October 2012 - Fractint - mailman.xmission.com

FOTD 04-10-12 (A Second Opinion [7])
by Jim Muth 05 Oct '12

05 Oct '12

FOTD -- October 04, 2012 (Rating 7) Fractal visionaries and enthusiasts: Today's image is another scene in yesterday's parent fractal, though instead of checking the large bud, we check the east edge of the main bay, just south of the broad peninsula that is trying, though not too successfully, to be an East Valley. The fractal patterns in this area are entirely different from those on the shore line of the large bud. Instead of loops, we see sharp-pointed, rather dark and ominous elements that would make a fitting cover for a paperback horror novel. The name "A Second Opinion" indicates that today's image is the second venture into the same parent fractal, and, as is the case with medical doctors, a second opinion sometimes brings an entirely different outlook. A rating of a 7 is entirely justified, at least in my opinion. The pattern surrounding the tiny central minibrot may be highly fractured, but it is regular enough to make a recognizable, semi-organized minibrot basin. The calculation time of 1-2/3 minutes is fast enough to leave time for fun or business. Time-saving joy may be found at the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> where the finished image is posted. Hi-def joy is online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are blissfully available at: <http://www.Nahee.com/FOTD/> Heavy clouds, fog and drizzle spoiled the entire morning here at Fractal Central. Some sun broke through in the afternoon, and the temperature reached 72F 22C, but by then the damage had been done and the fractal cats were in unhappy mode, demanding extra treats. The humans had another un-notable day, one that was peaceful to experience but boring to read about. The next FOTD will appear in a reasonable geologic time. Until that wondrous moment arrives, take care, and debate the debate. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Second_Opinion { ; time=0:01:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.442996736165/-0.063360789746/6e+007/\ 1/-85/0 params=1.5/0/51/0 float=y maxiter=1750 inside=0 logmap=144 periodicity=6 colors=000MF`LD_KCWF9QIAOG8LE6H00053D62IA75HB5LG5P\ K5TP4XT4bX4h_4mc3rf3wj3wm3wp3wn5wl6rj7mi8hg9ceAYcB\ VbCSwDPmENfFKdOH`cESmBQz9YzEgzJYzNNzSNmXMc`MUeLCiL\ BhKChJDgIEgHEgGFfFGfFGeEHeDIeCIdBJdAKdAKbBM`BOmCQw\ CSwDUhDWhEYhE_hFamFcZGeZGgZHiZHjIHkJIkJIlJImJImJJn\ JJoJJoJJpIKoJJpJJpJJpJJpJJpKJpKJqKJqKJqKIqKIqLIzD5\ zC5zB5zA5z95z85z75z65zOHzeTzvcftbdrabp``n_ZlZzjYzh\ XzgXzeWzcVzaUz_TzYSzWRzUQzTQzVPzXPzYPz_Pz`PzbPzdPz\ ePzgPzhPzjPzlPzmPzoPzpPzoOzoNznMznLzmKzmJzlIzlHzlG\ zkFzkEzjDzjCziBziAzi9zf9zb9zZAzVAzRBzNBzKBzLAzRUzT\ RzUOzVLzXIzYFz_Cz`9za6z_8zYAzXCzVEzTFzSHzQJzOLzNMz\ G6zE5zC4zB3zZfQhf9hfEhfIhfMffQcfUbfSafRafQ`fP_fO_f\ NbfMd_Lf`Ki`KkaJmaJpbIrbItcHwcGwzGwzFwzFwzHtzJpzLl\ zNjzQizThzVgzYfz_ezbdzdczgbzidzgfzehzcizakz_mzYnzW\ pzUrzStzQuzOwzMwzKwzIfzMczMazNZzNWzOTzOQzPOzPTzUXz\ ZazbezgjzlnzplznjzlQzbOza } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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|<a } END PARAMETER FILE=========================================

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FOTD 03-10-12 (Silver Horizon [8])
by Jim Muth 03 Oct '12

03 Oct '12

FOTD -- October 03, 2012 (Rating 8) Fractal visionaries and enthusiasts: Today's scene lies in the Mandeloid fractal that results when the formula Z^(1.5)+C is iterated 1.5 levels up the logarithmic hyper-spiral with no function applied. This parent fractal resembles a Mandelbrot set with an oversized main bud on the north shore line of the main bay. Today's scene is located on the southwest shore line of this oversized bud. I rated the image at an 8 because it is one of the finer minibrot scenes I have found in the fractals with exponents between 1 and 2. Although the pattern around the minibrot is filled with discontinuities, they are arranged so that the pattern appears quite regular, with some rather attractive curly filaments extending outward from the minibrot. The unusually brilliant colors also help with the rating. I sometimes wonder whether fractals like today's are actually true fractals at all. It seems to me that the MandelbrotBC3 formula invents a new kind of math, and while using it with its various functions, I am exploring possible alternate mathemati- cal systems rather than real fractals created with accurate math. It really doesn't matter however. The images are fractals, with all the characteristics of fractals, and real or not, they can still be unusually attractive. Do not be deceived by the name "Silver Horizon". The image is not one of those fantastic fractal scenes on other planets. It is a surprisingly attractive scene of just another irregular <2 >1 minibrot. The calculation time of 2 minutes is near the fractal average. The web sites can cut the wait notably. The finished image is online at: <http://www.crosscanpuzzles.com/Archives.html> The image is posted in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are available at: <http://www.Nahee.com/FOTD/> With partly cloudy skies, a temperature of 77F 25C and high humidity, today seemed more like an early August day than an early October day. The fractal cats would have preferred more sun, but they still found enough comfort on their chair by the southwest window. Except for a midday visit by the dryer repairman, who did his job quickly, the humans had a typical day. The next FOTD will be posted at the right time. Until whenever, take care, and I get the feeling that something is wrong with the world, but I can not track it down. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Silver_Horizon { ; time=0:02:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=+0.1154933507434394/+0.9603539171372509\ /7.500726e+008/1/-115/0 params=1.5/0/51/0 float=y maxiter=2500 inside=0 logmap=257 periodicity=6 colors=0009P07O05N03L02K02J00I00G00F00E10D20C20B52\ B85DAAFCEGEIHGNGJTGLZFOaHQcJTbLW_KZXIaTGdLOVEVL8`D\ 2e75i59l5Co5Fr5Ju5eu5ovSuz_zzzzzarzXmz3kz5ju5jr7hm\ 8hj8fe9fbAeZBeVBdSCdODbLEbIEaFFaCG_9I_7IZ3JZ2KX0LX\ 0LT0JP2GL5EJ9DFBBCE9AI87L53P31S20W10_00d00f01_2ATA\ LNGXGPdBZk7fp9jtCmzFpzJrzOuzVxzazzeuzkpOFmEDh5Ce5G\ z5Bj5AZ55W52V38S38Q37O37N35K25J25G25F23D23C35E35F3\ 7G58J59K5AL5BO5CP5DQ5ES7FV7GW7IX8J_8Ka8Lb8Nd9Of9Ph\ 9QjASmAToAVpAVrBTpCSoDQoEQmFPkGOkIOjJNhKLhLKfQKeWJ\ eZIdeIdKOaFV_B_Z7fX2mW0uV0zT0zW0xX0vZ0u_0sa0sb0re0\ pf0oh0mj1kk1km2jp2hr2fs2eu2XZ2_X1aW0dV0kT0pS0pQDmQ\ FoNKoJKoGQoDQpAXp8Xp5Xu2Xz0dz0kz0hfCzSAzV9zX9k_8kb\ 8Xe7Xh7Kj5Km53p52s51v30z30z32z9XsDXsIXsOXsTXsZXsdX\ skXsrkkxkkzkkzkkzkkzkkzkkzkkxkzxkzLkz0kz0kz0kz0kz0\ kz0kz0kz0kz0kz0kz0kz0kz0kz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zzozzmzzkzzazzZzzXzzVzzS } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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|<a } END PARAMETER FILE=========================================

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FOTD 02-10-12 (Negative Territory [5])
by Jim Muth 02 Oct '12

02 Oct '12

FOTD -- October 02, 2012 (Rating 5) Fractal visionaries and enthusiasts: We appear to be in one of those slow fractal periods here at FC. Today's humdrum image is the best I could dredge up in the day's fractal search. The image is a scene in the East Valley area of a Mandelbrot set corrupted by Z^(-21)+C energies. As is true of all Mandelbrot sets corrupted by negative energies, the deep minibrots retain the Z^2+C appearance. Since there are no minibrots in fractals of pure negative orders, the minibrots in negatively corrupted M-sets have nothing to change into. Perhaps the most surprising thing in today's image is the criticality of the bailout radius, (which is 16 more than the value assigned the real(p2) parameter, or 3.3). Decreasing this value results in a blank screen; increasing it results in the image first becoming more chaotic and finally breaking up and evaporating. The rating of a 5 indicates nothing of exceptional artistic value but implies enough fractal interest to make the brief calculation time of 45 seconds worth the effort. Enjoy extra leisure time by letting someone else do the calcula- tion. View the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And check the high definition and anti-aliasing at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are posted at: <http://www.Nahee.com/FOTD/> Rain fell here at Fractal Central today. The temperature of 64F 18C was pleasant enough, but with things so wet, it was wasted. The fractal cats saw the weather, then began chasing each other up and down the long hallway. The humans had so many other things to do that they hardly noticed the rain. The next FOTD will be posted in a number of hours. Until whenever, take care, and if you wish to rule the universe, the queue is on the right. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Negative_Territory { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=+0.3330817092270084/+0.0270745261371607\ /8.007146e+010/1/-166.25/0 params=-21/100000/-12.7\ /0 float=y maxiter=1500 inside=0 outside=real periodicity=6 mathtolerance=0.05/1 colors=000Q_pWdpaiofmogmkgmhgmegmbhm_hmXhmUhmRhmOi\ mLimIimFimCim9gnDfoGdpJcqMaqP`rSZsVYtYWu`VucYr`_pZ\ anXclUejSghQjeNlcLnaJp_GrYEtWCvUApTAjTAdTAZTATTANT\ AHTABTACVDCWGCYJCZMC`PCaSCcVDdYDf`DgcDifDjiDllDmnD\ pyGkwIfuKasMXqOSoPWhP_bPbWQfQQjJQmDKaKFRQ9GX45bE6_\ O7XX7Vf8So8QoINoSKo`IojFosDZbVJNkUZacjSmvIgtObrTXp\ YSncMlhHjmChrOW__JIYOFXSDVWAU`8Sd5Rh3Pb7OYAMTDLOG`\ QTWSe`YgabhVgjOmkHrmBwnQLZ_l0VK6RCC1JIJXOEWUAY_6ee\ 2ejCijLljUojbrjabctx0tb2ldBefKYhTRjaJljCnrFbdIRRLF\ DO30yKgxSkwZnveqvltoipifmccjY`gSYzMVzGmzAQz8RY7S_6\ Ta5Uc3Ve2Wg1Xi0Xk2Ze4_`5`W7oQ8cLAtGBeBDdFEdJFcMGcQ\ IbUJbXKazLazIIpGczDdNBez8fC6g77fN8ea9epzvDztJzrPzp\ Vzn_zlezjkRH3HVSrYMh`T_bZQddHfjdKKYPRRUYLZcEcjM7z0\ uksVzkPpdKfXFYQAOI5EB05J28Q4BX6Dd8GkAJrCLWGE9J7JUF\ TdNboU`nTZnSXnRVnQTnPRmOPmNNmMLmLKmKKkNKjQKhSKgVKe\ YKd_KbbKadK_gKZjKXlKWoKVq } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 01-10-12 (NewStuff [Low])
by Jim Muth 01 Oct '12

01 Oct '12

FOTD -- October 01, 2012 (Rating Low) Fractal visionaries and enthusiasts: Today's image has a low rating. Since I did not wish to embarrass myself, I did not state exactly how low, but it would be fair to state that the rating would be notably less than average. (A rating of 4 would be a good guess.) The image lies within the tiny bit of debris inside the Mandelbrot bud that appeared in the background of yesterday's image. Today's image is characterized by a near-hopeless nest of zigzag filaments overlying a totally chaotic background. The filaments are much like those found in the 'Siegel Disk' area of the Mandelbrot set. The name "New Stuff" is a bit misleading, since there is little new stuff in the image, which is really only a casual glance of what lies within a strange little eye-shaped bit of unevaporated debris. The calculation time of 8-1/2 minutes is a bit too much to pay for the image, but once again, the FOTD web sites charge to the rescue, saving both time and frustration. Be part of the charge. View the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Lots more older images are available at: <http://www.Nahee.com/FOTD/> Despite a few minor clouds here at Fractal Central today, the day brought the impression of a sunny one. The temperature of 68F 20C was quite pleasant for the start of October, and the fractal cats took full advantage of it in their southwest window as they watched the falling leaves outside. The humans made it through another day with nothing out of the ordinary happening, which is boring to report but quite pleasant to experience in person. The next FOTD will be posted whenever it is. Until then, take care, and be of sound constitution, but keep the sound level under control. You wouldn't want your noisy constitution disturbing the peace. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= New_Stuff { ; time=0:08:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=JulibrotMulti2 function=recip passes=1 center-mag=+0.0017245727/+0.0093780664/10151/1/82/0 params=6.5/-6.5/89/0/89/0/-1.626/0/0/0 float=y maxiter=4000 inside=0 logmap=382 periodicity=6 colors=000z1Sm8YfEbYKgRQlrzFgvIXtLNrNOpQOnTPlVRjYS\ h`TfbVdeWbhX`jZZm_Xp`VrZYkX_dWaYUcRSeKRgDTeEUdEVcE\ WbFX`FY_FZZG_YG`XGbTKdPOfMShIWjE_lBcn7gp4kn6il7hj8\ gh9ffAedCdbDc`EbZFaXG`VI_TJZRKYPLXNMWOQXPTXQXYQ_YR\ cYSfZTjZTmZUq_Vt_Vw_Uu`UtaUsbTrcTqdTpeToeSmfSlgSkh\ RjiRijRhkRgkL_fFSaQLh`Enk7tu0zs2xq4wo6vn7tl9sjBriC\ pgEoeGndHlbJk`Lj_MhYOgWQfVReSTgQUiOVkMWmKXoIYqGZsE\ _tKWoQSkWOgaKcgG_lCWjEVhGVfIUdJUbLTaNT_OSYQSWSRUTR\ TVQRXQPYPN_PLaOKbORUUYM_dDek5kj9jiCihFihIhgLhfOgeS\ feVfdYec`ebcdbfdZdaWc_TbYQ`WN_UKZSHXQEWOBVM8Tz5rz2\ ez6RQARZERgIRpLRyLYyLMz1bG4_N7XUAU`DSfGPmNzCMzBKv8\ Jr5In2Hk0Ii1Ih2Ig2If3Id4Ic4Ib5Ia5J_6JZ7JY7JX8JV9JU\ 9JTAJSAKQBKPCKOCKNDKLEKKEKJFKIFLHELHELGEMGDMFDMFDN\ ECNECNDCODBOCBOCBOCBPFDQHFQJHRMJSOLSQMTTOTVQUXSV_U\ VaVWcXXfZXh`YjbYlcjJQiIMhGIgFDfE9eD5eC1_J5VQ9PXCKc\ GFiJKePPaVTZ_j9Rl7Sn5Sp3S } frm:JulibrotMulti2 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p2*0.0055555555555556), b=pi*imag(p2*0.0055555555555556), g=pi*real(p3*0.0055555555555556), d=pi*imag(p3*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), aa=-(real(p1)-2), bb=imag(p1), c=p+flip(q)+p4, z=r+flip(s)+p5: z=(bb)*(z*z*fn1(z^(aa)+bb))+c |z|< 6 } END PARAMETER FILE=========================================

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FOTD 30-09-12 (Fractals-101 [7.5])
by Jim Muth 01 Oct '12

01 Oct '12

FOTD -- September 30, 2012 (Rating ?) Fractal visionaries and enthusiasts: The day we spent yesterday back at Old Fractal Central went quite well. But the fractal cats disapproved of our all day absence and our 10pm return. A quick treat of tuna and cheddar restored their good spirits. Today's image shows both the Mandelbrot and Julia aspects of the same Julibrot scene together at the same time. Since I will attempt to explain how this is possible, I have named the image "Fractals-101". The reddish outer parts outline the Julia aspect of the scene, while the bluish inner parts show the Mandelbrot bud aspect. The bluish Mandelbrot bud near the center is about 60 times its apparent size when it is viewed as a straight Mandelbrot shape. To see the pure Mandelbrot view, reset the real(p2) and real(p3) parameters to zero and reset the magnitude to 60. (The value of 60 is necessary because it is close to the value of the tangent of 89.) But how can a Mandelbrot image be enlarged by merely slicing it at a very sharp angle? The answer lies in the 4-dimensional shape of the high-iteration Mandelbrot features of the Julibrot, which are extended to infinity in two dimensions, and display the typical compact Mandelbrot shapes in the other two dimensions. Imagine an infinitely long cylinder in three dimensions with a circular cross-section. If it is sliced straight across, the slice is a circle. But if it is sliced at an ever increasing angle, the slice is an increasingly stretched oval. And slicing the cylinder along its length produces an infinitely long straight rod. The angle of the slice causes the expansion of one dimension of the slice. In four dimensions we may have an object that is circular in its two compact dimensions and extends to infinity in its two extended dimensions. Such an object may be sliced at two independent sharp angles. Doing this will give a 2-D slice that is stretched in two directions, and if the angles are equal, the cross section will be enlarged proportionally without being stretched. We have a Mandelbrot microscope. The Mandelbrot part of today's image was enlarged just this way. (Unfortunate- ly, we can get no extra magnification of Mandelbrot objects by doing this.) The image itself is pretty routine. The most interesting part is the curiously shaped bluish Mandelbrot bud at the center. The rating of a question mark means I don't really know how to rate the image. The calculation time of 2 minutes is reasonably fast, but the web sites are always there to make things even easier. Be happy! View the finished on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> without the need to calculate it. View the image in high-definition, with lots of added bells and whistles such as anti-aliasing at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> All the thousands of FOTD back images are online at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds, with a temperature of 64F 18C made today quite typical of the end of September here at Fractal Central in Central Pennsylvania. The fractal cats enjoyed the sunny periods on their shelf, and endured the cloudy times in sulk mode. The humans spent most of the day recovering from yesterday's trip to Old Fractal Central, where my sister is putting out food for the neighborhood cats that are starting to gather in increasing numbers for a free meal. The next FOTD will be posted in a reasonable amount of time. Until whenever, take care, and if we suddenly lost all our advanced technology, how many, I wonder, would survive and how many would curl up and expire. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Fractals-101 { ; time=0:02:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=JulibrotMulti2 function=recip passes=1 center-mag=0/0/1.572327 params=6.5/-6.5/89/0/89/0/\ -1.626/0/0/0 float=y maxiter=24000 inside=0 logmap=12 symmetry=xaxis periodicity=6 colors=000S05U17W28Y39_4Aa4Bc5Ce6Dg7Ei8Fk8Gm9HoAIq\ BJtCKwCLuEMsGMqINoKNmMOkOOiQPgSPeUQcVQbUPbUPbUOaUO\ aUNaTN`TM`TM`TM_TL_SL_SKZSKZSJZSJZSJVTKSULPVMLWNIX\ OFYPBZQ8_R5`S2`T9cQGeNNhKUjH`lEgoBnq8us5so9rlDpiGo\ eKmbNl_RkWViTYhQafMdeJhdGkdGkcHkcHlcHlcHlbIlbImbIm\ bImaJmaJmaJnaJn`Kn`Kn`Ko`Kz_Lz_Lz_Lz_LzZMzZMzZMzZM\ zYNzYNzYNzYNzXOzXOzXOzXOzWNzWNzWNzWNzWNzWNzWNzWNzW\ MzWMzWMzWMzWMzWMzWMzWMzWLzWLzWLzWLzWLzWLzWLzWLzVKz\ VKzVKzVKzVKzVKzVKzVKzVJzVJzVJzVJzVJzVEzVJzVJzVJzVJ\ zVIzVIzVIzVIzVIzVIzVIzVIzUHzUHzUHzUHzUHzUHzUHzUHzU\ GzUGzUGzUGzUGzUGzUGzUGzUFzUFzUFzUFzUFzUFzUFzUFzYKz\ XKzXKzXKzXKzXKzXKzWKzWKzWKzWKzWKzWKzVKzVKzVKzVKzVK\ zVKzUKzUKzUKzUKzUKzUKzaKz`Kz`Kz`Kz`Kz`Kz_Kz_Kz_Jz_\ Jz_Jz_JzZJzZJzZJzZIzZIzYIzYIzYIzYIzYIzYIzXHzXHzXHz\ XHzXHzWHzWHzWGzWGzWGzWGzVGzVGzVGzVFzVFzUFzUFzUFzUF\ zUKzKKzKKzMKzLKzLKzKKzKKz } frm:JulibrotMulti2 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p2*0.0055555555555556), b=pi*imag(p2*0.0055555555555556), g=pi*real(p3*0.0055555555555556), d=pi*imag(p3*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), aa=-(real(p1)-2), bb=imag(p1), c=p+flip(q)+p4, z=r+flip(s)+p5: z=(bb)*(z*z*fn1(z^(aa)+bb))+c |z|< 6 } END PARAMETER FILE=========================================

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