November 2010 - Fractint - mailman.xmission.com

FOTD 21-11-10 (By Sherry [Unrated])
by Jim Muth 21 Nov '10

21 Nov '10

FOTD -- November 21, 2010 (Unrated) Fractal visionaries and enthusiasts: Today's image is not my own. It is one I found on the CD that came with the second edition of the book "Fractal Creations". Since the book was printed in 1993, the image is over 17 years old. On the CD, the image is in a directory named 'Sherry'. I have no idea who this mysterious 'Sherry' person might be. I used the image virtually as I found it on the disk, though I did make it slightly smaller and add a few tints of color plus a few brilliant highlights. The image was calculated by the fn(z*z) formula hard-coded into Fractint. The name "By Sherry" indicates that I can take no credit for the image, nor can I give it a rating. I can only stand on the peak of the mountain that someone else carried me to the top of, and exclaim 'what a great view'. The calculation time is incredibly fast -- less than one second on my 2000mhz fractal-dedicated machine, which is very faithful, but now and then decides it does not want to start up unless its memory cards are reseated. The finished image is also available on the FOTD web site at: <http://www.Nahee.com/FOTD/> Too many clouds but otherwise benign conditions prevailed here at Fractal Central on Saturday. The temperature topped at a quite average 48F +9C, which was mild enough to keep the fractal cats happy. When their happiness waned, they amused themselves by chasing the toy laser beam up and down the hallway. They enjoy the laser so much that they come and ask one of us for action when they want their exercise. As for the humans, our day was average, which is the way we like it. The next FOTD, this time a J.M. original, will be posted in 24 hours. Until then, take care, and when we finally see the light, what will we do with it? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= By_Sherry { ; time=0:00:00.88-SF5 on P4-2000 reset=2004 type=fn(z*z) function=cosh center-mag=0/0/0.28548/1.3356/90/0 float=y inside=0 maxiter=500 potential=255/500/20 decomp=256 colors=000000gggffffffeeeeeeddddddccccccbbbaaaaaaa\ aa``````______ZZZZZZYYYYYYXXXWWWWWWVVVVVVUUUUUUTTT\ SSSSSSRRRRRRQQQQQQPPPPPPOOONNNNNNNNNMMMMMMLLLLLLKK\ KKKKJJJIIIIIIHHHHHHGGGGGGFFFFFFEEEDDDDDDCCCCCCCBBD\ BBEAAF99GAAHBBICCJDDKEELEEMFFNGGOHHPIIQJJRKKSLLTMM\ UNNVNNWOOXPPYQQZRR_SS`TTaUUbVVcWWcWWcXXcYYcZZc__c`\ `caacbbcccddddedegefifgkghmhioijqjksklulmwmmxmnyno\ zopzpqzqqzqszsszsszsszstzttzttzttzttzttztszsrxrqvq\ ptporqnprmnsmmtllukkvjjwiiwhhwggwffweewdduccsbbqaa\ o``m``k__iZZgYYeXXcWWaVV_UUYTTWRRUQQSPPQOOONNNMMML\ LLLLLKKKJJJIIIHHHGGGFFFzm0DDDEEEEEEFFFFFFGGGGGGGGG\ HHHHHHIIIIIIJJJKKKKKKLLLMMMMMMNNNNNNOOOPPPPPPQQQRR\ RRRRSSSSSSTTTUUUUUUUUUVVVWWWXXXXXXYYYYYYZZZ______`\ `````aaabbbbbbbbbccccccdddeeeeeefffgggggghhhiiiiii\ iiijjjjjjkkklllmmmmmmnnnoooooooooooonnnnnnmmmmmmll\ llllkkkjjjjjjjjjiiiiiihhh } END PARAMETER FILE=========================================

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FOTD 20-11-10 (Manipulated View [No Rating])
by Jim Muth 19 Nov '10

19 Nov '10

FOTD -- November 20, 2010 (No Rating) Fractal visionaries and enthusiasts: In yesterday's image a segment of the classic Mandelbrot shape appears in the background as the brilliant blue stuff. But the shape is so distorted that it is almost impossible to recognize the part of the M-set shape that is showing. In today's image we have taken yesterday's scene, rotated, twisted, and skewed it until we have restored the Mandelbrot shape to recognizable familiarity. Much to our surprise, we find we have cut a slice through the M-set shape that covers the main period-2 bud, the northwest part of the Main Bay and the northern period-3 bud. To find the slice, I totally winged it by eye. It might be possible by complicated trigonometry to determine the correct anti-distor- tion mathematically. It works quite well with simple single rotations, where all that is required is to enter the cosine or the reciprocal of the cosine of the angle as the X-magnification factor. But in yesterday's image, where four angles are involved, the mathematical method is too complex, at least for my Arithmetic-101 level of knowledge. At this point, I am left wondering which version of the same slice is more correct, yesterday's or today's. The actual Mandelbrot part of the Julibrot is a 4-D thing, kind of a nest of hypercylinders shaped like the M-set in the C-plane, but extended to infinity in the Z-plane. (Don't try to visualize the entire shape, it's impossible.) This Mandelbrot hyper- cylinder nest becomes distorted when it is sliced at an angle, as we did in yesterday's image. Today's image, which corrects this natural distortion, is actually the more distorted, and therefore the least correct image. But at the same time, it is almost impossible to tell our position when viewing yesterday's image, so I suppose this makes today's image the more correct one. All math and almost no artistic value equals no rating. The name "Manipulated View" tells it like it is. The calculation time of under 2 seconds is incredibly brief, and should be not be a factor. The finished image may also be seen on the FOTD web site at: <http://www.Nahee.com/FOTD/> Conditions here at Fractal Central on Friday were acceptable, with partly cloudy skies, a temperature of 48F +9C and cats that were fairly contented. The commercial work was about average, while the FOTD, is more a curiosity than a work of art. The next FOTD will be posted in 24 hours. Until then, take care, and try to uncover the alien plot before we end up on a slave ship to Arcturus. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Manipulated_View { ; time=0:00:01.88-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=0.177576/\ -0.440939/0.5850274/0.3595/142.341509490465285/\ -74.8871977088931544 params=152/105/-64/49/-1/0/\ 1.118/0 float=y maxiter=1800 inside=0 logmap=yes symmetry=none periodicity=6 colors=000C36D47E58F69G7AH8BI9CKADMCEOEFQGGTIHWKIZ\ NJbQKfWKi`KleKngKljKjjKhfKgcKe`Kc_KbZKcYKdXKeXKfXK\ gZKg`KkaKnaKqbKnbKlcKjcKhdKfdPdeUbaZ_gcYkhVpmTtrQy\ vOzzMzzJzzHzzFzzDzzAyz8xz6vz4uz4zzJzzXzz8zzWzzrrzb\ rzOrzLrzJrzHrzFrzDrzBrzCrzCrzCrzDrzDrzDrzErzErzErz\ MrzErzFrzFrzFrzGrzGrzGrzHrzHrzHrzHrzIrzIrzIrzJrzJr\ zJrzKrzKrzKrzXzzWzzWzzVzzVzzUzzUzzTzzTzzSzzSzzRzzR\ zzQzzQxzPwzPuzOszOrzNpzNnzMmzMkzLizLhzKfzKdzTdzScz\ RczQczQczPczOczNczNczMczLczKczeVzdWzcWzbXzaXz`Xz_Y\ z_YzZYzYZzXZzWZzV_zV_zU_zT`zS`zR`zQazPazPazObzNbzM\ bzLczKcz_zzXzzUwzSrzPmzMhz`zz_zzZzzZzzYzzYzzXzzXzz\ WzzVzzVzzUyzUxzTwzTvzSuzRszRrzQqzQzzPzzPzzOzzNzzNz\ zMzzMzzLzzLzzKzzGzzHzzHzzIzzIzzJzzJzzKzzKzzSzzPzzM\ zzNzzMzzLzzKzz6zz7zz8zz8zz9zz9zzAzzAzzBzzBzzCzzCzz\ DzzDzzEzzFzzFzzGzzGzzHzzHzzIzzIzzJzzJzzKzz4zz5zz6z\ z7zz8zz9zzAzzBzzPzzOzzNzz } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 19-11-10 (UnManipulated View [No Rating])
by Jim Muth 19 Nov '10

19 Nov '10

FOTD -- November 19, 2010 (No Rating) Fractal visionaries and enthusiasts: Today's image is presented exactly as it came off the press, with no manipulation such as rotating, stretching or skewing applied. What appears on the screen is all there is of the fractal. Nothing has been cropped. Such chaos is typical of Julibrot slices at such weird 4-D angles. The foreground features, which are colored dirty brown, are low iteration stuff that can go in any direction at all. The brilliant blue stuff in the background is high iteration stuff that defines the Mandelbrot set. This blue stuff is actually a very familiar segment of the Mandelbrot-set shape, though at the weird angle at which it is being viewed, it is unrecognizable. In tomorrow's FOTD however, I will post another version of today's scene, in which I have done all the manipulation needed to return the Mandelbrot part to its normal state. This will include substantial stretching and skewing, as well as a generous rotation. Since today's image is all math with almost no artistic intent, I could not give it a rating. The name "UnManipulated View" describes the image. Since the image is of such a low magnitude and maxiter, it calculates in a fireball 6 seconds. The image should also be available on the FOTD web site at: <http://www.Nahee.com/FOTD/> Heavy clouds and blustery conditions continued here at Fractal Central on Thursday, with a temperature of 50F 10C. The fractal cats kept happy chasing the point of light from a toy laser around the living room until they both began panting, and we decided they had had enough exertion for one day. As far as the graphic design work went, my day was slow. As for politics, in the morning paper I saw a column by a liberal woman columnist about how our schools are failing the young men, while the young women are excelling. I thought it was the women who are supposed to be suppressed beneath a glass ceiling by our patriarchal, male-dominated society. Regardless of who is suppressing who, the fractals are certainly not being suppressed. In fact, the next one will be posted in 24 hours. Until then, take care, and you can't have it both ways! Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= UnManipulated_View { ; time=0:00:06.04-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=0.967912/\ -0.1798/0.7473842 params=152/105/-64/49/-1/0/\ 1.118/0 float=y maxiter=1800 inside=0 logmap=yes symmetry=none periodicity=6 colors=000C36D47E58F69G7AH8BI9CKADMCEOEFQGGTIHWKIZ\ NJbQKfWKi`KleKngKljKjjKhfKgcKe`Kc_KbZKcYKdXKeXKfXK\ gZKg`KkaKnaKqbKnbKlcKjcKhdKfdPdeUbaZ_gcYkhVpmTtrQy\ vOzzMzzJzzHzzFzzDzzAyz8xz6vz4uz4zzJzzXzz8zzWzzrrzb\ rzOrzLrzJrzHrzFrzDrzBrzCrzCrzCrzDrzDrzDrzErzErzErz\ MrzErzFrzFrzFrzGrzGrzGrzHrzHrzHrzHrzIrzIrzIrzJrzJr\ zJrzKrzKrzKrzXzzWzzWzzVzzVzzUzzUzzTzzTzzSzzSzzRzzR\ zzQzzQxzPwzPuzOszOrzNpzNnzMmzMkzLizLhzKfzKdzTdzScz\ RczQczQczPczOczNczNczMczLczKczeVzdWzcWzbXzaXz`Xz_Y\ z_YzZYzYZzXZzWZzV_zV_zU_zT`zS`zR`zQazPazPazObzNbzM\ bzLczKcz_zzXzzUwzSrzPmzMhz`zz_zzZzzZzzYzzYzzXzzXzz\ WzzVzzVzzUyzUxzTwzTvzSuzRszRrzQqzQzzPzzPzzOzzNzzNz\ zMzzMzzLzzLzzKzzGzzHzzHzzIzzIzzJzzJzzKzzKzzSzzPzzM\ zzNzzMzzLzzKzz6zz7zz8zz8zz9zz9zzAzzAzzBzzBzzCzzCzz\ DzzDzzEzzFzzFzzGzzGzzHzzHzzIzzIzzJzzJzzKzz4zz5zz6z\ z7zz8zz9zzAzzBzzPzzOzzNzz } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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Mandelbrot Newtons
by Roger Alexander 18 Nov '10

18 Nov '10

Today's post is another mandelbrot newton hybrid. Ready made at http://maxitersfractalfollies.blogspot.com Mandelbrot Newton { ;fract520.gif ; blank ; calctime 0:45:28.17 ; created Nov 17, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=_m.frm formulaname=MandelbrotInNewton center-mag=-0.53594159502949720/+1.74212079795591200/1518260/1/-159.9999\ 99995772896/-6.8065392974658856e-009 float=y maxiter=1500 inside=0 logmap=123 colors=000CGUBET9DS8BR7AQ69P57O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAE\ TBGUCHVDIWFKXGLYHMZIO_JP`KRaLSbMTcOVePWfQXgRZhS_iTajUbkVclXemYfnZgo_ip`j\ qakrbmscntepufqvgrwhtxiuyjvzjvziuyhsxgrwfqvdoucntblsakr`jq_hpZgoYfnWdmVc\ lUbkT`jS_iRYhQXgPWfNUdMTcLSbKQaJP`IN_HMZGLYEJXDIWCHVBFUAET9DS8BR7AQ58P47\ O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAETBGUCHVDIWFKXGLYHMZIO_JP`KRaLS\ bMTcOVePWfQXgRZhS_iTajUbkVclXemYfnZgo_ip`jqakrbmscntepufqvgrwhtxiuyjvzjv\ ziuyhsxgrwfqvdoucntblsakr`jq_hpZgoYfnWdmVclUbkT`jS_iRYhQXgPWfNUdMTcLSbKQ\ aJP`IN_HMZGLYEJXDIWCHVBFUAET9DS8BR7AQ58P47O36N24M13L02K02K13L25M36N47O69\ P7AQ8CR9DSAETBGUCHVDIWFKXGLYHNZIO_JP`KRaLSbMTcOVePWfQYgRZhS_iTajUbkVclXe\ mYfnZho_ip`jqalrbmscntepufqvgswhtxhtxiuyhtxgrwfqveoucntbmsakr`jq_ipZgoYf\ nXdmWclVbkT`iS_hRZgQXfPWeOUdNTcMSbLQaKP`IO_HMZGLYFJXEIW } frm: MandelbrotInNewton(XAXIS) {; use float=yes: from CAL v4.0 by Tim Harris z = 0, c = pixel, cminusone = c-1: oldz = z nm = 3 * c-2 * z * cminusone dn = 3 * (3 * z * z + cminusone) z = nm/dn + 2 * z/3 |(z-oldz)|>=|0.01| ;SOURCE: mnewton.frm } Roger Alexander

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FOTD 18-11-10 (Stone Arch Bridge [6])
by Jim Muth 18 Nov '10

18 Nov '10

FOTD -- November 18, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image is an unfamiliar slice of the Julibrot, which I have named "Stone Arch Bridge". While searching for a name, I noticed the row of arches across the bottom of the image, and was reminded of the railroad bridge across the Susquehanna River at Marysville, which is just north of Harrisburg. The slice is centered at the western limit of the ever-smaller string of buds lined up out the negative X-axis of the Mandel- brot set. The orientation is at an angle rotated 31 degrees from the Parabolic toward the Oblate, though mostly Parabolic elements predominate. The rating of a 6 means I am only mildly impressed by the image, though, because of the spectacular coloring, I do consider it worth nominal FOTD status. The very brief calculation time of 8 seconds assures that very little effort will have been wasted if the resulting image lays an egg. To avoid the possibility of ending up with an omelet, I suggest checking to see if the image is posted on the FOTD web site at: <http://www.Nahee.com/FOTD/> After a heavy overnight thunder-storm, Wednesday dawned cloudy and blustery here at Fractal Central. The conditions continued most all day, with the clouds breaking only long enough to give a glimpse of the setting sun. The winds made the temperature of 52F 11C seem surprisingly chilly. The fractal cats made the most of things, checking every so often to be sure no unwanted cats were prowling nearby. My day was slow enough to enjoy, but not so slow as to cause concern. The next FOTD will be posted in 24 hours. Until then, take care, and be ever so cautious when the aliens from Sirius C are snooping about. They're as sneaky as a cat. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Stone-Arch_Bridge { ; time=0:00:08.27-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=0.572006/\ -0.350829/0.7022955/1/121/0 params=0/90/31/31/\ -1.40115519/0/0/0 float=y maxiter=950 inside=255 logmap=yes symmetry=none periodicity=6 passes=1 colors=00000A00C01E02G03I34K55M76O87RC8UF9WHAWIBYJ\ C`KDbKFeLGhNHjOImQJpSKtTLwVMyWNzVPxVRvUStUUpTVnTXk\ SZhS_zRazRbzQdzQfzPgzPizPjzOkzOlzOmzOmzOmzOmzNmzNm\ zNmzNmzNmzNmzNmzPmzRmzTmzUmzWmzYmzZmz`mzbmzdmzemzg\ mzimzjmzlmznmzomzgmz_mzTmzLpzEtzHszJrzMqzOqzRpzToz\ WozYnz`mzbmzemzgmzjmzlmzomzqmzpmzpmzpmzpmzpmzpmzpm\ zpmzpmzpmzpmzpmzpmzpmzpmzqmzqmzqmzqmzqmzqmzqmzqmzo\ mzmmzkmzimzgmzemzcmzamz_mzYmzWmzUmzSmzUmzVmzXmzYmz\ _mz`mzbmzcmzemzfmzhmzimzjmzlmzmmzomzpmzrmzsmzumzvm\ zxmzymzzmzxmzvmzumzsmzrmzpmznmzmmzkmzjmzhmzfmzemzc\ mzbmz`mz_mz`mz`mz`lz`kyajxaiwahvaguafubfubfvbfvbfv\ bfwcfwcfwcewcexcexdexdeydeydeydeyfmxgmwimvjmulmtmm\ tjmjgmaemTbmK`mB`mN`mY`mhamkammbgoblqakp`jo`in_in_\ hmZglYglYfkXejXejWdiWchVchUbgUmfTmfTmeSmdSmdPmeNme\ LmfImfGmfEmgCmg9mg7mh5mh3mh3mh3mi3mj3mk3mk3ml3mm3m\ n3mn6ml9mjCmhFmfImdLmbszz } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 17-11-10 (What Happened Here [!!!])
by Jim Muth 17 Nov '10

17 Nov '10

FOTD -- November 17, 2010 (Rating !!!) NEW FORMULA ALERT! UNUSUAL PICTURE SHAPE ALERT! Fractal visionaries and enthusiasts: Today's image will begin calculating toward the center of the screen. This is no error. Instead of a 4-3 width-height ratio, today's image has a much wider 2-1 ratio. Today's image rates a triple bang. This means it is of excep- tional mathematical interest, though of only moderate artistic value. The formula is a new one, so be sure to enter it into one of your formula files. The new formula takes the basic Mandelbrot expression and simply adds a variable function to both initial Z and C. The effect of the 'exp' (exponential) function that I applied to initial C in today's image is to virtually place the observer inside the plane of the image at the point assigned initial C, with the nearby elements appearing larger and the more remote elements, much smaller. In today's image I stationed the observer at -1.40115518995 on the X-axis, near the limit of the main body of the Mandelbrot set. The things this does to the set are dramatic, thus the rating of !!!. The question asked in the name "What Happened Here" will be answered when the image is viewed. In the actual M-set, the successive buds grow ever smaller as we travel out the negative X-axis. But by stationing the observer at the limit of the string of buds, as I have done in the image, I have negated this size decrease and made all the buds nearly the same size. The resulting image resembles nothing as much as a centipede with 15+ segments. Unfortunately, the image is a very slow one, growing ever slower as it progresses and taking nearly an hour to finish. I have sent the finished image on ahead to Paul at the FOTD web site. Hopefully, he will have it posted soon. The FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> To set things straight about how I feel about global warming, IMO, the earth is getting warmer because we're still coming out of the most recent ice age. And only a small percentage (one- percent or so) of this warming is due to man's activity. Little or nothing can now be done to slow the natural warming, so instead of futilely spending vast amounts to stop the warm- ing, we should be spending the money preparing for the minor but inevitable sea-level rise of an inch or two in the coming century, and at the same time developing renewable non-polluting energy sources. IMO, the most amusing part of the hyped-up global-warming 'crisis' is watching the hated big corporations using it as a sales pitch, and the easily manipulated masses buying 'green' products, thinking they are helping to save the earth when they are actually only enriching the hated big corporations Heavy clouds, steady rain and a temperature of 52F 11C kept man and cats alike indoors here at Fractal Central on Tuesday. There was enough work to keep the man's mind off the outside con- ditions, but the fractal cats seemed fascinated by the dripping rain and spent several hours on their window shelf, trying to make sense of all the water. The next FOTD will be posted in 24 hours. Until then, take care, and I see it's the cockroaches behind the conspiracy to end the world. That's a relief. I thought it was the aliens from the Herculean cluster. (Actually, the roaches might do the best job of running things.) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= What_Happened_Here { ; time=0:45:36.12-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotFunct function=ident/exp center-mag=-10.0738/0/0.1943703/0.6014 params=0/0/\ -1.40115518995/0 float=y maxiter=275000 inside=0 logmap=yes symmetry=xaxis periodicity=0 passes=1 viewwindows=1/0.5/yes/0/0 mathtolerance=0.05/1 colors=000rmIqmIpmIomJomJnmJnmJmmKmmKlmKlmLkmLkmLk\ mMkmMjmMjlMjlNjkNikNikOijOijOkkPijOhjOgjOfjOeiOdiO\ ciObiOahO`hO_hOYhNXhNWgNVgNUgNTgNSfNRfNQfNPfNOfNNe\ ONeONeONdPNdPNdPNcQNcQNcQMbQMbRMbRMaRMaSMaSM`SM`SM\ `TM`TL_TL_UL_ULZULZULZVLYVLYVLYWKXWKXWKXWKWXKWXKWX\ KVYKVYKVYIW_KVYMVXNVWPVVRUUSUTUUSWURXTQZTP`TNaTMcS\ LeSKfSJhSIjRHjRGjRFjREjQCjRDkRDkRDkRDkRDkRElRElSEl\ SEmSEmSEmSFmSFnSFmTFmTFmTFnTGnTGnTGnTGnUGoUGoUHoUH\ pUHqUHrUHtTFuUGtUHtUIrUIqUJqUKoUKoULnVMlVNlVNkVOkV\ PjVPiVQiVRgVRgWSfWTeWUeWUdWVcWWbWWaWXaXY`XZ_XZ_X_Z\ X`ZX`YXaXXbXXbWYcWYdVYeUYeUYfTYgTYgSYhRZiRZjQZjQZk\ PZlOZlOZmNZnLXqMYoNZnO_lP_kP`jQahRagSbeTcdTccUdaVe\ `WeZXfYXgXYgVZhU_iS`jR`jQakOblNclLdmKdnJenHfoGgpEh\ pDhqCirAjr9ks7lt6lu5kv6jw6iv6iz6hz6jz6lz6nz6qz6tz7\ wz7zz7zz7zz7zz7zz7zz7zz7zz8zzAzzKzzUzzczzmzztzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotFunct {; Jim Muth real(c),imag(c) z=fn1(p1), c=fn2(pixel)+p2: z=sqr(z)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 16-11-10 (Expect the Unexpected [6!])
by Jim Muth 16 Nov '10

16 Nov '10

FOTD -- November 16, 2010 (Rating 6!) Fractal visionaries and enthusiasts: One should always be prepared for the unexpected, even when it seems impossible. Today's slice through the Julibrot is a good example. The slice is centered on East Valley of the Mandelbrot set, and oriented 0.1 degree from the Oblate direction, which means the Mandelbrot stuff is stretched about 573 times its normal extent in one direction. In the image that I found before today's, I unstretched the Mandelbrot parts, but in so doing, I stretched the Julia parts about 573 times. The grossly stretched Julia stuff is visible near two corners of today's image. When I did this stretching, I had almost no hopes of finding any of the Mandelbrot stuff that I had presumedly returned to its normal proportions, but much to my surprise, I found one tiny open spot lurking in the upper left corner. When I closed in on the tiny spot, I found the better part of one of the twisted minibrots that fill East valley. At first I could not believe that any Mandelbrot features at all could remain when the Julibrot is sliced 89.9 degrees from the Mandel- brot orientation. But pictures do not lie, (unless they have been manipulated on a computer), and the twisted object at the center of today's image is most certainly the remains of an East Valley minibrot. The rating of a 6! means that almost all the interest lies in the mathematical aspect of the image. The artistic worth is minimal, though not entirely absent, and the features surround- ing the chopped-off minibrot certainly are curious. The name "Expect the Unexpected" relates my adventures on the way to finding today's image. The calculation time of 21 seconds takes almost all the work out of running the included parameter file. The calculation work can be eliminated entirely by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> The sun departed and the clouds moved in here at Fractal Central on Monday, while the temperature hovered around a mild 55F 13C. The fractal cats took it all in stride, concerned only about their next food treat. My day was uneventful. Until next time, take care, and beware of global warming -- it's got me worried. How long will it be before we wake up one morning up to our knees in the rising seas, and find polar bears extinct? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= ExpectTheUnexpectd { ; time=0:00:21.31-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=-0.023260073\ 46855092/-0.00735188243689156/2294.688/0.002601/\ -179.929980454595068/89.7871683432740895 params=0/0/89.9/0/0.277/0/0/0 float=y maxiter=2400 inside=0 logmap=22 periodicity=6 colors=000A0OA0PA0QA0RA0SA2TA4UA6WA8YAA_ACaAEcAGeA\ IgAKiAMkAOmAQoASqAUsAWuAYwA_xAayAczAdvAcrAZm9Uh8Pc\ 6KjNFiRFPYCK`CFcAAe85d70a90Y90R60L40720xy1tu0pq0lm\ 0hi0de0aa0YY0UV0QR0MN0JJ0FF0BB0770330KmNHeJEZGBSD8\ L95E6273USSPOOLKKHGGCCC888444PUvGKb8AJyfVnZPdSKVLF\ KEAA752Tg1JT09E8yM7rJ6kH5dE4YC3R92K71D4062jcxdZq_V\ jVQcQMXKHRFDKA8D546amLYhJVdHS`FPXEMTC_oGbeIeXJhOLj\ FMeFOaFPYFQUFSQFTLFUHFVDFX9FY5FZ1F_4M`6Sa9ZbBdcEkd\ GqdEpfDogCniAmj9ll8km7kn9loAlpBlpDmqEmqFmrHmsInsJn\ tLntMnuNovPovQowRowUkuXgsZcqa`odXmfTkiPilMgnIeqEct\ Aav7`uAYuCVtETtGQtJNsLLsNIsPGiRD`TBSU9NV8IW7EW79X6\ 4Y50Y56bABgEGkILpMQtQQuSQvUQwWQxYQy_cz`czbczdczfcz\ hcziczgczemzcmzamz_mzYmzWmzUmzSmzzmzzmzzmzzmzzrzzv\ zzzzzzzzzzzzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzznzzkzzgzzczz_zzXzzTzzPzz\ MzzLzzKzzJzzIzzHzzHzzFzzE } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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Another Newton Mandelbrot Mash-up
by Roger Alexander 16 Nov '10

16 Nov '10

Today's post is another newton mandelbrot mash-up. Ready made at http://maxitersfractalfollies.blogspot.com fractt517.gif { ; another newton-mandelbrot mash-up ; blank ; calctime 0:09:56.44 ; created Nov 15, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=_m.frm formulaname=mandel-newton-2 passes=1 center-mag=-0.61577/4.44089e-016/0.7788162 params=12/0 float=y maxiter=1500 inside=0 periodicity=0 colors=00000000100300400600800900B00C00E00G00H00J00K00M00O00P00R00T00U00\ W00X00Z00`00a00c00d00f00h00i00k00m01m03m04n06n07o09o0Ao0Cp0Ep0Fq0Hq0Iq0K\ r0Lr0Ns0Ps0Qs0St0Tt0Vu0Wu0Yu0Zv0`v0bw0cw0ew0fx0hx0iy0ky0mz1mz3mz5nz7nz9o\ zBozDozFpzHpzJqzLqzNqzPrzRrzTszVszXszZtz`tzbuzduzfuzhvzjvzlwznwzpwzrxztx\ zvyzxyzzzzyzzxzzwzzuzztzzszzqzzpzzozzmzzlzzkzzizzhzzgzzezzdzzczzbzz`zz_z\ zZzzXzzWzzVzzTzzSzzRzzPzzOzzNzzLzzKzzJzzIzzGzzFzzEzzCzzBzzAzz8zz7zz6zz4z\ z3zz2zz0zz0yz0xz0wz0uz0tz0sz0qz0pz0oz0mz0lz0kz0iz0hz0gz0ez0dz0cz0bz0`z0_\ z0Zz0Xz0Wz0Vz0Tz0Sz0Rz0Pz0Oz0Nz0Lz0Kz0Jz0Iz0Gz0Fz0Ez0Cz0Bz0Az08z07z06z04\ z03z02z00z00y00x00w00v00u00t00s00r00q00p00o00n00m00l00k00j00i00h00g00f00\ e00d00c00b00a00`00_00Z00Y00X00W00V00U00T00S00R00Q00P00O00N00M00L00K00J00\ I00H00G00F00E00D00C00B00A009008007006005004003002000000 } frm:mandel-newton-2 {; Sylvie Gallet [101324,3444], 1995-1996 ; Formula designed for Fractint 19.2 and modified for Fractint 19.3 limit = real(p1), test0 = 1, test3=0, iter = 1 z = pixel, c = z, b1 = 16 rad = 6, pix = (10*pixel+(8.0,-5))*(-0.1,-0.95) center = (1.0,0.1), zn = center+rad/(pix-center), b2 = 0.0001 : test0 = 1-test0, test1 = (iter<limit), test2=(iter!=limit) z = (z-zn)*test2 + zn z2 = z*z, z4 = z2*z2, z1 = (z4*z-1)/(4*z4 + (z==0)) z = (z2+c)*test1 + (z-z1)*(1-test1) test3 = (test3 || (|z|>b1)) z = z*(1-(test3 && test0 && test1)) iter = iter+1 ((|z|<=b1)*test1) || ((|z1|>=b2)*(1-test1)) ;SOURCE: gallet-n.frm } Roger Alexander

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Re: [Fractint] <Paul> I hope you're feeling better, Paul.
by Paul.N.Lee＠att.net 16 Nov '10

16 Nov '10

Hal Lane wrote: > > I hope you're feeling better, Paul. Yes, somewhat better. But very drained and tired. Hopefully, the doctors will think I have recovered enough to go home from the hospital in about 6 days or so. Jim Muth wrote: > > The finished image might be posted on the FOTD web site..... > ....but I am not sure Paul has the site up-to-date quite yet. And under my current health state, it explains why I only have finished the Oct.27th through Nov.07th web pages to get them up-to-date for the FOTDs. The rest will soon be up and available as I finish them over the next 36 hours. Sincerely, P.N.L. -------------------------------------- http://www.Nahee.com/PNL/Fractals.html http://www.Nahee.com/Fractals/

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Henon_JKO
by Mike Frazier 15 Nov '10

15 Nov '10

While looking through a used book I bought (Fractals Images of Chaos by Hans Lauwerier) I saw a formula I wasn't familiar with. The formula was discovered in 1969 by French mathematician M. Henon. I entered it into Fracton, played with it a bit, and found a few fractals I liked. Henon is listed in FractInt's built in formula list but I have never seen anyone use it. I have no way to tell if FractInt's Henon is the same as this one. Here is a page with an image: http://www.fracton.org/fmlposts/henon_jko.html Here is the par file used to generate the fractal: Henon_JKO { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20101115_0906 passes=1 float=y center-mag=0.32/0.15/0.53333334/1/0/0 params=-0.0235/0.488/4.6/0/0/0/0/0/0/0 maxiter=190 proximity=0 colors=000aaateOthNtjNtlMtnMtoLtqLtsKtuKswJswJsvJs\ uJsuJstJssJssJsrKsqKspKspKsoKsnKsnKsmKslLslLskLsjL\ siLsiLshLsgLsgMsfMseMseMsdMscMsbMsbMsaNs`Ns`Ns_NsZ\ NsZNsYNsXNsWOsWOsVOsUOsUOsTOsSOsSOsRPsQPsPPsPPsOPs\ NPsNPsMPsLQsLQsKQsJQsIQsIQsHQsGQsGRsFRsERsERsDRsCR\ sBRsBRsASs9Ss9Ss8Ss7Ss7Ss6Ss5Sr4Tq4Tp4To5Tn5Sl6Sk6\ Sj7Si7Rh8Rf8Re9Rd9QcAQbAQ`BQ_BPZCPYCPWDOWDOWDOWDOW\ DOWDOVDOVDOVDOVDOVDOUDOUDOUDOUDOUDOTDOTDOTDOTDOTDO\ TDOSDOSDOSDOSDOSDORCORCORCORCORCOQCOQCOQCOQCOQCOQC\ OPCOPCOPCPPCPPCPOCPOCPOCPOCPOCPNCPNCPNCPNCPNCPNCPM\ BPMBPMBPMBPMBPLBPLBPLBPLBPLBPKBPKBPKBPKBPKBPKBPJBP\ JBPJBPJBPJBPIBPIBPIBPIBPIBPHAQIBQJDQLEQMGQOHQPJQRK\ QSMQUNQVPQWQQYSQZTQ`VRaWRcYRdZRf`RgaRhcRjdRkfRmgRn\ iRpjRqlRsnSrnSpnSnnSmnSknSinSgnSfnTdnTbnTanT_nTYnT\ WnTVnTTnURnUQnUOnUMnUKnUJnUHnUFnVEnVCnVAnV8nV7nV5n\ V3nV1oW1oW1oW1oW1oW1pV1pV } frm:F_20101115_0906 { ; Henon's Expression ; From Fractals Images Of Chaos by Hans Lauwerier p126 ; x' = y ; y' = -x +2ay + by^2 ; Time = 0.4 sec at 640 x 480 with no anti-aliasing ; using Fracton on Mac Pro 2 x 2.8 GHz Quad-Core Xeon x=real(pixel),y=imag(pixel), a=2*real(p1),b=imag(p1),; p1 - Julia constant bailout=real(p2),; real p2 - bailout @beginloop, temp=y, y=a*y+b*y*y-x, x=temp, z=x+flip(y), |z|<=bailout } -- Mike Frazier www.fracton.org

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