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From: owner-fractint-digest@lists.xmission.com (fractint-digest)
To: fractint-digest@lists.xmission.com
Subject: fractint-digest V1 #551
Reply-To: fractint-digest
Sender: owner-fractint-digest@lists.xmission.com
Errors-To: owner-fractint-digest@lists.xmission.com
Precedence: bulk
fractint-digest Wednesday, April 18 2001 Volume 01 : Number 551
----------------------------------------------------------------------
Date: Fri, 13 Apr 2001 19:40:42 -0000
From: "Andrew Coppin" <orphi69@hotmail.com>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
>From: "Jonathan Osuch" <osuchj@qwest.net>
>Reply-To: fractint@lists.xmission.com
>To: <fractint@lists.xmission.com>
>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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------------------------------
Date: Fri, 13 Apr 2001 15:35:36 -0500
From: DeBow Freed <bmc1@airmail.net>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
<!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
bikenaga@marauder.millersv.edu
<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" <osuchj@qwest.net>
<br>>Reply-To: fractint@lists.xmission.com
<br>>To: <fractint@lists.xmission.com>
<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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fractint"</blockquote>
</html>
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------------------------------
Date: Fri, 13 Apr 2001 22:18:35 EDT
From: JimMuth@aol.com
Subject: (fractint) C-FOTD 14-04-01 (Squirt II [5])
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
jamth@mindspring.com
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\
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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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------------------------------
Date: Sat, 14 Apr 2001 16:11:17 +1200
From: "Morgan L. Owens" <packrat@nznet.gen.nz>
Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
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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------------------------------
Date: Sat, 14 Apr 2001 21:04:51 EDT
From: JimMuth@aol.com
Subject: (fractint) C-FOTD 15-04-01 (Deep in Hyperspace [7])
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
jamth@mindspring.com
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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------------------------------
Date: Sat, 14 Apr 2001 23:00:30 -0500
From: "Paul N. Lee" <Paul.N.Lee@Worldnet.att.net>
Subject: Re: (fractint) C-FOTD 15-04-01 (Deep in Hyperspace [7])
JimMuth@aol.com 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.
- --------------------------------------------------------------
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------------------------------
Date: Mon, 16 Apr 2001 08:59:28 EDT
From: JimMuth@aol.com
Subject: (fractint) C-FOTD 16-04-00 (Remotely Mandeloid [3])
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
jamth@mindspring.com
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\
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Aoz9qz8sz7tzRuzQuzPuzPuzO
}
END 20.0 PARAMETER FILE====================================
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------------------------------
Date: Mon, 16 Apr 2001 22:07:42 EDT
From: JimMuth@aol.com
Subject: (fractint) C-FOTD 17-04-01 (Fractal Celebration [5])
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
jamth@mindspring.com
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\
0Dy0Oz0Yz1ao3rz4jnIsyzc`fddzYVuXYxX_zX`zXczXdzXfz_\
aza_zdXzgTyjQxmOvpLssIrvFpyCoz9ixDdvI_sLVrPQpSSlOT\
gLVdIX`FXXCYT9_P4`M1`I0aD0cA0d60d30c10Y0CQ0OG0FG0F\
40A90DC0FF3II9JMFLPJOSPPVTS__TadVdiYgo_js`lvcmxdoy\
gozipzlrzmszpszruzuvzvvzxpzrlzlgzfaz`YzVTzPOzJJzDF\
z79z14z00z0Dz0Pm0``0mM0y90z00z00m4DVGSCSfzFJzCPyAT\
u9Yp6al4fg3jc0o_0sV0xX1vX4uX7sYArYFpYIp_Lo_Om_Sl`V\
j`Yj``iadgagfajdamdYg_VaVSYQOSMLOIIIDDC9A747104009\
01C17F4DJ6JM9PPAVSC`XFf_GlaJrfLxiOzlPzoQzi`zdis`ri\
Xz_SzQPzVOzYMz`LzcJzfIyiLvjMslOpmQomSloTipXfpYdr_a\
sa_scXudVvgSviPxjMylLydGr_MjTTcM`XGgPAiI3jA0l30m00\
o10p40r71sA4uD7vGAvJCvMFvPIxSLyVMzYGzSAzO4zJ0zF0zA\
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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------------------------------
Date: Tue, 17 Apr 2001 23:10:15 EDT
From: JimMuth@aol.com
Subject: (fractint) C-FOTD 18-04-01 (Fractured Fractal [6])
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
jamth@mindspring.com
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\
oaQpcOrdMsfLugJviIxjGylFzjFzlDzlCylAvmAslArlCplCol\
DmlDllFjjGijIgjJfjLdjMcjOajPajQajSaiQaiPagOagMagJa\
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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------------------------------
Date: Wed, 18 Apr 2001 00:08:41 -0500
From: "Paul N. Lee" <Paul.N.Lee@Worldnet.att.net>
Subject: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6])
JimMuth@aol.com 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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------------------------------
Date: Wed, 18 Apr 2001 17:56:35 -0000
From: "Andrew Coppin" <orphi69@hotmail.com>
Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6])
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" <Paul.N.Lee@Worldnet.att.net>
>Reply-To: fractint@lists.xmission.com
>To: fractint@lists.xmission.com
>CC: philofractal@lists.fractalus.com
>Subject: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6])
>Date: Wed, 18 Apr 2001 00:08:41 -0500
>
>JimMuth@aol.com 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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_________________________________________________________________________
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------------------------------
Date: Wed, 18 Apr 2001 16:33:04 -0400
From: "Zorba the Hutt" <zorbathut@uswest.net>
Subject: (fractint) The specter of schoolwork, and really really big fractals
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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------------------------------
Date: Wed, 18 Apr 2001 15:53:44 -0500
From: Programmer Dude <cjsonnack@mmm.com>
Subject: Re: (fractint) The specter of schoolwork, and really really big fractals
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 <Chris@Sonnack.com> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL |
|_____________________________________________|_______________________|
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------------------------------
Date: Wed, 18 Apr 2001 17:43:56 -0400
From: Sylvie Gallet <Sylvie_Gallet@compuserve.com>
Subject: (fractint) The specter of schoolwork, and really really big fractals
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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------------------------------
Date: Thu, 19 Apr 2001 00:16:05 -0500
From: "Paul N. Lee" <Paul.N.Lee@Worldnet.att.net>
Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6])
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.
- --------------------------------------------------------------
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------------------------------
End of fractint-digest V1 #551
******************************