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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.
-
- _________________________________________________________________________
- Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.
-
-
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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>--------------------------------------------------------------
- <br>Thanks for using Fractint, The Fractals and Fractint Discussion List
- <br>Post Message: fractint@lists.xmission.com
- <br>Get Commands: majordomo@lists.xmission.com "help"
- <br>Administrator: twegner@fractint.org
- <br>Unsubscribe: majordomo@lists.xmission.com "unsubscribe
- fractint"</blockquote>
- </html>
-
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
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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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- 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==================================
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
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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."
-
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
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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
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- 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==================================
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
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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.
- - --------------------------------------------------------------
- http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- 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\
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- }
-
- END 20.0 PARAMETER FILE====================================
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
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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==================================
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
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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==================================
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- 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
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- 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
- >
- >--------------------------------------------------------------
- >Thanks for using Fractint, The Fractals and Fractint Discussion List
- >Post Message: fractint@lists.xmission.com
- >Get Commands: majordomo@lists.xmission.com "help"
- >Administrator: twegner@fractint.org
- >Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- _________________________________________________________________________
- Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.
-
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
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- Administrator: twegner@fractint.org
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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
-
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- 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 |
- |_____________________________________________|_______________________|
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- 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
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
- Get Commands: majordomo@lists.xmission.com "help"
- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- 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.
- - --------------------------------------------------------------
- http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go
-
- - --------------------------------------------------------------
- Thanks for using Fractint, The Fractals and Fractint Discussion List
- Post Message: fractint@lists.xmission.com
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- Administrator: twegner@fractint.org
- Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"
-
- ------------------------------
-
- End of fractint-digest V1 #551
- ******************************
-
-