March 2005 - Fractint - mailman.xmission.com

Re: Fractint Digest, Vol 25, Issue 9
by JackOfTradeZ 20 Mar '05

20 Mar '05

Vortex Swirling wrote: "I still have the fantasy that some place in a fractal we find the signature of the creator or some other cool undeniable artifact. (This is similar to the idea in the book Contact by Carl Sagan - its in there, not in the movie)." Exactly! Why do you think I spend so much time and effort on this? ...Chaos is God's language and Fractals are His fingerprints... Long Live the Cult of Fractint! JoTz

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Re: Tessellations
by Vortex Swirling 20 Mar '05

20 Mar '05

THIS is the future of fractal generation. If I was about 20 years younger I'd start a sourceforge FractGrid project today. I'd ask permission to use parts of fractint like the parser and so on, but mostly it would attract a new generation of Stone Soupers. This isn't a trivial undertaking either. It would require specialized experience in parallel distribution... and a nodal network similar to bittorrent. If you consider a fractal image takes a day, if there was a way to split that up between even 100 internet users it might be feasible to get the image done in less than an hour. Start thinking big, 10,000 users, it would be so cool. -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.7.4 - Release Date: 3/18/2005 -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.7.4 - Release Date: 3/18/2005

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Re: Tessellations
by Vortex Swirling 19 Mar '05

19 Mar '05

JOT, I just want to say how incredible your animations are. I've been following your Universe series and its quite fascinating. Even with this I still can't comprehend how far this thing goes. I still have the fantasy that some place in a fractal we find the signature of the creator or some other cool undeniable artifact. (This is similar to the idea in the book Contact by Carl Sagan - its in there, not in the movie). I don't think I could reorganize the fractint code myself. If I had the money, I'd higher some good programmers to reorganize the fractint code such that the calculation part was completely separate from the user interface. That would free it up to be able to be able to run on any platform (except probably for dos). I would place a network layer into the mix so that you could use other fractint engines running on the grid to produce your image. And in fact I would rename the program FractGrid. All FractGrid users would be sharing their idle computer cycles. And it would still be free. This is probably the natural evolution anyway, I just may be several years ahead of myself. Who wants to wait for Moores law? Which isn't working so well with computer cycles anyway... The 18 month doubling says that an image that takes an hour now, should take 15 minutes in computers made 3 years apart. I don't see any such improvements. -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.7.3 - Release Date: 3/15/2005 -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.7.3 - Release Date: 3/15/2005

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FOTD 19-03-05 (Golden Arches [7])
by Jim Muth 19 Mar '05

19 Mar '05

FOTD -- March 19, 2005 (Rating 7) Fractal visionaries and enthusiasts: When I first saw today's moody atmospheric scene, which lies in the Rectangular orientation of the Julibrot, I considered giving it a poetic name such as "Blue Bayou" or "Transfigured Night", or even something bombastic such as "Ripples of Heavenly Peace". But then I turned, glanced out the side window, and saw in the distance the familiar golden arches that mark the location of the local fast-food emporium. When I turned again to the screen I saw the arches there also. I immediately got hungry, named the image "Golden Arches", and hurried out to pick up a couple cheeseburgers and a bag of fries. (Unfortunately for the store, I did not buy a soda, which is where they earn most of their profit.) Actually, the image reminds me of the 'lake' transformation, that makes fractals look as though they were half submerged in a lake and being reflected off the rippling surface. What we are seeing however is a true part of the Z^2+C Julibrot. The only special effect is that the scene has been stretched in the vertical direction. The horizontal stripes are the ever-smaller buds lining the valley leading to the larger period-6 bud on the northeast shoreline of the main bay of the Mandelbrot set. The golden arch is a different view of the debris that obscures the tiny buds as the imaginary part of initial Z of the Mandelbrot view of the area is changed from zero. Today's image is an improvement over yesterday's effort, but its rating of a 7 leaves room for more improvement. Two Rectangular images remain to be posted. That gives me two chances to do better. As in real life, success is never guaranteed, but it will be interesting to see how close I come. Today's image is a rather slow one that takes almost 15 minutes to render on my machine. But relief may be found on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> from where the image may quickly be downloaded. The temperature reached a high of 59F 15C here at Fractal Central on Friday. The wind was light, the sun was bright, and the fractal cats were happy. They wasted over three hours lurking in the thicket, watching for something that never came. Only a small treat of tuna was needed to end their day happily. Today is starting with some sun, and it is mild again, but rain is due to arrive later this afternoon, hopefully after the duo have finished their outing. For me it looks like an average day. The work is light, so I'll probably spend some time watching the games on TV before entering Fractal Land. The next FOTD will appear in 24 hours. Until then, take care, and there's a long time to come before entropy wins. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Golden_Arches { ; time=0:14:16.18--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=flip/ident passes=1 center-mag=0/-0.00537482249257776/131.833\ 9/0.01495 params=0/90/2/0/0/0/0.3750255321/0.21770\ 67886 float=y maxiter=6450 inside=0 logmap=70 symmetry=yaxis periodicity=10 colors=000nggnfgnfgnfgnegnegndgndgochochochobhobho\ ahoaho`ho`hmXho`hpchqghrjhsnhtqhuuhxziwyhvxhvxhuwh\ twgtvgsugsugrtgqtfqsfpsfprfoqfnqenpempeloelodkndkm\ djmdildilchkchkcgjcficfibehbehbdgbcfbcfaceaceacdac\ d`cc`cc`cc`cc`cc_cc_cc_cc_cc_ccZcbZcbZcaZcaYc`Yc_Y\ c_YcZYcZXcZXcZXcZXcZXcZWcZWcZWcZWcZWcZVcZVcZVcZVcZ\ UcZUcZUcZUcZUcZTcZTcZTcZTcZTcZScZScZScZScZRcZScZSc\ ZScZScZScZScZScZScZScZScZScZScZScZScZScZScZRcZScZS\ cZTcZTcZUcZUcZUcZVcZVcZWcZWcZWcZXcZXcZYc_Yc_ZcZZbZ\ ZaZ_`Y__Y`ZY`YY`XXaWXaVXbUWbTWcSWcRVcQVdPVdOVeNVeM\ VeLVdKVcJVcIVbHVbGVaFVaEV`DU`CT_BS_ARcAQcBPcCOcCNc\ DMcDLcEKcFJcFIcGHcGGcHFcIEcIDcJCcJBZKAZL9ZL8ZM7ZN6\ ZM7ZM7ZM7ZM7ZM7ZM7ZM7ZM7ZM7ZM7ZM6ZM6ZM6ZL7ZL7ZL7ZL\ 7ZL7ZL7ZL7ZL7ZL7ZL7ZL7ZL7ZL7ZK8ZK8ZK8ZK8ZK8ZK8ZK8_\ K8_K8`K8`K8aK8aK8bJ9bJ9cJ9dJ9eJ9fJ9gJ9hJ9iJ9jJ9kJ9\ lJ9mJ9mIAmIAmIAmIAmIAmIAm } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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FOTD 18-03-05 (False Seahorse [5])
by Jim Muth 18 Mar '05

18 Mar '05

FOTD -- March 18, 2005 (Rating 5) Fractal visionaries and enthusiasts: Today's image looks like just another trip to one of the Julia sets associated with Seahorse Valley. But look again! It is not even a Julia set. Real Julia sets are never filled with horizontal stripes such as those that fill the interior of the object in today's scene. Today's image shows a Rectangular set located off to the side of the Seahorse Valley of a tiny midget which is located on the negative stem of the M-set, near the point where the stem joins the main body of the Set. I named the image "False Seahorse". I gave it this name because at first glance it appears to be a Julia set, but closer examina- tion will reveal that it contains features that never appear in true Julia sets. I am not all that pleased with the coloring, which for some reason never came alive as I had hoped. Something more is needed to contrast with the hazy blue color of the interior of the Rectangular set. The rating of an average 5 reflects my lack of satisfaction. The rendering of today's image starts off fast enough, reaching 90-percent completion in the first couple minutes, but it slows to a near halt when it reaches the open stripe around the X-axis, and takes over 1/2 hour to finish. The frustration may be avoided by downloading the finished GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Well, today's effort might have fallen a bit short, but I have three more chances to produce a really outstanding Rectangular image before we move on to the Elliptic orientation. The clouds broke in mid-afternoon here at Fractal Central on Thursday, in just enough time for the cats to enjoy an hour in the sun on the porch. The hour must have been enough, for when the sun sank behind the trees, they came inside satisfied and ready for tuna. Today is starting sunny and it will likely be warmer. The duo should be happy. I have a little more than the usual amount of work stuff to put behind me before I will be happy, but the work will be finished and the next FOTD will appear on schedule in 24 hours. Until then, take care, and be yourself. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= False_Seahorse { ; time=0:33:24.06--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=flip/ident passes=1 center-mag=-0.00518053262314617/0/161638.\ 3/0.05557 params=0/90/2/0/0/0/-1.401913873518217/0 float=y maxiter=150000 inside=0 logmap=-230 symmetry=xaxis periodicity=10 colors=000R23S43T63V86WA9XCCZEF`GIbJLcLNgSQiYTmdWn\ jZrqastcpr`mqYjoVgnSelPbkM_iKXgHUeEScAPaKM_UJYcHWm\ TVmdLmcNmbPobRqaTtaUw`Xz`Yz_`z_azZczZezYfzYgz_fzae\ zcdzdczfbzhazi`zgZzfYzeXzcWzbVzaTz_SzZRzYQzXPzZOz_\ Oz`OzbOzcNzdNzeMzgMzhLziLzkKzlKzmKznKzcKzTKzJKzKKz\ LKzMKzJKzHKzFKzDKzBKz9Kz7KzBKzEKzIKzLKzPKzSKzWKzZK\ zbKzeKziKzlKzoKzqLzsMzSNzQOzPPzNQzMRzKSzJTzRUzYUzd\ UzdUzdUzdUzdUzdUzdUzdUzdUzdUzdUzPUzAUz9Uz8Uz8Uz7Uz\ 6Uz6Uz5Uz4Uz4Uz3Uz2Uz2Uz5Uz8UzBUzEUzHUzKUzNUzQUzTU\ zWVzZWzaXzdYzcZzc_zb`zbazabzaczadz`ez`fz_gz_hz_izX\ jzVkzTlzQmzOnzMozKpzHqzFrzDszBtz8uz6vz4wz2xzAyzHzz\ OzzVzzazzhzzozzmzzkzzizzgzzezzczzazz_zzYzzWzzUzzSz\ zPzzNzzLzzJzzHzzFzzDzzBzzEzzHzzKzzNzzPzzSzzVzzYzz`\ zzbzzezzhzzkzzmzzizzkzzmzzozzpzzqzzrzzszztzzuzzvzz\ wzzxzzyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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Wild Electric Dream
by Vortex Swirling 17 Mar '05

17 Mar '05

Has anyone seens this DVD? Is it worth acquiring? -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.7.3 - Release Date: 3/15/2005 -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.7.3 - Release Date: 3/15/2005

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Re: David Dollevoet web site
by JackOfTradeZ 17 Mar '05

17 Mar '05

Good luck Dave! I was there once - just put up my 1st site ... 4 years ago. Advise: put up a few thumbnail pics for your files / galleries to get attention; most people have broadband now and load time is not a factor. Spice it up a little.

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FOTD 17-03-05 (Alien Flowers [7])
by Jim Muth 17 Mar '05

17 Mar '05

FOTD -- March 17, 2005 (Rating 7) Fractal visionaries and enthusiasts: Happy Saint Patrick's Day fractal fanatics. In yesterday's FOTD discussion I remarked that today's image would be horrendously slow. I am not quite sure why I made that remark. Today's image renders in under 50 minutes even on my tired old clunker. This is not blazingly fast, but it is certainly not horrendously slow either, especially considering that in the past I have posted FOTD images that take over a full day to complete. Today's image is one I came upon and passed by while searching for a fractal of the variety seen in yesterday's image. The scene is located in the vicinity of the large midget on the negative X-axis of the Mandelbrot set. Since the Julibrot is four-dimensional, it is futile to try to describe the exact relation of today's image to the midget itself, other than to state that, despite its Julia-like appearance, the image is actually sliced in the Rectangular direction. The rating of a 7 is based largely on the coloring, to which I gave more than the usual amount of effort. It is now two days after the time I first saw the image however, and the picture is starting to look more like a 6 than a 7, but I must go with my first impression, so the rating of 7 will remain. The image reminds me of a cluster of flowers, such as might be seen on another planet lying in some remote corner of the galaxy. I named it "Alien Flowers". The fractal bouquet may be enjoyed by running the included para- meter file and waiting a half-hour or so, or by giving Paul a chance to run the file and post the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Despair not for the conclusion of the philosophy. It will eventually appear. The problem is that I have read some new material that has caused me to rethink several of my long-held conclusions about the nature of the self, and I must now re- codify my doctrine. And yes, I realize that I used the word 'doctrine'. Since I will be able to offer no proof of my eventual claims, they will fall into the category of a doctrine, to be believed or more likely rejected as the reader sees fit. Hopefully, all this will happen within a week, but no promise is given. The afternoon turned cloudy and chilly here at Fractal Central on Wednesday. The cats turned sulky when the sun vanished, and demanded their tuna before the official time for tuna arrived. But by evening, they had forgotten their bad afternoon and settled for a long sleep. Today is starting with about the same weather. I hope the cats' day is better, but fear a repeat. With only a little real work to put behind me, I expect my day to be acceptable. The next FOTD is due in 24 hours. There is a 99-3/4 percent chance it will appear at that time. Until that golden moment arrives, take care, and if an atom is a fractal, what then is a molecule of water, which is composed of three fractals? (Maybe an atom is not a fractal; maybe a molecule of water is a fractal.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Alien_Flowers { ; time=0:49:57.50--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=flip/ident passes=1 center-mag=-0.11570559494539450/+0.011693\ 05771904837/1734752/0.7588/41.8961562691883813/38.\ 6021046066249 params=0/90/2/0/0/0/-1.7541/0 float=y maxiter=40000 inside=bof61 logmap=57 periodicity=10 colors=000BCFCEHDGJFINGKRIMUJOYLQaMSeOUiOUmPWlPXlP\ ZkP_kPakQbjQcjQejQfiQhiQiiRjhRlhRmgRogRpgSqfSsfStf\ SveSweUwdSxeRxeQxfPxfOxfNxgLxgKxhJxhIyhHyiGyiEyjDy\ jCyjBykAyk5zm9zkDzjGzhKzgOzfRzhVzjZzlaznezpizrlzrm\ zrnzrozrpzrqzrqzrqzrqzrqzrqzrqzrqzrqzrqzrqzrqzrqzr\ qzrqzrqzrqzrqzrqzrqzrqzrqzrqzrqzrqzrqzrqzrqzrhxXhx\ YgxZgw_fw`fwaewbewcdvddvecvfcvgCubcvhasg`qf_oeZmdY\ kcXibWgaVd`Ub_T`ZSZYRXXQVWPTVOQUNOTMMSLKRKIQJGPIEO\ MIPQMQUQRXUS`YTdaUheVzXAkhWPzvRvsTsqVpnXmlZjikQveZ\ n_ggUp_QzUPyTPwSPuRPsQPqPOoOOmNOkMOiLOgKOeJNbJN`IN\ ZHNXGNVFNTEMRDMPCMNBMLAMJ9II7KH8MH9NGAPGBQFCSFDTEE\ VEFWDGYDHZCI`CJaBKcBLdAMfANg9Oi9Pj8Ql8Rl5Om7Qm8Rm9\ TmAUmBWmDXmEZmF_mGamHbmIdnKenLgnMhnNjnOknQmnRnnSpn\ TqnUsoUwnVtmVqlWokWljXjiXghYegYbfY_eZYdZVc_Tb_Qa`O\ ``L_`Jbhj`fk_dkZclYalX`mWZmVYnUWnSVoRToQSpPQpOPqNN\ qMMrLKrKJrpSWnUZmWakYdj_g } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 14-03-05 (Fêtes [4])
by Vortex Swirling 16 Mar '05

16 Mar '05

Paul, No. No such luck. I get the digest, so in order to reply to the list before I get that I just cut and paste the subject line from the list on the html page. My digest is one blob so I'd have to do that anyway, but for the record, what came in on the digest was the correct symbol (Eudora seems to work). Since I cut and pasted form the web page, I got the ? symbol instead since that is what is being displayed by IE. I tried the same page in FireFox which I have as a secondary browser and it shows up as ? as well. I replace the ? with Alt 136 here in this subject line. Now lets see what gets confused... -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.7.3 - Release Date: 3/15/2005 -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.7.3 - Release Date: 3/15/2005

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FOTD 16-03-05 (Rectangular Julia [4])
by Jim Muth 16 Mar '05

16 Mar '05

FOTD -- March 16, 2005 (Rating 4) Fractal visionaries and enthusiasts: The figure in today's image does not resemble a midget Mandel- brot set. Nor does it resemble a midget Julia set. It is some- thing entirely different -- a midget Rectangular set -- and it looks like nothing that could appear in the more conventional Mandelbrot or Julia fractals. On the surface, today's image suggests a midget Julia set, but Julia midgets are always symmetrical, and the thing in today's image is certainly not symmetrical. Its left side is entirely different from its right side. The left side is filled in, while the right side is open. And what about those brilliant straight elements in the background? Such straight elements never appear in Julia or Mandelbrot fractals. They appear only in certain odd slices between the two orientations. They are the give-away that we are in an odd orientation of the Julibrot. The location of today's scene is the vicinity of the northeast shoreline of the main bay of the large midget on the negative stem of the Mandelbrot set. It is located on the imag(z) axis, some distance from the actual Mandelbrot set, however. Some rotation and stretching was needed to bring the elements of today's scene to a more familiar proportion. I did no skewing, but the effect of the rotation, combined with the stretching, was to skew, or rather unskew, the image. The name "Rectangular Julia" is a simple description. The rating of a 4 is about what the image deserves. Such scenes have appeared numerous times in previous FOTD fractals, and the coloring is merely average. The render time of around 8 minutes is slightly slow, but com- pared to the horrendously slow image that will appear tomorrow, it is as fast as light. Luckily, relief is, and will be, at hand on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image has been posted, completed and ready for download. A sunny but chilly 48F 9C day on Tuesday here at Fractal Central limited the cats' outdoor time to under one hour, but in that time they had enough excitement for an entire day. While they were resting in the holly thicket, the tough gray-and-white cat from up the hill intruded in the yard, and it took immediate loud action by both Thomas and Tippy to chase him back where he belongs. When they came inside, I rewarded them with extra tuna and a bit of cheddar cheese. Today is starting partly cloudy and chilly again. We could be in for a repeat. For me, it looks like just another in an unending string of similar days. But this does not mean boredom. How could one be bored in a world composed of the fractals that we call atoms? The next FOTD will appear in 24 or so hours. Until then, take care, and relax. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Rectangular_Julia { ; time=0:07:54.89--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=flip/ident passes=1 center-mag=-0.10991105963559750/+0.006420\ 75384452202/11016.77/0.6894/-138.7784/65.942449468\ 6845151 params=0/90/2/0/0/0/-1.748/0 float=y maxiter=16000 inside=0 logmap=30 periodicity=10 colors=000KRNKRLKSJKTHKUFKVDKWBKW9KX7KY5KZ3K_1K_0K\ `1K`1L`1L`2M`2M`2N`2N`3O`3Oa3Pa3Pa4Qa4Qa4Ra4Ra5Sa5\ Sa5Tb5Tb6Tb6Ub6Ub6Vb7Vb7Wb7Wb7Xc8Yc8Zc8_c9`c9ac9bc\ 9ccAdcAedAfdAgdBhdBidBjdBkdCldCmdCmeCmeDmeDmeDmeDm\ eEmeEmeEmeEmdDmdDmcDmcDmbDmbDmbDmaDmaDm`Dm`Dm_Dm_D\ m_DmZDmZDmYDmYDmYDmXDmXDmWDmWDmVDmVDmVDmUDmUDmTDmT\ DmTDmSDmSDmRDmRDmQDmQDmQDmPDmPDmODmODmNDmNDmNDmMDm\ MDmLDmLDmLDmKDmKDmJDmJDmIDmIDmIDmHDmHDmGDmGDmGDmFD\ mFDmEDmEDmDDmDDnDDnCDnCDoBDoBDoBDnCEnCEnCFnDFnDFnD\ GnDGnEGnEHnFHnGInHInIInJJnKJnLJnMKnNKoOLnPKnQJnRIn\ SHnTGnUFnVEmWEmXDmYCmZBm_Am`9ma8mb7lc7lc6lc5lc4lc3\ lc2lc1lc1kc3kc4kc5kc6kc7kc8kc9kcAkczkczkczkczkczjc\ zjczjczjczjdzjezjfzjgzjhzjizjjzjkzjlzjmzinziozipzi\ qzirziszitziuzivziwzixziyzizzizzhzzhzzhzzhzzhzzhzz\ hzzhzzhzzhzzhzzhzzhzzizzhzzhzzgzzgzzfzzfzzfzzezzez\ zdzzdzzczzczzczzbzzbzzazz } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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