November 2005 - Fractint - mailman.xmission.com

FOTD 13-11-05 (A Julia Set for All-3 [7])
by Jim Muth 13 Nov '05

13 Nov '05

At 08:13 AM 11/13/05 -0700, you wrote: >Jim, >>> The name "A Julia Set for All-3" indicates that it is the third >in the series of similar Julia sets. << >What happened to "A Julia Set for All-2"? You sent an e-mail yesterday >with that title, but it was just a repeat of "A Julia Set for All-1"! >Lee I apparently made a mistake. I have just posted the correct FOTD for November 12. The curious thing is that no one noticed the duplication until now, or if they did notice, they didn't consider it important enough to comment on. Maybe the FOTD is nearing its last lap. We'll see how it goes. Jim M.

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FOTD 12-11-05 (A Julia Set for All-2 [5])
by Jim Muth 13 Nov '05

13 Nov '05

FOTD -- November 12, 2005 (Rating 5) Fractal visionaries and enthusiasts: Quite a while back, I received an e-mail from a forgotten someone who asked me why I so often end my FOTD discussions with such silly questions. Maybe it is because I am such a silly person. After all, why would any sensible person devote as much time and energy as I do to such a fruitless endeavor? But as for the questions, they are not supposed to be answered. They are merely philosophical thoughts in the guise of questions. Today's closing question for example asks about Julia sets on the head of a pin. It cannot possibly be answered because fractals are abstractions with no definite size. Anyone who tried to answer it would soon find themselves thinking about the true size of a fractal and would realize that a fractal is not the same kind of thing as a speck of dust or a planet. Today's image is a fractal. This much is certain. Yesterday's image was a Julia set of the south branch of Seahorse Valley of the Z^(2.01)+C Mandeloid as it appears 17 turns up the logarith- mic spiral. Today's image is a Julia set of the north branch of the same valley. But don't assume it is a repeat. The corres- ponding Mandeloid has no X-axis symmetry, and this makes today's image quite different. Yesterday's image consisted mostly of 'inside' stuff made active by the 'zmag' inside fill. Today's image shows a Julia set that consists totally of 'outside' stuff, quite a bit different from both yesterday's image and what would be expected in a conven- tional Julia set of Seahorse Valley of the familiar M-set. I named the image "A Julia Set for All-2". It is the second and maybe not the last in the series of similar Julia sets. The rating of a 5 indicates that I consider the image to be of average quality. The render time of 1-plus minutes assures that not too much time will be wasted if the image proves to be un- satisfactory. The finished product is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> from where it may conveniently be downloaded and the task of rendering completely eliminated. The partly cloudy skies and 52F 11C temperatures here at Fractal Central on Friday did not keep the cats from enjoying their usual time in the yard. The lack of wind made it easy for them to hear approaching danger. Today is starting cold, but it is sunny and the wind is calm. When it warms up this afternoon, the cats will have a good time. My day looks peaceful also. Until the next FOTD appears in 24 hours, take care, and how many Julia sets could fit on the head of a pin? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= AJuliaSetForAll-2 { ; time=0:01:16.95--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC passes=1 center-mag=0/0/0.9861933/1/-17.5/3.88578058619e-016 params=2.01/0/17/0/-0.7496/0.2947/0/0 float=y maxiter=1000 inside=255 periodicity=10 colors=000A0PA0PA0PA0PA0PA0PA0PA0PA0O90N90N80O80O7\ 0P70P60Q60Q50R50R80QB0QE0QH0PK0PM0PPLQWNVbP_hQdoSi\ uTnsTkrThqTepTboT_nTXmTUkTRjTOiTLhTIgTFfTCeTAWY_Mb\ ywQduScsTcqUboVbmWalXajYahZ`f_`d`_cb_acZ`dZ_eZZfYZ\ gY_hX`iXajWbkWckWdiUefTdcRc`QaYP_WNYTMUQLQOJOMINMH\ MOHMRHOVHTZHYbHcfHhjHnnHsrHxvHusIsqJpnKnlKkjLigMge\ NdcNb`O_ZPYWQVUQTSRRPSONTMLTJIUHGVFEVEGXEIYEKZDM`D\ OaDPbCRcCTeCVfBXgBYhB_jAakAclAen9go9hp9jq8ls8nt8pu\ 8qvCrqGsmJshNtdRt`UuWYuSavOdvJhwFkwBltDlqFlnGlkIli\ JlfLlcMl`OlZPmWRmTTmQUmNWmLXmIZmF_mCamAbfDa`GaVI`O\ L`IO_CQ_DRYDSXETVEUUEVSFWRFXPGYOGZMG_LH`JHaIIbGIcF\ IdELcINcLPbPRbSTaVVaZX`aZ`d`_hb_kd_n`VoYQpUSmQUjNW\ gJYdF_aCaZ8cW4eT1gR8iSEjTLlTRmUYoVcpVdoUemSflRgjQh\ iOigNjfMfgLcgK`gJYgIVhHShGOhGLhFIiEFiDCiC9iB6iB8jD\ 9jFAjHBjJCjLDjNFjPGjRHjTIkUJkWKkYMk_NkaOkcPkeQkgRk\ iSkjlJeoHdqFcsDbuCbpHcQLR } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(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|< p4+100 } END PARAMETER FILE=========================================

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FOTD 13-11-05 (A Julia Set for All-3 [7])
by Jim Muth 13 Nov '05

13 Nov '05

FOTD -- November 13, 2005 (Rating 6) Fractal visionaries and enthusiasts: For today's fractal we return to the Z^(2.01)+C Mandeloid and check it 300 levels up the logarithmic spiral, where it has rotated nearly 180 degrees, so that East Valley lies on the negative X-axis. The local elephant herd has has shifted west, perhaps in search of water. But once an elephant, always an elephant. Since elephants can not become seahorses any more than people can become elephants, the basic shape of the Julia set of our western East Valley is still what one would expect of an East Valley Julia set. This is where the similarity ends however. The fine-tooth-comb stuff that fills today's Julia set is a horse of a different color. I have never seen anything like it in any East Valley Julia set of the classic Mandelbrot set. The rating of a 6 is a bit above the average, which however is nothing to crow about. Perhaps if I had monkeyed around with the colors a bit further, I could have rated it at a 7, which would have made me proud as a peacock, but to be honest, the image really is little more than a humdrum Julia set of East Valley. The name "A Julia Set for All-3" indicates that it is the third in the series of similar Julia sets. I doubt that there will be a fourth in the series, and I'm not lion. I would be bats if I continued this unimpressive series. Today's image renders in only 1-3/4 minutes, which is quick as a bunny. Those with over-progressive machines that have forgotten how to do DOS may see the image by flying like an eagle to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and downloading the finished image from there. A totally perfect day here at Fractal Central on Saturday kept the fractal cats quite happy. Only the brief incursion of an unwelcome stray cat marred their happiness. But the other cat quickly departed when Tippy approached him and went into fight- ing stance. The day ended with both cats' noses in their tuna dish. Today is starting perfect again. My day will not be per- fect, as human beings have too many other things to be concerned about, but it looks like it will be pretty good. Until the next FOTD appears in 24 hours, take care, and will the real mystery please stand up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= AJuliaSetForAll-3 { ; time=0:01:XX.XX--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC passes=1 center-mag=0/0/1.041667/1/87.5/3.885780586188e-016 params=2.01/0/300/0/-0.267125/-0.006185/0/0 float=y maxiter=500 inside=255 logmap=yes periodicity=10 colors=000AcjAagAXcAWbAV`AUZASXAPVAMRAJOAGKADIACIA\ AIA9JA8JA9KAAKACKADLAGLAIMALMKNNUPNcPNkZszwytstoop\ ikldgh_cdX_`UXXQTTNPPJLLGHHCDD999665A57D59G5AJ4CN4\ EQ4FT3HW3I_3Kb2Mc2Nc2Pc2Qc3Oc4Mc4Lc5Jc5Ic6Gc6Fc7De\ 7Cc8Fa9I_BMYCPWDSUEVSFYQHaOIdMJgKKjILmHMpKLlMKiOJf\ RIbTI_VHXXGU_FQaENcEKcDGcCDcBAcB7cC8cD8cE9cE9cFAcG\ AcHFcHKcIPcJUcKZcKccHhcEmcCra9wX7z_BzbFzdIzgMzjQzl\ TzoXzq_znXzkUzhRzeOzbLzMrdMreNrfNsgOshOsiPsjPtkPtl\ QtmQunRuoRupSuqSvrTvsTvtTvuSsvSqwRoxRlyRjzQhzQezPc\ zPazPZzOXzOVzNSzNQzNOzMLzMJzMHzOOzPUzQ_zRezQbzP`zO\ YzNWzNUzMRzLPzKNzKKzJIzIGzHDzHBzG9zF6zE4zE2zLCzSMz\ YWzYZzYazYczYfzYizYkzYnzYqzYszXqzWozWnzVlzVkzUizUh\ zVfzVezWdzWczWbzX`zX_zXZzYYzYXzYWzWTzVRzTOzSMzQKzP\ HzNFzMCzKAzJ8zH5zG3zF1zG6zHBzIGzJLzKQzLUzMZzNczOhz\ PmzQrzRvzYgzdTzkEzr0zp4zo8znCzlGzkKzjNzhRzgVzfZzdb\ zcfzbiz`hz_hzYhzGazFdzFgz } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(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|< p4+100 } END PARAMETER FILE=========================================

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FOTD 12-11-05 (A Julia Set for All-2 [5])
by Jim Muth 12 Nov '05

12 Nov '05

At 11:55 AM 11/11/05 -0500, you wrote: > >FOTD -- November 11, 2005 (Rating 6) > >Fractal visionaries and enthusiasts: > >Today's fractal is a Julia set of the southern branch of >Seahorse Valley of the Z^(2.01)+C Mandeloid as it appears 17 >levels up the logarithmic spiral, where the Mandeloid has split >apart and rotated about 15 degrees. The image is a Julia set >for all, and that is what I named it. I added the '1' at the >end of the name because there might be more such Julia sets. > >A good part of the image consists of 'inside' stuff brought to >life by the 'zmag' inside fill option, which fills this set with >slightly organized chaos. The end result is a Julia set that >obviously is connected to Seahorse Valley, but is not quite what >we expect a Seahorse Valley Julia set to look like. > >A curious feature of the image is that its coloring changes as >the maxiter is raised or lowered. > >The rating of a 6 might be a bit overdone, but I rather like the >image, so the rating will remain. The render time of 10 odd >minutes borders on slowness. Luckily, rendering may be avoided >by downloading the completed image from the FOTD web site at: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > >A chilly, blustery, 50F 10C day on Thursday here at Fractal Cen- >tral kept the fractal cats unhappy. But a can of tuna came to >the rescue in the evening. Today is starting sunny but quite >chilly, and there is still a breeze. The cats will have to make >do with less than ideal conditions. My day will likely be close >to average. Until 24 hours from now when the next FOTD will >appear, take care, and relief is on the way. > > >Jim Muth >jamth(a)mindspring.com >jimmuth(a)aol.com > > >START PARAMETER FILE======================================= > >AJuliaSetForAll-1 { ; time=0:10:41.25--SF5 on a P200 > reset=2004 type=formula formulafile=allinone.frm > formulaname=JuliaBC passes=1 periodicity=10 > center-mag=0/0/0.9861933/1/-22.5/3.88578058619e-016 > params=2.01/0/17/0/-0.8075489172/0.039334604022/0/0 > float=y maxiter=1000 inside=zmag > colors=00030630840A40C50E50G60I60J70L70M70O80P80R9\ > 0S90UA0VA0XA0ZD0`G0bJ0cM0dP0eS0eV4gYCh`KidSog_ujcu\ > njuqcHTZBZUAcPAdKBdFCeCCeEDeFDfGEfIEfJFgKGgMGgNHhO\ > HhQIhRIiSJiUKjVKjWLjYLkZMk_MkaNlbOlcOlePmfPmgQmhQl\ > iRkjSjkTilUhmVgmWfnXeoYdpZcq_cq`braasb`tc_udZveYvf\ > XwgWxhVyiUzjUzjTxhTwgTveTudStbSsaSr`SqZSpYRoWRnVRm\ > TRlSRkRQjSQiUQhXQg_OebQfeSghUgkWhnYiq_itajwekzcjza\ > jz_izZizXizVhzThzSgzQgzOgzMfzLfzJezHezFezEdzCezAfz\ > 8gz9hz7iz6jz5kz4lz3my1nx2ow2pv3qu3rt4ss4ts5ur5vr6w\ > q6xq7yp7zp8zozzozzozznzznzzmzzmzzlzzlzzkzzkzzjzzjz\ > zizzizzhzzhzzdzzhzzlzzpzztzzxzzqzzkzzezz_zzTzzNzzH\ > zzBzzDzzFzzGzzIzzJzzLzzMzzOzzPzzRzzTzzUzzWzzXzzZzz\ > _zzazzbzzdzzfzzgzzizzjzzlzzmzzo9zrBzpCznDzlEzjFziG\ > zgHzeIzcJzaLz`MzZNzXOzVPzTQzSRzQSzOTzMUzKWzJXzHYzF\ > ZzD_zB`zAaz8bz6cz4dz3fz6hz9jzClzFnzIozLqzOszRuzUwz\ > Xyz_9zL8zJ7zH1zG7zFDzEIzD } > >frm:JuliaBC { ; Formula by Andrew Coppin > e=p1, p=real(p2)+PI, q=2*PI*floor(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|< p4+100 } > >END PARAMETER FILE========================================= > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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Re: Another Muth ZooM
by JackOfTradeZ 12 Nov '05

12 Nov '05

Zoom in animation of Jim Muth FOTD for 9/1/05, the Mandelbrot squared diamond. It is posted on my site; the direct link is: http://www.fractal-animation.net/vid/m_squared.zip WMV, 320x240, 60 sec, 4.2 MEG JoTz

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FOTD 11-11-05 (A Julia Set for All-1 [6])
by Jim Muth 11 Nov '05

11 Nov '05

FOTD -- November 11, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal is a Julia set of the southern branch of Seahorse Valley of the Z^(2.01)+C Mandeloid as it appears 17 levels up the logarithmic spiral, where the Mandeloid has split apart and rotated about 15 degrees. The image is a Julia set for all, and that is what I named it. I added the '1' at the end of the name because there might be more such Julia sets. A good part of the image consists of 'inside' stuff brought to life by the 'zmag' inside fill option, which fills this set with slightly organized chaos. The end result is a Julia set that obviously is connected to Seahorse Valley, but is not quite what we expect a Seahorse Valley Julia set to look like. A curious feature of the image is that its coloring changes as the maxiter is raised or lowered. The rating of a 6 might be a bit overdone, but I rather like the image, so the rating will remain. The render time of 10 odd minutes borders on slowness. Luckily, rendering may be avoided by downloading the completed image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A chilly, blustery, 50F 10C day on Thursday here at Fractal Cen- tral kept the fractal cats unhappy. But a can of tuna came to the rescue in the evening. Today is starting sunny but quite chilly, and there is still a breeze. The cats will have to make do with less than ideal conditions. My day will likely be close to average. Until 24 hours from now when the next FOTD will appear, take care, and relief is on the way. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= AJuliaSetForAll-1 { ; time=0:10:41.25--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC passes=1 periodicity=10 center-mag=0/0/0.9861933/1/-22.5/3.88578058619e-016 params=2.01/0/17/0/-0.8075489172/0.039334604022/0/0 float=y maxiter=1000 inside=zmag colors=00030630840A40C50E50G60I60J70L70M70O80P80R9\ 0S90UA0VA0XA0ZD0`G0bJ0cM0dP0eS0eV4gYCh`KidSog_ujcu\ njuqcHTZBZUAcPAdKBdFCeCCeEDeFDfGEfIEfJFgKGgMGgNHhO\ HhQIhRIiSJiUKjVKjWLjYLkZMk_MkaNlbOlcOlePmfPmgQmhQl\ iRkjSjkTilUhmVgmWfnXeoYdpZcq_cq`braasb`tc_udZveYvf\ XwgWxhVyiUzjUzjTxhTwgTveTudStbSsaSr`SqZSpYRoWRnVRm\ TRlSRkRQjSQiUQhXQg_OebQfeSghUgkWhnYiq_itajwekzcjza\ jz_izZizXizVhzThzSgzQgzOgzMfzLfzJezHezFezEdzCezAfz\ 8gz9hz7iz6jz5kz4lz3my1nx2ow2pv3qu3rt4ss4ts5ur5vr6w\ q6xq7yp7zp8zozzozzozznzznzzmzzmzzlzzlzzkzzkzzjzzjz\ zizzizzhzzhzzdzzhzzlzzpzztzzxzzqzzkzzezz_zzTzzNzzH\ zzBzzDzzFzzGzzIzzJzzLzzMzzOzzPzzRzzTzzUzzWzzXzzZzz\ _zzazzbzzdzzfzzgzzizzjzzlzzmzzo9zrBzpCznDzlEzjFziG\ zgHzeIzcJzaLz`MzZNzXOzVPzTQzSRzQSzOTzMUzKWzJXzHYzF\ ZzD_zB`zAaz8bz6cz4dz3fz6hz9jzClzFnzIozLqzOszRuzUwz\ Xyz_9zL8zJ7zH1zG7zFDzEIzD } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(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|< p4+100 } END PARAMETER FILE=========================================

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FOTD 10-11-05 (Crazy Trilobite [7])
by Jim Muth 10 Nov '05

10 Nov '05

FOTD -- November 10, 2005 (Rating 7) Fractal visionaries and enthusiasts: ;-) ;-) ;-) ;-) ;-) ;-) When I checked my e-mail box this morning, I found a letter telling me that I had been selected to be included in the next issue of Who's Who. I have no idea what I have ever done that makes me worthy of such honor. I didn't realize that fractals are so important. I also wonder why the publishers need me to submit my biography. They must have already known of my great fractals and my great graphic design ideas when they chose me for inclusion. But why did they notify me by sending a junky, poorly-written e-mail letter in HTML format, padded by random nonsense text? One would expect the notification of such an honor to arrive in a fancy snail-mail package or by a personal phone call. The next thing I know, they'll want me to pay for the honor of inclusion, which would make it no honor at all. ;-) ;-) ;-) ;-) ;-) ;-) While thinking of what to do about this, I'll turn to today's fractal, which is a Julia set of the Z^(1.5)+C Mandeloid as it appears 15 levels up the logarithmic spiral. The Mandelbrot point of today's Julia image is located in a truncated valley of the associated M-set. I named the image "Crazy Trilobite". For some reason it reminds me of one of those long-extinct creatures that once crawled in the slime of primordial sea floors. The rating of a 7 seems appropriate. Yes, I realize that the image has only one layer, but when it comes to fractals, one layer and a skilled fractalist are all that is needed. The render time of 4-1/2 minutes on my machine means that no one will be overly inconvenienced if they find the image not worth the effort. And as always, the completed fractal is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Despite the clouds that hung around all day Wednesday here at Fractal Central, the rain never arrived and the temperature reached 64F 18C. This was good enough for the fractal cats, who spent the afternoon out of sight in the holly thicket. Today is starting with sun and clouds, but the winds are up, and the cats dislike high winds that hide the sound of danger. We'll have to see how it goes. For me, the day coming up looks average. The next FOTD will appear in 24 hours. Until then, continue taking care, and wonder why so much care is necessary. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Crazy_Trilobite { ; time=0:04:27.76--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC passes=1 center-mag=0.244131/0.0250522/1.041667 params=1.5/0/15/0/-0.2492/0.0617/0/0 float=y maxiter=1500 inside=bof60 periodicity=10 colors=000j5Bg6Be6Ab7A`79Y89V98T98QA7OA7LB6IC6GK5D\ N5BP5FSBIVHLYNOaSReYUicXmh_plZtpYxrXyuXzzWueVudUub\ Uu`Tu_SuYmuWzuVmuTmuRzzQmvPmwNmxMSxLWqMZkMaeMd_M`a\ PYcRVeTSgVPiXMkZJm`PfdU`gZVkcPnhJqiMniPkiRhiUeiWbi\ Z_i`XicUieRihOijLimIioFirCitAfqLcnV`ldYinWgxXdwXbv\ X`uYZtYXsYVrYTqZRpZPoZNn_Lm_Jl_Hk_FjWLdSQZOVTK_NGd\ HCiCEgFFfHHdJIcMKbOL`QN_TOYVQXXRWZTV_VV_WU_YU_ZT_`\ T`aS`cS`eS`fR`hRaiQakQalPanPaoPaqO`tN_vM_mLUdLPWLJ\ NLEEL85L35P75TB5XF5`J5dN8eLqKnoMnmOojQohRofTpdVpaX\ p_ZqY_qWaqTcrRerPgrNhrdiSvj1qi2mh3ig4ef5ae6Ye7Ud8Q\ c9MbAIaBEaCGZDHXDJVDKTDLRDNODOMDPKDRIDSGDUDDVBDW9D\ Y7DZ5D_3DY5LW7TU9`SBhQDpPEwRCsTBoVAlX8hZ7d`6ab5Yd3\ Uf2Rh1Nj0Kg5JdAJaEI_JIXOHUSHRXGPaGMeFJjFGoEEsEFpFF\ nGGlHGjHHgIHeJIcKIaKJZLJXMKVNKTNMPLOLJQHIQHIQHJQHJ\ QIJQIJPIJPIJPJJPJJPJJPJJPJJPKJOKJOKJOKJOKJOLJOLJOL\ JOLJF`LNLJNMJNMJjGBlACm4C } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(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|< p4+100 } END PARAMETER FILE=========================================

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Re: [Fractint] Triternions Ikenaga and Lambda
by Russell Walsmith 10 Nov '05

10 Nov '05

Thanks for your interest in the triternion formulas, Gilles. List members may enjoy your elegant galleries at http://www.mathsong.com/casaraku/ Ciao, Russell ----- Original Message ----- From: "gilles nadeau" <gillesnadeau56(a)videotron.ca> To: fractint(a)mailman.xmission.com Subject: [Fractint] Triternions Ikenaga and Lambda Date: Sun, 06 Nov 2005 02:41:50 -0500 > > Hello all, > > I am new on this list but I use Fractint since 1994. I have > difficulty in include/understand English and I use a translator. > I would like to propose two new models of "Triternion". T_Ikenaga > and T_Lambda. The formulas triternion are mysterious. > I read that those would be 6-d. I am not a mathematician and I > does not know exactly what that means. > Here two formulas. > > Gilles Nadeau > > > T_Ikenaga-XZ {; 6-dimensional M-Set > ; based on formulae by Russell Walsmith > ; Gilles Nadeau, March, 2005 > ; > x=y=t=u=v=w=0 > cx=real(pixel) > cy=real(p1) > ct=imag(pixel) > cu=imag(p1) > cv=real(p2) > cw=imag(p2) > : > tx= x^3+t^3+v^3-3*(x*y^2+t*u^2+v*w^2)+6*(x*t*v-x*u*w-y*u*v-y*t*w) > ty=-y^3-u^3-w^3+3*(y*x^2+u*t^2+w*v^2)+6*(y*v*t-y*w*u+x*w*t+x*v*u) > tt= 3*(t*x^2-t*y^2+v*t^2-v*u^2+x*v^2-x*w^2)-6*(t*u*w+x*y*u+y*v*w) > tu= 3*(u*x^2-u*y^2+w*t^2-w*u^2+y*v^2-y*w^2)+6*(x*v*w+x*y*t+t*u*v) > tv= 3*(v*x^2-v*y^2+x*t^2-x*u^2+t*v^2-t*w^2)-6*(u*v*w+x*y*w+y*t*u) > tw= 3*(w*x^2-w*y^2+y*t^2-y*u^2+u*v^2-u*w^2)+6*(t*v*w+x*y*v+x*t*u) > dx=cx*x-cy*y+cv*t-cw*u+ct*v-cu*w > dy=cy*x+cx*y+cw*t+cv*u+cu*v+ct*w > dt=ct*x-cu*y+cx*t-cy*u+cv*v-cw*w > du=cu*x+ct*y+cy*t+cx*u+cw*v+cv*w > dv=cv*x-cw*y+ct*t-cu*u+cx*v-cy*w > dw=cw*x+cv*y+cu*t+ct*u+cy*v+cx*w > x=tx+dx-x-cx > y=ty+dy-y-cy > t=tt+dt-t-ct > u=tu+du-u-cu > v=tv+dv-v-cv > w=tw+dw-w-cw > z=x+flip(t) > z2=y+flip(u) > z3=v+flip(w) > |z|+|z2|+|z3|<=64 > } > > T_Lambda-XZ {; 6-dimensional M-Set > ; based on formulae by Russell Walsmith > ; Gilles Nadeau, March, 2005 > ; > x=0.5 > y=t=u=v=w=0 > cx=real(pixel) > cy=real(p1) > ct=imag(pixel) > cu=imag(p1) > cv=real(p2) > cw=imag(p2) > : > tx=x*x-y*y+v*t-w*u+t*v-u*w > ty=y*x+x*y+w*t+v*u+u*v+t*w > tt=t*x-u*y+x*t-y*u+v*v-w*w > tu=u*x+t*y+y*t+x*u+w*v+v*w > tv=v*x-w*y+t*t-u*u+x*v-y*w > tw=w*x+v*y+u*t+t*u+y*v+x*w > dx=x-tx > dy=y-ty > dt=t-tt > du=u-tu > dv=v-tv > dw=w-tw > x=cx*dx-cy*dy+cv*dt-cw*du+ct*dv-cu*dw > y=cy*dx+cx*dy+cw*dt+cv*du+cu*dv+ct*dw > t=ct*dx-cu*dy+cx*dt-cy*du+cv*dv-cw*dw > u=cu*dx+ct*dy+cy*dt+cx*du+cw*dv+cv*dw > v=cv*dx-cw*dy+ct*dt-cu*du+cx*dv-cy*dw > w=cw*dx+cv*dy+cu*dt+ct*du+cy*dv+cx*dw > z=x+flip(t) > z2=y+flip(u) > z3=v+flip(w) > |z|+|z2|+|z3|<=128 > } > > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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FOTD 09-11-05 (She Sells Sea Shells [6])
by Jim Muth 09 Nov '05

09 Nov '05

FOTD -- November 09, 2005 (Rating 6) Fractal visionaries and enthusiasts: She sells sea shells down by the seashore. It's an old tongue- twister that I learned back in the middle of the last century. The first four words, "She Sells Sea Shells", is the name of today's fractal, which reminds me of a pile of colorful sea shells washed up on some remote beach. The image, which is a 50-50 mixture of inside and outside stuff, was created by combining generous portions of Z^(-0.2) and Z^(-5.5) then adding (1/C). To create some extra excitement, the inside was set to 'fmod' with a proximity of 5, while the outside was set to 'tdis'. The parent fractal appears as a circular hole with some unim- pressive features scattered inside it. Only a small area shows potential, and it is this area that I chose to investigate. IMO, today's image rates a 6. A recent note on the list sugges- ted that I might rate the FOTD's according to more than simply how much effort I put into the coloring. I am considering an expanded rating system which will break the rating into two parts -- a fractal part and an artistic part. We'll see what I eventually decide to do. Today's image takes 4-3/4 minutes to come to life on my old and impossibly-outdated fractal-dedicated machine. Newer machines will bring it into existence in only a fraction of that time. Of course, the completed image has been posted as always to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> There wasn't much sun here at Fractal Central on Tuesday, but the temperature reached a high of 70F 21C, which kept the frac- tal cats quite happy. They spent a long uneventful afternoon lurking in the holly patch, watching for unwanted tomcats. But today is starting cloudy with rain in the area. I doubt that the good day will be repeated. The next FOTD will be posted in 24 hours, give or take an hour or two. Until then, take care, and what's it all about? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SheSellsSeaShells { ; time=0:04:43.58--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.07359315904045856/+0.004686271523444\ 79/2.673082e+007/1/-90/3.88578058618804789e-016 params=20/-0.2/16/-5.5/0/0 float=y maxiter=1500 inside=fmod proximity=5 outside=tdis periodicity=10 colors=000K7LJ7PH7TG7X_ZAaY8cW7dU6fS5hQ3jO2lM1mL0l\ N2lO3kP5kQ6kS8jT9jUBjVCiXEiYFhZHh_IhaKgbLgcNgdOifP\ jhPljQmlRopQnmRmjRlgSkdSkbSj_TiXThUTgRUgPUfMUeJVdG\ VXDkdEVg2HkEEoQCr`Avl8yw6wsAvoEukIshMrdPq`ToYXnU`m\ QdlNghPeeQcbRaZS_WUZTVXPWVMXT1VZJYSe`O__MVZLQZKLYI\ GXHAYFBXGCXGDXHEXHFWHGWIHWIHWIIVJJVJKVKLVKMUKNULOU\ LN`GOULQLQPOPPROPUNOXMO_LOaKOdJNgINjHNmGNoGWpXdpla\ miZjgWheTecQbaN`_LYYIVWFTUCQS9NQ6LO3IM1GK7IICJHHKF\ MLERMDWNB`OAeP9jQ7oR6sY0tS5uMAvGFx7KwBKvFKvJKuNKtR\ KtUKsYKraKreKqiKpmKryLppKogKm_KlRKjIKj3LiAKhGKgNJf\ TJe_IdeIdkIbfNaaS`XXZSaYNfXIkVBsWDoWFlXHhXJeXLbYNZ\ YPWROYYQTgTKdSObSS_SWYS_VScTSgQSkOSoMSsIhfFyVIwUKu\ TMsSPqRRoQTmPWkOYiN`iN_hMZhLYgLXgKWfKVfJVeJUeITdIS\ dHRcHQcGQcGOdLMePPgVLeTHdSDbR8`PAaQCbREcSGdTIeTKfU\ LgVNhWPiWRjXTkYVlZWlZHITIHSIGRIFQIFQJEPJDOJDNJCNKB\ MKBLKAKK9KL9JL8IL7HN8CL7H } 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 PARAMETER FILE=========================================

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Re: Fractint Digest, Vol 33, Issue 5
by JackOfTradeZ 09 Nov '05

09 Nov '05

""I'm still stoked on this formula. Morgan Owens and Hiram Berry should see this! Oh yeah, and Lloyd Garrick (aka Jack O'Tradez; http://www.sonic.net/~jot/ufvp.html) should consider animating it, IMO..."" Exactly which formula are you refering to? There were many in the last couple mailings and I will check it out after the current projects; I am zooming into Jim Muth recently posted "squared" mandelbrot, the "diamond", and also continuing the 2nd MuthZooM to the terminal minibrot at e+26, almost done. BTW, my handle is JaÃ§k Of TraÃeZ. Get it right. Margaret, As for the number of frames in a zoom sequence, you need to find that by experiment, there is no rote formula. Too few and it will zoom in too fast and be dissapointing. Too many is better cause it goes nice and smooth and slow but it takes much longer to render the sequence. Trust me, I have had some experience with this ... Also, for AVI, the default standard is 15 FPS, which is just barely adequate for a smooth zoom, you will see a slite jerkiness. I have found 24 FPS is perfect, any more than that makes no significant improvement. So assume 24 FPS, then you know how many seconds your sequence will be if you know the total frame count. You can plan it out from there. JoTz

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