October 2003 - Fractint - mailman.xmission.com

Classic FOTD 17-11-98 (The Omega Point)
by Jim Muth 19 Oct '03

19 Oct '03

FOTD November 17, 1998 (The Omega Point) Fractal visionaries: The weather today was so dull that I can barely remember it. Oh yes, it was partly cloudy with a temperature of 60F 15.5C and a south wind at 12kph. Regardless, it was a perfect day for scrounging in fractal land for that one perfect fractal that might exist among the infinity of infinities of fractals that might exist. Unfortunately, tonight has become totally cloudy, and the meteor storm, if it happens, (which I doubt), will be invisible from fractal central. But I'll be up around 5am just in case a hole opens in the clouds and the meteors are there. The fractal I found was created by the next in my series of 12 MandNewt formulas, MandNewt10. This formula, as well as numbers 11 and 12, has six variable parameters. Since the six parameters are limited to real numbers, the resulting fractals always have X-axis symmetry. In some cases, the extra variable parameters are redundant, simply increasing or decreasing the values of other parameters, but overall the result is totally unpredictable, which is the way I like my fractals. I named the picture "The Omega Point" because as I studied it, I wondered if there could possibly be a last fractal. Actually, that's the way I name most of my fractal pictures -- I stare at them until a name comes into my head. The picture is a lot like my "Fractoland" picture of several days ago, though I'm not blaming this one on Dr. J. The picture has vague buds half obscured by bits and pieces of ectoplasmic fractal material, and areas of chaos offset by organized areas of quasi-order. But this image has at least a hint of order amid the most chaotic disorder. The spiral occupying most of the top third has no corresponding feature in the earlier picture. This spiral reminds me somewhat of the images produced by the Barnsley formulas. The GIF file has been posted to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> And now I suspect that the honorable thing to do would be to wrap this up and see if I can get it posted. Until next time, when I shall likely be a bit more settled, take care, and remember that no matter how far you search, you will never find the last fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PARAMETER-FORMULA FILE============================ The_Omega_Point { ; 16 min on a P200, 640x480x256 reset=1960 type=formula formulafile=mandnewt.frm formulaname=MandNewt10 passes=1 center-mag=-0.7352\ 27/1.28731/1.153329/1/-75/-2.50563458870090017e-014 params=3.524/1.979/-3.263/1.769/0.733/0.736 float=y maxiter=12000 inside=0 logmap=yes periodicity=0 colors=000HELHEMGDNGDOFDPHFRFDPE7ODANC9MB8LABPEATI\ 9XMCWLi_KmZJlYIjXHiWGhVFfUDeSCcRBbQAaP9_O8ZNAYODXP\ FWQHVQKVRMUSOTTQSUTRVVQWXPW_OXaNYcMZfM_hL`jK`lJaoI\ bqHcsHctIdtIdtJetJetJetJetKfuKfuKfuKfuLguLguLguMhu\ MhuMhuMhuNiuNivNivNivOjvOjvOjvOjvPkvPkvPkvQlvQlvQl\ wQlwRmwRmwRmwRmwSnwSnwSnxRmxRlxRlxRkxRkxRjxRjxRixR\ hxRhxRgxRgyRfyRfyReyRdyRdyRcyRcyRbyRbyRayR`yR`yR_y\ R_yRZyRYyRYyRXyRXyRWyRWyRVyRUyRUzRTzRTzRSzRSzRRzRQ\ zRQzRPzRPzROzROzRNzRMyQLyQLyRLyRLySMySMyTMyTMyTMyU\ MyUMyVNyVNyVNyWNyWNzXNzXNzYOzYOzYOzZOzZOz_Oz_Oz`Pz\ `Pz`PzaPzaPzbPzbPzcQzcQzcQzdQzdQzeQzeQzeQzfRzfRzgR\ zgRzhRzhRzhRziSziSzjSzjSzkSzkSzkSzlTzlTzmTzmTzmTzn\ TznTzoUzoUzpUzpUvqQqrNlsJfsFatCXu8Sv4Mu1Nu1Nu1Ov2P\ v2Pv3Qv3Rv4Rv5Sw5Tw6Tw6Uw7Vw8Vx8Wx9Xx9XxAYxAZyBZyC\ _yC_yD`yDayEazEbzFczGczGdzHezHezIfzJgzJgzKhzKizLiz\ LjzMjzMkzNlzOlzOmzPnzPozQ } frm:MandNewt10 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-b)*z-g j=c*z^d+g z=z-e*h/j, f <= |h| } END 19.6 PARAMETER-FORMULA FILE==============================

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Classic FOTD 31-03-98 (Symphony in P-Flat)
by Jim Muth 18 Oct '03

18 Oct '03

F.O.T.D., March 31, 1998 (Symphony in P-flat) Fractal visionaries: This first paragraph was written on October 18, 2003. I wonder whatever happened to Doctor J. in the 5-1/2 years since the rest of this discussion appeared. And things are looking good for the resumption of the ongoing FOTD by the end of the month. START MARCH 31, 1998 DISCUSSION=========================== I see that Dr. J is loose again on the internet. I heard his mad-scientist laughter the moment I signed on. I only hope he can keep himself firmly in three-space. We've been losing far too many good fractalists into the fourth dimension lately. As the doctor zipped past my place, he dropped off a fractal that looked like two M-sets, one on top of the other. To view the image properly, I needed my red and blue glasses. Luckily, I found them still tucked inside my "Fractal Creations" book. The glasses showed not two but three M-sets -- a red one that looks like a snowman and two overlapping blue sets. I had several questions to ask, but the doctor flashed away before I had a chance. Today I had planned, I had honestly planned on describing how I stumbled upon what I consider to be one of the most incredible of fractal objects -- the perfect rectangle at Z=0.00019,0.07388 in the Julia set of the Z^2.003+C figure with a starting point of C=-1.7435,0.0. I started out well enough on the article, and had it nearly half finished, when an unexpected rush job arrived that took longer than expected. Rather than rush the article to comple- tion, I decided to postpone it until tomorrow, when I will have time to get it right. But not to disappoint anyone, I have a fractal for today -- an admitted quickie. It looks rather like a Pollock painting, where streaks and splotches of paint are dripped and splashed around the canvas. But this one is a pure fractal. It is a scene in the (-Z)^(-0.95)+C figure, made more presentable by the epsiloncross inside fill, which adds the streaks to the splotches, which are part of the fractal. I named the picture "Symphony in P-flat" because it reminds me of a scene in an old Disney animated musical film. (I think it is the 'After You've Gone' segment of the film 'Make Mine Music'.) The image is sliced in the Parabolic direction. This particular image could really benefit from anti-aliasing to correct the fine lines which have broken into dashes. But even in its imperfect state, it is worth a look. The picture has been posted to: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Tomorrow, I'll tell the tale of the vanishing rectangle -- I really will -- honest! Until then, take care and . . . Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PARAMETER-FORMULA FILE=========================== Symphony_in_P-flat { ; 38 seconds at 200mhz reset=1960 type=formula formulafile=slices.frm formulaname=ParabolicMiN passes=1 center-mag=0.0\ 860258/0.0841156/0.8239817/1/-57.5 params=-0.95/\ 0/0/-1/0/0.4 float=y maxiter=252 bailout=25 inside=epsiloncross logmap=yes symmetry=none periodicity=10 colors=000kBXP0mK_JnpEz0z000tzZJI\ bZCfd4J0v0HdGYNVpWmoJkHC5Y9Q3wNYpYfTcBT7VHRV9D\ <2>i6amV4nMInEWkMRmE`T7R<2>i6eRp5<2>hH_eSShKYkDc\ FcCRSObHZBBqP9na7kPzIK8xV7sd6n17E<2>b6a`7OCwjWXi\ 5iMLWU_Jac5d<2>l6hZThzwW<2>qJftjV<2>oGfpsC<2>nIa\ WG89Zi6JJ`N7<2>kA`EMQRGXbBcB2UNab<2>gEhrJ1jobl_e\ mLgXiabWdhJg`Cyafl<2>kFiFN3<2>eA_WOeeFghVdkIgU7L\ <2>i6cvb8B_mPQkaGjczOiYZrGfq`BpQNoGZC4WW5b4kL<2>\ cGcf4c<2>l6hrzPpY_fDfj9hRlyZYsfKnDLmQGkbBjRdgbNh\ 7GLhIqjEnlAk6vMLdU_NaXoZEnZR_bbLfNCb7F0<2>c8ZWdw\ `WseNpjEln7N<2>n6d7SjTHi5Wn<2>cCj0V9HMMYEYdY`hOc\ kFfwOZiH5<2>m8_lJemCgQpiZ`ifLisAyp8q`dG`y5efJjOX\ UcqdNmt4Ur5_p6dpli<2>nGi5ly<2>cGmnfSnUYnIclvu<2>\ nJlECnRAlb8jggjkPiqLLea2QcKBeaT8R<2>mM2<2>9up3i5\ TNHS_QSkZQhYPeXPSIPF3W4M<3>o11Uczn4OgGJiDQ } frm:ParabolicMiN {; Jim Muth b=p1, z=imag(pixel)+p2, c=real(pixel)+p3: z=(-z)^(b)+c, |z| <= 16 } END 19.6 PARAMETER-FORMULA FILE=============================

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Classic FOTD 10-10-99 (Mandelbrot Maestro)
by Jim Muth 17 Oct '03

17 Oct '03

CLASSIC FOTD October 10, 1998 (Mandelbrot Maestro) Fractal visionaries: It was cloudy today here in fractal land, with a few light showers in the evening. The high temperature of 68F 20C was perfect for exploring a hyperfractal, which I did with my Mandel_4-D formula. Every fractal explorer knows that when the starting point of Z is perturbed, the features of the resulting image are distorted. But when the fractal is a four-dimensional Mandelbrot set, the distortion can be downright grotesque, as today's image shows. The mis-shapen object in today's picture is the prominent midget on the negative tail of the 4-D hyper-M-set, viewed in a remote perturbed plane. I have named the picture "Mandelbrot Maestro" because that phrase popped into my head as I studied the image. I can't begin to explain why the image appears as it does. Nor can I explain exactly what the formula does. At times, the fractals drawn by this formula don't make sense, leading me to suspect that some of the images are artifacts. I'll need to do quite a bit of testing before I can add comment lines -- something that I have resolved to start doing with all my formulas. (Nothing is more annoying than having a formula and not knowing how to make it work.) The GIF file of today's quick image has been posted to: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Tomorrow . . . who knows? I'll be here again with another fractal -- that's for sure, but as to what type of fractal it will be -- I won't know until I actually see it. Even then I may not know. So until then, take care, and didn't someone once claim that the fractals of Autumn are the best of the entire year? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PARAMETER-FORMULA FILE============================ Mandelbrot_Maestro { ; 25 seconds on a P200 at SF5 reset=1960 type=formula formulafile=jim.frm formulaname=Mandel_4-D center-mag=-1.75909/0.0021\ 9158/69.70197 params=0/0/0/1.137/0.001/0 float=y maxiter=1200 inside=0 logmap=yes periodicity=0 colors=000KYN<8>1u43n7029<3>06H47H<4>TEOYAPbGQg7R\ lISmCTnPUoIVpVWpOXq`YrPZsc_oNzsb_lHgkaekJckZakL_k\ WYkNXkYVkPTkVRkRP<3>kVIkWGlYH<12>hD0<7>4p0<13>l7y\ <3>DRq0_r<7>VA_Z7Yb1X<13>R_MRaMPcO<6>EpWHxa<2>BhZ\ 4f`<12>u9N<2>lTCi_9dd3<12>sg_<15>a38<10>SgUNoMJwF\ <14>ZaV_`W`ZZ<9>bPx<3>lxe<6>ZrmYrnWpl<9>L``<2>GlZ\ KcQNVIfJHy7HdALKDOVLY<3>NWQ } frm:Mandel_4-D {; 4-D Mandelbrot, 8-D Julibrot a=(p1), b=(0,0), d=p2+2: f=sqr(a)-sqr(b)+pixel b=d*a*b+p3 a=f |a|+|b| <16 } END 19.6 PARAMETER-FORMULA FILE==============================

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Classic FOTD 19-05-99 (Bed of Hot Coals)
by Jim Muth 16 Oct '03

16 Oct '03

CLASSIC FOTD May 19, 1999 (Bed of Hot Coals) Fractal enthusiasts: Yesterday's fractal showed a view of the bottomless pit. Today's fractal shows the bed of glowing coals at the bottom of the bottomless pit. Yes, I realize that a bottomless pit has no bottom, but for the sake of convenience, we'll give our pit a bottom. The scene of today's image usually is filled with imps, hopping around on the coals, crying, "ouch!" Unfortunately, none of these unpleasant entities appear in the picture. I named the picture "Bed of Hot Coals" as a description. Don't worry if the first three inches of the picture are featureless. The detail is in the bottom half of the image. The image is actually a zoom into the left edge of yesterday's FOTD. I changed the color palette only slightly, to achieve a more sinister effect in the sky. This scene itself has some interesting zooms in it, so we'll see what tomorrow brings if I decide to go zooming. The parameter file runs in a few minutes; the picture file is posted to: <alt.binaries.pictures.fractals> and to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I've noticed that on the UF list, they're discussing whether fractals are art. Having thoroughly thought about the situation, and noting the effort that goes into the creation of some of these images, I can state in no uncertain terms that yes, fractals are indeed art. Whether my fractals are art is another question, however, and one which I have not yet answered. Some of the fractals being posted to ABPF have been achieved only after hours, even days of work. The average length of time I spend working on my images is about 15 minutes, draw time excluded. I doubt if art can be created on such a production line basis. But, art or not, I'll be here again tomorrow with another fractal, perhaps a closer look at today's bed of coals, perhaps a skewed view of a great spiral. And perhaps some philosophy. For now, I'm going to ponder whether the eight diagonals of a tesseract intersect at right angles. (I'll bet not!) Until next time, take care, and be at peace with peace. Jim Muth jamth(a)mindspring.com START 19.6 PARAMETER-FORMULA FILE========================= Bed_of_Hot_Coals { ; 0:05:50.82, p200, SF5 reset=1960 type=formula formulafile=mandnewt.frm formulaname=mandnewt05 function=atanh passes=1 center-mag=2.22365/1.06229/10.4956/1/77.5/-3.77822\ 773067748585e-014 params=1.172/-1.191/0.957/-0.004\ /-4.046/0.798 float=y maxiter=250 inside=bof60 logmap=yes periodicity=10 colors=000zZ9yW9uS9pO8lK8hG8eG8bF8_E7XD7UB7RB7PA7M\ 97K87K77K87KA9KAAKABKACKADKAEKAFKAFKAFKAFKAFKAFKAF\ KAFKAFKAFKAFKAFKAFKAFKAFLAFNAFPAFRAFTAFUAFWAFYAF_A\ F`WIbWHdWHfWGgWGiWFjWFkWEnWEoWDqWDrXBtXBvXAwXAw_Aw\ c9wf9wi8wk8wk8ogGh`M`USUNYQB_RGcSJfXNjaQm`Rj_Si_Tg\ ZUfYVdYWcXXaWY`WZZV_YU`WU`VTaTSbSScQRdPQeNQfMPgKOh\ JOiHNjGNkFMmDJp4Ln8MmBOjGPjJQhMSgQTeTVcXWa_X`bZZf_\ XiaVmbTodRtdRscSrcSrcSqbTpbToaUoaUnaUn`Vn`Vm`Vk`Vk\ _Wj_WjZXjZXiZXhZXgYYgYYfYZfXZeXZdW_dW_cW_bUZdVZcX_\ bY_aZ_`_`_a`Zb`XcaWdaVfaUgbThbSjcRjcQkcPmdOndNodMp\ eLreKsfJtfIufHwgGxgFygEygDzgByhEyiFyiGyjHxjIxkJxkK\ xkLxmNxnOwnPwoQwoRvpSvpTvpUvqWurXusYusZut_tt`tuatu\ bqrdnofknhjjjghkdemaco_`pXZrUWtOVySVuWUrZUnbTjaTj_\ TjZUiYUiWUiVUiUUhSUhRVhPVhOVgNVgLVgKVgJWfHWfGWfFWf\ DWfBWeAWe8We7We6We7Uf8Tf9Rg9QgAOgBNgDLhEKhFIiFHiGF\ iHEiIBjAAjAAjAAjBBjBBjBBj } frm:MandNewt05 {; Jim Muth z=c=fn1(pixel): a=z^2+(c-p1)*z-c b=p2*z^2+c-1 z=z-1*a/b p3 <= |a| } END 19.6 PARAMETER-FORMULA FILE===========================

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Lost
by Brian Rankin 16 Oct '03

16 Oct '03

Help! I have lost my Fractint front end.I would be obliged if anyone could tell me where to find it. Brian

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Classic FOTD 20-04-99 (Hyper-Spherical)
by Jim Muth 15 Oct '03

15 Oct '03

October 15, 2003 This FOTD image and discussion originally appeared on April 20, 1999. I present the image today in an improved version with fine-tuned colors. The discussion has been edited to remove some irrelevant stuff, and a few new comments about the fourth dimension have been added. ======================================================== CLASSIC FOTD April 20, 1999 (Hyper-Spherical) Fractal enthusiasts: What does a 4-D hypersphere look like? We shall never know. Speculation is futile. A hypersphere is not a visual object; it is an abstraction. Trying to visualize a hypersphere is as hopeless as trying to visualize any other abstraction, such as honor. But it is still fun to try to see what a hypersphere would 'look like' if we were four-dimensional beings. Of all the higher-dimensional figures, the hypersphere is the simplest. Any 3-dimensional slice of a hypersphere of any number of dimensions is a 3-D sphere. For example, any 3-D slice of a 4-D hypersphere is a sphere. Any 2-D slice is a circle, and any 2-D slice of a hypersphere of any number of dimensions is a circle. Today's fractal is a revelry of circles, which I assume, though I have not checked, are slices of 4-D hyperspheres. The three-dimensional effect is due entirely to the coloring, to which I devoted an unusual, (for me), amount of time and effort. The image resembles nothing as much as a scene in orbit around a giant planet in some far away galaxy. The entire picture is composed of circles colored to appear as spheres. These circles are arranged into interesting sheets and tendrils, which need investigating. Anyone out there who would like to investigate further, go ahead. I've got too many more fractals waiting, to have time to spend more than one day on a given image. I named the picture "Hyper-Spherical" more out of hope than fact. I hope that these circles are slices of near-perfect 4-D hyperspheres, but I have a strong suspicion that they are not. The GIF file has been posted in all its planetary glory to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather at fractal central has not changed. Partly cloudy skies with occasional sprinkles of rain and a temperature of 57F 14C made it a chilly spring day, yet a perfect day for finding fractals. I shall now close down the fractal shoppe for another evening, and call it a day. But I'll return tomorrow with more fractal blather. Until then, take care, and keep the fractal faith. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PARAMETER-FORMULA FILE========================= Hyper-Spherical { ; time=0:12:57.80--SF5 on a P200 reset=1960 type=formula formulafile=mandnewt.frm formulaname=MandNewt12 passes=1 center-mag=+0.7897\ 05601237999/-0.02843030167377993/477729.2/1/30 params=-4.3808/-0.5139/-1.2595/1.0881/-0.81/2.519 float=y maxiter=250 inside=bof60 logmap=yes periodicity=0 colors=000zzYyxYxuXwqWvmVukUtiTsgSrf\ RqeQpdPocOnbNmaMl`Lk_KjZJiYIhXHgWGfVFeUEdTDcSDbRCa\ QC`PB_OBZNAYMAXL9WK9VJ8UI8TH8SG7RF7QF6PD6OA5N75M98\ LBAK75J66I66H008WT8WT8WT8WT8ZV8`Y8c_8fa8ic7kf7nh7q\ j7tl7vo7yqAwqDurHrrKpsNnsQltTjtWhu_eubcveavh_wkYwn\ WxrTxuRyxPyuMqsIipF`nBTk8Lj9KhAJgBIfCHeCGcDFbEEaFD\ `GCZHCYIBXJAWK9UL8TL7SM6RN5PO4OP3PP4QP6RQ7SQ8TQAUQ\ BVQCWREXRFYRHZRI_RJ`RLaSMbSNcSPdSQeSRfTTgTUhTViTXj\ TYkUZlU`mUanUboUdpUeqVgrVhsVitVkuVlvWmwWoxWpwYmuZk\ t`hrafqccpd`nfZmgWliTjjRilOgmMfoJhpKipLkqMmrNosOps\ PrtQstRrqSqoSplSojSnhSmfSmcSlaSk_SjYSiVShTSgRSfPSe\ MSdKScISbGSbDSaBS`9S_7SZ4SY2SY0SZ1R_1R_1R`2Qa2Qa2Q\ b2Qc2Pd2Pd3Pe3Pf3Of3Og3Oh3Oh4Ni4Nj4Nj4Nk4Ml4Ml5Mm5\ Mn5Lo5Lo5Lp5Lq6Kq6Kr6Ko7Jl7Ji8Ig8Id9Ha9GZAGWAFTBER\ BEOCDLCDIDCJEDKGFKHGLIIMKJNLLOMMOOOPPPQRRRSSSTTSVV\ TWWUXYVZZW_`W`aXbcYcdZdc_dcwTgwSgwRgwQg } frm:MandNewt12 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-1)*(z-b) j=c*z^d+g z=z-e*h/(f*j), .0000000000000000000000000000005 <= |h| } END 19.6 PARAMETER-FORMULA FILE===========================

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Classic FOTD 12-03-99 (Edge-on Galaxy)
by Jim Muth 14 Oct '03

14 Oct '03

CLASSIC FOTD March 12, 1999 (Edge-on Galaxy) Fractal enthusiasts: Today was bright and sunny, but chilly here at Fractal Central. The temperature of 41F 5C was perfect for a journey through fractal land. My journey took me to the same area as yesterday's shamrock fractal. I wrote a new formula just for the trip, which will let me view the scene from an entirely new direction. The angle of the slice has been turned -10 degrees from the Rectangular direction toward the Oblate direction, giving the effect of a galaxy seen edge-on through clouds of interstellar dust. I named the picture "Edge-on_Galaxy" as a straightforward description. And yes, once again I have sinned by loading the GIF file into a graphics program for some fine-tuning: The gently illuminated galaxy is visible on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where you will find links to lots of hyper-dimensional stuff, and some pretty far-out hyper-fun-stuff also. I've been busy today, so I'll have to cut the discussion short, but the fractal is good enough to make up for a lack of words. After all, one picture of a three-dimensional object is worth a thousand words, so a picture of a four-dimensional object must be worth a million words. Until tomorrow, take care, and don't get lost in the stars. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PARAMETER-FORMULA FILE========================= Edge-on_Galaxy { ; 0:01:43.64--SF5 on a P200 reset=1960 type=formula formulafile=allinone.frm formulaname=multimin-xz-yw-new passes=1 center-mag=+0.05750247255816/+0.00097963198354/204\ .5845/0.04123 params=90/-10/3.5/0/0.03907/-0.28621\ /0.8042/0 float=y maxiter=1200 bailout=25 inside=0 logmap=16 periodicity=10 colors=000RAWQAVPAUOATNASMARLAQLAQKAPJAOIANHAMGALF\ AKEAJD9JB9J89I6BI4BI1BG0BG0BG0BE0BE0BD0BE0BE0BE0BG\ 0BG0BG0BI0BI0BI0BJ0BJ0BJ0BJ0BL0BL0BL0BL0BN0BN0BN1B\ O1BO1BO1BO2BQ2BQ2BQ4BR4BR4BR6BT6BT6BT6BT8BV8BV8BV9\ BX9BX9BX9BXBBYBBYBBYDB_DB_DB_DB_E9aE9aE9aG9bG9bG9b\ I9dI9dI9dI9dJ9fJ9fJ9fL9gL9gL9gL9gN9iN9iN9iO9kO9kO9\ kO9kQ9lQ9lQ9lR9nR9nR9nT9pT9pT9pT9pV9qV9qV9qX9sX9sX\ 9sY9tY9tY9tY9t_9w_9w_9wYDt_9w_8xa6za4za1zb0zb0za0z\ a0zb0zb0zb0zd0zd0zd0zd0zd0zf1zf1zf2zf2zf2zg4zg4zg4\ zg6zi6zi8zi8zi8zi9zk9zkBzkBzkDzkDzlEzlEzlEzlGxnGxn\ GxnIxnIxnJxpJxpJxpLwpLwpNwpNwqOwqOwqOwsQwsQtsQtsRt\ sRttTttTttVttVttVswXswXswYswYsxYsx_sx_sxaqxaqzaqzb\ qzbqzdqzdqzdqzfpzfpzgpzgpzgpzipzipzkpzknzlnzlnzlnz\ nnznnzpnzpnzplzqlzqlzslzslztlztlztlzwkzwkzxkzxkzxk\ zzkzzkzzkzxlzxlzwlzwlzwlzwnzwnzxpzzqzzszztzzwzzxzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:multimin-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=(-z)^(p2)+c, |z| <= 36 } END 19.6 PARAMETER-FORMULA FILE===========================

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Classic FOTD 17-02-99 (A Little Lotus)
by JimMuth＠aol.com 13 Oct '03

13 Oct '03

FOTD February 17, 1999, (A Little Lotus) Fractal visionaries: It was a bright and sunny day here at the Fractal Place -- unusually warm for winter, but pleasant nonetheless. The temperature of 64F 18C was perfect for hunting fractals, and as you might expect, I hunted. Yesterday's FOTD was a bit disappointing, so I decided to post an extra impressive fractal as today's FOTD. The workhorse MandelbrotMix4 formula once again did its job when I needed it, turning up today's lotus-like picture after only 15 minutes of searching. The scene I stumbled upon resembles an unfolding lotus blossom, so I named it "A Little Lotus". The parameter file runs slow, but as always, the GIF file of the image has been posted to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Now, I must make a confession. I hate to disappoint my philosophy lovers, but I've got no words of wisdom today. I've been irritable all day from a job that went sour, and it's hard to philosophize when you're in a bad mood. Tomorrow is another day, however, and it will bring another fractal. It might even bring some babble, so check then to see. Until next time, take care, and don't stare too long at any one fractal. They do strange things if they're stared at too intensely for too long a time. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PARAMETER-FORMULA FILE============================ A_Little_Lotus { ; 21 min on a P200 SF5 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.43928832160053900/+0.04139571017709617\ /1.414159e+010 params=100/0.9/101/-1.1/-0.985/100 float=y maxiter=12000 bailout=25 inside=0 logmap=361 symmetry=xaxis periodicity=12 colors=000jT0jT0iT0gT0fT0dT0cT0aT0`T0_T0YT0XT0TT0Q\ T0ST0QT0PT0QT0ST0QT0TT0SV0SV0VV0TX0TX0VX0VX0TY0XY0\ VY0VV0YV0YT0YS0_S0_Q0_O0cP0cO0dO0dM0dL0dJ0gJ0gI0gG\ 0iG0iF0iD0mF0mC0mA0oC3oA3o93rA7r97r77u70r77o69m6Dm\ 6Gi6Mg1Og1Td1Yc1``1dc3mc1rc3yd4zc4zc6zd7zf9zgCziFz\ lGzmIzoLzpMzrPzsQzuTzuVyxYyx_xycxzfxzfxycuxasu_ru_\ rrXooVmoTmmTmiPiiPiiMigMidJgdJgcIg`Ig`Fg_FdXCdXCdX\ 9dT9cQ7cQ7cP4cL4_J1_G1YD0XC0VAiu0ez0az0Yz0Ux0Qr0Mm\ 0Ig0Ec0Aa0E_0Ia0Mc0Qe1Tg1Wi4Yk4Zm9_o9aqCcmCdmDdoDf\ oGgrGirJjuJluMmxMoxPpyPryTrzTuzVvzXxzYyz_yz`zz`zzd\ zzdzzgzzgzzizzjzzmzzmzzpzzpzzuzzuzzxzzxzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 19.6 PARAMETER-FORMULA FILE==============================

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Classic FOTD 23-12-98 (Ceremonial Radical)
by Jim Muth 12 Oct '03

12 Oct '03

CLASSIC FOTD December 23, 1998 (Ceremonial Radical) Fractal visionaries: Today seemed a lot more like winter here at fractal central. The afternoon temperature of 28F -2C and forecast of snow for tomorrow made it perfect for a fractal hunt. I hunted in the MandelbrotMix7 formula, experimenting with the parameters in a whimiscal manner to see what I might find. What I found was today's image, a strange fractal with a ceremonial aura about it. I named the picture "Ceremonial Radical" because of the effect of deep symbolism in the image. As I understand it, a radical is almost the same as a bud, but differs from a bud in that the word "radical" refers to the entire set of features connected with a bud, such as sub-buds, stars, filaments, etc. In today's picture, the radical is the bud at lower center, along with all the associated debris. Toward the top of the picture lies a very distorted M-set, with its period-2 bud larger than its main bay. Today's GIF file, (a small one), has been posted to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tomorrow, I'll return with more wonders from the world of fractals, and maybe a fractal limerick or two. Until then, take care, be cynical if you wish, and be true to your fractals if you want them to be true to you. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PARAMETER-FORMULA FILE============================ Ceremonial_Radical { ; 0:05:37.79 on a P200 SF5 reset=1960 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=2.87321/-9.76996e-015/0.259034/1/-90 params=10/0.5/-10/0.5001/1150/0 float=y maxiter=1200 inside=0 logmap=yes periodicity=10 colors=000M5EL5FK5GI5HH5IG5JF5KE5LD5MB5NA5O95P85Q7\ 6R67SP6XH5XS5aU7`VA_XC_YEZ_HY`JXbMWcOVeQVfTUhVTiXS\ k_RlaRncQogPqhOrmNtmMuqMwrLxrKxtKwsJwsJwrIwrIvrHvq\ HvqGupGupFuoFtoEtoEtnDtnDsmCsmCslCqkEpjFohHngImeJl\ dLkaMjaNiZOhZQgWRfZSgWThZUiYVjZWk_Xl`YmaZnb_oc`pda\ qe`rf_sgZthYuiWvjVwkUxlTymSznRzoQzpPzqPzrQzsQztQzu\ RzvRzwRzxSzySzzTzzTzzTzzTzzUzzUzzUzzVzzVzzVzzWzzWz\ zWzzXzzXzz`zzczzgzzkzzozzrzzvzznzzfzzZzzRzzSzzSzzT\ zzUzzVzzVzzWzzXzzYzzYzzZzz_zz`zz`zzazzbzzczzczzdzz\ ezzfzzfzzgzzczz_zzXzzTzzPzzLzzQzzUzzZzzbzzgzzkzzPz\ z2zz4zz6zz8zzAzzCzzEzzGzzIzzKzzMzzOzzQzzSzzUzzSzzQ\ zzOzzMzzKzzIzzGzzEzzCzzAzz8zz6zz4zz7zz9zzCzsFzsIzs\ KztNztQztSztVzuYzu_zubzzdzzgzzizzhzzgzzfzzfzzezzdz\ zczzdzzfzzgzzhzzhzzizzizzjzzkzzkzzlzzmzzmzznzzAzzc\ zzUzzJzzLzzLzzKzzKzzKzzKzzJzzJzzJzzJzzIzzIzzIzzHzz\ HzzHzzHzzGzzGzzGzzGzzFzzF } 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 19.6 PARAMETER-FORMULA FILE==============================

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Classic FOTD 21-12-97 (Lost Midget)
by Jim Muth 11 Oct '03

11 Oct '03

Classic F.O.T.D. December 21, 1997 (Lost Midget) Fractal visionaries: Happy Solstice! This, after all, is what the season is really about. In the Northern Hemisphere it's the shortest day of the year; in the Southern Hemisphere it's the longest day of the year; at the equator it's just another 12-hour day; while at the North Pole it's the middle of the six-month-long night, and at the South Pole it's high noon of the six-month-long day. Here at coordinates 39.20 north 76.30 west, the sun sets at 4:45pm, which is not too bad when one considers places like Norway and Sweden, which receive almost no sunlight at all at this time of year. But the shortage of sunlight certainly does not imply a shortage of fractals. Today's fractal is ample proof of this. I've named it "The Lost Midget" because, like yesterday's FOTD, (which BTW was wrongly dated 19-12), it illustrates one of those obscure midgets that instead of actually existing, has merely a tendency to exist. I chose this particular midget because it best illustrates the effect of a ghostly something that is not really there. The formula is a generalized one of the form, (Z^n+C)+(C^n+Z). It is one of an experimental series that I worked up a few months back and then laid aside. I've actually got versions of this formula that draw all six perpendicular planes. (I do this with most all my formulas.) Some of the odd planes of this series are most unusual, so expect to be seeing more of them in the near future. The image has been posted at 640x480 resolution to Paul's web site at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Tomorrow will bring a longer (or shorter) day and a new fractal. At this time, I can't say what I'll decide on, but what ever it is, it will be interesting. So until then, take care and never choose a fractal when you play charade. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE====================================== lostmidg { ; 0:01:14.20 SF5 on a P200 reset=1960 type=formula formulafile=test.frm formulaname=MandelbrotZC passes=1 symmetry=xaxis center-mag=-0.601331/1.52656e-016/31.61269 params=1.26/0/0.5/-2/0.5/1 float=y maxiter=100 bailout=25 inside=bof60 logmap=yes periodicity=10 colors=000i`2Uc3TAmLIQYA_THROQJzKBuCAzU0wHSzm0VQ\ WzUyKZetLBkKB_F8QB5KA50hz<6>0hzcA8SN6Hb4MQ6RD8WA\ A_ACkAXwAp3D0aH4<2>RBwSU3NJhKRVHZHKeYmkosA1YAIMA\ _JHPGUEKAnSAFLH9hUAT`6ScULeGQLlMTXI_IlkAVh6BgTCf\ KDfBCKGGAyFAeERMXb5YA2RD3KS3EAGECBES7JT2HY3Fb3JL\ AZEUSOLLYC6`8<2>Ce45XlAaQZGE3A19AaCKKD_5UZcOaRJd\ FpZUXbGOiQJgE9RpCZSqYCVA0MAAKC8IM6GX45dj<2>CfExA\ 2MQ3IZ30cC7e7vADQCSMNJIXBIjFaZU<2>Kd90BG<2>BZ64A\ m7Aa9IQCVEcACRO7ZDT6_M9bFCd9sAL0gSLAzIDfGSNDCJES\ BmaC<2>Ne5IJHGVAKQ7VA8MH5_A7SB5LR4PLeJWMek46GwkA\ SVQFBR6CV5DZ4Eb3DE0<2>E_34Xo<2>CdFSexKiR<2>Ff9LP\ yDTdEYSEbFGPgFVUE`GEJq<2>E`FocnXeRyA4iD3US38CuAN\ bCXLqVcjQt_WbPaLHRIGVEFZAEb6FFvETV`J8<2>J`4NhA\ <2>Gf4UAzMOXsRy<2>ObHAA`CEKyNtaXU8KBBW7Je6Gf4WMy\ <2>IaHkWa0F37T3dK1<2>Ka3cGyRUWiAwpAxfAiXGWNUH } frm:MandelbrotZC {; Jim Muth z=p1, c=pixel: z=real(p2)*(z^imag(p2)+c)+real(p3)*(c^imag(p3)+z), |z| <= 100 } END PARAMETER FILE====================================

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