> we change sheets", but we could just as easily draw it along the negative
> real axis, or either imaginary axis or anything in between. Wherever you
> place it, you can extract a sheet out of the surface that covers the
> entire complex plane (except of course for the origin) by cutting along
> your chosen axis on any sheet and an adjacent sheet.
>
> It should be pretty obvious that these lines I've been talking about are
> the branch cuts. Conventionally, the log() function is cut along the
> negative real axis. So is the square root function, for that matter,
> while the arctangent function is cut along the negative imaginary axis
> starting at 0-i and extending downwards towards -infinity.
>
> To provide a bit of a summary, I'll describe the Riemann surface of the
> z^(1/2) function. Since this function is at most two-valued (the only
> exception being of course z=0, which has one value), the Riemann surface
> is made by stitching two sheets together. Laying them atop each other,
> we see that they have to actually meet at z=0 (because they have the
> same value there). Now, what do the two values of z^(1/2) have in
> common? They're negations of each other, of course, which on the complex
> plane is equivalent to rotation about the origin of 180 degrees (or
> more appropriately, pi radians). So if we were to start at one value and
> walk around the origin and arrive back at our starting point, we'd
> find ourselves on the other sheet. Another walk around and we really
> will be back where we started. We can manage this by cutting the sheets
> as follows. Starting at the origin, we cut a slit out to infinity
> (conventionally as I mentioned above), join the lower edge of the lower
> sheet to the upper edge of the upper sheet, and the upper edge of the
> lower sheet to the lower edge of the upper sheet. Don't worry if this
> violates your three-dimensional imagery - it's not a stunt that can be
> pulled off in 3D without the optical illusion of the two sheets
> apparently interpenetrating. And there's the surface. The (illusory)
> crossover line along the axis can be waved and wiggled about all over
> the complex plane - as long as one end remains rooted at the origin -
> and every such wave and wiggle can be used to define a branch cut for
> separating the surface back into sheets again.
>
> Its precisely the positioning of the branch cut for the log() function
> that is explored by the MandelbrotBC formula. If you build an animation
> where you steadily increase the branch cut parameter, you can almost see
> the spiral staircase effect as you climb higher and higher.
>
> See also:http://library.wolfram.com/examples/riemannsurface/
>
> Morgan L. Owens
> "I _had_ to ask..."
>
> --------------------------------------------------------------
> Thanks for using Fractint, The Fractals and Fractint Discussion List
> Post Message:   [e-mail]
> Get Commands:   [e-mail] "help"
> Administrator:  [e-mail]
> Unsubscribe:    [e-mail] "unsubscribe fractint"


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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  29-04-01  (Veil-Nebula [6])
Date: 28 Apr 2001 21:32:04 -0400 (EDT)


Classic FOTD -- April 29, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

In the constellation of Cygnus, which is directly overhead in
the summer months at a latitude of 39N, there is a delicate
nebula, the remnants of a supernova explosion that took place
some 25,000 years ago.  It is called the Veil nebula.

The delicate traceries surrounding today's midget remind me so
much of that celestial sight that I named the image "Veil
Nebula".  After naming it, I gave it a rating of 6, since it's
not at all a bad picture, though the somewhat excessively
intense colors keep it from a higher rating.

The image once again takes advantage of the MandelbrotBC
formula, this time applied to the Z^2.003+C Mandeloid.  This is
the fractal with that most curious rectangular object in the
Julia set of the East Valley area of the prominent midget on the
infinitely-divided negative stem.  I found today's scene when I
went looking for that object in the JuliaBC formula, and failing
to find it, turned instead to the MandelbrotBC formula to have
some fun with the Mandel aspect.

Using Fractint's evolver feature, I located the section with the
most interesting branch cuts and started exploring.  Within 10
minutes I had found a whole nest of midgets just past the midget
on the stem, a stem which in this case points in the positive
direction.  Today's midget is a minor member of that nest.

With a render time of just over 2 minutes, the parameter file is
probably the best way to view the scene.  But for those who
enjoy travel, the file of the GIF image will soon be available
on the WWW at:

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

and at:

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

The weather today, fractal weather that is, was near perfect.
Only a slightly chilly temperature of 65F (18C) kept it from
being absolutely perfect.  The fractal cats helped me enjoy the
day by watching me trim the grass, keeping safely out of the way
whenever the mower drew near.

Due to too much enjoyment, I had little time for idle
philosophical pondering.  I ponder best while working on dull
routine jobs or while waiting for fractals to generate.  I
ponder very poorly while trimming lush wet grass with a lawn
mower with a blade in need of sharpening.

But the next FOTD is only 27 hours away, 39 hours if I don't
post it until Monday morning.  That is ample time in which to
ponder.  To see whether or not I actually ponder, check then.

Until then, so long for now!


Jim Muth
[e-mail]


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

Veil_Nebula        { ; time=0:02:12.54--SF5 on a P200
  reset=2001 type=formula formulafile=branchct.frm
  formulaname=MandelbrotBC passes=1 float=y
  center-mag=1.78204/0.00403291/4113.286/1/-99.999
  params=2.003/0/1040.877965636158/0 maxiter=1500
  inside=0 logmap=33 periodicity=10
  colors=000J0EL0EN0HP0KR0NU0QW0TY0W_0Zb0ad0df0gf0jh\
  0mh1pk5sk8unCwnHznJzpNzpRzsWzs_zudzuhzwnzwszwuzupz\
  skzphzndzkbwhYsfWndRhbPd_L_YJWYFPWCLU8HR7CP38N15L0\
  1J00H00F00C00C00A00A00A10A70AC0AJ3AP5AW8AbCAhHApJA\
  wNAzRAzUNzdYznhzzuzzzzzzwzzwzzuzzuzzuzzszzswzsuwps\
  wpnwpkunhunfunbsk_skYskWphUphPphNnfLnfJnfHhdAfb7db\
  3b_0__0WY0UY0RW0PW0NU0LU0PP0RL0UJ0WF0YC0_80b70d30f\
  10h00k00p00s00u00w00z00z00z00z00z00z00z00z00z00z00\
  z00z00z00w00u30s73sC8pHCnNHkRNhYRfYWdYbbYf_Yk_YpdY\
  hfYdhYYkYUnYNpYJsYCuY8wY3zY0zY0zY0zY0zY0zY0zY0zY0z\
  Y0zY0kY0WY0FY01Y00Y00Y00Y05Y0AY0HY0WYCkNRzCfz3wz0z\
  z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\
  zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\
  0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\
  z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\
  zz0zz0zz0zz0zz0zz0zz0zz0z
  }

frm:MandelbrotBC   { ; Formula by Andrew Coppin etal
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<100
}

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


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

From: Guy Marson <[e-mail]>
Subject: (fractint) evolver bug?
Date: 29 Apr 2001 19:40:55 +0200

Hi Fractinters,

in an .frm working with 4 functions (fn1-fn4) I need to play with fn1-fn3
but not with fn4. Fn4 is set to 'sinh' and has to stay so. Starting the
Evolver with the 'fn4=no' option (but set to 'sinh' in the Z-screen) all
the pictures are generated with 'fn4=sin' except the first one..

One more observation: I think that the first disabled function (in the
evolver) is always set to sin and not to the wanted function. E.g.:
fn1=random fn2=no fn3=no fn4=random then fn2 is set to 'sin' by the Evolver..

Is it a feature or a bug?


cheers,


Guy



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

From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) evolver bug?
Date: 29 Apr 2001 17:01:58 -0500

Guy,

> Is it a feature or a bug?

I'll have a look after I've finished uploading the various files for
20.1.08.

Jonathan



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

From: "Chris Curnow" <[e-mail]>
Subject: (fractint) Acknowledgments due?
Date: 29 Apr 2001 23:54:55 +0100

This is a multi-part message in MIME format.

------=_NextPart_000_0019_01C0D107.CA2B8580
Content-Type: text/plain;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

I have been interested in the various discussions regarding the =
proprietary rights to fractal images.  Poor old, (young), Zorba the Hutt =
who spent hours generating high resolution versions of fractals to =
delight others with slower machines, is then shamed into deleting them =
because they are the 'property' of the esteemed Sylvie Gallet, (may her =
.map files continue to delight us all).  On the other hand Jim Muth, =
absolutely correctly, goes to some pains to ensure that the MandelbrotBC =
formula is marked as 'belonging' to Andrew Coppin et al.

Surely fractal images, in the raw so to speak, are 'found' objects.  =
Acknowledgment is due to the creator of the formula; be it Mandelbrot =
himself.  The colouring scheme, however, is an aesthetic operation with =
two functions.  Firstly it is needed to display some features of the =
'raw image' which may not be obvious, and secondly it serves to make the =
object a pleasing picture, (a piece of artwork).  So we all generate or =
download Jim's images every day looking for an aesthetic experience, the =
maths is fun but the image is king.  I have tried to better Jim's colour =
scheme usually with abysmal results, so Jim you're an artist (even if =
your Mum doesn't think so! 'C-FOTD 20-4-01')  On the other hand I've =
very often found a 'more interesting' area in one of Jim's FOTDs.  (That =
is, more interesting to me) - not something new that I have 'created'.

As for the 'new' sinusoidal map generation utility posted by Rupert =
Millard on 26th April.  A note of acknowledgment that he received the =
source code for the basic algorithm from me on 4th April would have been =
courteous, here I *do* have a proprietary interest :-)   I'm working on =
using the Bezier function to define the three R, G, & B curves but the =
maths is a bit steep so this utility program may be some time coming.  =
Any VB6 programmers interested in joining in the endeavour can contact =
me direct and I'll send the source code, (and problem list!), so far.

Regards,
Chris Curnow
[e-mail]


------=_NextPart_000_0019_01C0D107.CA2B8580
Content-Type: text/html;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 5.50.4611.1300" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>I have been interested in=20
the various discussions regarding the proprietary rights to fractal =

images.  Poor old, (young), Zorba the Hutt who spent hours =
generating high=20
resolution versions of fractals to delight others with slower machines, =
is then=20
shamed into deleting them because they are the 'property' of the =
esteemed Sylvie=20
Gallet, (may her .map files continue to delight us all).  On the =
other hand=20
Jim Muth, absolutely correctly, goes to some pains to ensure that the=20
MandelbrotBC formula is marked as 'belonging' to Andrew Coppin et=20
al.</FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2></FONT> </DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>Surely fractal images, in the =
raw so to=20
speak, are 'found' objects.  Acknowledgment is due to the creator =
of the=20
formula; be it Mandelbrot himself.  The colouring scheme, however, =
is an=20
aesthetic operation with two functions.  Firstly it is needed to =
display=20
some features of the 'raw image' which may not be obvious, and secondly =
it=20
serves to make the object a pleasing picture, (a piece of =
artwork).  So we=20
all generate or download Jim's images every day looking for an aesthetic =

experience, the maths is fun but the image is king.  I have tried =
to better=20
Jim's colour scheme usually with abysmal results, so Jim you're an =
artist (even=20
if your Mum doesn't think so! 'C-FOTD 20-4-01')  On the other hand =
I've=20
very often found a 'more interesting' area in one of Jim's FOTDs.  =
(That=20
is, more interesting to me) - not something new that I have=20
'created'.</FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2></FONT> </DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>As for the 'new' sinusoidal =
map=20
generation utility posted by Rupert Millard on 26th April.  A note =
of=20
acknowledgment that he received the source code for the basic algorithm =
from me=20
on 4th April would have been courteous, here I *do* have a proprietary=20
interest :-)   I'm working on using the Bezier function =
to define=20
the three R, G, & B curves but the maths is a bit steep so this =
utility=20
program may be some time coming.  Any VB6 programmers interested in =
joining=20
in the endeavour can contact me direct and I'll send the source code, =
(and=20
problem list!), so far.</FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2></FONT> </DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>Regards,</FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>Chris Curnow</FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2><A=20
href=3D"mailto:[e-mail]">[e-mail]</A></FONT><=
/DIV>
<DIV><FONT face=3D"Comic Sans MS" =
size=3D2></FONT> </DIV></BODY></HTML>

------=_NextPart_000_0019_01C0D107.CA2B8580--


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

From: "Jonathan Osuch" <[e-mail]>
Subject: (fractint) Fractint version 20.1.08
Date: 29 Apr 2001 18:20:26 -0500

Folks,

Fractint version 20.1.08 is now available at the developer's web site.
www.fractint.org

Features in this patch:
Added truecolor support to Fractint thanks to Bert Tyler.  While in a
  truecolor mode, the following features are disabled/changed:\
    Color Cycling\
    Palette Editor brings up the contents of the MAP directory\
    Saving the image still only produces a 256 color GIF\

  Removed Bert's truecolor test code used with the test fractal type.

  Updated Paul de Leeuw's contact information.

Jonathan



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

From: Lee Skinner <[e-mail]>
Subject: (fractint) Acknowledgments due?
Date: 30 Apr 2001 09:05:32 -0400

Hi Chris,

>> Poor old, (young), Zorba the Hutt who spent hours generating high
resolution versions of fractals to delight others with slower machines, i=
s
then shamed into deleting them because they are the 'property' of the
esteemed Sylvie Gallet, (may her .map files continue to delight us all). =

<<

Fractint and Ultra Fractal do not always generate identical images from t=
he
same par file. In this case, Sylvie generated the images with Fractint an=
d
posted Fractint pars.  Zorba generated the hi-res images with UF instead =
of
Fractint - they appeared differently (having a different texture)than
Sylvie originally generated - and so she had them removed mainly for that=

reason - they were no longer her images, and so Zorba's saying that they
were her images was inaccurate.  Had he generated them with Fractint, she=

may have approved, assuming that her permission was obtained first.  I
don't think Zorba was aware of the differences when he posted them.

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

From: Lee Skinner <[e-mail]>
Subject: (fractint) Fractint version 20.1.08
Date: 30 Apr 2001 09:05:33 -0400

Jonathan,

>> Fractint version 20.1.08 is now available at the developer's web site.=

>> Features in this patch:
>> Added truecolor support to Fractint thanks to Bert Tyler.  =


I presume that there is no way to save a true-color par file yet either.

Is there any mechanism yet for manipulating the true colors?

Lee

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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  30-04-01  (A Ghostly Spectre [4])
Date: 30 Apr 2001 10:01:42 -0400 (EDT)


Classic FOTD -- April 30, 2001 (Rating 4)

Fractal visionaries and enthusiasts:

Today's hasty fractal was created by the formula
2Z^(-2.1)-2Z^(-1.9)+(1/C).  I named it "A Ghostly Spectre" when
I noticed that the seahorse-like detail surrounding the midget
is clearly visible only when certain broad color palettes are
applied to the image.  With a narrow color scheme such as F2,
the detail vanishes and the image becomes a featureless screen
full of fractal sand.

The location of today's image is in an elephant trunk in the
East Valley area of a larger midget, which is resting in a
chaotic part of the parent fractal.

I rated the image at a 4.  This is all I could give to a fractal
that I found and colored with so little effort.  With a running
time of exactly 15 minutes, the parameter file might not be the
best way of viewing the image, which will be available for
download and viewing in an hour or so at:

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

and at:

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

One of these days when things settle down, I'm going to gain
convenient access to ABPF, and resume posting the images there.
But so far I haven't had the chance to recover from the move of
Fractal Central auxiliary.

With sunny skies and a temperature of 68F (20C), the fractal
weather today was so good that I took the day off.  When I
returned, the cats scolded me for not being there to let them
out to enjoy the fine weather.  To soothe them, I gave them a
treat of tuna and promised to do better next time.

And speaking of next time, it will come in about 13 hours.
Until then, take care, and watch out for those fractal ghosts.


Jim Muth
[e-mail]


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

A_Ghostly_Spectre  { ; time=0:15:00.01--SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+1.584484530091595/+1.150509782717139/7\
  774320/1/132.5 params=1/-2.1/-1/-1.9/1/300 float=y
  maxiter=1800 inside=0 logmap=205 periodicity=10
  colors=000i_zg_zg_zfYzfYzdYzdYzbWzbWzbWzaWzaVz_Vz_\
  VzYVzYTzXTzXTzSRzVTzVTzXTzXVzXVzYVzYVz_Wz_Wz_WzaWz\
  aYzbYzbYzbYzd_zd_zf_zf_zf`zg`zg`zi`zibzibzkbzkbzlc\
  zlczlczncznfznfzpfzphzqhzqhzqhzsizsizuizuizukzwkzw\
  kzxkzxnzxnzznzzozzpzzpzzqzzqzzszztzztzztzzwzzwzzwz\
  zxzzyzzzzzzzzzzzzzzxzzxzzvzzuzztzzszzpzzpzzpzzpzzn\
  zxnzxnzwnxumwumwsmusmsqksqkqpjpshsqfqpdpnbplank`ni\
  _lgZlfYkdXkbWiaVi_UgYTgXSfVRfSQdRPbPObONaMMaKL_JK_\
  JJYHIYFHXEGXCFVAEV8DS7CS6BR4AP29P18O07O07M07M07K07\
  K07J07J07H07H07F07H07F07F07F07F07E07E07E05E07C07C0\
  7C07C17C47A68A68A7BA8B8AD8CE8EE8FF7FF7HC7JE7KE7MG6\
  OG6PH6RK6RL4SO4VQ4XR4YU1_V1aY1b_1b`1db0fb0gc0if0kf\
  0lh0lh0ni0pk0qk0sm0um0wn0xp0xp0zr0zr0zs0zu0zu0zw0z\
  w0zx0zx0zx0zx0zx0zx0zx0zz0zz1zz1zz4zz4zz6zz6zz7zz7\
  zz8zz8zzAzzAzzAzzAzzAzzAzzAzzAzzAzzAzzAzzAzzAzzAzz\
  AzzAzzAzzAzzAzzAzzAzzAzzA
  }

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

From: "Andrew Coppin" <[e-mail]>
Subject: (fractint) Linux Fractint
Date: 30 Apr 2001 14:50:31 -0000

I don't know who did the Linux Fractint post, but HATS OFF TO THEM!

Yesterday, after wanting to have a Linux Fractint for AGES, I got someone to
download the source for me. I let him compile it, thinking it would be a
nightmare. The guy typed "make", half a million lines of text flew past, and
an executable appeared. He executed it, and it just worked.

I would never have believed it if I hadn't seen it for myself!

BTW, this was on an Athlon 1GHz machine. Once I reached arbitary precition
mode, it was *still* rapping off 2 lines per second! Man, I *want* his
machine!!!

Once again, a big thanks to whoever it was who made this thing!

Thanks.
Andrew.

_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.


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

From: Sylvie Gallet <[e-mail]>
Subject: (fractint) Acknowledgments due?
Date: 30 Apr 2001 12:12:43 -0400

Hi Chris,

>> Poor old, (young), Zorba the Hutt who spent hours generating high
>> resolution versions of fractals to delight others with slower machines=
,
>> is then shamed into deleting them because they are the 'property' of t=
he
>> esteemed Sylvie Gallet,

  I can't let you say that I _shamed_ him into deleting these images.  He=
re
is what I wrote:

<<<<<<<<<<<<
  All of the images are different from their Fractint version, and in lot=
s
of them, UF replaced the nice texture with banding so, I'd like you to
remove them or redo them with Fractint (maybe in a standard 1600x1200
format).
>>>>>>>>>>>>

  Cheers,

        - Sylvie

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

From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) Re: C-FOTD
Date: 30 Apr 2001 12:17:58 -0500

Jim Muth wrote:

> When one is working with fractals, it is obvious that CPU speed is
> important.  I do not need to state the fact.  When I do state it, I am
> merely repeating the obvious.  I have no memory of stating that one
> should go out and spend money they cannot afford on a new computer,
> though I suppose it could be implied in my words.

FWIW, I've never gotten that impression from any of your FOTDs.  As you
say, it's self-evident that a faster machine == faster rendering, but
I've never gotten the impression you were egging us on in any way.

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

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

From: "Chris Curnow" <[e-mail]>
Subject: (fractint) No hard feelings
Date: 30 Apr 2001 22:52:36 +0100

This is a multi-part message in MIME format.

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Oh dear!  I really put one of Jim's cats amongst the pigeons!
I owe Rupert Millard and Sylvie Gallet each a public apology. =20

Here it is Rupert.  I'm sorry for implying that you 'stole' anything. =20
But it's a real bummer when you spend umpty-tump hours trying to=20
design a decent user interface for a program written only to find a=20
similar program posted!  And, yes you're right; my program uses the=20
negative cos function to generate a sinusoidal curve.  (And it's not=20
as good an implementation as yours!)

I still think the Bezier function would transform these gradient type=20
of map generators.  Really no hard feelings from my side so I'll send=20
you the bit of source to your email address, (I may persuade you to=20
spend a few moments on the 'problems'!)

Sylvie, I didn't mean to imply that *you* were the one that shamed him.  =

(English is my native tongue but sometimes I have trouble with my =
worms!) =20
The point I was trying to make was that what Zorba had done, although=20
based on your work, was something different and therefore valid; and=20
yet, he felt that he should delete them.  The question still hangs =
there. =20
Why did he, or anybody, feel that his version was in any way 'inferior'=20
to the original?  Put it another way, how come Andy Warhole could=20
charge zillions for a picture of a can of Campbell's Soup?  Was the =
money=20
his, or the graphic designer who drew the original can label? =20

I suspect that Lee Skinner sums up the problem as I see it........

>Zorba generated the hi-res images with UF instead of
>Fractint - they appeared differently (having a different texture)than
>Sylvie originally generated - and so she had them removed mainly for =
that
>reason - they were no longer her images, and so Zorba's saying that =
they
>were her images was inaccurate.  Had he generated them with Fractint, =
she
>may have approved, assuming that her permission was obtained first.

Why ask for permission?  The images were different and "no longer her =
images"!
Zorba gave acknowledgement that the .par files had been produced by =
Sylvie=20
but he *did* feel that it was the right thing to delete them.  I really =
don't want=20
to put Zorba on the spot over this, so Zorba, if you're listening I'm =
not asking=20
you to reply!  I just don't understand; but then I'm probably being =
thick!

So..... any comments from the Fractint List on the premise that fractals =
are=20
'found' objects, or is that a dead duck? =20
(Dead duck image copyrighted by Jan Vermeer (1623-75)=20
Still life  "Dead Duck with Kalashnikov")

Best regards,

Chris

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<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 5.50.4611.1300" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>Oh dear!  I really put =
one of Jim's=20
cats amongst the pigeons!</FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>I owe Rupert Millard and =
Sylvie Gallet=20
each a public apology.  </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2></FONT> </DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>Here it is Rupert.  I'm =
sorry for=20
implying that you 'stole' anything.  </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>But it's a real bummer when =
you spend=20
umpty-tump hours trying to </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>design a decent user =
interface for a=20
program written only to find a </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>similar program posted!  =
And, yes=20
you're right; my program uses the </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>negative cos function to =
generate a=20
sinusoidal curve.  (And it's not </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>as good an implementation as=20
yours!)</FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2></FONT> </DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>I still think the Bezier =
function would=20
transform these gradient type </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>of map generators.  =
Really no hard=20
feelings from my side so I'll send </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>you the bit of source to your =
email=20
address, (I may persuade you to </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>spend a few moments on the=20
'problems'!)</FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2></FONT> </DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>Sylvie, I didn't mean to =
imply that *you*=20
were the one that shamed him.  </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>(English is my native tongue =
but=20
sometimes I have trouble with my worms!)  </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>The point I was trying to =
make was that=20
what Zorba had done, although </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>based on your work, was =
something=20
different and therefore valid; and </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>yet, he felt that he should =
delete=20
them.  The question still hangs there.  </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>Why did he, or anybody, feel =
that his=20
version was in any way 'inferior' </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>to the original?  Put it =
another=20
way, how come Andy Warhole could </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>charge zillions for a picture =
of a can of=20
Campbell's Soup?  Was the money </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>his, or the graphic designer =
who drew the=20
original can label?  </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2></FONT> </DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>I suspect that Lee Skinner =
sums up the=20
problem as I see it</FONT><FONT face=3D"Comic Sans MS"=20
size=3D2>........</FONT></DIV>
<DIV> </DIV>
<DIV>>Zorba generated the hi-res images with UF instead =
of<BR>>Fractint -=20
they appeared differently (having a different texture)than<BR>>Sylvie =

originally generated - and so she had them removed mainly for =
that<BR>>reason=20
- they were no longer her images, and so Zorba's saying that =
they<BR>>were=20
her images was inaccurate.  Had he generated them with Fractint,=20
she<BR>>may have approved, assuming that her permission was obtained=20
first.</DIV>
<DIV> </DIV>
<DIV>Why ask for permission?  The images were different and "no =
longer her=20
images"!</DIV>
<DIV>Zorba gave acknowledgement that the .par files had been produced by =
Sylvie=20
</DIV>
<DIV>but he *did* feel that it was the right thing to delete them.  =
I=20
really don't want </DIV>
<DIV>to put Zorba on the spot over this, so Zorba, if you're listening =
I'm not=20
asking </DIV>
<DIV>you to reply!  I just don't understand; but then I'm probably=20
being thick!</DIV>
<DIV> </DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>So..... any comments from the =
Fractint=20
List on the premise that fractals are </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>'found' </FONT><FONT =
face=3D"Comic Sans MS"=20
size=3D2>objects, or is that a dead duck?  </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>(Dead duck image copyrighted =
by Jan=20
Vermeer (1623-75) </FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>Still life  "Dead Duck =
with=20
Kalashnikov")</FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" =
size=3D2></FONT> </DIV></FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2>Best regards,</FONT></DIV>
<DIV><FONT face=3D"Comic Sans MS" size=3D2></FONT> </DIV>
<DIV><FONT face=3D"Comic Sans MS" =
size=3D2>Chris</FONT></DIV></BODY></HTML>

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

From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) No hard feelings
Date: 30 Apr 2001 17:18:09 -0500

Chris Curnow wrote:

> Why did he, or anybody, feel that his version was in any way 'inferior'
> to the original?

I shouldn't speak for someone else, but perhaps not "inferior" so much as
treading on private ground?  Like, you can run across someone's yard, but
if they indicate they don't like it, you respect that and don't?

Or closer to the copyright issue: is music "discovered" or invented?  You
*could* suggest that--mathematically--all songs (and books) already exist
as a permutation of a fairly basic set of "primatives" (notes/words).

But "discovering" a permutation that pleases others, ah, that's the ART!

> Put it another way, how come Andy Warhole could charge zillions for a
> picture of a can of Campbell's Soup?  Was the money his, or the graphic
> designer who drew the original can label?

(IMO obviously) His.  Warhol's art was in drawing our attention to the
presence of graphic art all around us in everyday life.  He was pointing
out that a (probably trained) artist created that soup can label.

THAT's why his work is worth gazillions and mine--if I aped it--ain't.

>> ...and so Zorba's saying that they were her images was inaccurate.
>
> Why ask for permission?  The images were different and "no longer her
> images"!

But she did the original legwork to "discover" the image and--in a moral
sense--has *some* sense of ownership which someone else might respect.

> So..... any comments from the Fractint List on the premise that
> fractals are 'found' objects, or is that a dead duck?

Considered a dead duck by many.

My vote: yeah, fractals are largely discovered, but the framing, coloring
(and these days, overlaying of multiple images) is clearly art, so I don't
see the answer being all Yes or all No.  To me, it's the amount of effort
and *personal* input by the "artist" that makes it art.

If I boot FractInt, zoom in randomly for a while, generate a random color
palette.... is that art?

If I boot FractInt, spend a bit of time finding an image that seems
pleasing to the eye, seems somewhat unique in my experience and then
spend time finding a color palette that brings out the best of the
fractal..... is THAT art?

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

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

From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) Fractint version 20.1.08
Date: 30 Apr 2001 17:20:26 -0500

Jonathan Osuch wrote:

> Features in this patch:
> Added truecolor support...
> [....]
>     Saving the image still only produces a 256 color GIF

???  So you can look, but not save?

Given that you've GOT an image and that free PNG libraries exist, I'm
curious why you can't save a t/c image?

Not raggin' on ya, just curious...

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

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

From: "Fernando Bresslau" <[e-mail]>
Subject: Re: (fractint) Fractint version 20.1.08
Date: 30 Apr 2001 20:08:29 -0300

isn┤t there a way of capturing the screen? maybe some third party software?
Fernando Bresslau, who hasn┤t tried it yet.
http://www.fractal.art.br


----- Original Message -----
Sent: Monday, April 30, 2001 7:20 PM


> Jonathan Osuch wrote:
>
> > Features in this patch:
> > Added truecolor support...
> > [....]
> >     Saving the image still only produces a 256 color GIF
>
> ???  So you can look, but not save?
>
> Given that you've GOT an image and that free PNG libraries exist, I'm
> curious why you can't save a t/c image?
>
> Not raggin' on ya, just curious...
>
> --
> |_ CJSonnack <[e-mail]> _____________| How's my programming? |
> |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
> |_____________________________________________|_______________________|
>
> --------------------------------------------------------------
> Thanks for using Fractint, The Fractals and Fractint Discussion List
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-------------------------------------------------------------------------------

From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) Fractint version 20.1.08
Date: 30 Apr 2001 18:20:46 -0500

Chris,

> ???  So you can look, but not save?

Not exactly.  The images you can currently generate are still using the 256
color palette.  So, to save the image, the truecolor pixel on the screen is
read and converted to an index value into the 256 color palette.  This
conversion may make the saved image look different than if it were done
directly in a 256 color mode.

> Given that you've GOT an image and that free PNG libraries exist, I'm
> curious why you can't save a t/c image?

Memory.  Because of the memory model we are using (medium), we can't fit the
PNG libraries into Fractint.  There are solutions.  We have tried compiling
the Xfractint code using djgpp, but it needs work.  Any volunteers?  We have
the experimental code which incorporates the Allegro graphics package but no
way as yet to save images.  We could add the PNG libraries to Xfractint and
stop developing the DOS version.

We will eventually have to dump the current DOS source code, but would like
to at least have something place for Windows before we do this.

Jonathan



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

From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) Fractint version 20.1.08
Date: 30 Apr 2001 18:02:36 -0500

Lee,

> I presume that there is no way to save a true-color par file yet either.

The images that can currently be generated still use the 256 color palette,
and will generate the corresponding PAR.  Once we add different coloring
schemes I don't see any way to generate a PAR that makes sense.  Depending
on how the coloring schemes are generated.

> Is there any mechanism yet for manipulating the true colors?

No.

Jonathan



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

From: Lee Skinner <[e-mail]>
Subject: (fractint) Fractint version 20.1.08
Date: 30 Apr 2001 19:55:13 -0400

Jonathan,

>> I presume that there is no way to save a true-color par file yet
either.<<

> The images that can currently be generated still use the 256 color
palette, and will generate the corresponding PAR.  Once we add different
coloring schemes I don't see any way to generate a PAR that makes sense. =

Depending on how the coloring schemes are generated. <

I am not an Ultra Fractal user, but doesn't it generate par files of
true-color images?  (Perhaps some UF user could shed light on how this
might be implemented.)

Lee

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

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  01-05-01  (Decorative Minibrot [6])
Date: 30 Apr 2001 23:01:26 -0400 (EDT)


Classic FOTD -- May 01, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Before attempting to run the parameter file of today's image,
notice that it has been drawn by an updated version of the
MandelbrotBC formula, which I have named MandelbrotBC1.  This
new version is identical to the old version except that I have
replaced the fixed <trunc> function with a variable function,
and replaced the fixed bailout radius of 100 with a variable
parameter entry.  Since I've lost all track of those who worked
on this formula, I have credited it to 'several Fractint users'.

Today's image uses the <floor> function, which curiously enough
draws exactly the same images as the <trunc> function.  I have
not yet tested the various trig functions, though hopefully they
will draw some interesting if not quite correct variations.  The
variable bailout is useful mainly with negative-exponent
fractals, which I have not yet worked with.

I also see that a developer's version of Fractint with
rudimentary true-color capability is available, though at the
present time, one can only see the image on the screen, say
'wow', stare at the image a while, and then shut down their
computer.  It's a start, but before I switch the FOTD to a true-
color version of Fractint, the program will need the ability to
cycle and change the colors, to save the image in true-color
with data intact, and also to save the true-color image as a
parameter file.  And there's also the possibility that my
stripped-down computer, used only for finding fractals, will not
be able to display true-color with its meager 1 meg of video
memory.  But that's a problem I'll concern myself with if and
when it arises.

Today's fractal is quite decorative, an attribute that inspired
the name "Decorative Minibrot".  The irrational number entered
as the real(p1) parameter may appear familiar.  Actually, it is
familiar.  It is the square root of 3, a number I entered hoping
to create midgets with 3-way symmetry.  As of yet, I have found
no such midgets, though I did find today's midget, which bears a
curiously close resemblance to a standard quadratic midget.
Only the chopped-off main bud reveals the midget's true nature.

The parameter file is unusually fast, rendering in under two
minutes.  Of course, the download, which may be found at:

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

and at:

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

is equally fast.  I leave it to the viewer what route to take.

The fractal weather today was clear as a crystal, with a
temperature of 77F (25C), conditions that Thomas and Tippy, the
fractal cats, consider ideal.  Since they were deprived yester-
day of their rightful time outdoors, I treated them to all the
outdoor time they wanted today.  My only concern is about a fox
that has been seen lately in the neighborhood.  The cats haven't
confronted it yet, and I have no idea of what might happen if
they meet.

But right now, the dynamic duo are sleeping in their beds, a
sign that it's time for me to shut down the fractal shoppe and
call it a night.  Until next time, take care, and if true-color
is true, does that mean that 256-color is false?


Jim Muth
[e-mail]


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

DecorativeMinibrot { ; time=0:01:52.60--SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=mandelbrotbc1 function=floor passes=1
  center-mag=-0.73763/0.15494/2498.371/1/-124.999
  params=1.732050807569/0/28.4/0 float=y maxiter=1000
  inside=0 logmap=36 periodicity=10
  colors=000mA9jBPnCHqDHtFDwGAzH5zH2zM4zS5zW7za8zeAz\
  jMzp_zzmzzzbsfFPO0D70ID1PK4YP8cWClaGrhIwmMriPmeUha\
  WcZ__VbVQfQOiMKmHGpDCuAAw45z12z00z11z42z83zC4zG4zK\
  5zO7zS8zW8y_AycByhCylClSPaAaQ0mS0pU2rU7sVCuWHvWMwY\
  SyZYzZazeVmjO_pIMpMLpPKpUKpWIp_HpbHQYP2SW1WS0ZO0bL\
  0eH0hD0lB0o70s40v10y00z00z00z0ovzpszrryrpwsouumsul\
  rvjpwhmwflyejzcizbfzaez_czZbzYazW_yVZwVYvUWuSVuSUs\
  QSrPQpOPoOOmMMlLLlLLhKMcKOaIPYIQUHSQHUMGVKGWGFYCFZ\
  AD_5Da2Cb0Cc0Be0Be0If0Pf0Wh1ch3ji4ri7sf8ueAvcCvbDw\
  aFyZGzYIzWKzVLzUMzSVzKbzDiz5rz0yz0wv3vsDupOulZsiir\
  furczsczscyucvucsvcpvcmwcjwchyceycbzc_zcYzcVzcUwcZ\
  sccpchycfzcfzc_zeUzfMzhHyiKsjMmlO0m02o04p27r3Bs4Du\
  5Hv8KwAMyBQzCUzFYzG_zHbzIZzFWzBSz8Pz4Lz1Iz0Fz0Cz0A\
  z0Dz2HzGKzUFzLAzD4z57zB8zFBzICzMFzOHzPKzPMzQPzQSzS\
  VzSYzU_zUbzVezVhzWizWjzUjzQlzPlzMmzLmzImzHozGpzFpz\
  DlzFWzHWzHVzIVzIVzKUzKbzY
  }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a
}

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


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

From: "Morgan L. Owens" <[e-mail]>
Subject: (fractint) Re: [philofractal] C-FOTD  01-05-01  (Decorative Minibrot [6])
Date: 01 May 2001 17:23:57 +1200

At 15:01 01/05/2001, Jim Muth wrote:

>Classic FOTD -- May 01, 2001 (Rating 6)
>
>Fractal visionaries and enthusiasts:
>
>Today's image uses the <floor> function, which curiously enough
>draws exactly the same images as the <trunc> function.  I have
>not yet tested the various trig functions, though hopefully they
>will draw some interesting if not quite correct variations.  The
>variable bailout is useful mainly with negative-exponent
>fractals, which I have not yet worked with.

Not that surprising: trunc((28.4+PI)/(2*PI)) = floor((28.4+PI)/(2*PI)). The
two functions differ in how they deal with negative numbers (trunc rounds
towards 0, floor rounds towards -infinity).

Morgan L. Owens
"I remember when all we had to worry about was good old Int."



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