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FOTD 11-11-09 (Magenta Lining [7])
by Jim Muth 10 Nov '09

10 Nov '09

FOTD -- November 11, 2009 (Rating 7) Fractal visionaries and enthusiasts: The random parameters for today's image show that the parent fractal was created by the 'evolver' feature of Fractint, a good thing to use when the inspiration is lacking, as it was today. This parent fractal is a Mandelbrot set rotated 180 degrees, so that its main spike is facing east. This set is surrounded by a field of debris, which is particularly noticeable extending west- ward in the shape of an arrowhead from the East Valley of the M-set. Today's scene is located near the tip of the southern branch of this arrowhead-shaped field of debris. I named the image "Magenta Lining" when the area surrounding the M-set reminded me of the sun breaking through storm clouds. The rating of a 7 might be a bit liberal considering the routine nature of the image. The calculation time of almost exactly 3-1/2 minutes seems just about what the image is worth. Those who would rather surf than calculate may view the image already calculated on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A cloudy but dry day with a temperature of 61F 16C here at Frac- tal Central on Tuesday went unappreciated by the fractal cats, who spent the day watching for a tough new tomcat that has been prowling the area the past few days. As far as I know, the un- wanted cat never appeared. My day was comfortably busy. The next FOTD will be posted in 24 hours. If all goes well with the next FOTD, it will be an im- provement over today's. Until then, take care, and there's a lot more to life than meets the eye. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Magenta_Lining { ; time=0:03:30.01-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ passes=1 function=ident center-mag=-1.634006631643/-0.301637495589/3297436\ /1/-50/0 params=1.631336405529954/0.71065401165807\ 06/-0.3385723441267128/3.40971098971526/0/0 float=y maxiter=1500 inside=0 logmap=190 periodicity=10 colors=00080M90N91OA1PA2QB2RB3SC3TC4UD4VD5WE5XE6YD\ 6ZE7_F7`F8aG8bG9cG9dHAeHAfLBfQFiXJl`NneQqiVskYvmZx\ naxo_xn_ym`yl`zlazjbzjbziczjczidzhdygcxfcwecvecudb\ tcbrbbpabo`an_am_alX_jVYhTXgQVeOUdMSbKRaHP_FOZDMX7\ JYAKWDMUGNSJPQMQOQSMTTKWUIZWGaXEdZCg_Aj`8lbCmcFndJ\ oeMpfPqgSrhWsjZtkaulevmhwnkxonyprzquvpqsomonjlnfhm\ belZakWZjSViOSiKOhHLgDHf9GbLP`QOXRNUTMTULTVKNXJMYJ\ M_IL`HFaG9cF8dE8fD7gC6iB5jA5l94m83n74u74r84o84l83j\ 93g93d93aA3ZA3WA3TB3QB2OB2LC2IC2FD1CC2DC3DC4EB5EB6\ EB7FB8FA9FAAGABGACGADH9EH9FH9GI9HI8II8JJ8KJ8LJ8MK7\ NK7OK7PL7QL6RL6SM6TM6UM6VN5WN5XN5YO5ZO4_O4`P4aP4bP\ 4cQ3dQ3eQ3fR3gR2hR2iS2jS2kS0lR1mR2mR4nR5nR6oR7oR8p\ RApRBqRCqRDrRErRGsRHsRItRJtRKtRMuRNuROuRmvRmvRmvSm\ wSmwSmwSzwSzxSzxSzxSzxSzySzySgySiySkySmySozSrzStzS\ vzSxzSyzSzzSzzSzzUzzZzzczzhzzmzzrzzvzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 10-11-09 (The Right Angles [No Rating])
by Jim Muth 09 Nov '09

09 Nov '09

FOTD -- November 10, 2009 (No Rating) Fractal visionaries and enthusiasts: I wrote today's formula, which is part of a series, long ago, well before the start of the FOTD. But despite its apparent complexity, the images it produces have a boring similarity. Today's image is typical of the images created by the formula. With six parameters and four functions in the formula, the variety it produces is almost unlimited, but a little experimen- tation will soon reveal the boring sameness that led me to shelf the series of formulas. I named today's image "The Right Angles" because it is filled with squares and rectangles. And then I rated it at a 7, but a few minutes later I grew quite disappointed and, rather than rate it at something like a 4, decided to let it go without a rating. The calculation time of 17 seconds is no cause for disappoint- ment however. Neither is the trip to view the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The temperature continued mild here at Fractal Central on Monday, with a high reading of 68F 20C, but the almost total lack of sun made the fractal cats unhappy. My day was average, as are most days. And tomorrow is likely to be average again. But with any luck, the fractal will be above average. Until next time, take care, and if nothing but gravity can escape from a black hole, then gravity must move faster than light. (Something's wrong here but I'm not sure what.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Right_Angles { ; time=0:00:17.71-SF5 on P4-2000 reset=2004 type=formula formulafile=jim.frm formulaname=TowerMinExp04a function=sin/sqr/sinh/\ sinh passes=1 center-mag=1.28568/0/0.0827/1/90/0 params=1.5/0/0.333/0/0.8/0 float=y maxiter=500 inside=bof60 logmap=yes periodicity=10 colors=000000IVzb0NNLWNLVNKUNKVNKWNKXNJYNJZNJ_NJ`N\ JaNIbNIcMIcMIcMHcMHcMHcMHcMHcMGcMGcMGcMGcMFcMFcMFc\ MFcNEcOEcOEcPEcPEcQEcREcREcSEcSEdTEeTEfUEgVEhVEiWE\ jWEkXElYEmYEnZEoZEp_Eq_Er`EsaEtaEubEvbFwcGxdHydIze\ JzeKzfLzfMzgNzhOzhPziQziRzjSzkTzkUzlVzlWzmXzmYznZz\ o_zo`zpazpbzqczqdzpezpfzpgzphzpizpjzokzolzomzonzoo\ zopzoqzorzoszotzouzouznvznvznwznwznwznxznyznzznzzn\ zynzxmzwmzvmzumztmzsmzrmzqlzplzolznkzmkzljzljzlizm\ izmhzmhzmgzngznfznfznezoezodzodzoczpczpbzpbzpazqaz\ q`zq`zr`zr_zr_zrZzsZzsYzsYzsXztXztWztWztVzuVyuUyuU\ yuTyvTxvSxvSxvRxwRwwQwwQwwPwxPvxPvxOuwOuxOuyNtzNtz\ NtzNtzMszMszMszMszLrzLrzLrzLrzKrzKqzKqzKqzJqzJpzJp\ zJpzIpzIozIozIozHozHozHnzHnzGnzGnzGmzGmzFmzFmzFlzF\ lzElzElzEkzEkzDkzDkzDkzDjzCjzCjzCjzCizBizBizBizBhz\ AhzAhzAhzBgzBfzCfzCezCezDdzDczDczEbzEazEazF`zF`zF_\ zGZzGZzGYzHXzHXzHWzIWzIVz } frm:TowerMinExp04a {; Jim Muth z=pixel, c=p2+(p3*pixel): z=z^fn1(z^fn2(-z^fn3(z^fn4(-z+p1))))+c, |z| <= 100 } END PARAMETER FILE=========================================

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FOTD 09-11-09 (The Great beyond [No Rating])
by Jim Muth 08 Nov '09

08 Nov '09

FOTD -- November 09, 2009 (No Rating) Fractal visionaries and enthusiasts: I recently watched one of those shows claiming that the world will end in December of 2012. I was already taking the doomsday stuff very lightly, when an ad appeared for an automobile that they claimed could run for 15 or 20 years before finally wearing out. When I heard this, I started laughing, wondering if the auto designers realized they were wasting their efforts creating an auto that would run for up to 20 years when the world has only 3 years to go. But then, maybe the auto will be able to travel the road to heaven. Far more important is the problem of fractals in heaven. Without fractals, heaven would be more like the place down below, at least to me. But then, maybe they have computers of infinite speed in heaven. Today's image is a repeat of a very early FOTD image, which appeared in April of 1997 under the name "Gothic". This time around, I recolored the original image, backed off a bit and slightly stretched the entire scene. The image is a scene in the 4-dimensional Hypermandelbrot set, which is just about all I can say about it. I named the image "The Great Beyond". The background bud in the shape of a gothic arch, or ogive, is totally beyond reach. For over 10 years I have tried futilely to find a way to bring this background arch to the foreground. I guess the arch will remain forever in the great beyond of the fractal world. Since the image is a virtual repeat, I could not give it a rating. The calculation time of 6-1/5 minutes will drag on most machines. To avoid impatience I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday was perhaps the best November day of all time here at Fractal Central, with cloudless skies, light winds and a temper- ature of 66F 19C. The fractal cats actually had more sun than they desired before becoming overheated and stretching out in a shady corner by a north window. My day was well with reason, even though my opinions often are not. The next FOTD can reasonably be expected to be posted in 24 hours. Until then, take care, and prepare for who knows what. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Great_Beyond { ; time=0:06:12.88-SF5 on P4-2000 reset=1950 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-1.754864785812205/0/285446/1.0969/90/0 params=0/0/0/0/18/0/1e-035/0 float=y maxiter=5000 inside=0 logmap=-414 periodicity=0 colors=00AIAAIAAIAAIAAIAAIAAIAAIAAIAAIAAIAAIAAIAAI\ AAIAAIAAIAAIAAIAAHAAHAAHAAHAAHAAGAAGAAGAAGAAGAAFAA\ FAAGBBKCCKDDJEEJFFJGGJHHJIIIJJIKKILLIMMHNNHNOHOPHP\ QHQRDRSESTFTUGUVGVWFVXFVYFW_FWaFWcEWeEWgEWiEWkEWmD\ WoDWpDWqDXrDXsCXtCXuCXvCXwCXxBXyBXzBXzBXzBYzAYzAYz\ AYzAYz9Yz9Yz9Zz9_z9`z8az8bz8cz8dz8ez7fz7gz7hz7iz7j\ x6kx6jx6kx6lx6mx5mx5my5my5my5my4my4my4my4my4mz3mz3\ mz3mz3mz3mz2mz2mz2mz2mz1mz1mz1mz1mz1mz0mz0mz0mz0mz\ 0mz0mz0mz0mz0mz0mz0mz0mz0mz0mz0mz0mz0mz0mz0mz0mz0m\ z0mz0mz0mz0mz0mz0mz0mz0mz0mz0mz0mz0mz0mz0mz0mz0mz0\ mz0mz0mz1mz2mz3mz4mz6mz8mzAmzCmzEmzGmzImzKmzLnzMnz\ NozOozPpzQpzRqzSqzTrzUrzUszUtzUuzVvzWvzXvzYvzZwz_w\ z`wzawzbxzcxzdxzexzfyzgyzhyziyzjzzkzzlzzmzznzzozzp\ zzqzzrzzszztzzuzzvzzwzzxzzyzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD for 11/06/09
by Paul.N.Lee＠Worldnet.att.net 07 Nov '09

07 Nov '09

Brian Prentice <bprentice(a)webenet.net> wrote: > > Very interesting formula Jim, here are three more details: > > http://linuxenvy.com/bprentice/Fractals/Set%2013/BP_13_69a.png > http://linuxenvy.com/bprentice/Fractals/Set%2013/BP_13_69b.png > http://linuxenvy.com/bprentice/Fractals/Set%2013/BP_13_69c.png > I must agree with the previous comments, the "69b" rendering is quite good. Well done!! Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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Re: [Fractint] FOTD for 11/06/09
by Maryetta Campbell 06 Nov '09

06 Nov '09

Mike Traynor replied on Philofractal list: > > Thanks for sharing those images, especially 69b. > It is one of the most beautiful images of any > kind, fractal or other, I've ever seen. Wow > doesn't begin to cover it. > > > Brian Prentice wrote on Philofractal list: >> >> Very interesting formula Jim, here are three more details: >> >> http://linuxenvy.com/bprentice/Fractals/Set%2013/BP_13_69a.png >> http://linuxenvy.com/bprentice/Fractals/Set%2013/BP_13_69b.png >> http://linuxenvy.com/bprentice/Fractals/Set%2013/BP_13_69c.png >> > Yes, "BP_13_69b" is very good indeed!!! Great coloring choice. :-) And "BP_13_69c" is the second best of these.

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FOTD 07-11-09 (A Minibrot in the Sand [8])
by Jim Muth 06 Nov '09

06 Nov '09

FOTD -- November 07, 2009 (Rating 8) Fractal visionaries and enthusiasts: I was going to name today's image "Sandy Claws", but I decided to name it "A Minibrot in the Sand" instead. The image is a scene on the main stem of the chaotic Mandeloid that results when Z^(2) and Z^(-2) are combined in a crazy way. When a negative exponent of Z is involved in a formula, the resulting fractal is highly dependent on the bailout radius. The 3000000 entered as the second parameter acts as somewhat as a bailout radius. I set this parameter at the point where the image is on the verge of evaporating, and let it rip. The result was interesting enough to be FOTD for today. The rating of an 8 might be a bit optimistic, but I feel the image is worth it. The calculation time of 2-3/4 minutes is certainly a bargain. The most convenient way to view the sandy image however is to surf out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and be exalted in its radiant glory there. Total sun but chilly temperatures prevailed here at Fractal Central on Friday. The fractal cats enjoyed the sun while it was beaming in the window, then took their places by the hall radiator. My day was average, which is just about all I can say about it. Due to a trip back to Old Fractal Central on Saturday, there will be no FOTD for November 8. But the FOTD for November 9 will be posted on schedule. Until then, take care, and don't get caught up in the feel-good craze. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Brot_in_the_Sand { ; time=0:02:44.05-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip float=y passes=1 center-mag=-1.785765881132176/0/3.218e+008 params=-2/3000000 maxiter=5000 inside=0 logmap=400 symmetry=xaxis periodicity=10 mathtolerance=0.05/1 colors=000gEahBeiFfiJfiNfiRfiUfiYfiafiefihfilfipfi\ tfiwf0ZU3WT5TT7QT9NSBKSEHSGESIBRK8RM5RO3RN5SM6TM7U\ L8VK9WKAXJBYIDZIE_HF`GGaGHbFIcFJcMRYSYSYeMclG_mIWm\ JTzKPzLMzMIzOzzzBzzzzz4zzzzz3zzzzz6zzzzzAzzzzzDzzz\ znGzpzzsJzuzztNpsOnrQlqSjqThpVfoXdnYbm_`maZlbXkdVj\ eUjhTfjSclR`oQYqPVsOSqNPoMNnMLlLJjLHiKFgKDeJBdJ9cI\ BcHDbGEbGGaFIaEJaEL`DN`CO_BQ_BSZATZ9VZ9WU8XQ7YM6YI\ 5ZE4ZGAcIGgKMkMSpOYtPbxO`wNZvMXuLVtKTsKSsJQrIOqHMp\ GKoGJoFHnEFmDDlCBkCAkFEiHHgJKfMNdOQcQTaTX`V_ZXbY_e\ WahVckTzn0et0ez0_p0zf0zY0mO0GEBB5CA4A949938837836L\ BJYJWjRhvZun_tf`tZataPpdDlf1hdDjbPl``nZlpXxr`tkcpd\ glZjhSmdMieNfeObeO_ePWeQTeQPeRMeSIeSFeTCeTAgV8hW6i\ X4jY5i_6ha6gb7gd7ff8eg8di9dk9clAbnAboGmELmAPm7Tm4Y\ mPami`mk_mnZmpZwrYwpXwoWwmVzlUzjXznLzcAzTBzRCzPDzN\ DzLEzJFzHGzFGzDHzBIz9Iz7HzBHzEHzIHzLGzPGzSGzWGzZGz\ bFzeFziFzlFzpFzsdzNezSfzX } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 06-11-09 (Sixteen Candles [8])
by Jim Muth 05 Nov '09

05 Nov '09

FOTD -- November 06, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's image is named "Sixteen Candles", and it is not hard to see why. The sixteen brilliantly colored basins surrounding the central minibrot certainly do stand out like candles in a dimly lit room. The parent fractal involves Mandeloids of orders 2 and minus-3. I'll not try to describe the parent fractal this combination produces, but it's certainly worth a quick look. After a moment's consideration, I rated today's image at a rather impressive 8, not too bad for an image created during a half-hour work break. But I must admit that most of the coloring was created not by me, but by a stroke of the <enter> key. The calculation time of just under 2 minutes will pass like a flash in the dark. To avoid all risk of impatience, the completely rendered image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Periods of brilliant sun alternated with heavy clouds and sharp showers here at Fractal Central on Thursday. Just before sunset a rainbow appeared in a passing shower, ending the day with a burst of splendor. The fractal cats, who do not enjoy showers and rainbows, thought the temperature of 46F 8C was too chilly for comfort and spent most of the day near the hallway radiator. My day was spent working at the FC computer, which is positioned with a window to the side, allowing a view of the outside condi- tions with a glance to the left. Unless something unexpected comes up, the next FOTD will be posted in 24 hours. Until then, take care, and don't be caught texting or you'll be twittered. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Sixteen_Candles { ; time=0:01:55.80-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip float=y center-mag=+28.3662156592203/0/2.48e+011/1 inside=0 params=-3/-1000000000 maxiter=3200 symmetry=xaxis logmap=405 periodicity=10 mathtolerance=0.05/1 colors=000NAD000E0KHIBH5DH7FH9IGBKGDMGFPGHRFJTFLWF\ NYFP_FRaEVODZBFZEHZHJZKLZNNZQPZTRZWTZZVZ`PNLJC5IE6\ IG7IH8HJ9HKAHMBGNCGPCGQDFSEFNFFHKENHEbIEcIDWGCUFBR\ EAPCANB9KA8I97G76D66B559346234132045457769A7BE8DH9\ FK9HNAJRBLUCNXDP`ERcFTfFViKRkONlTJmXFnaBoe8pb7q`6q\ Z6rX5rV4sT4sQ3tO2tM2uK1uI0vG0vH4uH8uICuIGuIKuJOtJS\ tKWtK_tKcteiXfVdYMaVUbSacPidMpdOmeQjeSheUeeWczYmz_\ ZzamzcTzeRzgOfiMfkJflHfkFdjEciDbiBahA`g9_f7Yf6Xe5W\ d3Vc2Uc1TYHYSWbMkgHzkGrlFkmEcnEXoDPpCIqCBrMvYFhK8W\ 69PG9IQ9Bs94zP6mc8Qr9Hl8Jg8Kb8MX7NS7PN7QI7RJATKCVL\ EWMHYMJ_NL`ONbPQdQSeQUgRWiSZjT`lUbnUdoVapWZqXWrYTs\ ZQt_Nu`LvaJrbIocHldGieFffEcgD`gCYhBViASj9Pk8Ml7Jm6\ Gn5DnKAoP9pU9pZ9qc8qh8rm8sr7sv7tz7tk6uz6us6pz9krBg\ zDbqFZzIUqzPpzzpzKpzzozLozzozRqzUrWXtz_uZbvzexhhyz\ kzrnzzqzztzzwzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 05-11-09 (Beyond Belief [7])
by Jim Muth 04 Nov '09

04 Nov '09

FOTD -- November 05, 2009 (Rating 7) Fractal visionaries and enthusiasts: There is an extra paragraph in the philofractal version, but it's hardly worth getting excited about. Today's image is an infinitesimal scene on the main stem of its parent fractal, which is a Mandelbrot set already showing cubic tendencies. Perhaps the most interesting feature is the periodicity of the elements surrounding the central cubic minibrot. I see rings of 6, 9, 12, 18, 24, and 27 elements, with higher numbers closer in. The name "Beyond Belief" might be somewhat of an exaggeration, but it does get attention. The rating of a 7 is near FOTD average. The calculation time of just under 3 minutes leaves lots of time for other projects. The finished image is posted as always on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Too many clouds and too little warmth here at Fractal Central on Wednesday spoiled the fractal cats' day. The high temperature reached only 48F 19C, which kept Nicholas and Cassie glued to the warmest radiator, the one in the long hallway. My day was perfectly average. The next FOTD will be posted in 24 hours. Until then, take care, and I fear the best times for the human race are already in the past. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Beyond_Belief { ; time=0:02:57.48-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip float=y center-mag=-1.562268212787373/0/1.7402e+012/1/-90/0 params=3/10 maxiter=2000 inside=0 logmap=352 periodicity=10 mathtolerance=0.05/1 colors=000AAHAAIAAJAAKAALAAMAANAAOAAPAAQAASAAUAAWA\ AYAA_AAaAAcAAeAAgAAiAAkAAmAAoAAqAAsAAtAAuAAvAAwAAx\ AAyAAzAFzAFzAFzAKzAKzAKzAKzALzAMzAPzAPzAPzAPzAPzAQ\ zARzATzAVzAWzAXzAYzAZzA_zC`zDazEbzGbzHbzIbzKbzLbzM\ azE_zDYzDWzDUzDSzCQzCQzCQzCQzBQzBQzBSzBUzETzGTzISv\ KSrMRmORhQQgSQfVQdXPcZPb`OabO_dNZfNYhNXfMVdMTbLRaL\ P_KNYKLWJJVJHTJFRIDPIBOH9MH7KG5IG3HG1IF2JE3KD4LC5M\ B6NA7N98N89N7AN6BN5CO4DP3DN7ELBFJFGHJHFNICRJ9VK6cL\ 4hM6mOmrQzvRAzTzvVDrWFmYGh_Ic`JbbLadMaeOagPaiQajbm\ TelUgkUjkVljVniWqiWshXuhXuiYujYukYulYumYunYuoYupZu\ qZurZusZutZuvmzzzzzZtqWtlUtfRsaPsWNsRKrLIrGFrADr5B\ oENlNZTGvSJuSMtSPtRRsRUsRXrQGmQNlQdqPlzPjzzqzOozzw\ zOtzPuzmmzQizYYVZKZZVb_`gSQ_QT_NW`L_`IbaGeaEiaBlb9\ ob7rb9scBscDscFtcHtdItdKudMudOzzQzzRzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE=========================================

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Re: [Fractint] AOTD 11-3-09
by JackOfTradeZ＠comcast.net 04 Nov '09

04 Nov '09

. Animation of Jim Muth's FOTD -- October 28, 2009 (Spirit Of The All) is posted: http://www.fractal-animation.net/vid/spiritofchaos.zip 14 Meg, 74 sec, 640x480 WMV Enjoy! JoTz .

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FOTD 04-11-09 (Third From the Left [7])
by Jim Muth 03 Nov '09

03 Nov '09

FOTD -- November 04, 2009 (Rating 7) Fractal visionaries and enthusiasts: Check the philofractal version for a longer discussion. Today's image shows an unusually attractive order-7 minibrot that lies in the East Valley area of the large minibrot on the main spike of the parent fractal, which on the surface is a perfect Mandelbrot set. Since I put most of the day's writing energy into the philosophy in the philofractal version, I will cut today's fractal discus- sion short. But what can really be said about an image such as today's, which speaks for itself, (silently of course). The rating of a 7 puts the image above average. The name "Third from the Left" means absolutely nothing. The calculation time of 43 seconds means a total lack of impatience. The fact that the completely rendered image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> means total satisfaction is at hand. A mixture of sun and clouds made Tuesday a questionable day here at Fractal Central. The fractal cats enjoyed the periods of sun and grumbled when the sun disappeared. The temperature of 57F 14C was reasonably comfortable. For me the day was somewhat busier than normal. Tomorrow will likely be the same. The next FOTD, which will be posted in 24 hours, will hopefully be an improvement over today's. Until next time, take care, and don't be distracted by the gadgets. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Third_From_TheLeft { ; time=0:00:43.12-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip float=y center-mag=-1.747885166579884/+0.0005600637725752/\ 3.81e+009/1/-77.5/0 params=7/7777777 passes=1 maxiter=375 inside=0 logmap=50 periodicity=10 colors=000zzzzyzwxzrwzmuzhsvcprZmmUhhPccKZZGUUFNPE\ AKzsCznBzhBzZBpSBgIBW0BE0B8MzAKrBJjCIbDGYEFRFEK3zw\ 4zq5vb6r`7mZ7jX6FW6FW3DY4EX5FW6FW7GV8GV9HU9HTAISBJ\ RmONmPMmPMmQLmQPmRPmROmSOmTSmTSmURmUQmVVmVUmWUmWTm\ XzmYzmYzmZzmZzm_zm_zm`zm`zmazmbzmbzmczmczmdzmdzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhzzgzzg\ zzfzzezzdzzdzzczzbzzazz`zz`zz_zzZzzYzzXzzzzGzzGzzG\ zzGzzGzzGzzHzzHzzHzzHzzHzzHzzHzzHzzHzzHzzHzzIzzIzz\ IzzIzzIzzIzzIzzIzzIzzIzzIzzIzzHzzHzzHCzzCzzCzzCzzC\ zzDzzDzzDzzDzzDzzDzzDzzDzzEzzEzzEzzEzEEzDEzDEzDEzD\ FzDFzCFzCFzCFzCFzCFzBFzBGzBGzBGzBGzAGzAGzAGzAGzAHz\ 9Hz9Hz9Hz9Hz9Hz8Hz8Hz8Iz8Iz8Iz7Iz7Iz7Iz7Iz7Iz6Jz6J\ z6Jz6Jz6Jz5Jz5Jz5Jz5Jz5Iz6Iz6Iz6Iz6Iz6Iz6Iz6Iz7Iz7\ Iz7Iz7Iz7Hz7Hz7Hz7Hz8Hz8Hz8Hz8Hz8Hz8Hz8Hz9Hz9Hz9Gz\ 9Gz9Gz9Gz9Gz9GzAGzAGzAGzA } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 01-11-09 (High and Unmighty [No Rating])
by Jim Muth 03 Nov '09

03 Nov '09

FOTD -- November 01, 2009 (No Rating) Fractal visionaries and enthusiasts: A longer discussion appears on the philofractal list. The FOTD is late because of a surprise antiquing trip on Saturday and a flood of 'trick or treat' goblins Saturday evening. Today's image gets no rating because it's kind of an automatic thing -- a minibrot lying near a larger minibrot deep in the East Valley of the even larger minibrot on the main spike of the parent fractal, which on the surface is an everyday Mandelbrot set. The name "High and Unmighty" refers to the extreme magnitude of over 10^13, which makes the mathtolerance entry necessary; and also the not-so-mighty final result of all the calculating. We have seen this kind of thing countless times before, which brings the rating of the image so low that I dared not mention it. Instead, I let the image go with no rating at all. The calculation time of 5 minutes is a bit slow for such an everyday type of image. But salvation is at hand on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is waiting to be viewed at leisure. A sunny morning here at Fractal Central on Saturday gave way to an afternoon of clouds and rain. The temperature of 72F 22C was unseasonably warm however, and made the wet conditions not as unpleasant as they might have been. The fractal cats complained about the lack of afternoon sun, and curled up to sleep off their dis-satisfaction. My day was pleasant enough, even if a good part of it was spent looking at the old junk someone else threw out. The next FOTD will be posted in about 4 hours. At least, it is scheduled to be posted then. Whether it appears on time is another story. Until whenever, take care and don't worry about the small things. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= High_and_UnMighty { ; time=0:05:01.34-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip float=y center-mag=-1.749855480585885/+0.00000000728024242\ /1.158437e+013/1/-47.5/0 params=13/3e+030 passes=1 maxiter=2500 logmap=539 periodicity=10 inside=0 mathtolerance=0.05/1 colors=000AAIAAJAAKAALAAMAANAAQAATAAWAAZAAa8AdFAgM\ HjTOm_VpfaskhUpoUuvcwzmzzzzzzzzzzzzzzzzlzzdzzYTzQR\ zJQZCP_JU`PY`Vaa`ebfiblm_fgX`bUVYRQSOKNLEII9DRHN_O\ XhVeqaozhxwgqufjredpdYmcRkcLS`E8Y8C`EGbKKdPNfVRh_V\ jeYljjZtQNtSMsTLsUKsVKsWJsXIsYIsbRog_kgecgkWgqOgwH\ jmRld_nWhpNqrEzVWaPaRJfGE`MAVS6QY5PZ4P_3P_3O`2O`1O\ a1Oa7WfDbkJjpPquUxzZvecmUhccmUmrMzvFzm8mcAfZBcUCXP\ CNKC5AC6AC7AC8AC9FCAKFCPIDUKEXNFUQHRSIOVJMWKJV0IUA\ IUJ12v84tF5rM6pT7nZ8m4ndGaaSQZbEWrGPbbseckhdckdWne\ OpeHibNc_TXXZRUdKRjEOoCIkACh86d70aR`kVWiYSg`NecJdc\ JfcKhcKi_IgWGfSEeOCdKAbG8aC6`84_hHcbIbXIbRIaLIasIa\ p`_mmYzwWzzXzuYDtZBt_9s`6ra4qb2qbBeNJU8JVGJVNJWUJW\ `JXgJXnHTkGQiENfDKdCGbAD_9AYcMEPF9U74_CNc9Hm6Bz35z\ kfzWSzGEz1Zz0Qz0Hz08zcdzeKzhF5mo9rVqvH_zBIz5Azy5zV\ zz_zzwzzkzzNzzBzzbzzFzzxzzczzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 03-11-09 (Numbers Without End [7])
by Jim Muth 02 Nov '09

02 Nov '09

FOTD -- November 03, 2009 (Rating 7) Fractal visionaries and enthusiasts: Hooray! Today's quickie image actually rates a 7. It's a scene in the parent fractal that results when 1.34 parts of Z^(-1.2) are subtracted from 0.83 part of Z^(1.2) and (1/C) is added. Since time is at a premium, I'll make no effort to describe the image, but with a calculation time of a mere 35 seconds the included parameter file can be run with little risk of bitter disappointment. The risk of let-down may be totally bypassed by viewing the completely calculated image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Lots of sun on Monday here at Fractal Central, combined with a temperature of 57F 14C, gave the fractal cats a pleasant afternoon in the sun. My day was quite busy. The next FOTD will probably be posted in 24 hours. Until then, take care, and be alert for minor discrepancies. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= NumbersWithout_End { ; time=0:00:35.85-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.823047589/+0.837390532/5261/1/-160/0 params=-1.34/-1.2/0.83/1.2/0/0/0/0 float=y maxiter=350 inside=0 outside=tdis periodicity=10 colors=000pQPqOVkKYeG_`DbV9dQ6fY4jd3nl2rs1vz0yy7ry\ EkyLdyRlxYRzbKzrDxq7wg6vY5uP4tFjs6nl73e74Z75S86L87\ E888897D9FI9KO9UV9c`9mgczzmmhcccMUZTzUZEPdzMkIJqzH\ wJczzRrHWoH`mzekFjhEofEtdzwdGzdHzdHwdImdJcdK`dKZdQ\ Y`WYXaYTgXPmXLrXHkWFeWEZWDTVCMVBGVAHT8HR7HP6HN5HL4\ HJ3HI2KEDMBOO7ZQ4iS1sRBaQLKPU3SPBVKJXGR_BZa7fzzdzz\ bzzazz_zzZzzKzzKzzJzzJJzzIzzHzzHzzGzzFzzFzzzzGzzGz\ zbzz_zzXzzzLzzJzzHzzFzzmzMkxLjvLiuLhsLgrLfzKezKdzK\ czKbzKazK`zJ_fJZdJYcJXaJW`JUZITYISWIRVIQTIPSIOQHNP\ HMNHLMHKKHJJHIHGHGGGEGFDGEBGopQlmPjjOhhOeeNccNa`MZ\ ZLXWLVUKTRKQPJOMIMKIJHHHFHFCGgJkfIjeIidIhcIgcHgbHf\ aHe`Hd`Gc_GcZGbYGaXG`XF_WF_KpcHniEloCjuGitKhsOgrSf\ qVeqP`mJXiDTe7Pa1LY8QZFVZMZZTcZ_hZflZaiWXfUTcSO`QK\ YOFVMBSKHYYNbkGZY9VL3S8`fmuQ_v4xFldNaVUSMJgoOhnTin\ YjnbknglmlmmqnmvomuintdnsZosUorOoqJppDpp8pplroc`nV\ JnN1oO3pP5qQ6rR8sS9tTBnTI } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 02-11-09 (The Root Has It [No Rating])
by Jim Muth 02 Nov '09

02 Nov '09

FOTD -- November 02, 2009 (No Rating) Fractal visionaries and enthusiasts: Another late fractal. I'm still getting caught up. Today's image lies in the parent fractal that results when the formula Z^sqrt(2)+C is calculated a whopping 4321 levels up the logarithmic ladder, a level I chose purely on a whim. It is an unusually good image for such a low exponent of Z. Since the image was found in a hurry, I could not give it a rating, but the calculation time of under 2 minutes means that no one will have wasted much time if the image turns out to be disappointing. The name "The Root Has It" came to mind as soon as I shut down my brain, (which I am told takes very little effort). To see the rather dark image, either run the included parameter file or visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Monday here at Fractal central featured sunny skies, a temperature of 57F 19C, and happy cats. My day was quite busy, but I still managed a fast FOTD. The next FOTD is due in about 6 hours. Check then, but do not be disappointed if it is late. Until next FOTD, take care, and be happy in your fractal work. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Root_Has_It { ; time=0:01:58.84-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=+0.8737443818\ 611416/-1.340159768589525/9.624077e+009/1/87.5/0 params=1.414213562373/0/4321/0 float=y maxiter=1500 inside=0 logmap=241 periodicity=10 colors=0009AZ7AZ4AZ2AZ0AZ3AY0AW3AV5AT7AS9AQABPCCND\ DMEELGDIHCGJBDK9BL89N76L64K02F0IzzfUU1LI5OK9SNDWPH\ _SLbUPfXTkZXoa`tcdxfhzhlzjpzeltaipYfnTcjP`eLX`HUWC\ RT8OR4LP0II1NG2SF3X84a24e47f5Af6CfAFfFIfKGePEbUPfZ\ RccT`hVYmXVrZSv`PzaMvdWrgeminhhjchfZgcVf_SeXQdTNbQ\ LYMIVJFRFDRCAQ88P58PB8PH8QM8RS8SY8Tb8Zh8cn8ds9er9f\ s9fv9gx9hz9hzAizAizAjzAkzAkzAlzAlvBjrBhmCghCezDdzD\ bzEazE_zFZzFXjGWjGUjGTjFQkFNjELiDIhDFhCDgBAgB8gA9f\ 99f89f8Af7Af6Af6Af8Ff9JfBOfCSgEWhF`iHdjIhkJbgKXcKS\ `LMXMGTMBQN5MN0JNIARJEVJIYKMaKPdLThLXkM`oMcrNgvNky\ NnzMZzLJzK4cL66L76L86LA6LB6LC5ME5MF5MG5MI5MJ5MK5ML\ 6ON7PP8QR8RS9SUATWAUXOXUYZS``PcbNheKmgIriFwkDzmBvl\ CqlCmlChkDejDaiDYhEUgERgEUhGWhHZiJ`iKbiMekNgkPilQl\ mSnnTpnUqpKrqGssDtt9uu6vv7ww8xz8yz9zz9zzAzzAzzBzzC\ zzCzzDzzDzzEzzEzzNzzVzzbzzczzczzczzczzdzzdzzdzzdzz\ ezzezzezzezzfzzfzzfzzfzzc } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(p/(2*PI)), r=real(p2)-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 31-10-09 (Oasis [No Rating])
by Jim Muth 30 Oct '09

30 Oct '09

FOTD -- October 31, 2009 (No Rating) Fractal visionaries and enthusiasts: We end the month of October with another blast from the distant past -- May, 1997 to be exact -- when virtually the same image appeared under the name "Martian". To update the image I have slightly re-cropped it, tweaked a few colors, and changed the outside to 'real'. The name "Oasis" refers to a slight tinge of green on the horizon at the left edge of the image, which I took to be a distant oasis of green on the otherwise desolate planet Mars. Or it could be the desert planet otherwise known as 'Dune' in the well-known series of fantasy novels pretending to be science fiction. Since the image is another repeat, I gave it no rating. There is not much more to be said about the image, which speaks for itself, other than repeating that the way to see it is to run the included parameter file and wait 30 seconds, or to surf out to the glorious FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the completed image in relaxed serenity there. The Friday weather here at Fractal Central was a repeat of the past 2 days' conditions -- heavy clouds but dry, and a tempera- ture of 55F 13C. The fractal cats gave up early and spent the rest of the day in the coziest warm places they could find. For me the day was just one more in a seemingly endless string of routine days. (Not that I find anything wrong with this.) If all goes well, and even if it doesn't, the next FOTD, the first of a new month, will be posted in 24 hours. Until then, take care, and don't judge another until you have walked in his shoes, (or something like that). Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Oasis { ; time=0:00:30.08-SF5 on P4-2000 reset=1821 type=manzpower center-mag=-0.4202216978\ /-0.0000124324/144032/2.3247/-5/0 params=0/0/3.25/0 float=y outside=real maxiter=550 inside=1 logmap=yes colors=000RINmYblXdjXehXggXheWjdWkbWm`Wn_VpYVqjY_b\ YZVYZMXYEXY6XXrY_qY_qY_pY_pZ_oZ`oZ`nZ`mZ`mZ`lZ`l_`\ k_`k_`j_ai_ai_ah_ah`ag`ag`af`ae`ae`ad`bdabcabcabba\ brY_qZZpZYp_Yo_Xn`Wm`VlaVlaUkbTjcSicShdRhdQgePfePe\ fOdgNdgMchMbhLaiK`iJ`jJ_jIZkHqZZp`YoaWncVmdUlfSkgR\ iiQhjOglNfmMeoKdpJpX_nVZlUZiSYgRYePXcOW`MWZLVXJVVI\ USGUQFTODSMCSJARH9RF7QbWQNTG7Q5rZawY9r`crberchrejr\ gmpfmnemldmjclhblfald`lb_l`ZkZYkXXkVWkTVkRUkOSjMRj\ KQjIPjGOjENiCMiALi8Ki6Ji4Ih2Hh0Gh2Gh4Gh5Hi6Hj6Ik6J\ k6Lk6Mj7Ni9NhBOgDOgFOgHOgKOgNOfQOfTOfWOfYPf_PfaPfb\ QfdRffSfhTejUelWenWepXerXdrXcvXkzXjzXZxZYz_Ww`VubT\ rcSodQlePjfNgfMdfKXfIUfHCgF9iDAgCAeBBcABa9C_8CY7DW\ 7EU6ES5FQ4FO3GM2GK1HI0JK3KM5MO8OPAPRDRTFTVIUXKWZNY\ _PZaS`cUbeXcgZeiagjchlfjnhlpkmrmotpqurrwutywryroyl\ kygzeUzeUxhUwkcukmukmfrPllUctZercXidO`fERg5Ih7Jh9K\ gBLgEMgGNgIOfKPfKPfOReQSe } END PARAMETER FILE=========================================

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FOTD 30-10-09 (The Second Time Around [No Rating])
by Jim Muth 29 Oct '09

29 Oct '09

FOTD -- October 30, 2009 (No Rating) Fractal visionaries and enthusiasts: Now and then I sneak in a blast from the past, in which I do a slight reworking of an earlier FOTD image -- today's image is a reworking of an early image indeed. The first version appeared over 12 years ago in April of 1997 -- the first month of the FOTD, at a time when I was interested in what I call 'ghost buds', vague ghostly high-iteration things that often appear in the background of the perturbed Mandelbrot sets. (These ghost buds appear because regardless of where the points start, if they do not escape first, they eventually settle into the same orbits as the points that start at 0,0.) The effect of the monstrous banded elements in the foreground was created by the 'ranges' feature of Fractint, a little used feature that, as far as I know, can be accessed only through the command line. The scene lies in the perturbed M-set with a starting point of the square root of 0.777,-0.555. (For some reason, the type=mandel fractals are calculated with a starting point equal to the square root of the entered complex number.) The scene is located on the north shore of the main bay, just west of the large period-3 bud. The large ghost bud in the background has a periodicity of 14. The smaller buds have a much higher periodicity. The maxiter of 32767 is actually too low to fully resolve the image, but the 'ranges' option does not work with a maxiter higher than this. The name "The Second Time Around" admits that today's image is a near-repeat of one that appeared over 12 years ago. I could hardly give a rating to a repeat, so I let the image go unrated. The calculation time of a fireball 19 seconds will bring no hardships. And as always, the finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds that hung on all day made Thursday unpleasant here at Fractal Central. The temperature of 57F 14C did nothing to improve things. The fractal cats found comfortable spots and slept through most of the day. For me, the day was about average, even though the fractal was not quite up to FOTD standards. The next Fractal of the Day will be posted in 24 hours. Until then, take care, and wait for what you wish for. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_2nd_TimeAround { ; time=0:00:19.19-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.2620\ 037/+0.6428974/76.368/1/-13.5/0 params=0.777/-0.555 float=y maxiter=32767 bailout=100 inside=0 periodicity=25 ranges=0/-1/300/600/1000/1600/2400/\ 3600/5000/10000/32767 colors=000K9DjOOYIrKSzKcpKhwKmzKrzmwzzzzzzzSPRPSVM\ WYr0s`IiSzNRvPPrROnTNjVLfXKbZyx2nqBckKTdT9IdBLcCNc\ EQbFSaHVaIX`oUHkVKgVMcWPZXRVXURYWNZZHRHITMIVRJXWyi\ QrgSkeUccWXaYQ__vzdlscblbTeaUeZSc_Qb_gbYdYXaSXZNW`\ NRbMNdMIfLEhL9dgS2Z7GO5TC3f11bBAYKKUUTPbaXMNSRSNVX\ GhXHdZIa_IbRIbSIaUJaVJ`WJ`YJ_ZJZ_LKLLMNKOPKQRKSTKU\ VJWXJYZjUhcVfXXdQYba6JZAMWEOUJRRNUORWLVZdDwaGtZJpW\ NmSQjPTfMWcEFDHPPGebHdbHcaIbaIaaJ``J_`ScGRbJQbLPaO\ N`RM_UL_WKZZbReZTdVVcRWbNYaYKpWMnUOlSQjQShOUfMWdKY\ b1`D7_LDZTjYNdYQ_ZTUZWOZZV3TT7USBVQFWPJXNNYMRZKV_M\ T9U`iyR_jU`XX`eQXbRYZTYWUZTV_PX_MY`vuCprGjnJekN_hR\ UdUOaYrVsmWqiWndXl`XiWYgSYdNZba69SLN4Lf9QdEVbC2XE9\ YFGZHM_IT`cYDLV1LW6KWBKXHKYMJYRJZWYumWrkUojSlhQifO\ fdMccK`a1I_4L_7O_AR`DU`GX`pCW_OZZVDXWHUWKSXOQYRNYV\ LZYBT8DVFFWNHYUez1UlJT57S9BQDFPHJOKMNOQLSUKWYhrBWh\ OgOkdPjaRhZSgVUeSVdPXbMYa } END PARAMETER FILE=========================================

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FOTD 29-10-09 (My Name is Fractal [6])
by Jim Muth 28 Oct '09

28 Oct '09

FOTD -- October 29, 2009 (Rating 6) Fractal visionaries and enthusiasts: To begin, let me make it perfectly clear that my name is not Fractal -- the name of today's image is "My Name is Fractal". Now that this perplexing problem has been solved, let's turn to the FOTD image of the day. To begin, the image lies in the parent fractal that is created when various parts of Z^(-10) and (1/Z) are combined and (1/C) is added. This fractal resembles nothing as much as an over- sized splat. The rating of a 6 seems about right. The image is nothing that we haven't seen countless times before. The calculation time of 3-1/4 minutes is perhaps a bit longer than the result is worth, but what the heck, those who do not calculate the parameter file will never know what they missed. The way out of this quandary is to make a quick trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoy the finished image there without the task of running the parameter file. On Wednesday afternoon FL made one of those comments that gets me thinking. I wrote a few politically-oriented paragraphs that I intended to post here, but I counted to 10, and then, to avoid an off-topic debate, I deleted them. After all, what more could I add to what is already filling the news? Wednesday here at Fractal Central started with rain and ended with clouds. The temperature of 61F 16C would have been fine if the sun had been shining. The fractal cats gave up early and spent most of the day searching for places to curl up and sleep. After deleting my original political comment, my day was quiet enough. As for the next FOTD -- look for it in about 24 hours. Until then, take care, and the elimination of sickness and death would solve the health-insurance problem, but it would be bad news indeed for the health insurance industry. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= My_Name_is_Fractal { ; time=0:03:16.12-SF5 on P4-2000 reset=2001 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=-3.22306139553/-1.16948742835/390528.7/\ 1/0.5/0/0 params=-0.6/-10/-10/-1/0/0 float=y maxiter=3600 inside=0 logmap=363 periodicity=10 colors=000HCRHCSKCWNCZPCbSCeVCiYAm`BpcCrfCuiDwITBG\ QCENDCKEAHF8EF6BG48H25I37H49H5CG6EG7GF7IF8KE9MEAPD\ BRDCTCDVCEZBGcBHeAJhARlAYp9es9lw8nzCmw7eu8_r8To9Kk\ 9KjAKiAKhBKgBKgCKfCKeDKdDKcEJbEJaFJ`FJ_GJZGJZHJYHJ\ XIJWIJVJJUJKTHJUIIUJHVKGVLGWNFXOEXPDYQCYRBZSA_T9ZT\ AZUBZVBZWCZWDZXEZYF_ZG__G_`H_aI_aJ_bK_cL_dL_eM_fN_\ gO_gP_hP_iQ`jR`kS`lT`mU`mU`nV`oW`pX`q_dvZctZbsY`qX\ _pWZnWYlVWkUViTUgTTfSRdRQcQPaQO_PMZOLXNMVMJULKSLGQ\ KFOJENIDLIBKHAIG9HF8F707929C4CE7EG9GJBILDLOFNQHPSK\ RVMUXOWZ_Yak`cwbfydhyfizfjzfjzhbvkYyw`AzdDwcGrYJhR\ MZQPUPSPLOBMRFOTKPWOQZSS`XTc`UfdYPeWZgVhhXkjWmjVoj\ UqjUriTtiSviRxiSwhTvgUueVtdWrcYqbZp`_o_`nZamYblWck\ VdiUehTfgRgfQhePjdOkcMlbLm`Kn_JoZHpYGqXFuYBvYCvZEw\ ZFw_Gw`HwaIxbJxcKxdLyeMyfNygOyiPykQzmRzoSzqTztUzwV\ zzWzzXzzYzzQzzTzzWzzZzzazzdzzgzzjzzkzzlzzlzzmzzmzz\ nzzozzozzpzzqzzqzzrzzrzzs } frm:MandAutoCritInZ {; 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)+(p4)), 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] FOTD 28-10-09 (Spirit of the All [7.5])
by Jim Muth 28 Oct '09

28 Oct '09

At 04:05 PM 10/27/09 -0400, you wrote: > >FOTD -- October 28, 2009 (Rating 7.5) > >Fractal visionaries and enthusiasts: > >Today's image takes us back to one of the formulas of the old >MandNewt series. (Number 11 to be exact.) I long ago forgot >what these formulas were originally intended to do, but >regardless, as today's FOTD shows, they still make interesting >images. > >I named the image "Spirit of the All", leaving it to the viewer >to decide what the word 'all' refers to. In my opinion, 'all' >could only mean the multiverse, including everything both >objective and subjective, which would make the spirit of all >this stuff equal to God. But I see nothing unusually godlike in >the image, so the exact meaning must forever remain an enigma. > >Whatever the meaning of its name, the image rates a solid 7, >with an added 1/2 point for the effort I put into smoothing the >colors. > >The calculation time of 3-1/4 minutes will try the patience of >no one but the most impatient. Those impatient few may save >time by flying out to the FOTD web site at: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > >and viewing the already-calculated image posted there. > >Heavy clouds, drizzle, and a temperature of a raw 52F 11C made >conditions unpleasant here at Fractal Central on Tuesday. The >fractal cats gave up hope for a pleasant day early, and spent >most of the day curled up, sleeping near the heat. > >Except for the fractal, my day was uneventful. The next FOTD >will be posted in 24 hours. Until then, take care, and be at >peace with your lot, even if it's only a few hundred square feet. > > >Jim Muth >jamth(a)mindspring.com >jimmuth(a)aol.com > > >START PARAMETER FILE======================================= > >Spirit_of_The_All { ; time=0:03:13.41-SF5 on P4-2000 > reset=2001 type=formula formulafile=mandnewt.frm > formulaname=MandNewt11 passes=1 center-mag=0.25415\ > /0/3.9/1/-90/0 params=-1.38/-0.99/-1.98/0.47/-0.48\ > /3.46 float=y maxiter=250 inside=bof60 > logmap=yes periodicity=0 > colors=000zzzzyzzxzzwzzuyzsyzqyzoxzmxzkxzixzhwzgwz\ > fwzewzdvzcvzbvyavx`uw_uvZtuYttXssWsrVrqUrpTqoSqnRp\ > mQplPokOojNniMmhLlgKkfJjeIidHhcGgbFfaEe`Dd_CcZBbYB\ > aXB`W9_V9ZU9YT9XS9WR8VQ8UP8TO8SN8RM6QL6PK6OJ6NI6MH\ > 6KG5KF5IE5GD5GC5EB3DA3D93B839739628526426325223113\ > 11201101101001000000000000000000000000000000000000\ > 00000000000000000000000000000000000000000010020030\ > 0500600800900B00D00G00I00K00M00O00Q00S00U00W00Y00W\ > 00U00U00S10S10Q20Q30O50O60M60M80K90KB0ID0ID0GE0EG0\ > EI0DK0DK0BM0BO09Q09S08U08U06W06Y05_05a03a02d02f01h\ > 01j00j00l00o00q00s00w00zK0zP0zU0zX0zU0zP0zK0x00u00\ > s01q02o05l06j08f0Bd0Da0G_1IY3MW5OU7SS9UQBWQDUQFSQH\ > OQJMQLKQNIQPGQRDQTBQV9QX8QZ5Q`3Qb2Qd1Qf0Qh0Qj0Ql0Q\ > m0Wl0_j0fh1jf3od5ua8zYBzYEzXIzXKyYPw_UubZsecqhhokm\ > mnrkquitxhwzfzzdzz_zzYzzUzzSzzQzzMzzKzzIzzEzzDxzBs\ > z9oz6lz5hz3dz2_z0Wz0Sz0Oz } > >frm:MandNewt11 {; 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-f >j=c*z^d+g >z=z-e*h/j, >.0000000000000000000000000000005 <= |h| } > >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: [Fractint] Spirit of the All
by JackOfTradeZ＠comcast.net 28 Oct '09

28 Oct '09

. Spirit of the All - a solid 10 pointer Jim! Although I might have named it "Alien Cyclops" or something. Cool colors too. I haven't had much luck animating anything recently, I'll see what I can do with this one ... .

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FOTD 28-10-09 (Spirit of the All [7.5])
by Jim Muth 27 Oct '09

27 Oct '09

FOTD -- October 28, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image takes us back to one of the formulas of the old MandNewt series. (Number 11 to be exact.) I long ago forgot what these formulas were originally intended to do, but regardless, as today's FOTD shows, they still make interesting images. I named the image "Spirit of the All", leaving it to the viewer to decide what the word 'all' refers to. In my opinion, 'all' could only mean the multiverse, including everything both objective and subjective, which would make the spirit of all this stuff equal to God. But I see nothing unusually godlike in the image, so the exact meaning must forever remain an enigma. Whatever the meaning of its name, the image rates a solid 7, with an added 1/2 point for the effort I put into smoothing the colors. The calculation time of 3-1/4 minutes will try the patience of no one but the most impatient. Those impatient few may save time by flying out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the already-calculated image posted there. Heavy clouds, drizzle, and a temperature of a raw 52F 11C made conditions unpleasant here at Fractal Central on Tuesday. The fractal cats gave up hope for a pleasant day early, and spent most of the day curled up, sleeping near the heat. Except for the fractal, my day was uneventful. The next FOTD will be posted in 24 hours. Until then, take care, and be at peace with your lot, even if it's only a few hundred square feet. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Spirit_of_The_All { ; time=0:03:13.41-SF5 on P4-2000 reset=2001 type=formula formulafile=mandnewt.frm formulaname=MandNewt11 passes=1 center-mag=0.25415\ /0/3.9/1/-90/0 params=-1.38/-0.99/-1.98/0.47/-0.48\ /3.46 float=y maxiter=250 inside=bof60 logmap=yes periodicity=0 colors=000zzzzyzzxzzwzzuyzsyzqyzoxzmxzkxzixzhwzgwz\ fwzewzdvzcvzbvyavx`uw_uvZtuYttXssWsrVrqUrpTqoSqnRp\ mQplPokOojNniMmhLlgKkfJjeIidHhcGgbFfaEe`Dd_CcZBbYB\ aXB`W9_V9ZU9YT9XS9WR8VQ8UP8TO8SN8RM6QL6PK6OJ6NI6MH\ 6KG5KF5IE5GD5GC5EB3DA3D93B839739628526426325223113\ 11201101101001000000000000000000000000000000000000\ 00000000000000000000000000000000000000000010020030\ 0500600800900B00D00G00I00K00M00O00Q00S00U00W00Y00W\ 00U00U00S10S10Q20Q30O50O60M60M80K90KB0ID0ID0GE0EG0\ EI0DK0DK0BM0BO09Q09S08U08U06W06Y05_05a03a02d02f01h\ 01j00j00l00o00q00s00w00zK0zP0zU0zX0zU0zP0zK0x00u00\ s01q02o05l06j08f0Bd0Da0G_1IY3MW5OU7SS9UQBWQDUQFSQH\ OQJMQLKQNIQPGQRDQTBQV9QX8QZ5Q`3Qb2Qd1Qf0Qh0Qj0Ql0Q\ m0Wl0_j0fh1jf3od5ua8zYBzYEzXIzXKyYPw_UubZsecqhhokm\ mnrkquitxhwzfzzdzz_zzYzzUzzSzzQzzMzzKzzIzzEzzDxzBs\ z9oz6lz5hz3dz2_z0Wz0Sz0Oz } frm:MandNewt11 {; 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-f j=c*z^d+g z=z-e*h/j, .0000000000000000000000000000005 <= |h| } END PARAMETER FILE=========================================

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FOTD 27-10-09 (Space Exploration [7])
by Jim Muth 26 Oct '09

26 Oct '09

FOTD -- October 27, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image exists in the parent fractal that magically appears when 0.4 part of Z^(-0.8) is subtracted from Z^2 and (1/C) is added. This fractal is a grossly oversized networky thing with a curiously distorted Mandeloid near its origin. Today's image is located in the vicinity of this Mandeloid. I rated the image, perhaps a bit liberally, at a 7. Actually, the image is little more than just another minibrot with a quirky pattern around it. The name "Space Exploration" refers to something that will never happen in our lifetimes. The calculation time of a relatively brief 3-2/3 minutes may be eliminated entirely by checking the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted for immediate enjoyment. Cynical political comment is in the philofractal version. Read it at your own risk. Sunny skies and a temperature of 63F 17C made the fractal cats happy here at Fractal Central on Monday. Getting the work finished early made me happy. The next FOTD will be posted in 24 hours. Until then, take care, and those younger than 40 years will likely end their lives without ever having seen men walking on the moon. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Space_Exploration { ; time=0:03:40.13-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.185093095538751/-0.7198843055345714/\ 3.6e+010/1/67/0 params=1/2/-0.4/-0.8/0/0/0/0 float=y maxiter=1500 inside=0 logmap=248 periodicity=10 colors=000AGPAJPAMPAPPASPAVQAYMA`IAcEKiAUoKctUozcz\ zzzzznzVntSnpPkkNiiMghKefJceHacG_bEY`DVZBTYAzzzzzm\ zz5qz4zzczu1zk4zf6zb5zX5zR5mU4hP4cK4ZF3UA3PA3KA2FA\ 29A28A17A16A16A59CABDFEEKGFPIGULHZNIcQJhSKmULrXMvc\ NzhYzodzzizdgOaeQ_dTXcWVaZS`aQ_dNYfKXiIWlFUoDTrASu\ 8RwCPtFNqIMnLKkOIhRHeVFbYD_`CXcAUf8Rj7OqBRzFUzJWzN\ ZzQazUccYfbahadk`hn_lpZpsZsuWorUkoShmPdjN`gLYeIUbG\ R`ENYBJV9GT7CQ59OADQEHSILUMPWQTYUX_Y`aadceheilgmoi\ imffkdbjb_h_WfYTeWQcXObXLaYJ`YG_ZEZZCYZ9X_7W_4V`2U\ `0T`2S_4S_6S_8S_AS_CS_ES_GR_IR_KR_MR_ORZQRZSRZURZW\ QZYQZ_QZaQZcQZeQZgQZhQZhP_hO`hN`hMahLbhKbhJcDwiFnh\ HegJYfLPfNHeP8dR0dLBUGMKBXA6f0Ae5Dd9GdDJcHMcLQbQTa\ UWaYZ`aa`ee_jhZnkZrnYvqYzrZus_pt`kuafvbawbXuaWtaWs\ aVzzVzzUzzUzzTzzTzzSzzSzzRzzRhzQgzQlythzadzKaz2jz5\ rz8nzBjzDgzFczI`zKXzMUzPQzRNzTJzWGzYCz_9zb5zd2zf6z\ jAzmEzpIztMzwQzzOziozaozZ } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 26-10-09 (Half of Everything [8])
by Jim Muth 25 Oct '09

25 Oct '09

FOTD -- October 26, 2009 (Rating 8) Fractal visionaries and enthusiasts: Do not be concerned if the top half of today's image appears all too routine. A huge change happens at the exact center, leading to the bottom half, which is totally different. The image is divided into two halves. The top half is outside stuff, while the bottom half is inside stuff brought to life by the 'bof60' inside fill. Any more talk would be superfluous. Unless the sound is turned off, the image will speak for itself, so I recommend running the parameter file and waiting with bated breath for the big change that appears halfway through the calculation. The name "Half of Everything" makes little sense, though it does refer to the schizoid personality of the image. The rating of an 8 indicates that the image is well worth the 3-3/4 minutes spent calculating it. If, for some reason, calculation is impractical, the finished image may be viewed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But be prepared to stare in awe and wonder. Perfect late October weather prevailed here at Fractal Central on Sunday -- not a cloud in the sky, light winds, and a tempera- ture of 61F 16C. The fractal cats spent the entire afternoon fighting for the best spot on the sunny shelf in the southwest window. My day was uneventful. The next FOTD is due in 24 hours. And if all goes well, it will actually be posted around that time. Until then, take care, and isn't it a crying shame -- the entire universe out there waiting, and we're stuck on the surface of a minor planet with minds of steel trapped in bodies of kleenex. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Half_of_Everything { ; time=0:03:45.69-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip float=y passes=1 center-mag=-0.05540299/+0.56101401/568/1/\ 88.9/0 params=0.941455/1.5 maxiter=15000 passes=1 inside=bof60 logmap=yes periodicity=10 colors=000zzzpppjhjfbbeZ_dWXcTUbRRaPO`NL_LIZJFYHCX\ F9WDAVAAUAATAASAARAAQAAPAAOABNABMABKABI9BG6BE3BC0B\ A0BA0DA0FACHAEJAGLAHNAJPAKR9MT8OV7PX6RZ5S_6U`7Va7W\ a8Xb8Yc9Zc9_dA`eBaeBbfCdgCegDfhDgiEhiFijFjkGkkGllH\ mmHnmIokJpjJphKqgLreLrdMscNtaNt`OuZOuYPvWQwVQwURxS\ SyRSyPTzOTzNhhVwRatS`rS_oT_mTZjUYhUYeUXcVW`VWZWVWW\ UUWURXTPXSMYSKYRHZQFZQCZPA_O7_O5`N2`M0`MBZJLYGWXDe\ WBdVEcUGbTIbTKaSM`RO_RQ_QSZPUYPXXOZXN`WNbVMdVDZWBd\ X9kY6rZ5Y_4COGQCSzBTz9Vz8Xz6Zz5`z3bz2dz0cz3bz6`z9Y\ wCVsFRjIOa0LV0FA0AA0AB0AAaXCeaChfDlkEVj8Dh268c5Da4\ IZ3NW1TTHhVXxYevfospypzylvygrxbmxYiwTdqcZknTezNfsT\ gkZhceiWkkOrkQnlSimUenW`oYXp_SqbN_jLIrIKhRNZ`QPjTF\ tOFiIEYCDMLCFUA824281u73p66j58d4BZ3DT2GN1JH3OG5UE7\ ZC9dABi8Do6Ft4Hz2YlCnZMkZUg_bc_k_`t_ZrZWpZUnYRkYOi\ XMgXJeWGbD9ANIAXRAf_AbcFZgLVkQRpWTmYVj_XgaZdc`aebZ\ hUUfLOcSOcZNbfMahMUkMMnME } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 25-10-09 (Fractal Dissolution [9])
by Jim Muth 24 Oct '09

24 Oct '09

FOTD -- October 25, 2009 (Rating 9) Fractal visionaries and enthusiasts: Today's image is unusual enough to earn a rating of a lofty 9. It is a scene in the parent fractal that results when various negative parts of Z^(-1.4) and Z^(-4.4) are combined and (1/C) is added. One full point of the rating is due to the extra effort I put into the coloring and the bit of luck I had with bringing up random color palettes. The parent fractal is a typical double-negative thing, with a prominent 'fan' extending east from the origin and filaments that terminate in rings. Today's image is located toward the eastern edge of the 'fan'. The name "Fractal Dissolution" refers to the appearance of the image, which gives the impression of being caught in the act of evaporating. BTW, the image is not 'evaporated'. The evapora- ted version is too chaotic. The calculation time of 2-3/4 minutes is thankfully brief, and will make the image available to everyone who wishes to calculate it. Those who do not consider calculation their cup of tea may find their tea on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted. The weather on Saturday left much to be desired here at Fractal Central. The temperature of 68F 20C was mild enough, but the day was spoiled by heavy clouds and torrential rain during the late morning. The fractal cats spent the day distracting themselves with various diversions, while my day was average. The next FOTD will be posted in 24 hours. Until then, take care, and miracles do indeed happen. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FractalDissolution { ; time=0:02:44.30-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.874477823124435/-0.03584207960073543\ /1.2e+009/1/-127/0 params=-4/-1.4/-0.4/-4.4/0/0/0/0 float=y maxiter=1400 inside=0 logmap=192 periodicity=10 colors=000ABKA1PK1PA1PA1KA1PK1PA1PA1KA1PK1PA1PA1KA\ 1PK1P61Q73K84S96QA7OA9NBALCCJEDIHFHJGHMIGPJFSLDUMC\ UNFUNIUNLTOOTORSOUSPXRP_RPbQQeQQhPQkPRnORqORsLUoJX\ lPZnVcp`hrfmtlrvrvxzzzzzrpnjmmbilVekNbkFIT`MRbPPdS\ OfVMgYKi`JkdHlgGnjEpmCqpBss9uv8vsDsqIpoNnlSkjXihaf\ efcckaapZ_tXUoROjLIfGCaA7Y57Uz7U07Uz7U77Uz7U77Uz3U\ 3RUrDURmUikZhjcghhfgleemdcncbnb`oa_p`Yq_XqZTlcQhhN\ cmK_rHWvIYqJ_lK`gKbbLcYMeTMgONhJOjEOkAPhDPfGPdJQaM\ Q_PQYRRVURTXRR_SObSMdSKgTHjTFmTDpTBrw0zr4tn8njBhfF\ bbIXZMRVQLRTFNX9J_3DPL7Ea14r3Dj4Mc5VW7cP8lH9uAErJJ\ oRNm_SjgXgp`exbdtcdqddmfdjgdfhdcjc_kcXlcTncQocMpcJ\ fRKXFKVGNUHPTHRSIURJWQJYPK`OKbNLdMMgLMiKNkJOnIOpHP\ rGPtEUdCZPBbAF`9JZ9NY9RW9UV9YT8aR8eQ8iO8lN8`WLPcYS\ gWVkUYoS_sRbvPexNgzMjzKmzIpzGrzFuzDxzBzzAqzKhzT_za\ RzjIzsJzrJzqJzqKzpKzoKzoLznLznLzmMzlMzlMzkMzkOzcPz\ WQzOSzGTz8Uz1Tz5Sz9RzCQzG } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 24-10-09 (Forever Onward [8])
by Jim Muth 23 Oct '09

23 Oct '09

FOTD -- October 24, 2009 (Rating 8) Fractal visionaries and enthusiasts: Due to a lack of time, today's FOTD is dated October 24 and the discussion is brief. No FOTD exists for October 23, which is no loss, since there never was one. Today's unusually colorful and festive image speaks for itself, so no words are necessary. In my opinion, the rating of an 8 is honest. The name "Forever Onward" refers to the endless nature of the fractal depths. The calculation time of X-1/X minutes may be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> BTW, plans are being discussed for a FOTD fractal and business web site, though things are going slowly so far. Stay tuned. With ample sunshine and a temperature of 73F 23C, Thursday was a day to be remembered here at Fractal Central. When the sun went behind the trees, the fractal cats remembered that the time for their treats had arrived. Friday brought more clouds, more wind but a continued mild temperature of 66F 19C. Both days were quite busy for me, but unless more work intervenes, the next FOTD will be posted in 24 hours. Until then, take care, and Halloween is near! Many sensible people know that ghosts are not real, yet despite being told that ghosts are merely images created in the brain and projected outward, why do the rest of the sensible people still claim to have seen a real objective ghost? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Forever_Onward { ; time=0:XX:XX.XX-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.0000175777426223/-2.825716026845529/\ 1.1362e+009/1/10/0 params=1/-1/-1/1/0/0/0/0 float=y maxiter=2000 inside=0 periodicity=10 colors=000W6ddJzcJzbIzaHz`Gz_FxZEwYEuXDtWCrVBpUAoU\ AmT9lS8jR7iQ6gP6eO5dN4bM3aL2_L2ZP8`SEaVKbYQdaVed`f\ gfhjlimqjdneWl`NjWEhR6fgElTMzzrKTzsEYjb`dbb_bdUbgO\ biIbkDbeFZ`HVWJSQLOLNKGPHJQIMQJPRJSRKVSKYSL`SMcTMf\ TNiUNvU9oU9zX8s_8x`8vc8yd8zg8zh8gYOUSOGLO2F93H83J8\ 3K84M84O84P75R75T75UM5WM6YM6ZL6`L7bL7cL7eL7fLGSLOE\ LPGKPHKPIKPJKPKKQLJQMJQNJQOJQPJQQJRRIRSIRTIRUIRVIR\ WISXHSYHSZHS_HS`HSaHU`HV_HX_HYZH_YH`YHbXHzWzdWHcUJ\ bTLbSMaRO`QP`PR_OS_MUZLWYKXYJZXI_XHaWGbVEdVDfUCgUB\ iTAjS9lS8mR6oR5qQ4rP3tP2uO1wO0xP3yP5zQ8zQAzQCzRFzR\ HzRKzSMzSOzSRzTTzTWzTYzU_zUbzUdzVgzVizVkzTnzRqzPts\ NvmOslOqlPokPmkPkkQijQgjQejRciRaiR_iSYhSWhSUhTRgTP\ gUNfULfUJfVHeVFeVDeWBdW9dW7dX5cX3cfTmY3eZ4g_5i`6ja\ 7lb8nc9odAqeBsfCugDvhExiFzjGzkHzlIzmJznKzoLzpMzpNz\ oMznLzmLzlKzlJzkJzjIziIzhHzhGygGxfFweEueEtdDscDrbC\ paBoaBn`Al_9kZ9jZ8hY8gX7f } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 21-10-09 (Star in the Night [6])
by Jim Muth 20 Oct '09

20 Oct '09

FOTD -- October 21, 2009 (Rating 6) Fractal visionaries and enthusiasts: Today's image is named "Star in the Night". The image is a good example of a curious fractal phenomenon known as anti-bifurca- tion, where instead of converging toward an area of infinite iterations and bifurcating as it converges, the fractal flow diverges from a point of low iteration and bifurcates as it diverges. The low point of divergence appears near the center of the frame, appearing as a brilliant star in the deep blue surrounding night But despite its mathematical interest, the image makes only an average artistic impression, which holds the rating to an average 6. The calculation time of a speedy 1-3/4 minutes should try the patience of no one. In addition, the finished image is posted for all it is worth on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With total sunshine and a temperature of 68F 20C, Tuesday was a day to be remembered here at Fractal Central. The fractal cats remembered it for at least 2 seconds when meal time came. My work day was rather busy, but I got FL to help a little. The next FOTD will be posted in 24 hours. At least it is scheduled to be posted then. But I have a funny feeling that a big job will come in sooner than expected, so stay tuned to see how things work out. Until next time, take care and keep waiting for the miracle. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Star_in_the_Night { ; time=0:01:47.83-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip float=y center-mag=-0.39282165939/+0.59824259947/342911/1/\ 12.5/0 params=10/10000000000000000.0 passes=1 maxiter=1000 inside=255 logmap=50 periodicity=10 colors=000zwzvyzrxzmwzhuzcszZqzUozPnyKmxFlwGkvGjuH\ itIhsJguJfvMdrObnQ`kS_gUYdWW`YUX_TUaRQcPNeNJgMFiNC\ kO8mP5mQNmRPmSQmTRmUSmVUmWVmXWmYXm_YnY_nW`nUboScoQ\ eoOfoMgpKipIjpGlqEmqCoqApq8qo7pm6ol6nj5mh4lg4ke3jc\ 2ib2h`1g_1gYElSKiOPdKScGUbCWY8WU5VS6TQ7RO9PMAOLBML\ CKKDJKEIJGHJHGIIFIJEHKDHLCHKBJJBLIBMHBOHAQGARFATEA\ VDAWD9YC9ZB9`A9b99c98e88g78h68j68k79l7Al8Bl8Bl9Cl9\ DmAEmAEmBFmBGmCHmCHnDInDJnEKnEKnFLnFMoGNoGNoHOoHPo\ IOqHPoHPnGQmGQkGQjFRiFRhESfESeESdDTbDTaDT`CU_CUYBV\ XBVWBVUAWTAWSAWRDQVGLZIGbLAfO5jQ0nP5hP9cODYOITNMNN\ QIMPKLOMKNNJMPILQIKSHJUGIVFHXEGYDF_DEaCDbBCdABe9Ag\ 47g99hEBiJDjOEjTGkYIlbKmpQtfLmXGfNB_D6T32M45N48O4B\ O4EP4HQ5JQ5MR5PS5SS5VT1aQ5XT8SWCOYFJ`JEcMAeOFfQKgS\ PhUUhWZiYcjZhjXjnWkqThiQeaNbUL_MOWNQSOTPPVLQYIQ_ER\ bBSd7Tf4Ti5Xl6`n7dq8ht9lv9p8PvARtBTrCVpDWnEYlF_jGa\ hIbfJddKfbLh`MiZNkXOmV7GX } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 20-10-09 (Mystic Conspiracy [7])
by Jim Muth 19 Oct '09

19 Oct '09

FOTD -- October 20, 2009 (Rating 7) Fractal visionaries and enthusiasts: The parent fractal of today's image is a Mandelbrot set with cubic characteristics in its depths, and today's image lies quite deep indeed. The scene is located in one of the east- style valleys of a larger cubic minibrot on a filament extending from the large northern bud of the parent M-set. Since I rather like the color scheme, I rated the image at a 7. The name "Mystic Conspiracy" refers to the unfinished pyramidal shape surrounding the minibrot. Some would have us believe that such a shape, especially with the all-seeing eye hovering above it, is a symbol of a conspiracy to take over the world. I think the conspirators are supposed to have been plotting the takeover for over a thousand years, and the plot might even involve space aliens. If so, the aliens must be pretty inept. The calculation time of 6-1/4 minutes is a bit slow. A faster way to see the finished image is to view it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An absolutely cloudless sky, light winds and a temperature of 55F 13C made Monday one of the best days of the autumn here at Fractal Central. With total sunshine on their window shelf, the fractal cats were as happy as cats can be. With the work finished, my day was acceptable. Unless something goes awry, the next FOTD will be posted in 24 hours. Until then, take care, and wait for the aliens to uncloak. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mystic_Conspiracy { ; time=0:06:13.03-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip float=y center-mag=+0.02385231181558285/+1.022424410500009\ /2.4e+012/1/100/0 params=3/13 passes=1 maxiter=6000 inside=0 periodicity=10 mathtolerance=0.05/1 colors=0009aeA`dA_dA_cAZcAZbAYbKKUvfcrddn`enV`bNXY\ FTU8PzGKzOFRWAzjV8yzzxiExzzwazwYzwTOvzzvLzvHzeDGP9\ z867C45F32J20M13Q45T67W89_BBbDDeFJfJPfMVfP`fSffVkf\ YegZ_g_Vg`PgazwbEgcIdZLaVO_RRXNUUIXSE_PAbN6hYBnhFf\ nE_tETyEUuJUqNUmSUiWUe_UadUYhUUlQTnNTpKTqHTsETtBTz\ 8Tz9Vz9Xc9YU9_K9aA9b1Dh5Hn8LtBPyEUvFYtGbrGfpHknIol\ IfgKZbMRZOJUQBQRDUyGTuISqLRnNQjPPfSOcUN_WMXeaWf`Tf\ _PfZLgYIgXEhWBhV7hU4iW5iX5iY6iZ6i`7ia7ib8ic8ie9if9\ igAihAijBikBilCimChkHhiMhgRheWgc`gaeg_jgYogXshZqh`\ ohbmhdlhfjhhhhjfhkeimcioaiq_isZiuXiwViyTizSfzSdzSb\ zT_zTPgkPgkPgkPgkPgjQgkRgkQgkRgkSgkSgkShkShkRhkRhk\ RhkQikQikQikPikPikPjkPjkOjkOjkOjlNklNklNkmMkmMknMm\ nMnoLooMppNqpOrrPrrQrrRrrSrsTstUsuVsvWswXsxYtyZtz_\ tz`tzatzbuzcuzduzeuzfuzguzitzktzmtzotzqtzsszutzwuz\ yvzzwzzxzzyzzzzzzzzzzzzzzzzzzzzzzzzzzzzyyyuuumvucr\ sUmoKhk8ch9cg9cg9bf9bf9ae } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 18-10-09 (Simply Outstanding [8.5])
by Jim Muth 19 Oct '09

19 Oct '09

FOTD -- October 18, 2009 (Rating 8.5) Fractal visionaries and enthusiasts: Little can be said about today's image, which must be seen to be believed. Unmatched in its extravagance, it is truly an image, that speaks for itself. The parent fractal also must be seen to be believed. The most incredible part of this Mandelbrot set parent is that only half of it is there. The western half has moved on to a higher dimension, and has been replaced by a field of scattered stars and planets. Today's image is located just beyond the large period-5 bud on the northwest shore line of the main bay of the parent half-M-set, almost exactly on the line where the M-set is vanishing. It is located a curious area of chaos in the East Valley of a larger minibrot. There is so much of interest in the image that I failed to find a single theme in it that might inspire a name. I finally named it "Simply Outstanding", which says it all. Actually, the colors of the image are a bit too disorganized to earn a top rating. The rating of 8-1/2 is high enough however. The chief drawback is the calculation time of over 22 minutes, though this time may be cut to a minute or so by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But due to the odd hour of this posting, give Paul a chance to get it posted on the site. Heavy clouds and a steady cold rain mixed with a few snowflakes left Saturday a day with much to be desired here at Fractal Central. The fractal cats were so disgusted that they passed most of the day squatted down and sulking. Except for the better-than-expected fractal, my day was uneventful. The next FOTD will be posted in 8 hours, more or less. Until then, take care, and when the going gets tough, get tough and get going. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Simply_Outstanding { ; time=0:22:25.04-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip float=y center-mag=-0.4910502171778077/+0.6046112975128152\ /6.404988e+011/1/27.5/0 params=0.5/31.67 passes=1 maxiter=13500 inside=0 logmap=2675 periodicity=10 mathtolerance=0.05/1 colors=000RpgRpgRphSphSpiSpiSpiSpjSpjTpkWDyODyHDzA\ Dz4Ml5Sf5Y`6bW6hQ7nK1tE4sF7sFAsGDsGGsHJsHMrIPrISrJ\ VrJYrKatL`sK`rK`qK`qJ`pJ_oJ_nI_nI_mI_lHZkHZkHZjGZi\ Gbh9`iDZiGYjKWjNUkRTkURlXPl`OmcMmgKnjIlgHidGfaFc_B\ TN7IA9HCBHDDHEFHFHHGJHHKGIMGJOGKQGLSGMUGNUDLVFNVGO\ VHPVIQVJSVLTVMUVNVVOXVPYVRZVS_VTaVUbVVcTXcVWdWWdYW\ eZWe_VfaVfbVfcVgeVgfUhgUhiUijUi_0KoVlkUihTfeScbR`_\ QYXPVUOSROPONMLMJILGFKDCJA9I76H43H29M6ERAJVDP_HUdL\ ZhOzzSizWnzZzzRzjKzdCzX2zY4zZ5m_7c`8Ya9XbBVbCUcESd\ FReGPfIOgJNgKSjUXmcaolbijbdicZhcUgdOedJdeDce8b_D_U\ HYOLWJPTDTR7XP2`N3YQ3WT3TW3RZ3P`3Mc3Kf3Hi3Fk3Dn3Al\ 38o36q6Ao8DmAGkCJjENhHQfJTdLWcN_aPbdSebUhaWl_YoY_r\ WauVOp`BkeAib9m`9mZ8mX7mU7mS6mQ5XO5mMKmRKmRKmRKmSK\ mSKmSLnTLnTcnUmnUmnUmnVmnVmnWmnWmnWmnWmnXmnXmnYznY\ znYznZznZznZzo_zo_zo`zo`zo`zoazoazobzobzobzoczoczo\ dzodzodzoezoezoezpfzpfzpg } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 19-10-09 (Cubical Quadratic [6])
by Jim Muth 19 Oct '09

19 Oct '09

FOTD -- October 19, 2009 (Rating 6) Fractal visionaries and enthusiasts: With an unexpected improvement in the weather, an unexpected antiquing trip erupted on Sunday, which was yesterday, and explains the lateness of today's FOTD. The image pictures a simple cubic minibrot with some not-so- typical surroundings. The parent fractal is a Mandelbrot set slightly stretched in the north-south direction on its west side. Today's scene is located in a rather shallow part of East Valley. I named the image "Cubical Quadratic" because it contains elements of both types of fractals. Then I rated it at a 6, which is a fair rating. The calculation time of 3-1/2 minutes is well within reason except for those who simply find nothing of interest in fractals, but those few will not be calculating the image to begin with. The finished image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The skies cleared here at Fractal Central on Sunday and the fractal cats' mood imporved at once. The temperature of 55F 13C felt just about perfect for the middle of October. My day was busy but not too unpleasant. The next FOTD will be posted in about 12 hours, (no promise). Until next time, take care, and look for the meaning of it all. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cubical_Quadratic { ; time=0:03:33.98-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip center-mag=+0.331618271858/-0.01773386681/1.5e+007\ /1/57.5/0 params=3/13 float=y maxiter=2250 inside=0 logmap=300 periodicity=10 colors=000UfkUfkUfkTgkTgkTgkSgkSgkShkShkRhkRhkRhkQ\ ikQikQikPikPikPjkPjkOjkOjkOjkNkkNkkNkkMkkMkkMlkMlk\ LlkLlkLlkKmkKmkKmkKmkJmkJnkJnkInkInkInkHokHokHokHo\ kGokGpkGpkFpkFpkFpkFpkEolDomComBonAon9no8no7np6np5\ nq5nq5nq6mp6lp6lo6ko6kn6jn7jm7im7il7hl7hk7gk8fj8fj\ 8ei8ei8dh8dh9cg9cg9bf9bf9ae9aeA`dA_dA_cAZcAZbAYbBY\ aBXaBX`BW`BW_BV_BV_CUZCTZCTYCSYCSXCRXDRWDQWDQVDPVD\ PUDOUENTENTEMSXKkXKkXKkWKkWKkWKkVKkVKkVKkUKka32_53\ Y74X94VB5TD6SF6QH7OJ8NL8LN9JPAHRBGTBEVCCXDBZD9`E7b\ F6dF4fG2hH1jHZGQ`FPaEPbDPcDPdCPeBPfBOgAOh9Oi9Ok8Ol\ 7Om6On6No5Np4Nq4Nr3Ns2Nt2Ns5Mr7MqALpCLoFLnHKmJKlMK\ lOJkRJjTJiVIhYIg_IfbHedHfiFefHddJcbKb`MaZN`XP_VQZS\ SYQUXOVWMXVKYUI_4GBHGOUG`eCxfErfGlfIgfKafLXgNRgPLg\ RGgTAoV6gU5_U4SU3LU3NW4PY5R_6Ta7Uc8We9YgA_iB`kCbnD\ dqEftFhwGizHkzImzJozKpzLrzMtzNvzORzMgzOwzPtzQrzQpz\ RmzRkzRizSfzSdzSbzT_zTYzT } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE=========================================

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Re: [Fractint] Tile Wall 13-Oct-09
by JackOfTradeZ＠comcast.net 19 Oct '09

19 Oct '09

. Hey Jim - that certainly IS a fractal! Although the esthetic / artistic impression is not extreme, it definitely illustrates what a fractal is - endless repetition and self similarity. I have never seen one like this - awesome! Zooming OUT creates a finer and finer patchwork which seems to stop at around E-005, and you cant zoom out further than that for some reason I dont know. Zooming IN looks like a normal mandelbrot, but squashed a bit along the IMAG axis. A zoom animation may not be spectacular, but I will investigate. Maybe a morph - I will see. .

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FOTD 13-10-09 (Tile Wall [No Rating])
by Jim Muth 18 Oct '09

18 Oct '09

FOTD -- October 13, 2009 (No Rating) Fractal visionaries and enthusiasts: Late fractal alert! New Formula Alert! No, this is not how the bathroom wall here at Fractal Central is decorated, but some fractal fanatic somewhere might find it interesting. As for me, I prefer the old-fashioned plain square tiles. I'm not sure whether today's image is a fractal or not. I came up with the formula while noodling around with some old formulas in one of my overstuffed and forgotten formula files. With four changeable functions, this formula creates an apparently limit- less variety of fractal tessellations of any chosen point of the Mandelbrot set. In today's image I chose the large minibrot on the main stem, which appears, shining brilliantly, at the tile intersections. The formula name "TileWall" is also the name of the image, and this well might be the only time I use this particular formula. The reason for the name is apparent once the image is seen. Since I'm not even sure the image is a fractal, I could give it no rating. The calculation time of 1 second is ceratinly one of the briefest of all time. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will not be quite as fast, but it will be more fun. Heavy clouds and a chilly temperature of 50F 10C put a damper on all outdoor activity here at Fractal Central on Monday. The fractal cats slept through most of it, doing all their sulking in their dreams. Otherwise my day was average. The next FOTD will be posted in 24 hours. Until then, take care, and what the heck does the <logmode=fly> entry in the parameter file mean. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Tile_Wall { ; time=0:00:01.13-SF5 on P4-2000 reset=1960 type=formula formulafile=jim.frm formulaname=TileWall function=conj/cos/ident/cos passes=1 center-mag=0/0/0.1032964 params=-1.766/0 float=y maxiter=500 inside=253 logmap=yes logmode=fly symmetry=xyaxis periodicity=10 colors=000eUOaVPYWQUWQQXRMYScpzcpzcpzapzkpztoD0030\ 03aPLVdNP`Q7I3DQGdIJUQO_W4YW7WXAUXDRXGPXJNYMLYPi5a\ e9`aDZYIYUMWQQVMUTZvcWqaTlZPgXMbU`S7XTBUVGQWKMXOpg\ NgdO_bQR_RPvWMkUUTJOWOkkEfiGafJXdLSaON_QvWphXgWY_u\ OJaTOarISgNmAihEfcIcYM`TQYOUV5X67X99XCBYGDYJFYMHYP\ TSTOVS5sl8ohBjdEf_HaWQ49OCEMJJKROsBE`NLKvMJsNJoOJj\ PJfQJaRSEuRHqQJmPMiNOfMRbLTZKWVTnRRkRPhROeSMbSK_SC\ 6`FGYHPVnq8N4aLEYKOVdvi`qeWlbSgZNbV0Zp0Rh3Se6TbAV_\ DWXGXUbKNTRQUaKS`LR`MP_ONZPMZQKYRLidLgbKe`KcYJaWJ_\ UnoVs6JfGMVPP72WalynVtzElqMfhU```VShPJpJXnJimJwkJm\ eNc`QTVUJPXTHVa9Uk1SiLfgcutlGohGidGd`G_XHUSHPOHJKH\ EGHDKLCOOARS9VV8ZZIabTegbhkmlpwotdUlN9eMAbMB_LCXKC\ UKDRJEOJELGRWEbeCnoAvy8sv7ms6gq5an4Vl3Pi2Jg1DdEOiQ\ ZnbhrnswdW`W8EOKSFWf7gtDgpJglPghWgeafagfYmfUsfQq_N\ oSLmLIkeTivbfvcctdareZofXmgUjgShhPeiHXSNceMaaL`ZKZ\ VLY71gX4eW6dV9bUzzzE_THZS } frm:TileWall {; Jim Muth ; p1=Mandelbrot set coordinates z=c=p1+.05*(fn1(fn2(real(pixel)))\ +flip(fn3(fn4(imag(pixel))))): z=sqr(z)+c, |z| <= 100 } END PARAMETER FILE=========================================

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FOTD October 18, 2009 (Simply Outstanding [8.5])
by JimMuth＠aol.com 18 Oct '09

18 Oct '09

FOTD -- October 18, 2009 (Rating 8.5) Fractal visionaries and enthusiasts: Little can be said about today's image, which must be seen to be believed. Unmatched in its extravagance, it is truly an image, that speaks for itself. The parent fractal also must be seen to be believed. The most incredible part of this Mandelbrot set parent is that only half of it is there. The western half has moved on to a higher dimension, and has been replaced by a field of scattered stars and planets. Today's image is located just beyond the large period-5 bud on the northwest shore line of the main bay of the parent half-M-set, almost exactly on the line where the M-set is vanishing. It is located a curious area of chaos in the East Valley of a larger minibrot. There is so much of interest in the image that I failed to find a single theme in it that might inspire a name. I finally named it "Simply Outstanding", which says it all. Actually, the colors of the image are a bit too disorganized to earn a top rating. The rating of 8-1/2 is high enough however. The chief drawback is the calculation time of over 22 minutes, though this time may be cut to a minute or so by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But due to the odd hour of this posting, give Paul a chance to get it posted on the site. Heavy clouds and a steady cold rain mixed with a few snowflakes left Saturday a day with much to be desired here at Fractal Central. The fractal cats were so disgusted that they passed most of the day squatted down and sulking. Except for the better-than-expected fractal, my day was uneventful. The next FOTD will be posted in 8 hours, more or less. Until then, take care, and when the going gets tough, get tough and get going. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Simply_Outstanding { ; time=0:22:25.04-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip float=y center-mag=-0.4910502171778077/+0.6046112975128152\ /6.404988e+011/1/27.5/0 params=0.5/31.67 passes=1 maxiter=13500 inside=0 logmap=2675 periodicity=10 mathtolerance=0.05/1 colors=000RpgRpgRphSphSpiSpiSpiSpjSpjTpkWDyODyHDzA\ Dz4Ml5Sf5Y`6bW6hQ7nK1tE4sF7sFAsGDsGGsHJsHMrIPrISrJ\ VrJYrKatL`sK`rK`qK`qJ`pJ_oJ_nI_nI_mI_lHZkHZkHZjGZi\ Gbh9`iDZiGYjKWjNUkRTkURlXPl`OmcMmgKnjIlgHidGfaFc_B\ TN7IA9HCBHDDHEFHFHHGJHHKGIMGJOGKQGLSGMUGNUDLVFNVGO\ VHPVIQVJSVLTVMUVNVVOXVPYVRZVS_VTaVUbVVcTXcVWdWWdYW\ eZWe_VfaVfbVfcVgeVgfUhgUhiUijUi_0KoVlkUihTfeScbR`_\ QYXPVUOSROPONMLMJILGFKDCJA9I76H43H29M6ERAJVDP_HUdL\ ZhOzzSizWnzZzzRzjKzdCzX2zY4zZ5m_7c`8Ya9XbBVbCUcESd\ FReGPfIOgJNgKSjUXmcaolbijbdicZhcUgdOedJdeDce8b_D_U\ HYOLWJPTDTR7XP2`N3YQ3WT3TW3RZ3P`3Mc3Kf3Hi3Fk3Dn3Al\ 38o36q6Ao8DmAGkCJjENhHQfJTdLWcN_aPbdSebUhaWl_YoY_r\ WauVOp`BkeAib9m`9mZ8mX7mU7mS6mQ5XO5mMKmRKmRKmRKmSK\ mSKmSLnTLnTcnUmnUmnUmnVmnVmnWmnWmnWmnWmnXmnXmnYznY\ znYznZznZznZzo_zo_zo`zo`zo`zoazoazobzobzobzoczoczo\ dzodzodzoezoezoezpfzpfzpg } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE========================================= </HTML>

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FOTD 17-10-09 (Everyday Fractal [6])
by Jim Muth 16 Oct '09

16 Oct '09

FOTD -- October 17, 2009 (Rating 6) Fractal visionaries and enthusiasts: Another very busy day here at FC left little time for a proper fractal discussion. The image shows an order-7 minibrot very deep in the East Valley of its parent fractal, which is the familiar Mandelbrot set. The rating of a 6 reflects my dis-satisfaction with the colors, which strike me as far too gaudy, with no obvious unifying theme. The name "Everyday Fractal" shows that the image is typical of those I often pass by on the way to the real image of the day. The calculation time of 6-2/3 minutes is on the slow side, so why not view the finished image, which is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A mixture of cold rain and wet snow fell all day here at Fractal Central, making the fractal cats very unhappy. The tuna treat only partly eased their displeasure. Otherwise, the day was quite busy. The next FOTD is due to be posted in 24 hours. Until then, take care, and the whole world is waiting for the light. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Everyday_Fractal { ; time=0:06:39.88-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip center-mag=+0.2620305801459116/-0.0021712604450317\ 4/1.023753e+012/1/-172.5/0 params=7/1000000000000.0 float=y maxiter=4200 inside=0 logmap=912 periodicity=10 mathtolerance=0.05/1 colors=000HUAIXAJZBKaBLdBerG_oEVlDQiCG81IK5KW8nPod\ VaV`O_tEWpDSmCOfBUbU6SV88SADQCINENLGSIIXGKaDUh0Vc0\ _X0eS0eN4fI5eD6aI7ZN8VS9SXAOaBK2bejV_iQVhLQgGG9sII\ gJQXKZM0b03c26c38d5Bd6Ee7Ge9JfAy7yrDpkJhdP_YVSR`Jg\ eQafMWfIQfEStcgJXjIUlHRnGNpFKrEHtDEvDBpE9kE8fE6aE5\ XE4UF5SG5PH5NI5KJ6IK6FL6DL6FKAHJDJIGLHJNGMPFPRESTE\ VWG_YIc`JgbLkeNogOsjDgl3WgAQbHKYNETU8O_3Qb8ReDSgIT\ jNVmSWoXXraYteJDUMHWOKYQNZSR`UUaWXcY`e`cfbfhdjifmk\ hpmjtnlwpnzqkvpispgpoemocjoagn_dnYanUeoRhpNkqKnrHq\ sLltOgtRbuUYuYTv`OvcJwfEwy0xu1sq2om3ki4ge5c`9aXD_T\ HZOLXKPWGTUCXTAQS9KR8DQ77PA6TC5WE4ZH3aJ2dL1gN0jzrD\ a_7EI1FM3GP4HS5IV6JY8K`9WFTLcAeMebP`_SXXVSUYOR`JOc\ F3mZ7kUBjPEhKzgFws0mo3OV6MimzLkVLURMNOzH_w_YuWWtTU\ rQSqNQoKOnHMlEszcnwZitVdqR_nNVkJQhFGVsHXlIZfJ`_JLU\ KINLeHm4vFO9GRAJiAHl9Fm8Eo7Cq6As58u4mw3zz2zz1zz0zz\ 1zz2zz2zz6zz9zzCzzFzzJzzM } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 16-10-09 (Much of Nothing [6])
by Jim Muth 15 Oct '09

15 Oct '09

FOTD -- October 16, 2009 (Rating 6) Fractal visionaries and enthusiasts: Today's image lies in yesterday's image. And that's about all I have to say about it. The image is perhaps a bit more colorful than usual, but nothing more than just a bit above a rating of average. The name "Much of Nothing" is an oxymoron that has absolutely no meaning beyond the sound of the words. The calculation time of 4-2/3 minutes is a bit more than the image is worth, so I advise a trip to view it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Today's discussion is short because I let myself fall into another useless debate with FL, who remarked that she is still waiting for our latest president to fulfill some of his campaign promises. Needless to say, she is disappointed, while I wonder if it is yet time to say, "I told you so." A most unpleasant day prevailed with the weather as well here at Fractal central on Thursday, as a sloppy mixture of rain and snow fell all day, while the temperature hovered just above free- zing. The fractal cats watched the flakes fall past the window for a while, then retired to their cozy places near the heat. My work day was average. The next glorious FOTD fractal will be posted in 24 hours. Until then, take care, and when will Superpresident fly out of the phone booth and save us? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Much_of_Nothing { ; time=0:04:20.23-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip float=y center-mag=-1.739211970904733/+0.00050860216317744\ /6.443154e+011/1/-127.6/0 params=0.85/4000 passes=1 maxiter=2000 inside=0 logmap=-569 periodicity=10 colors=0000Kb0Ka0Ka0K`0K`0K_0K_0KZ0KZ0KY0KY0KX0KX0\ KW0KW0JV0JU0IT0IS0IR0HQ0HP0HO0GN0FM0FL0FK0FJ0FI0FH\ 0FG6BF_X0e`0jd0kUFlJUz8hz2VzmjzIizOazUVz_NzmGvUDuJ\ Au87`5GH2PD5WA7b79i4Bp1DvIFpZGjnHdiFZeDTaBNY9ITKJO\ VKKdKPZITUHXPG`JEdEDh9Cl4B_LANa9Bq9WSOo3bq2Ur2Mt2D\ u25_TXFrwDomCldAiV9fM7cC6a3Ga6Pa9YaCfaFoaHTX86T0RU\ sNUqKUqHUnDWoBYn8`o8co8eq8kt8rw8zzA7em`OzoT88m97g9\ 7a96W62R96QCAPEEOHHNJLMMPLPWJOUKOSLOQMKP9QOHOPMNQR\ LQWKR`JSeHSjGToEOyFTsGXnHaiIedJiZKnULrPDuRMvKXH4Ix\ 2Pw8VwDavIqXkliZgvNVuu9G8ALFBQL1Pa5RY8TUBURFWNIXKL\ ZGO_DRZJUYOWXUZWZaVdDXjRWicViVPLxUutUopUilUciUYeUS\ aUMYzzYzzWzzVzzTzzUzzzzzzzzzzzzzzzzOzzKzzFzzAzz1zz\ 6zzHzzSzzjzzazzTzzLzzCzz4zz_zzWzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzFziFzkFzmFzoFzq0zs0zt\ AztKzuUzvczwhzxmzyrzzvzzzzz_zZczUazNczOezOgzPizPkz\ Q0z9lzQkzMjzJizFhzCgzHfzL } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 15-10-09 (Fractal Spiderworks [7])
by Jim Muth 14 Oct '09

14 Oct '09

FOTD -- October 15, 2009 (Rating 7) Fractal visionaries and enthusiasts: By all rights, today's image should show a minibrot of order 0.85. But such a thing is an impossibility, since such a minibrot would have minus 0.15 lobes, which is nonsense. Instead, we have a normal quadratic minibrot at the center of the image, with a curiously symmetrical east fragment of another quadratic minibrot just to its east and a lot of interesting things happening in between. To see this situation clearly however, another in-zoom is needed. I named today's image "Fractal Spiderworks" because the elements surrounding the minibrot remind me of spiderwebs covered with dewdrops. Then I rated it at a 7. The image does have a certain attractiveness about it. The calculation time of only one minute means no one will waste much time calculating an image they find disappointing. And the finished image is posted as always on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday began promisingly here at Fractal Central, with blue skies, sparkling sunshine and a temperature of 43F 6C. But by mid-morning the clouds moved in, leading to a cloudy and chilly day that brought little pleasure to the fractal cats until the tuna appeared late in the afternoon. My day was both thoughtful and productive. And no one was obliged to agree with the thoughtful part. In all likelihood, the next FOTD will be posted at this same place in about 24 hours. Until then, take care, and don't make an unjustified leap from the particular to the general, (or even to the major). Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FractalSpiderworks { ; time=0:01:03.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip center-mag=-1.749456597407157/+0.000001271090939/\ 8.829e+009/1/177.5/0 params=0.85/1000000 float=y maxiter=5000 inside=0 symmetry=none periodicity=10 colors=0005HG5HG5HG6HG6HG6GG6GG6GG6GH6GH_X0e`0jd0k\ UFlJUz8hz2VzmjzIizOazUVz_NzmGvUDuJAu87`5GH2PD5WA7b\ 79i4Bp1DvIFpZGjnHdiFZeDTaBNY9ITKJOVKKdKPZITUHXPG`J\ EdEDh9Cl4B_LANa9Bq9WSOo3bq2Ur2Mt2Du25_TXFrwDomCldA\ iV9fM7cC6a3Ga6Pa9YaCfaFoaHTX86T0boxXovSouNosIorDop\ 8oo8oo8no8nn8nn8mnA7e9VOQbT88m97g97a96W62R96QCAPEE\ OHHNJLMMPLPWJOUKOSLOQMKP9QOHOPMNQRLQWKR`JSeHSjGToE\ OyFTsGXnHaiIedJiZKnULrPDuRMvKXH4Ix2Pw8VwDavIqXkliZ\ gvNVuu9G8ALFBQL1Pa5RY8TUBURFWNIXKLZGO_DRZJUYOWXUZW\ ZaVdDXjRWicViVPLxUutUopUilUciUYeUSaUMYzGYz1Wz6VzBT\ zGUzNTzMSzLEzYJzTNzORzKWzF_zARz1cz6XzHQzSMzjJzaGzT\ 0zL0zC0z40z_0zW0zT0zP0zQ0zO0zN0zMYzLXzKWzJWzISzK0W\ _LYaI_cEaeFcgFeiFgkFimFkoFmq0os0qtArtKsuUtvcuwhvxm\ wyrxzvyzzzz_QZcKUa9NcBOeDOgFPiHPkJQ029lKQkHMjFJiDF\ hBCgAHfALe9Pd9Tc9XMFN4KD4KE4KE4KE4KE5JE5JE5JE5JE5J\ F5JF5IF99L5IF5IF5IF5IF5HF } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 14-10-09 (Talons of Doom [5])
by Jim Muth 13 Oct '09

13 Oct '09

FOTD -- October 14, 2009 (Rating 5) Fractal visionaries and enthusiasts: Today's image is not a scene in any Mandelbrot set, warped or otherwise. It is a an oblique scene in the Z^2+C Julibrot, which encompasses all the warped Mandelbrot sets as well as all the Julia sets. The orientation of the image is double-rotated 5 and 5 degrees from the true Julia direction. The banded effect of the foreground elements was achieved with the 'ranges' feature of Fractint, a little used and probably almost unknown feature. The three-dimensional effect of ghostly half-obscured Mandelbrot buds in the background arises because points that do not escape will eventually settle into the same orbits regardless of where they begin their journeys. The rating of a 5 indicates that I'm not very satisfied with the image, which is not quite worth the 8 minutes required to run the parameter file. The name "Talons of Doom" refers to the talon-like effect of the converging foreground stuff on the right side of the image. The most convenient way to view the image, as always, is to view it in finished form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday here at Fractal Central was marked by dark scudding strato-cumulus clouds and blustery northwest winds. The temperature of 61F 16C felt more like 50F 10C. The fractal cats needed an extra tuna treat to keep their spirits up. My day was spoiled (or made) when I got into a heated political discussion, which I might elaborate on and post on the philo- fractal list in a day or two. (Politics sure can be fun.) The next FOTD will be posted in 24 hours. Until then, take care, and maybe I should win the Nobel Prize for easy fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Talons_of_Doom { ; time=0:08:09.72-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=multirot-XY-ZW-new function=flip/ident passes=1 center-mag=-1.85151/1.376/9.59/1/158.35/0 params=85/85/2/0/-1.41/1.382/0.244/-0.738 float=y maxiter=32767 inside=253 periodicity=10 ranges=0/\ -1/250/260/275/295/325/360/400/450/600/1500/32767 colors=000cK0F0FKMzPQzUUzZYzcazhezmizrmzwtrzzj0000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 0000000000000000c_z000000 } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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FOTD 12-10-09 (Mystic Elliptic Set [7])
by Jim Muth 11 Oct '09

11 Oct '09

FOTD -- October 12, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's scene lies in the upper right quadrant of yesterday's image, and uses much of the same color palette. It is actually an Elliptic set (It is not a Julia set!) lying close to one of the apparitions of the large minibrot on the main stem of the larger minibrot on the main stem of the parent Mandelbrot set, which is nowhere to be recognized in this Elliptic orientation of the Julibrot. Because of the effect of a near-blinding aura of light that might surround something as mystical as the Holy Grail, I named the image "Mystic Elliptic Set". But there is nothing sacred about the image. It is all done with mere numbers. (Then again, perhaps numbers are not so simple. Maybe God creates His works with numbers.) The rating of a 7 is my fair estimate of the value of the image. The calculation time of 4-3/4 minutes makes running the included parameter file almost a breeze. The full breeze may be enjoyed by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image in breezy comfort there. A mix of clouds and sun let through just enough sun to keep the fractal cats happy here at Fractal Central on Sunday. The temperature of 59F 15C was on the chilly side, but the sun was shining warm on the shelf in the window, so the cats were toasty warm. My day was peaceful while FL visited a nearby friend. The next FOTD will be posted in 24 hours. Until then, take care, and how does one know what's right if he doesn't recognize what's wrong? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= MysticEllipticSet { ; time=0:04:45.20-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=-1.785734063956232/-0.22039446\ 49006539/1.395829e+008/0.1291/54.82991160555688/-7\ 1.010913634439 params=90/0/2/0/0/0/0/0.0001 float=y maxiter=10000 inside=255 logmap=35 periodicity=10 colors=000u4TrCUoKUmSUjZUhfUenUcuUdl_ddddWidOndGsZ\ NtUUuP`vKfwFmxAty5zz5zz5zz8zzAzzCzzFzzHzzJzzMzzOzz\ QzzTzzVzzXzzYzzZzz_zz`zzazzazzbzzczzdzzezzfzzqzzkz\ zdzzZzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzSzzN\ Le0Me0Ne0Oe3Pe5Qe8RfASfCTfEUfGUfIVfLWfNXfPYgRYgTZg\ V_gY`m_bradvcgzejzgmzjozloznpzpqzrrztszvtzwuzxvzyw\ zzxzzyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzyzzyzzxzzxzzwzzwzzvzzvzzuzzuzztzztzzszzszzrzz\ rzzqzzqzzpzzozznzzmzzlzzkzzjzzizzhzzgzzfzzezzevyer\ xemwehvedvectfcsgcrgcqhcoicnicmjclkcjkcilchmcgncen\ cdoccpbbpbaqb_rbZrbYsbXtbVubUubTvbSwbQwbPxbOybNybM\ wcNvdOtdPseQrfRpfSogTngUlhVkiWjiXhjYgjZfk_dl`clabm\ b`mc_ndZoeXofWpgVphWqeWqbXr`XrYXsWYsTYtRYtOZuLZuJ_\ vG_vE_wB`w9`x6`x4ay5by5cy6hy6my7ry7vy8wy8zy8zy9zzL\ zzJzzHzzFzzDzzBzzAzz9zz8zz8zzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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FOTD 11-10-09 (Near Point Zero [7.5])
by Jim Muth 10 Oct '09

10 Oct '09

FOTD -- October 11, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is a view of the large minibrot at -1.75 on the negative spike of the Mandelbrot set. Yes, I realize it has nothing at all about it that would suggest it is a minibrot in the M-set, but this image is not sliced in the Mandelbrot direction. It is sliced in what I call the Elliptic direction, which is the orientation determined by the real(c) and imag(z) axes of the 4-dimensional Julibrot. Today's image is actually a reworking and re-coloring of a similar image that appeared several years ago. The original image is very similar. Anyone who cares to go searching for it will have a lot of fun before stumbling upon it. The name "Near Point Zero" refers to the imag(c) value of 0.0001, which is the tiny departure from zero necessary to produce the image. The rating of 7.5 includes 1/2 point for the coloring effort, even though a good part of the coloring is carried over from the original image, which was posted several ears ago. The calculation time is a fireball 10 seconds, almost as fast as the speed of light. If it had been a little faster, it would have exceeded the speed of light and finished 10 seconds before it was started. All such troublesome paradoxes may be forgotten however by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds continued here at Fractal Central on Saturday, but the overnight rain ended before daybreak. This was not good news however, for the rain was replaced by a blustery northwest wind, which with a temperature of 61F 16C, dampened the fractal cats' enthusiasm. Once again, their complaints were silenced by a generous second serving of chunk-light tuna in water. With all the cat activity, the rest of the day was thankfully uneventful. The next FOTD will be posted in 24 hours. Until then, take care, and if it makes you feel good, believe it; otherwise don't believe it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Near_Point_Zero { ; time=0:00:10.07-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=-1.76526/0/15.9369/0.2252/-90/0 params=90/0/2/0/0/0/0/0.0001 float=y maxiter=10000 inside=0 logmap=18 periodicity=10 colors=0000DP7LV5Qe8RfASfCTfEUfGUfIVfLWfNXfPYgRYgT\ ZgV_gY`m_bradvcgzejzgmzjozloznpzpqzrrztszvtzwuzxvz\ ywzzxzzyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzgzzgzzgzzfzzfzzfzzfzzezzezzezzezzdWt\ dYud`udbvddvectfcsgcrgcqhcoicnicmjclkcjkcilchmcgnc\ encdoccpbbpbaqb_rbZrbYsbXtbVubUubTvbSwbQwbPxbOybNy\ bMwcNvdOtdPseQrfRpfSogTngUlhVkiWjiXhjYgjZfk_dl`cla\ bmb`mc_ndZoeXofWpgVphWqeWqbXr`XrYXsWYsTYtRYtOZuLZu\ J_vG_vE_wB`w9`x6`x4ay5by5by6cy6dy7dy7ey8ey8fy8gy9g\ y9hyAhyAiyBjyBjyCkyCkyClyDmyDmyEnzEnzFozFpzGpzGqzG\ qzHrzHszIszItzJtzJuzKvzKvzKwzLwzLxzMyzMyzNzzNzzNhz\ YRzhAzs9zq9zp8zo8zn7zm7zl7zj6zi6zh5zg5zf5ze8zbAz`C\ zZFzXHzVJzTMzQOzOQzMTzKVzIXzGYzKZzO_zS`zVazZazbbzf\ czidzmezqfzuqzEkzDdzCZzCYzEYzGYzHYzJYzKYzMYzNYzPYz\ QYzSYzTYzVYzWSzPNzJIzDDz7 } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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FOTD 10-10-09 (Blues in the Dawn [6])
by Jim Muth 10 Oct '09

10 Oct '09

FOTD -- October 10, 2009 (Rating 6) Fractal visionaries and enthusiasts: Today's image, with its royal blues and oranges, lies in the parent fractal that results when Z^(1.1) is subtracted from Z^(-1.1). This parent fractal is a grossly oversized thing consisting of two Mandeloids, one of them a peanut-shaped thing, the other a partially cut-off Mandelbrot set. These two large Mandeloids are connected by a stream of debris, with today's image located near the midpoint of this debris. Royal blue and orange are my old school colors, so I gave the image an extra point in the ratings. If I had gone to another school, the image, with the blues that just don't look right, would rate only an average 5. The name "Blues in the Dawn" is appropriate for one who is going home after a rough, disappointing night out. The brief calcula- tion time of 1-1/2 minutes kind of makes up for that bad night. But all these problems may be eliminated by viewing the image in finished form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Too many clouds prevailed here at Fractal Central on Friday, and the temperature of 63F 17C was too chilly for total comfort. As a result, the fractal cats were dis-satisfied and needed an extra treat of tuna to keep them quiet. My day was busy, which explains the late FOTD. The next FOTD will be posted in 24 hours. Until then, take care, and be right up there with the big-time thinkers. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Blues_in_the_Dawn { ; time=0:01:33.30-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.728552855008/-1.64484287301/1239049\ /1/152.5/0 params=1/-1.1/-1/1.1/0/0/0/0 float=y maxiter=1800 inside=0 outside=tdis periodicity=10 colors=000IBbJBcLBcNAcPAcQ9cS9cU9czzzzzzZ7c`7ca7dc\ 6de6df5dh5dj5dl4dzzzzzzq3dr3dp4eo4en4el5ek5ej5ei6e\ zzzf6fe7fd7fb7fa7f`8fZ8fY8fX9gW9gU9gTAgSAgRAgQRmPQ\ lOPlNOlMNkLMkWijVhjUfjSeiRdiQchPbhN`hM_gLZgJYfIWfH\ VfFUeETeDSdBQdAPd9Oc7Nc6Mb5Kb3Jb2Ia1Ha0Ga2Fb4Fb6EY\ 7EY9DYBDYDDYECYGCYKPmKOlKOlKNlKNlKNlKMlKMlKLlKLlKL\ lKKlKKlKJlKJlKJlLIlMIlNHlOHlPHlQGlRGlSGlTFkUFkUEkU\ EkUEkUDkUDkUDkUCkUCkUCjUBjUBjUBjSAjQAjOAjM9jK9jI9j\ B1OD3NF5MH7LJ9KLBJMDJOFIQHHSJGULFVNFXPEZRD`TCbVBcX\ BeZAg`9ib8kd7zpFzjBze7zb8z_8zX8zU8zR9zO9zL9zI9zFAz\ CAz9Az6Az17z28z09z3Az0Bz5Cz0Dz0Ez0FzUGzUHzUHzUIzUJ\ zUKzULzUMkUNlUOlUPmUQsURpUQmUQjUPgLPdOOaRO_TOXWNUZ\ NRzMOzMLzLIzLGzLHzKHzJHzJIzIIzIzzHzzHzzGzzGzzFzzFz\ zEzzEzzDLLDLJCMHCMGBMEBNCANAAz89R38z79JBAzFB5C4zIB\ GNHzSNQXTza__fezkkipqzuw4zJzyI7yHzyHAyGzxGDxFzxFGx\ EzwEJwDzwCMwCzvBXiWWkVUlT } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 09-10-09 (Light Versus Dark [7])
by Jim Muth 09 Oct '09

09 Oct '09

FOTD -- October 09, 2009 (Rating 7) Fractal visionaries and enthusiasts: The FOTD is late. That's the way of it sometimes. Today's image is an evaporated one in the fractal that results when various negative portions of Z^(-1.2) and Z^(-7.5) are mixed and (1/C) is added. Due to heavier work than expected, I spent less time than usual finding the image. The short time made little difference however, as the image still rates a higher-than-average 7. The name "Light Versus Dark" refers to the donut ring of contrasting light and dark elements surrounding the nearly- obscuerd minibrot at the center. (I could just as easily named the image "Planetary Nebula".) The calculation time of 8 seconds more than 12 minutes is admittedly slow, so why not avoid all risk of impatience by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image at leisure there. Thursday started sunny here at Fractal Central, but clouds arrived in the afternoon, blocking the fractal cats' time in the sun and making them crabby. A treat of tuna settled them down and brought back their sunny dispositions. My day was averagely busy. The next FOTD will be posted in 24 hours. Until then, take care, and when light is mixed with darkness, light always wins. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Light_Versus_Dark { ; time=0:12:08.69-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+4.694759696683037/+0.06501194903217314\ /2.403471e+009/1/32.5/0 params=-5/-1.2/-0.8/-7.5/0\ /1e+100/0/0 float=y maxiter=5000 inside=bof61 periodicity=10 colors=0002Td2Td2TdDhf000j`RjXUiUXhQ_hNbgJegGhfCkf\ 9ng8mh8lh7ki7ji6ijchk5gk5fl4el4dm3cn3bn2ao2`o2_aBY\ PKXBTV0aU1YW4VYmSz9P`BMaAOdAQgARjATmAUpAWsAXuDazFf\ mHkjKobMsVPwNRzFSyHSwJSuLSrNSpPSmQSkSShUSfWScYSaZS\ _`SYbSVdSTfSSgUQeVOcWMaYK`ZIZ_GXaEWbCUcASe8Rf6Pg4N\ h2Mf1Pd1Rb0Ta0V_0XY0_W0aV0cT0eR0gQ0iS0gT1fV3dW5cY7\ aZ9`_BZaDYDEeEHcFKbGNaHQ_JTZKWXLZWMaUNdTOgSYHhXGgW\ FfVFeUEdTEcSDbRCaQCaPB`OB_NAZM9YL9XK8WJ8WQ7SW7Ob6K\ h6Gf5Me4Sd3Yb2ca1i`0o_0ua2rb4pc6me8kfBhgDfiFdjHakK\ _mMXnOVoQTnTSnWRmZQmaPmdOlgNljMkmLkpKkrKmgMnYOpNPq\ DRr3Sn6Rk9RhCReFQbHQZKQWNPTQPQTPNVPQSOSQOUOOWMNYKN\ _INbFMdDMfBMzhLj7LzZLz3LzUKz2JzPJX1Ic1HP1H00000000\ 00500A00F0000zPBzzvzZAzm9th9riDqjGpjKokNmkRllUklYj\ m`hmdgngfnkeondoqWepOWpGMo8CoAAnB9mC8lD7lE5kF4jG3i\ H2iMAfRIcWP``XYecVjkSnrPdkTWdXNgzMVYLSzKPUKMSJJQIG\ OHDMAAASOIlaGmnFwjIkgLkcO } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 08-10-09 (Golden Apples [7])
by Jim Muth 07 Oct '09

07 Oct '09

FOTD -- October 08, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that is produced when various negative portions of Z^(-5.0125) and Z^(-1.0125) are combined and (1/C) is added. This parent fractal resembles an oversized circular disk lying east of the origin, with scalloped edges on the east side and a circular bay on the west. Today's image is located in a valley leading to this bay. The name "Golden Apples" has little to do with the image, other than the golden area inside the blue surroundings. The rating of a 7 indicates that I consider the image above average. The calculation time of 3-3/4 minutes may be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds and high winds spoiled Wednesday here at Fractal Central. Annoyed by the lack of sun, the fractal cats spent most of the afternoon sleeping, stirring only when a noisy tomcat fight broke out nearby. My day was spent trying to finish the work. The next FOTD will be posted in 24 hours. Until then, take care, and raise the Hamiltonian. (Whatever that means.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Golden_Apples { ; time=0:03:47.55-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.745899025154062/-0.9887844877387386/\ 1.8e+010/1/166.5/0 params=-1.1/-5.0125/-5.1/\ -1.0125/0/0/0/0 float=y maxiter=1500 inside=0 logmap=118 periodicity=10 mathtolerance=0.05/1 colors=000A8_A8`A8aA8bA7cA7dA7eA7fA7d67d37c7AbAC`D\ FZGHXKJRNMMgXOTQOjYL_VIj_Fe_Cla9ld6oc3rh0sd1sg2tg2\ ug3vg3xg4yg4zi5zg6yg6xg7wg7wg8wg8tc7q`7nY6kU6hR5eJ\ 5bK4_H4XE3UA3R72O42P75Q98RBASDDTFFUHIVJLWLNXNQYPSZ\ RV_TXlc4eZ8ZUCTQFd`7pk0xGnuLcrPToTIlX8cPJWIUNBdF4n\ J7pNAqRDsUFtWKaYOK_S2_ogXXDVaNTfXoLmfUjZbhZAK47SAI\ WGS_MacdeCZxnj6`GJLKTTOb_w5jlKhaYgg6ZbH`ZRbVadW15T\ POt0VeO`m5VP9NOlMXXSUd_S81RSMc1sXPl1dJd8m`IkYSiUag\ `dzYfuWhpTjkZ7SVS_cRg_XfXafUffA0XGG`MWcXvas6XdRaK7\ UMIYOS`Qach4M_QXkvodrlYniIoyNmoUr54pBCnMKlXCEwiDY9\ suEqqIomNmiWLQUSVTZZSeb`qqs78iLK_ZWQHfRPfRXfRdfCwL\ KqWwBNUBHTLOSUURb`mrjVJVURYTY`SdcrnhkmgdlgYkfgjQak\ WWkaYDVVPZT`bUB8TOKS_WsNrVgLTiTSj_5Mm8KRuYsjbn`gj4\ NZAU`G_bMedPhHQjUuL1`kK9OdN1ix`JldRahZaF`WWcP_bQed\ 89ZZ3lVQiAiKJjWpmMXz0VvBUrMSnXUEUTNYSV`RccJUmNbi7p\ uHmmOMfRvNRpXnAjq9jm8ki8k } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 07-10-09 (Seventy Times Seven [No rating])
by Jim Muth 07 Oct '09

07 Oct '09

FOTD -- October 07, 2009 (No Rating) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's formula is a new one. I named it "AllNewDivideBrot". It is a modification of the NewDivideBrot formula, which at a cost of a slight increase in calculation time, eliminates the tendency of the resulting fractals to grow in size beyond all bounds as the second parameter is increased. Before you copy it into a formula file, remove the 'frm:' before the name. The formula still has some problems to be worked out, so there might be an updated version in a few days. The parent fractal is a normal sized Mandelbrot set pictured about 2/3 of the way through the process of morphing into an order-7 Mandeloid. Today's image lies in a backward valley very near the negarive X-axis. The image shows an order-7 minibrot in unusually rich surround- ings. In fact, the surroundings are so grossly overdone that I could not give the image a rating. I think the name "Seventy Times Seven" is a phrase from the Bible, indicating how many times we are to forgive our enemies. Why the phrase came to mind is a mystery, since I am no saint. My patience would run out at about the second offense. The calcuation time of a little under 8 minutes is slower than I would prefer, but relief may be found on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed image is posted. Morning sun, afternoon clouds and a temperature of 66F 19C made Tuesday a typical early Autumn day here at Fractal Central. The fractal cats enjoyed what little sun they found, and spent the rest of the time finding various other trouble to get into. My day was once again quite busy. Most likely tomorrow will be the same. The next FOTD will be posted in 24 hours. Until then, take care, and the last fractal will never be found. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SeventyTimes_Seven { ; time=0:07:51.87-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot function=recip float=y center-mag=-1.515507963309433/-0.00007503378442631\ /1.372161e+010/1/45/0 params=7/7 passes=1 maxiter=7500 inside=0 logmap=410 periodicity=10 colors=000q_PrZPrXPsWPsVPtUPtSPuRPuQPvOPvNPwMPwLPv\ NQuPRtQRsSSrTSqVTpXUpYUo_Vn`VmbWldXkeXjgYjhYliUniQ\ piNrjJtjGvjCxj9sbEoWImYKlZMk_Ni`PhaRgbSecUddWceXaf\ Z`g`_haYicXjeWkfUlhTmjSnkQomPpoOqpMloLgnJbnIYmGTmF\ OlEJlILiMNfPPcTQ`WSY_UVcWSfXPjZMm`JqbGtcDjbIabNTaS\ KaXJ`VI_UHZTGYSGYRHZPI_OJ`NJaMKbLLbKMcJOdIQeHSfGUg\ FWgEYhC_iBajAck9el8gl7im6kn5mo4op3qq2sr1us4wu6xw8z\ zAZfCZdEZbG_`I_ZK_WN`UP`SR`QT`OVaMXaKZaI`aGbeFciEd\ mDeqCfuBgyAgvBftBerBdpBcnBblBajB`hB_fBZdBYaBXZBWVB\ VQBULBPIBKGBFABAABAABAABAABAABAABAAEA6HA6KA6NA7QA7\ TA6WC5ZE5aE4dD3gC2jK2lK5kz8jFAiGDhIGgJIfLLeMNdOQcP\ TbRVaSY`U__VbZXeYYgX_jW`lVboUcrTetSfwRhyRizQjzPjzO\ jzOjzNjzMjzLjzLjzKjzJjzJjzIjzHjzcjzcjzcjzcjzcjzcjz\ cjzcjzcjzcfzcczc`zcXzcUzcRzcNzzKzzHzzDzzAzz7zz6zz5\ zz4zzBzzHzzOzzUzzTzzszzrzzqzzpzzozznzzmzzlzzkzzjzz\ izzhzzgzzfzzPzzPzzPzzPzzP } frm:AllNewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=b*(z^2*fn1(z^(a)+b))+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 06-10-09 (The Bat-fractal [5])
by Jim Muth 05 Oct '09

05 Oct '09

FOTD -- October 06, 2009 (Rating 5) Fractal visionaries and enthusiasts: Things were quite busy here at F.C. on Monday, so to save time I returned to the same parent fractal that gave us yesterday's FOTD image and checked an area that appeared to have East Valley characteristics. After a hurried search of the area, I found today's scene lurking not very deep. The outside=fmod option showed the way to the minibrot. This option surrounds minibrots with circular bull's eyes. I named the image "The Bat-fractal", perhaps thinking of a certain comic hero. Then I rated it at a measly average 5. It's really not worth anything more. The one redeeming feature is the calculation time, which at a mere 55 seconds, will cause no one to grow impatient. All possibility of impatience may be eliminated by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A mixture of sun and clouds let just enough sun through to keep the fractal cats happy here at Fractal Central on Monday. The temperature of 66F 19C kept the people happy. My day was more than busy enough to keep me happy. The next ground-breaking, (I hope), FOTD will be posted in 24 hours. Until then, take care, and wait for something really new. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Bat-fractal { ; time=0:00:55.60-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.461660097395/-0.098463200739/2906449\ /1/-50/0 params=1.5/0/-16/0 float=y maxiter=1600 inside=0 logmap=68 periodicity=10 colors=000`ADcABfAJiARlAUoAYrAXuBOxCGrDFmDFhDEbEEY\ EDTEDOEDDZX3uz7tzAszErzHqtLpzOozSnzzmzqlzkkzijzViz\ UhzTVaSVYRVTQVOPVKOVFNVANV6LV8KV9zmcmmCGWDFWFEmGDW\ HCXJAXK9WL8WN7WO6WPATSERUIOXLMZPJ`THcWEe_Czc9zf7zj\ 4zn2zz0zr8zsFzzMztTzqSzzRzzQziQzgPzdOzbNz_NzXMzVLa\ SKeQKhNJkLInIHqGHtEFvDDxFEuGErIEoJElLEiMEfKEcPE`QE\ YSEVYJETESUEPWEMXEJZEG_ED2zh5ve7sc9paClZEiXGfVJcTL\ _QNXOQUMSRKUNHXKFZHDC`eEZbGX`HWZJUXLTVMRTOQRQOPRNN\ TLLVKJWIHYHF_FDomYkdSgWMcNGpU0oT1nS2mR2lQzkPzjOziN\ zhMzgLzfKzeJzdIzcHzbGzaFz`Ez0ez3cz5az7`z9ZzBXzEWzG\ UzISzKRzMPzONzRMzTKzVIzXHzZFzemzdkzdzzdzzdzzczzczz\ czzczzbzzbzzbzzbzzazzazzazzazz`zzzzEzzCzzIzzHzzHzz\ GzzGzzFzzFzzEzzEgzEfzDezDdzCczCbzBazB0z25z39z4Dz5H\ z6Lz7Pz8Tz9zzAzzCzzBzzBzzBzzBIzBMzBPzBSzBVzBYzBszi\ rzgqzepzcozanz_mzYlzXkzVjzTizRhzPgzNfzMezKdzIczGbz\ EazCOzdSzXVzQFzNGzKHzIIzF } 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 05-10-09 (The Forever Valley [No rating])
by Jim Muth 05 Oct '09

05 Oct '09

FOTD -- October 05, 2009 (No Rating) Fractal visionaries and enthusiasts: Yes, I know that today's FOTD is late, but I have an alibi. On Sunday FL was bitten by the antiquing bug, which sent us on a trip to an antique emporium in Bellefonte, which is 2 miles northeast of the geographic center of the state of Pennsylvania. Actually I'm glad we went. I found a 35-year-old 35mm SLR film camera in perfect working condition, offered for sale at $15. Film cameras are pretty much a thing of the past, but how could I resist such a bargain. The camera cost $250.00 new in 1974. Today's image lies in the fractal that results when the formula Z^1.5+C is calculated 16 levels down the logarithmic hyperladder and no function is applied. The parent fractal is shaped much like the minibrot at the center of today's image. The scene is located rather deep in a valley leading to a bud on the shore line of the main period-2 bud of the parent. Having put so little effort into the image, I was unable to give it a real rating, but considering the muddiness, a rating of a 5 would be about right. The name "The Forever Valley" is a poetic phrase. It has little connection with the actual appearance of the image. The calcula- tion time of 6-1/3 minutes is brief enough to keep doubts of the worth of the calculation at bay. And those who do not consider fractal calculation to be their cup of tea, may view the image effortlessly on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather here at Fractal Central on Sunday was a bit too cloudy for absolute perfection, but there were enough periods of strong sun to keep the fractal cats satisfied. My day was unexpectedly pleasing. The next FOTD is due to be posted in 8 hours. It might make it; it might not. Check then to find out. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Forever_Valley { ; time=0:06:20.58-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=+0.762519089/+1.109746278/5982/1/45/0 params=1.5/0/-16/0 float=y maxiter=16000 inside=0 logmap=-312 periodicity=10 colors=000P6DS9ITCNUFSVIWVHUXGSVFRTEPRDOOCMMBLKBJI\ AIG9GD8FB7D96C75A559HBESHIcMMzKQzYUzcVzmVzhWzcWzUX\ pUXnTYmTYkSZjSZgR_eR_bQ`_Q`UMaTJbSGcRDdQ9eQ6fP3gN0\ hK3UK6GKBNKFTKJZSNeKRzDVzCQzBMzAHz9Dz88S74N76O78P7\ AQ7CR7DS7FT7HU7JV7KW7MX7OY7QZ7R_6QX6PU5OS5NP5MN4MK\ 4LI4KF3JD3IA3I8BNEJRKRWQZ_Wfc`eeYegVdiSdkzcmzcoKbq\ HbsEbuC`zD_nzzzzzgzzzzV`zTYzSVzRREPOEOKENHELEEKAEJ\ 7EI4ECQN6kW8lYAlZCl_El`GlaIlbKlcMldOleQlfSlgUlhWli\ Ylj_lk`llckmejngjojipliqnhrqhssgtugtoioijkclgYmbTo\ ZNpVHrQBsM5uI0vE2pF3jF4dG5ZG6TH7NH8HH7b`6xtCrnHmiN\ hdSbZYYUbTP__QXfRUmSStTUqSVnRWkRXhQYfQZcP_`P`YOaWO\ ZYQXZSU`USaWPcYNdZLf`IgbGidDjfBlh9mi9nh9oh9og9pg9q\ g9qf9rf9sf9se9te9ue9ud9vd9zd8z`7zz7zz6zz6zz5zz5zzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 -- October 05, 2009 (The Forever Valley [No Rating])
by JimMuth＠aol.com 05 Oct '09

05 Oct '09

FOTD -- October 05, 2009 (No Rating) Fractal visionaries and enthusiasts: Yes, I know that today's FOTD is late, but I have an alibi. On Sunday FL was bitten by the antiquing bug, which sent us on a trip to an antique emporium in Bellefonte, which is 2 miles northeast of the geographic center of the state of Pennsylvania. Actually I'm glad we went. I found a 35-year-old 35mm SLR film camera in perfect working condition, offered for sale at $15. Film cameras are pretty much a thing of the past, but how could I resist such a bargain. The camera cost $250.00 new in 1974. Today's image lies in the fractal that results when the formula Z^1.5+C is calculated 16 levels down the logarithmic hyperladder and no function is applied. The parent fractal is shaped much like the minibrot at the center of today's image. The scene is located rather deep in a valley leading to a bud on the shore line of the main period-2 bud of the parent. Having put so little effort into the image, I was unable to give it a real rating, but considering the muddiness, a rating of a 5 would be about right. The name "The Forever Valley" is a poetic phrase. It has little connection with the actual appearance of the image. The calcula- tion time of 6-1/3 minutes is brief enough to keep doubts of the worth of the calculation at bay. And those who do not consider fractal calculation to be their cup of tea, may view the image effortlessly on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather here at Fractal Central on Sunday was a bit too cloudy for absolute perfection, but there were enough periods of strong sun to keep the fractal cats satisfied. My day was unexpectedly pleasing. The next FOTD is due to be posted in 8 hours. It might make it; it might not. Check then to find out. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Forever_Valley { ; time=0:06:20.58-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=+0.762519089/+1.109746278/5982/1/45/0 params=1.5/0/-16/0 float=y maxiter=16000 inside=0 logmap=-312 periodicity=10 colors=000P6DS9ITCNUFSVIWVHUXGSVFRTEPRDOOCMMBLKBJI\ AIG9GD8FB7D96C75A559HBESHIcMMzKQzYUzcVzmVzhWzcWzUX\ pUXnTYmTYkSZjSZgR_eR_bQ`_Q`UMaTJbSGcRDdQ9eQ6fP3gN0\ hK3UK6GKBNKFTKJZSNeKRzDVzCQzBMzAHz9Dz88S74N76O78P7\ AQ7CR7DS7FT7HU7JV7KW7MX7OY7QZ7R_6QX6PU5OS5NP5MN4MK\ 4LI4KF3JD3IA3I8BNEJRKRWQZ_Wfc`eeYegVdiSdkzcmzcoKbq\ HbsEbuC`zD_nzzzzzgzzzzV`zTYzSVzRREPOEOKENHELEEKAEJ\ 7EI4ECQN6kW8lYAlZCl_El`GlaIlbKlcMldOleQlfSlgUlhWli\ Ylj_lk`llckmejngjojipliqnhrqhssgtugtoioijkclgYmbTo\ ZNpVHrQBsM5uI0vE2pF3jF4dG5ZG6TH7NH8HH7b`6xtCrnHmiN\ hdSbZYYUbTP__QXfRUmSStTUqSVnRWkRXhQYfQZcP_`P`YOaWO\ ZYQXZSU`USaWPcYNdZLf`IgbGidDjfBlh9mi9nh9oh9og9pg9q\ g9qf9rf9sf9se9te9ue9ud9vd9zd8z`7zz7zz6zz6zz5zz5zzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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========================================= </HTML>

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FOTD 04-10-09 (No Discontinuities [No rating])
by Jim Muth 04 Oct '09

04 Oct '09

FOTD -- October 04, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image shows a minibrot on the main stem of its parent fractal, which is a Mandelbrot set about 1000 times the size of the true M-set. Today's scene lies at -1749 on the stem, at a depth where the minibrots look like those of order 2.5. But unlike true Z^2.5 minibrots, there are no discontinuities around today's minibrot. Creating fractional minibrots without discontinuities is the main feature of the DivideBrot series of formulas. I could give no rating to today's image, especially since it takes a longer-than-usual 7-1/2 minutes to calculate. But the calculation may be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A perfect early Autumn day here at Fractal Central on Saturday was thoroughly enjoyed by the fractal cats, who spent several hours in the sun. The temperature of 72F 22C made the day ideal for humans as well. For me the day was near average, which is peaceful but un-interesting. The next FOTD is due to be posted in 24 hours. With only a little luck it will actually appear as planned. Until then, take care, and look up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= No_Discontinuities { ; time=0:07:38.30-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=DivideBrot6 center-mag=-1749.639999374\ 908/0/9.060976e+009/1 params=2/3/1000/10000000 float=y maxiter=12000 inside=0 logmap=-1850 symmetry=xaxis periodicity=10 mathtolerance=0.05/1 colors=000WJ4VK3VL2UM1UN1SO2RP2PQ2OQ2MR2LS3JS3IT3G\ U3FU3DV4CW4VM4YM47P46Y49X7CX9EXCHXEJWGMWJaQL`RNUSQ\ WVSZVV`VXcVZfVahQckUemUhpUjtWnrUllLkkQjmQilPhjOghK\ fgLeeKddIcbHb`G`_E_YDZXCYVAXT9WS8VQ6UP5TN4SM4RM3RK\ 9UJEXIJ_GPbFUeEZhE`jDckEejFgiFhiGjhGkgHmgHnfIpeGrf\ IqeJpeKodLndMndNmcOlcPkcQjbRjbSibThaUgaVfaWf`Xe`Yd\ `Zc__b_YZb`b_beYdhWfkUhnSjqQltOmqNmnNmlNmiMngMndMn\ bMn_LoYLoVLoTKoQKpOKpLKpJJpGJqEJqBIq9Iq6It2Kq4Po5U\ m7Zk8chAhfBmdDrbEv_GzYHzWJzUKzRMzPNzNPzLQzISzGTzEV\ zCWzAXz9Wz9Wz9Wz8Wz8Wz8WzKFyFFzBEz5DzYnzZpz_qz`rza\ tzbuzcvzdxzeyzfzz7zzzzAzzAzz9zz9zz9zz8zz8zz8zz7zz7\ zz7zz6zz6zz6zz5zz5zz2zz5zz8zzBzzEzzGzzJzzMzzPzzSzz\ UzzXzz_zzbzzezzvzzgzzUzz5zzGzzRizanzklzikzhjzfizeg\ zcfzbez`dz_czZczWczUczRAzcBzdBzdBzdCzdCzdCzdDzdDzd\ DzdEzdEzdEzdFzdFzdFzdGzdGzdGzdHzdHzdHzdJzaLzZNzWPz\ UQzTRzTSzSTzSUzRVzRWzQXzQ } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 03-10-09 (Spidery Zodiac [6])
by Jim Muth 02 Oct '09

02 Oct '09

FOTD -- October 03, 2009 (Rating 6) Fractal visionaries and enthusiasts: Today's scene lies far out on the main negative spike of an oversized Mandelbrot set. Yes, I realize that the minibrots on the spike of the M-set are all quadratic, but though it looks like a Mandelbrot set, the parent fractal of today's image is a M-set only on the surface. In its depths it is a combination of quadratic and cubic elements, and with a magnitude of 10^10, today's scene lies deep enough to have cubic tendencies. Most of the effect was achieved by rendering the image with the outside set to 'tdis'. The rating of a 6 means I consider the image to be merely adequate. The calculation time of 19 seconds makes the trip to the FOTD web site hardly necessary, though the trip is always a lot more fun. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday here at Fractal central began with heavy clouds and light rain. The rain ended by 10am but the clouds remained throughout the day, holding the temperature to 63F 17C. The fractal cats passed the time wishing for sun. My day was close to average. The next FOTD will be posted in 24 hours. Until then, take care and don't be disappointed. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Spidery_Zodiac { ; time=0:00:19.07-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=NewDivideBrot function=recip center-mag=-999.9986621984146/0/9.90551e+009/1/90/0 params=3/500 float=y maxiter=62000 inside=0 outside=tdis periodicity=10 mathtolerance=0.05/1 colors=000zzfcMfcLbbLYbKUbJPbJLZNQVQVRU_OXdK`iGcnD\ frGeoIelLeiNefPdcSd`UdYWdWM`eCYn3VwATuHRsOPrVNpaLn\ gJmcQm`XmYcmVjmRmgNoaKqXGsRCuL9wG2GXENWPTW`_WkeWvk\ WmfSebPXYMPUIGPF8LC0H9HTCXdFVaIU_LSXPQUSORVqTjlXjh\ `icei_ihVmhRqhWmd_jacfZgcWk_ToXQsTNwQKJ_m_gaUlsWjr\ YhrZfq`dqacqZglXjgUmcSqZPtVuzzuzzHuOEpQAkR7fT4bUIi\ PWpLiwHhtJhqKhnLhkMhhNheOhTPhYQj`Xfhcuzzozp3ULEXGP\ _CQb8OdCDdGJeNPeUUe__efdelZboT`qNYtHWvGZtFasFcrEfq\ DipDkoDloDloEinEgnEenEcmEamFZmFXlFVlFTlFRkGEjGOkGM\ kGKjGIjGGjXZOVXQUVSTUURSWQQXPPZNN`MMbLKcJIeIHgHFi`\ zeZvfYsfXpfVmgUjgTggRdhQahPZhNWiMTiLQiJNjIKjHHj3tR\ 4qS5oT5mU6kV7iW7gX8dY9bZ9`_AZ`BXaBVbCTcDQdDOeEMfFK\ gFIhGGiltekrfjqfipfhofgmfflfekfdjgchgbggafg`eg_dgZ\ bgYahX`hW_hWYhVXhUWhTVhSTiKKKKKKPQiOPiNNiMMiLLjKKj\ JIjIHjHGjGFju1Qs2Rr2Sq2Sp3To3Tn3Um4Ul4Vk4Vj5Wi5Wh5\ Xg6Xf6Ye6Yk`Grh7maNhVadOp } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 02-10-09 (Infected with H1N1 [7.5])
by Jim Muth 01 Oct '09

01 Oct '09

FOTD -- October 02, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Today's little diversion holds both quadratic and order-10 elements. The overall pattern is typical of those in the East Valley areas of quadratic minibrots, but the 9-lobed minibrot at the center is clearly of order-10. I named the image "Infected with H1N1" becuase it shows an everyday scene in any quadratic East Valley infected with the Z^10+C virus. I chose the name because of the closing od several schools, where the students are coming down with the latest trendy influenza virus. After a modicum of indecision, I rated the image at a 7.5, the extra half point being for the extra 15 minutes or so of effort I put into the coloring, which BTW, was not achieved in a sepa- rate graphics program. The calculation time of 39 seconds is brief by any standards except for the lifetimes of some of the more exotic sub-atomic particles. But don't be a computer nerd, view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A mixture of sun and clouds made Thursday a rather scenic day here at Fractal Central, but the temperature of 55F 13C was just a little too chilly to enjoy the scenic conditions. The fractal cats spent the afternoon leaping onto their shelf when the sun appeared and leaping down when it went behind a cloud. My day was un-notable. The next FOTD will be posted in 24 hours. Until then, take care, and don't think about it, do it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Infected_with_H1N1 { ; time=0:00:39.59-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=NewDivideBrot function=recip float=y center-mag=-17.42830500282003/+0.01711881042215816\ /3.566635e+011/1/10/0 params=10/10 periodicity=10 maxiter=750 inside=0 logmap=82 mathtolerance=0.05/1 colors=000K4OJ6QI8SHAUGCWFEYEG_DIaCKcFNeEQgDTiCXlB\ `oAdr9hv8jzCkzFfvJarMXnQSjTNfWJa_FWbAQfAKiAFmACpHC\ sPCuUIvZOxeUyi_zmeyi_veVtaPrWKqSFpODpMCoLAoK9nJ8nI\ 6mJ5mJAnKKoKUpKcoKelLfiTgf_hcmi`zzzzzzzzhzzlmrjNnh\ RkgVheZddcazzZzzVzzSzzPzzSzzUzgWzcYz__zXbzTdzPfLLh\ KHjJElTJgaObjTYsYTqXSpWRoVQnUPmTOlSOkRNjQMiPLhOKgN\ JfNJhOIiPIjQHkRHlSGmTGnUFoVFpWEqXErYEqTJpPOoLSnGXm\ C`l8el4ij6fh8dfAbdC`cEZaGW_IUYKSWMQR2XO1ZL0_m`FmaE\ mbDmcCndBneAnf9ng8ng8pi9rkAtmBvnBuoCuoCuoCtoCtoDto\ DtpDspDspEspErpErpErqErqFqqFqqFqqFpqGprGprGprGorGo\ rHorHnsHnsHnsInsImsImsImtIltJltJltJztzztzzuzzuzzuz\ zuzzuzzuzzvzzvzzvzzvzzvzzvzzyzzvzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzIzzIzzIzzIzzIzzIzzI\ zzIzzIzzJzzJzzJzzJzzJzzJzzJzzJzzJzzJzzKzzKzzKzzKzz\ KzzKzzKzzKzzKzzKzzLzzLzzLzzzzbzzczzdzzdzzezzezzfzz\ fzzgzzgzzhzzhzzizzizzjzzj } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 01-10-09 (Basic and Basicer [6])
by Jim Muth 30 Sep '09

30 Sep '09

FOTD -- October 01, 2009 (Rating 6) Fractal visionaries and enthusiasts: Today's image is another hurried one, but still worth a look. It's a quintic Minibrot lying on the unusually ragged east shore of the large north bud of its parent fractal, which is a near- Mandelbrot set about 5 times the normal size. About the only thing going for the image is the ring of 25 red- yellow highlights surrounding the four-lobed minibrot. These mostly-accidental highlights earned the rating of a 6. The name "Basic and Basicer" makes about as much sense as spending over an hour every day searching for fractals and writing about them. Actually, the name is also the names of the Fractint formula files I use most often. In keeping with a hurried day, the included parameter file runs in a lightning fast 53 seconds, so no time will be wasted doing something for nothing. But why not do something for something and hurry out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image there. Tuesday was cloudy and blustery here at Fractal Central. Wednesday was only slightly less blustery, with a temperature of 61F 16C. The fractal cats disapproved of both days. In my department both days were busy. The next FOTD will be posted in 24 hours, give or take a few. Until then, take care, and be a fractal whisperer. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Basic_and_Basicer { ; time=0:00:53.02-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=NewDivideBrot function=recip inside=0 center-mag=-0.1500974292445382/+3.620143085850874/\ 3.17549e+010/1/-5/0 params=5/5 float=y maxiter=1500 logmap=81 periodicity=10 mathtolerance=0.05/1 colors=000CCSEEUFFWGGYHH_IIaJJcKKeMMgOOiQQkSSmUUoW\ WqYYs__uaawccxhhymmzrrzvvzzzzzzzzzzzzzzzczvOzmezbS\ zSFvH2rDHmAVh8Xc6ZZ6aU6UPBKKMANXKIimDozTrzTtzSvzSz\ z_zzeTrWVmNZcXbUYfKZeDSbFL_Hm2VdARWIONQLcLyVPjMTWQ\ `Fl`Jl_ImYHnXGnWFoUEoTDpSCqQBqPArO9sM8sL7tK6vF2tJ5\ rN8zRBnVEzZHjbKzfNfjQznTbrWzvZazazy`Xy_zyZSxYQxYzx\ XMxWzwVHwUzwUCvTzvS8vRzzP4xQzvR8uSzsTBrUzpVFnWGmXI\ kYKjZMh_Ng`PeaRcbTbcU`dW_eYYf_bdZXfYRhaKmLoaNjcQed\ S`fVXhXSj_NkaImdDou3yp5vk7sf9paBmXDjSEhzGeIIbDK_8M\ XzNV4OU5OU6OTzPT7PT8PS9QSzQRAQRBRRzRQCRQzSPESPzSPF\ TOGTOzTNHUNIUNzUMJVMKVMzVLLWLMWKzWKzXzOXzPXzzYzQYz\ RYzzZzTZzTZzz_zV_zV_zz`zX`zz`zYazzaDzazzZDz`zzaDzb\ zzcDzdzzeDzfzzgDzhzziDzjzzlDzmzznDzoDzpDzqDzrDzsDz\ tDzuDzvDzwEzwEzwEzwEzwEzwEzwEszEszErzErzEqzEqzFqzF\ pzFpzFozFozFnzFnzFnzFmzFmzFlzFlzGkzGkzGkzGjzGjzGiz\ GizGhzGhzGhzGgzGgzHfzHfzH } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 29-09-09 (3-Way Intersection [6.5])
by Jim Muth 28 Sep '09

28 Sep '09

FOTD -- September 29, 2009 (Rating 6.5) Fractal visionaries and enthusiasts: Things are rather rushed here at FC today, so the discussion will be short, leaving the image to speak for itself. The image, which shows a cubic minibrot lying in the Scepter Valley of its Mandelbrot parent, rates a 6.5. I don't know why I added the extra half-point. The coloring is not that great. The name "3-Way Intersection" has nothing to do with traffic engineering. It refers to the cubic nature of the scene. The calculation time of 1-2/3 minutes will keep the doctor away, but the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image there, will even pay the doctor's bill. Monday started sunny here at Fractal Central, but by mid-morning clouds moved in and by noon moderate rain was falling. The rain culminated in a sharp heavy shower around 2pm, followed quickly by a clearing and brisk wind. The temperature of 70F 21C was near ideal. The fractal cats noticed the changes and then went back to sleep. My day was as usual. Due to a work-connected trip on Tuesday, there will be no FOTD for September 30. The October 1 FOTD will be posted on schedule. Until then, take care, and be somewhat enlightened. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= 3-Way_Intersection { ; time=0:01:40.39-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=NewDivideBrot function=recip center-mag=-3.581162722144/+0.066980258199/2754663\ /1/57.5/0 params=3/3 float=y maxiter=1800 inside=0 logmap=171 periodicity=10 colors=000oU7pW7qY8r_9saAtcBueCvgBwiCvgCueCscDraDq\ ZDoXEnVEmTElREjOFiMFhKFfIGeGGdDGbBHa9H`7Hb2J_5HX7G\ U9FSBEPEDMGCKIBHKAEN9CP89R76T64V56U78U8AT9CTAESCGS\ DIREKRFMQHOQIQPJSPKYQKUPLQPLNPLJOMFOMCOMzzNzvNzrNz\ mKzkHziEzgCzeDzcEzaEz_FzYGzWGzUHzSHzQIzOJzMJzKKvIK\ rCImBGhAEc9Ca8A`7A_6AZ5AY4AX3AW3AV5AU6AT7AS8AR9AQA\ APBAKCAFDAEEAFFAFHAGIAGJAHKFHLKIMPINUJOZJPcKQhKRmK\ TeKU_KVTKWNKXGKYAL_3KZ4KY5KX6JW7JW7JV8IU9ITAITAHSB\ HRCHQDGQDGPEGOFFNGFNGFMHELIEKJEKJHJIJIHLHHNHGPGGRF\ FTEFWEEYDE_CDaBDcBChFCmKBrPBvUAzZAzc9zh9vc8rU8mK7h\ CKcEUZG`XIzUKzRKzPKzMKzJIzHFzEDzBBz7Az99zA9zB9XC9W\ E8UF8TG8SH8QJ8PK7NL7MM7LO7JP7IQ6GR6FT6DU6CV6BW59Y5\ 8Z56_55_33`54a74b95cB5dD5eF6fH6gJ6hL7iN7jO7kQ8lS8m\ U9nW9oY9p_AqaArcAseBtgBviAukBumBuoBuqCusCuuCuwDvxD\ wyDxzEyzEzzEzzFzzFzzFzzGzzHzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 28-09-09 (Spiderwork Minibrot [7])
by Jim Muth 27 Sep '09

27 Sep '09

FOTD -- September 28, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the same parent fractal as yesterday's image. Its exact location lies in scattered debris near the X-axis in the vicinity of Seahorse Valley. Most of the scene consists of inside stuff in the shape of circular rings made visible by rendering the image with the inside set to 'fmod'. The name "Spiderwork Minibrot" refers to the lacy network of debris filling the frame. The rating of a 7 seems about right. The calculation time of 9-1/2 minutes may be cut significantly by rendering the scene with the 'passes=g' option in effect, though doing so will tear apart the lacy network. All these difficulties may be eliminated however by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday morning rain here at Fractal Central ended with a heavy shower at 3pm, followed by a clearing sky. The fractal cats enjoyed the few minutes of sun that fell on their window shelf. My day was average, which means there was nothing worth mention- ing. The next FOTD will be posted in 24 hours. Until then, take care, and be sharp. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SpiderworkMinibrot { ; time=0:09:27.15-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=NewDivideBrot function=recip passes=1 center-mag=-2.145015465107/+0.013780976681/4991130 params=3/3 float=y maxiter=1500 inside=fmod logmap=yes periodicity=10 colors=00083C83AB2IE2PG1WJ1bL0iO0pQ0wP5tO9rOEoNImN\ MjMRhMVeLZcKc`KgZJkWJpUItRIxPLsOOoOQkOTgNVcNY_N`WM\ bSMeOMgKLjGLmCLo8Kr4Kt0Km4Ig7GaAEWDCQGBKJ9EM78P52S\ 41V31X31Z31`31b2zzzzzzzxmzvcztUzrKtpAmn4cl6Uj9KhBE\ fDGdGJbIL`KOZNQXPTVSVTUYRW_PZbN`dLbaO`_Q_XSYVUXTWV\ QYUO_SMaRO_SQZTSYUUXUWVVYUW_TWaSXcQYePYgOZiN_kL_mK\ `oJaqIalKYhMVcOS_POVRLRTIMVFIWBDY89_55`2Bc6HeAMgES\ iHYkLbmPhoTmqWloVknUjmUjlTikShjShiRggQffQeePedOdcO\ cbNcaN69j7Fd8L_9RVAXQBbKChFDnAEt5Ey0Ds5Dn9DhDCcICY\ MCTQBNVBIZBDbEEcHEcJEcMEcOEcREdTEdWEdZEd`EdcEeeEeh\ EejEemEeoEekNdgVccbc_jbWrbtFVnGXiHZdI`_JbVKcQLeLMg\ GNiBOjDPkFQlHQlJRmKRmMSnOToQToSUpTUpSVrSWsUZrWarYd\ r_grajrcmreprgsrivrkyrjwpiuohsmgqlfojemidkgcifbgda\ ec`ca_a`Z_ZYYYXWWWUVVSTURSTSVTSYTS_TSbSSdSSgSTiSTl\ RTnRTqRTsRTvRTxPQqOOjNLdLJYKGSJELHBFF8kE7hE7fD7cD6\ `C6YC6WB5TB5QA4NA4L94I93F } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 27-09-09 (Absolute Minimum [7])
by Jim Muth 27 Sep '09

27 Sep '09

FOTD -- September 27, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image is late for the usual Saturday reasons. It's a scene deep in a spurious valley on the negative X-axis of the parent fractal, which is an oversized Mandelbrot set just starting to change into a Z^3 Mandeloid. The rating of a 7 is what I consider the image worth; the name "Absolute Minimum" means almost anything one may wish. The calculation time of 7 minutes will pass like a freight train, so why not side track the train by viewing the finished image on the FOTD web site at. <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Morning clouds gave way to steady afternoon rain here at Fractal Central on Saturday, while the fractal cats' hope gave way to disappointment. The chilly temperature of 59F 15C added to their discomfort. My day was somewhat below average yet not too bad. The next FOTD will be posted in about 8 hours. At least I hope so. Until then, take care, and check back here later. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Absolute_Minimum { ; time=0:06:59.30-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=NewDivideBrot function=recip float=y center-mag=-3.866279368698615/-0.00000085627868251\ /9.63e+011/1/-90/0 params=3/3 mathtolerance=0.05/1 periodicity=10 maxiter=3200 inside=0 logmap=847 colors=000veKpdKkcKgbKeaKc`Ka_KbYKcWKdUKeSKfQKgOKh\ MKiKKiILiGLiDMhBMg8Mg6Ng3Nf1Nd2Md3Mc3Mc4Mc5Mb5Mb6M\ d7Lg7Lh8Li9Lh9LhALhALeFKcKJ`OJYTIWXHTaHQeGNjFLnFNh\ JObMPYQQSTRMWSH_TBbU6eTOUSdITeLUfNVfQWgSWgUXhXYiZZ\ ia_jc_jeZldZncZpbZrbZtaZv`Zx_Zz_WwWTtTQqQNnNKkKHhG\ EeDBbA8_76X48Z8A`BCbEEcHGeLIgOKhRMjUOlXQn`SocUqfWs\ iXtlYpkZmk_jj`gjacib`icYhdVheRhfOggLghIfiEfjBek8el\ 5e_`lSJOL10K44J78zzCzwFztJzmNzcQzUUvPYmR`cPYUNWKLT\ CJRBHOBGMCILDKLEMKFNKGPKIRJLTJOUIRWIUYIX_H_bHbeGeh\ KhkOknSnqWqt_tucrugqsjoqlmoolmrjkuiiwfftcdq`bnY`lV\ ZiSWfPUdMSaJQZHOXKMVMLTPKRRJPUHNVGLXFJYEH_CF`BDcAB\ e99g87hCCiFGjJLjMPkQUmTYoXap_frcjzzzzzzzzzzzzzzzn`\ zlVzjPzhJzfDzdezbJc`PP__AZZFYYKXYOVZPTzPR_zP`QNazL\ aRKbRIczGcSEdTCezAeU8fz7zU9czB`zDZzEzzGUWIRzKPXLMz\ NKzPHYQFzTHzVJ_XLz_NaaPzcRzeTzhVzjXzlZzn`zqbzszzuf\ zwgzqizlkzflzanzTrzNgzHXz } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 26-09-09 (Wheel in the Sky [8])
by Jim Muth 25 Sep '09

25 Sep '09

FOTD -- September 26, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's hasty image combines various unlikely negative portions of Z^(-1.05) and Z^(-5.5). When (1/C) is added, the resulting parent fractal is a grossly oversized thing consisting of a nearly circular main bay with a kind of dimple on its eastern edge. Today's image is located in a bit of fractured chaos in the vicinity of this dimple. The extreme magnitude of the image makes the mathtolerance entry necessary. The name "Wheel in the Sky" was the first phrase that came into my head when the time came to name the image. It might also be the name of an old song. The rating of an 8 indicates that I think the image is pretty good. The calculation time of 8 minutes is slightly dragging, but the trip to the FOTD web site, where the finished image is posted, is much faster. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A sunny day with a temperature of 70F 21C was just what the fractal cats ordered here at Fractal Central on Friday. They were totally satisfied with the afternoon sun. My day was rather busy but otherwise acceptable. The next FOTD will probably be posted in 24 hours. Until next time, take care, and it's double or nothing. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Wheel_in_the_Sky { ; time=0:08:04.83-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-3.216611489264435/+0.5748460602506144/\ 2.053771e+012/1/51.5/0 params=-2.475/-1.05/-0.275/\ -5.5/0/0/0/0 float=y maxiter=12000 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000hfcfdbecadb`ba_a`Z`_YZZXYXWXWVVVUUUTTTSS\ SRQRQPQPOOOMNNLMMKLLIKKHJJGIIFHHHJJJLKLMMMONOPOQRQ\ RSRTUSVWUWXVYZW__YaaZbb_ddaffbggciielkgnniqpltsnww\ wxxxyyyzzzyyysssrrrmmmmmmamlemljmlnhlrhlmhlihmfhmc\ hm`imYimVinSjnPjnLjnIknFkoCkp9lq6lr3ms0nt2nu4nv6ow\ 8oxAoyCnzElzFjzHiyJgwLfuNdsPcqRcoSbmUamWamY`m__ma_\ mcZmdZmbYlaXk`Wj_WiZVhYUgXUfVTeUSdTScSObRQaQM`PF_N\ LZMAYLJXKAWJHTIAUHARGASDA9FACHFFKGKMHPRIUUKZYLc_Lh\ cMmfMrhNvjNzmOzpOzsOzvOzuOzlHtgGobFiYEdTDZOBUKAOG9\ JC8D87846355555655855955A55C55D54F54G54H54J54K54M5\ 4N54OA8PFCQKGRPKRUOSZSTcWUgZUfYTfYTb_W_`YWa_TcbPdd\ MefBSIBTJBUJAUKAVKAWLAXLAXLBWMCVNCUNDTODSPERPEQQFM\ RGIR0ES0AT00T00P00A00Y00A00c00ALEmMDZMCmLDYKUzJDYJ\ EmIEYHUzGFXGFmFFXEUzDGXDGmDESDDmDCmDBmDAmD96D82F76\ H79J6CL6FN5IP5LR4OT4RV3UX3XZ2_`2bb1ec1hb3ga5f`7e_8\ d_AcZCbYEaXFaeRSfVVgZYhb` } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 25-09-09 (TDIS For All [8])
by Jim Muth 24 Sep '09

24 Sep '09

FOTD -- September 25, 2009 (Rating 8) Fractal visionaries and enthusiasts: I was playing around with one of the older MandelbrotBC formulas (MandelbrotBC2) on Thursday when I came up with today's surpris- ingly good image. It is so good in fact that I crowned it FOTD for Sep 25. The parent fractal is a Mandeloid of the formula Z^(1.99)+C, as it appears 10 levels up the logarithmic ladder. This parent is a slightly distorted and rotated Mandelbrot set. Today's image is located in the Seahorse Valley of its parent. The striped effect was achieved by rendering the image with the outside set to 'tdis'. The 'tdis' outside also inspired the name "TDIS For All". The rating of an 8 is a fair comment on what I think of the image. The calculation time of 1-2/3 minutes will waste no one's time, that is unless they are totally disappointed with the result. The way to eliminate all risk of wasted time is to view the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday appeared to be a loss until 3pm, when the sun suddenly burst through the clouds just in time to give the fractal cats their hour in the sun. The temperature of 77F 25C could hardly have been better. My day was average, with little more to be said about it. The next FOTD will be posted in 24 hours. If it does not appear as scheduled, you will know it did not make it. Until next time, take care, and ponder the improbable. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TDIS_For_All { ; time=0:01:41.79-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=-0.7431880192\ 1538760/+0.00305014005282306/1.955000e+011/1/11/0 params=1.99/0/10/0 float=y maxiter=1200 inside=0 passes=1 outside=tdis periodicity=10 colors=000883TISmSoRhq5ys4pl3gf2Z_2QU1HN08H00B77DE\ EELLGSSHZZIbWKeULiRMlPNoMPsKQvHRyFSlWFfTF`QFVNFQKF\ KHFEEF8BF39F2RM1gT1xZHUvQSuZRtfQtdUpcYlb`hadd`h`_k\ XZoTYrP_sOatNcuNdvMfwLhxLjyKkzKijNgWQeGTc1V_7WWCWS\ HWPNWLSWHXUEaUC_UBXmAUm9Rh8Oc7LZ6JU5HP6GK7FE8EG9DH\ ACJCBLDA0EA0FA0GA0HA0IA0JA0IE0II0IL0IP0ITQcWPc_Ozc\ NzfMzjLzmKzoPUqU_rZetbkugqwlvxpstqpqrnmrkjsigtfctd\ `uaYuZUvXRwUNwSKzPHzNDzKAzI7zOEzTKzYQqcXohblmhzrnz\ pnzonznnzlnzknzjnzhkzfhzdfzbcz``zZZtXWtVTzTRzROzPL\ zNJzLGzJDzHBzJCzKCzLDzNDzODdPEbRE_SEYTFVVFSWGQXGNZ\ GK_HI`HFaHDgx2OsB4oK8pKCpKGpKJqKNqKRqKVrKYrKarKesK\ isKlsKptKttKwtKrrInpHjoGfmFblEYjCUiBQgAMf9Id8Ec7I_\ BLXFOTISQMVMQYJTWGRUEPSCNQAMO8KM6IL4HQBMVHQ_NUdUZi\ _bmefkjYjoPbggV_zTXwSVtQSqPQoOUhNYaMaVMePBhe1juFkn\ SlhemarnWqlSqkOqiKphGpfCpe9uBonHmgNl`TjUZiNdgGjf9p\ d2vc1rf1nhHrbXuXkxSpRNUHD } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(p/(2*PI)), r=real(p2)-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 24-09-09 (Bubbles in the Blue [9])
by Jim Muth 23 Sep '09

23 Sep '09

FOTD -- September 24, 2009 (Rating 9) Fractal visionaries and enthusiasts: A FOTD fractal with a rating of a 9 is a rare beast, but today we have one, a welcome relief from the string of 6 and 7 rated images. The parent fractal came about when I subtracted 0.2 part of Z^(-7) from 0.2 part of Z^3 and added (1/C). This parent resembles nothing as much as a network looking like an overdone pancake with various shaped holes scattered about. The largest hole is a twisted Mandelbrot set with a wedge pointed at its East Valley. Today's scene is located on the shoreline of this wedge. The unusual effect was achieved by rendering the scene with both the outside and inside set to 'fmod' with a proximity of 1. The image is divided about 50-50 between inside and outside parts. One glance at the image will show why I rated it at a 9. A second glance will explain the name "Bubbles in the Blue". The calculation time of just over 1 minute will make taking the glances a very brief task. But there are always those overquali- fied computers that will not run DOS fractint. Those with such units may view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> My Wednesday ponderings were on the four-dimensional phenomenon known as double rotation, where an object such as a hypersphere may be subject to two totally independent and distinct rotations at the same time. Of all the unvisualizable things possible in 4-D space, this is perhaps the most intriguing, for unlike most other 4-D stuff, it has no analog in 3-D space. Morning sun gave way to afternoon clouds here at Fractal Central on Wednesday, while the temperature reached a summer-like 82F 28C. The fractal cats are still more concerned with their power- ful new catnip rats than the weather. My day was about average. The next FOTD will be posted in 24 hours. Until then, take care, and what we need is a fractal tea party. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Bubbles_in_theBlue { ; time=0:01:07.12-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.110714075944/+0.083632827962/4955856\ /1/87.5/0 params=-0.2/-7/0.2/3/0/0/0/0 float=y maxiter=500 inside=fmod proximity=1 outside=fmod logmap=yes periodicity=10 colors=000zzzvyvrxrmwmhvmcumZtmUsmPrmKqmFpmAom6nm6\ mm6mm6mm6lm6lm6km6km6jm6jm6im6im6hm6hm6gm6gm6gm6fm\ 6fm6fm6fm6em6em6em6em6dm6dm6dm6dm6cm6cm6cm6cm5bm5b\ m5bm5bm5am5am5am5`m5`m5`m5`m5_m5_m5_m5_m5Zm5Zm5Zm5\ Zl5Yk5Yj5Yi5Yh5Xh5Xh5Xh5Wh5Wh5Wg5Wf5Ve5Vd5Vc5Vb5Ua\ 5U`5U_5UZ4TZ4TZ4TZ4TZ4SZ4SZ4SZ4SZ4RZ4RZ4RZ4QZ4QZ4Q\ Z4QZ4PZ4PZ4PZ4PZ4OZ4OY4OY4OY4NY4NY4NY4NY4MY4MW4MW4\ LW4LV4LU4LU4KT4KT4KS4KR3JR3JR3JP3JO3IN3IM3IL3IK3HI\ 3HG3HE3HC3GB3GA3GA3FA3FA3FA3FA3EA3EA4EA6EA8DBADCCD\ DEDEGEFIEFKEFMEFOFFQFFSFFUFFWFFYFF_FP`FPaFPbFPcFPd\ FPeFPfFPgFPhFPiFPjFPkFPlFPmFPmCQnEPnFPnGPnHPoJOoKO\ oLOoMOpNOpPNpQNpRNqSNqUMqVMqWMrXMrYMr_Lr`LsaLsbLsd\ KseKtfKtgKthKtjJukJulJumJupIvsIvvIzzmzzzzzmvvItrIs\ oIrmIpkIoiImgIlfIkdIibIh`IgZIeXIdVIbTIaRI`QIZOIYMI\ WKIVIIUGISEIRCIQBISCHTDGUDGWEFXFFYFE_GE`HDaHCcICdJ\ BpKMnKNmJOlJPjIQiIRgHSfHT } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 23-09-09 (Agitated Iterations [6.5])
by Jim Muth 22 Sep '09

22 Sep '09

FOTD -- September 23, 2009 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image is a scene on the infinitely fractured main negative stem of the Z^(2.001)+C Mandeloid as it appears at ground level of the logarithmic ladder when no function is applied. The precise location is in the East Valley of the large minibrot on this fractured stem. The name "Agitated Iterations" sounds like much but means nothing. It was the first thing that came to mind when I put my brain into idle, which I often do. The rating of 6-1/2 includes a 1/2 point bonus for about 5-minutes extra effort I devoted to the coloring. The calculation time of 1-1/2 minutes is close to average. The trip out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image may be seen instantly, is always average. My ponderings for Tuesday were largely upon the degrees of freedom in the fourth dimension. As is usual, I came to no conclusion, but it was a lot of fun. The gloom brought on by the heavy clouds here at Fractal Central on Tuesday was mitigated by the dry weather and a pleasant temperature of 77F 25C. The fractal cats spent the day worrying about the fresh new catnip rat. They were unconcerned with the lack of sunshine. My day was normal. Unless the world ends, the next FOTD will be posted in 24 hours, and it is likely to be a fractal never before seen in the entire history of human investigation. Until then, take care, and where will all the fractals go when the power goes off? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= AgitatedIterations { ; time=0:01:33.85-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=-1.748190276984/+0.019122558784/5e+007/\ 1/-105.5/0 params=2.001/0/0/0 float=y maxiter=1750 inside=0 logmap=168 periodicity=10 colors=000UJdTIcSHbRGaQF`PE_ODZNBYM9XL7WK5VE0U90T3\ 0P00K00F00A005000000000000000000gW7jV8lU9oTAqSBtRC\ vQCpXGkcKejO`qRbnPdlOfiNhgLjdKlbJm_HoYGqVFsTDuQCwO\ BxMAsz7nz4kv8hr8fo8dl8bi8`f8Yc8W`8UY8SV8QS8OP8NNDN\ LPMJUMHZLFcLDhKBmKKrJNzJUzIZzIYzMRvPNrT9nWBi_DfbFc\ fH_iJXmLUpNQtPNwRKvQLvPLuOLuNMtMMtLMsKNsJNrINrHOqG\ OqGOsMPuSQwXRybSzgSj_ZWSdVReVQeVPeVOeVNeVMfVLfUKfU\ JfUIfUHgUGgUFgUEgUDgRFcOG_LIWJJTLLUNMVPOVRPWTRWVSX\ WTXYVY_WZaYZcZ_e`_ga`hb`lUeoLjrCnnIkjOhgTecZb`d`Xi\ YUoVQuSNzQcxJtwCqvEnuFkuGitHfsJcsKarLZrMWqOUpPRpQO\ oRMnTJnUGmVEmWCsbAxhCwiEwjFwkHwlIvmKvnMvoNvpPuqQur\ SusTusPppMkmIfkFahBXe8Sc4N`1IZ6P`BVbG`dKffPlhUrjYx\ lawcevWiuNltFmqHmnJnlLniNngPodQocSodUpeWpfYpgZkhYf\ iXbjXYkWUlWYmV`nVcoUgpUjqTmrTjsVgtXduZbv`_wbXxdUyf\ SzhUziWzjXzkZzl_zlazmczndzofzpgzpezqdzrczrazs`zs_z\ tZztXzuWzuVzvUzvSzwbz6dz6 } 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 22-09-09 (Something Else [8])
by Jim Muth 21 Sep '09

21 Sep '09

FOTD -- September 22, 2009 (Rating 8) Fractal visionaries and enthusiasts: Due to a lack of time, today's discussion will once again be short. The parent fractal is the same as yesterday's but the scene has shifted to a blunt valley of a large hole just to the northeast of its main bay. I named the image "Something Else" because it's something else in the same fractal. The rating of an 8 might stretch the worth a bit, (Is the image really better than yesterday's?). The minibrot at the center does strike me as above average for the Z^1.9 range however. The calculation time of 1-1/4 minutes will pass in a flash. The trip to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will pass in a flash also. The clouds moved in fast here at Fractal Central on Monday, though the rain held off until well after dark and the temperature reached a pleasant 75F 24C despite the lack of sun. The fractal cats ignored the weather, enjoying instead the fresh catnip rats we picked up on Sunday. Cassie got a bit tipsy. My day was uneventful; even the work was humdrum. If nothing unexpected comes up first, the next FOTD will be posted in 24 hours. Until then, take care, and after listening to the 'music' blaring from a passing car this afternoon, I am left to wonder why the young people of today seem to enjoy being kept angry. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Something_Else { ; time=0:01:14.53-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=+0.71021616856/-0.05517047022/443232.9/\ 1/60/0 params=1.9/0/1/0 float=y maxiter=3200 inside=0 periodicity=10 colors=000bpGasEZoDWlCTiBRfAOc9L_8IX7GU6DR5AO48L4C\ K7FKAIKCMJFPJHSJKWIMZIPaIRbLPbOOcQMcTLcVJdYId`GebF\ eeDegCfjAfm9go7gr6gt5bmAYgFT`KOVPJPUEIZ9Cc46h85gB5\ fF4eI4dM4cP3bT3aW3aZ2`b2_e1Zi1Yl1Xp0Ws0Vv0Vr5To9Rl\ EPhIOeNMbRKZWJW_HTdFPhEMmCJqAGu9CnI8gQ4`Y7_V9ZTBYR\ DXPFWNGWTHWZHWcKVdMVdOVeQVeSVfUVfXVfZVg`VgbVhdVhfV\ hbYgZ`gVbgRegOhfKjfGmfCpf9rfAngAjgBfgBbgCZgCVgDRgD\ NgEJgEFgFBgF7gL9jRBlXDobEqhGsnIvtKxyLzwKwvJttIrsIo\ rHlpGjoFgmFdlEbkD_iCXhCVfBSeAPdANcDQcGScIVbLXbN_bQ\ aaTdaVfaYi`_k`bn`dpZfkXhgVjcTl_RnWPpRNrNLtJJvFHxBF\ z7RhKbRWgAggJ_`STU`LNszOuzPhPQgURlzSozTfiUeoSexWiy\ UdxScxQbwOawMavK`vI_uGZuEZuFXsGVqHToHRmIPkJNiJLgKJ\ eLHcMFaMD_NBYO9WO8UN7NN7HN7BMDELIGKOJJTLIYOHcQGhTF\ mVJiSNeQRaOUYMYUJaQHeMFhIDlEApA8t66w24s36o48k49g5B\ c6C_6EW7GS8HO8JK9KGAMCAO8BP4CR1CS5HV8LYBP`EUbHYeKa\ hNejMdgMceMbcMa`M`ZL_XLZU } 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 21-09-09 (On the Right Line [7])
by Jim Muth 21 Sep '09

21 Sep '09

FOTD -- September 21, 2009 (Rating 7) Fractal visionaries and enthusiasts: This FOTD is late because FL and I took an antiquing expedition to Lewisberry on Sunday. It's not an excuse; it's just an expla- nation of the lateness. Today's better-than-average image lies on a filament extending from the large period-2 bud of the largest minibrot on the main stem of the parent Mandeloid, which not surprisingly is shaped like the minibrot at the center of the frame. This parent was created when I calculated the formula Z^(1.9)+C at one level up the logarithmic ladder when no function is applied. Since time is at a premium, I'll let the image do most of the speaking for itself. (I think it's one that can speak for itself.) The rating of a 7 indicates that I consider the image to be worth the 1 minute, 33 seconds needed to run the included parameter file. The finished image may also be viewed already calculated on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> which is the simplest way to see the image, but I'm not sure you will hear it speaking for itself if you view it this way. Lots of sun and a temperature of 73F 23C here at Fractal Central on Sunday gave the fractal cats lots of time to stretch out and relax while we were away. The rest of the day was uneventful. The next FOTD will be posted as soon as I finish it. Until then, take care, and where does an event go after it happens? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= On_the_Right_Line { ; time=0:01:33.16-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=-1.102794620148859/+1.459219711739321/\ 6.156207e+010/1/30/0 params=1.9/0/1/0 float=y maxiter=2500 inside=0 logmap=126 symmetry=none periodicity=10 mathtolerance=0.05/1 colors=000_F_ZFZYFYXFXWFWVFVTFURFTOFRLFPIFNFFLCFJo\ _7aT8OM8C79BC8FTEGQDSOCaMBcKApI9azKXoISeGOZEJTCEMA\ zzKmjHWaELQBnp3UY6xY4gS6RM779q9DVnC8zP8mE8XE8RF8LF\ 8FG8SIkOHcKHWHGODGG8Nn9JTpNWVJKnNc`KTNIIC5moLlzHjx\ OewV`vaXthSsoNrvJmtMhsPcrSZqVUpYPo`LncUjYafTibNqZI\ yWDrSGkOIdKKYGMRCPK8RD4T71VFA`MJfURl`_rggwaemWccRb\ VNwiMrgLnfLjeKfdJbcJZbBI8GSSDMI9V7AT8AR8AP8AN8AL8A\ J8AH88jc9_TAQIRlVMcPIWJEODLHNIGKGGHEGECGB`axVXmQTb\ KOTFKIyOulMh_KXNIKem4`h5Wc6SZ6NU7JP7EK8bscXkcRccLW\ cFOcJZcHWcGUcFUcEUcDUcCUcBUcGUcEUcDUcBUcgUcbVcZVcV\ VcRWcMWcIXcEXcSYcPYcMYcKZcHZcFZcCZcocaQcfKcVFcJ`ca\ VcWQcQKcKFcEUcYRcUOcQLcMIcJFcFCcBzr4zl5zf6za6zz7zz\ 7zz8zzGzzDzzAzzVGrzFszEtzDuzCvzBwz0xz3yz5zz8zz8zz9\ zzxzz8zz8zz8zzzzEzzGzzGzzGzzGzzGzzGzzGzzGzzGzzFzzD\ zzCzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 20-09-09 (A Brief Diversion [6])
by Jim Muth 19 Sep '09

19 Sep '09

FOTD -- September 20, 2009 (Rating 6) Fractal visionaries and enthusiasts: Believe it or not, we're still in the same area of the same parent fractal. I don't seem able to let go of it and move on. The most interesting thing about this particular area is the unpredictability of the shape of the many minibrots, if they actually are minibrots, that is. The minibrot at the center of today's image however is an every- day Z^2 one, though it is invisible at the magnitude of today's image. Most of the action was achieved by rendering the scene with the outside set to 'tdis' and the inside set to 'atan'. I named the finished product "A Brief Diversion" and rated it at a very ordinary 6. The calculation time of just over 3 minutes borders on slowness, especially on clunkers. For those with clunkers or with over-qualified units that panic when they see the letters D.O.S., calculation may be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A totally cloud-free sky and temperature of 68F 20C made condi- tions nearly ideal for late summer here at Fractal Central on Saturday. The fractal cats took full advantage of the unbroken sunlight falling on their shelf in the southwest window. In my department, the re-do job has been redone and things have set- tled down to about average. The next FOTD is due in 24 hours. I give it a 75-percent chance of appearing on schedule. And a more careful calculation shows that we actually still have 1188 days before the world ends, presumably on 21 December, 2012. Until next time then, take care, and make fractals while the sun shines. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Brief_Diversion { ; time=0:03:09.77-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.372291100014543/-0.04221711007309\ /1.171e+008/1/58.5/0 params=1/4/2/3/0/0/0/0 float=y maxiter=1500 inside=atan outside=tdis periodicity=0 colors=0009j91q5PgJkZWgaSdcPaeLZgIWiFTkBQm8No5KkBI\ gGFdMD`RAXW8Ua5Qf3NkNZVTeUZlTcsSYlOTfLO`IJUEEOB9I8\ 7JdEPgKUiR_lXdncjzirzpzzzzzuwmunmufSh`YWVbJPg6JlG`\ 8Ke5Oj2So0XYIaGZ_F_ZE`XD`WDaVCbTBbSAcRAcZFceJclNcs\ RcddCYgKSiSMkZGnfApn4ru9nkDkbIhTMeKRbAV_1ZY5aW8eVB\ hTElSHoQKrPNlDRf1Uc6RmcYpWksPypUwmYukathfrfjqcnoar\ n`qk_phZoeYnbXm_WlXVkUVkSTeXR``PWeORiMMnKHrJCvXLdj\ TNw`6kWK`SXQOjFKwEOnDReDUXCYOB`FBc7KeCTgGaiKikOjfQ\ kaTkYVhSQfMMdGHbAD`59UARNEgHIxCozwxdbXQI6BO8JTAQZB\ YcDdiFlnGsjKngNjdReIWqGSqEOqDLqEOrFRsGTsHWtIKuJ`uK\ WoLSjLNeMJ`NFWNARO6MO2HOBQOKZOTgO`oC_d0ZUSWMsTFnQL\ jORfMXbKbZHhVFnRDtNByMGvMLtMPrLUoLYmLbkLfiFgnAhs9_\ p8jn8kl7lj7lh9mgBmgCngEngGnfHofJofKofUnQbnA`lG_kLY\ jQXhWVc`hFWTejLknDqr5vu7ed8PO35YF3_R1`PThOsoPljQee\ Q_`RTWSMRSGMYLabQqhOqnNqiOmePiaPeYQapUYPRULSQ0ZNKM\ MMGLOALb9Qq8VhGQ_OMRVIIbD } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 19-09-09 (Terrible Terraces [7])
by Jim Muth 18 Sep '09

18 Sep '09

FOTD -- September 19, 2009 (Rating 7) Fractal visionaries and enthusiasts: We're still in the same area of the same parent fractal of the past 3 or 4 days. The little minibrot at the center has been livened up by rendering the scene with the outside set to 'tdis' and the inside colored a brilliant white. The rating of a 7 is becoming so average that I might change the rating system to make such images rate an average 5 rather than an above-average 7. The name "Terrible Terraces" makes little sense, but then fractals and even life itself make little sense, so why not give the image such a name. The calculation time of 1-1/2 minutes is fast enough to prevent impatience yet slow enough for a bit of enjoyment. Total enjoy- ment may be found on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is posted fully finished for total satisfaction. Mostly sunny skies and a temperature of 77F 25C here at Fractal Central on Friday made up for the fractal cats' disappointment on Thursday. They enjoyed their sunny shelf to the maximum. My day would have been average if one of the customers had not unexpectedly added a full-page ad to his 16-page program, which made it necessary to re-work 8 of the 16 pages. When the late ad came in, I showed a bit of temper and FL asked if I thought my angry outburst would help the situation. When I said that temper displays only make things worse, she asked me why then was I wasting so much energy. I told her that I had gotten angry not to help things, but because we had to do half the already-finished job over, which put the discussion back where it started. To keep the argument from going in a circle, we let it drop and got to work, me grumbling and FL remaining silent. But I think I should have answered her with something like, "since you have reminded me that anger will do no good, I now realize that I am only making things worse. I have decided to calm down and do the job in a sensible manner . . . and after all, we *will* get extra money for re-doing half the job." Now that the silly "Dear Abby" style advice is out of the way, I must disclose the great news that the next FOTD is scheduled to be posted in 24 hours. But since perfect weather is expected on Saturday, do not be surprised if it fails to appear until some- time Sunday. Until whenever, take care, and I hear the world will end in 824 days. Hmmmm . . . maybe I'll do a count-down. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Terrible_Terraces { ; time=0:01:29.37-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.3519918957555/-0.0011234773843/\ 1.42084e+008/1/161/0 params=1/4/2/3/0/0/0/0 float=y maxiter=1500 inside=255 outside=tdis periodicity=10 colors=000VwHUuSTtbSrmRqxNnwJkwFhvBev7bvJWkVQ`eKRb\ PN_UKXZGVbDSg9Pl6Np3No5No7Nn9NnBSgJW`R_UZcNfgGnkAu\ eAo`AiWAcRAYMASHAMCAHSdfdefpefumkztpmjoaanQSmEcl2c\ k7UgBKdFH`KKYOMUSORWQOSRMPRLLRJIRIESGBSF7SD4SC9XHD\ `MIeQMiVRnZVrcZvgQqhHmh8ii0ei9imHmpQpsYtvewy_vlVu_\ QtNRoORkORgORcOR_ORWORSOROOZWNfcNnkNurNomQihTdcWZZ\ ZUUaOPdJKfFUfCcf9mfJneSodapcjqbsqamgUgZNaPFXG8fEOo\ CbxBqtDlpEglGbhHZdJU`KPXMKTNGOSNJWTE`_AdeFjdKpcOub\ LkVIaNFSFCI7A80BFBCMMDTWE_fFfpPUcZIS`ORaTQbYPcbOdg\ NelMfqLgvLWYTLA`ZR_kgZxxYpvUhtR`rOTqKLoHDmE5lB7mL9\ mUBmbCmkMpmWsodvqbxoazn`qj_if_`cZT_ZKXYCTY4QTBMOII\ JOEEVA9a64g2Bc9I`FPXMVUSaQYhNdoJjuGpqJknLfkNbhPYdS\ TaUPZWKWYGNSYENoJJqOGrTDtY9ub6wg3xl0yaBXSM5QP9ORDM\ UHLWLJYPH`TFbXEd_OcUXbOeaIn`Cw_7v`Jv`Vu`fu`rvZpvXo\ wVmwTlxRjxPiyNgyMfsJcnG`iEYcBWZ9TU6QP4OYF_fQjn`uA9\ MjzEVV`UWYT_WjrfetV`wIzzz } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 18-09-09 (Mass Confusion [None])
by Jim Muth 17 Sep '09

17 Sep '09

FOTD -- September 18, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image is the third in the same area of the same parent fractal. The confusion is obvious. The parent fractal came about when portions of Z^3 and Z^4 were mixed together, so where does the Z^6 minibrot on the left come from? And what is it doing right next to a Z^3 minibrot? This is not the only problem. On the filament connecting the two large minibrots lies another minibrot, this one a near- perfect Z^2 one. I'm not about ready to try to determine what's going on here. I simply think it makes a rather interesting image, interesting enough to be the FOTD for today. And I'll continue to examine this area in the next few FOTD's. Though I gave the image no rating, if I had rated it, I would have given it a rating around a 6. The name "Mass Confusion" refers to the puzzle of the wrong minibrots. The calculation time of an incredibly brief 21 seconds will make running the included parameter file almost a pleasure. For total pleasure surf to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. Far too many clouds were overhead here at Fractal Central on Thursday, and the temperature of 66F 19C was not quite warm enough for cat comfort. The additional problem of early morning rain made the day pretty much a bust. The fractal cats made the most of things but were obviously annoyed when the afternoon sun failed to warm their window shelf. My day was average. The next FOTD will be posted in 24 hours. Until then, take care, and search for the quantum solution. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mass_Confusion { ; time=0:00:16.22-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.352018653/-0.000853932/4434.36/1/72/0 params=1/4/2/3/0/0/0/0 float=y maxiter=1500 inside=0 logmap=22 periodicity=10 colors=00000000000000000000000000070370165B6AK5FU5\ Kb5OkDUmL_rTeu`oznwzzzzxrvsltogrj`pfUnbNmfQjiThmWe\ pYcgP`_HYS8VK0TH9XFH`DQdBYh9fl7np9pjBqeDs_FtVHuPJw\ KLxENy9RsFUmKXgQ_aVbW`eRehPdkOdnMdqLdh40Z5DP6PF7`N\ 8cV9fa9iiAlqBoxBr1Toeatb_l`ZeZXZXWSVVLTTERS7PR0ZU1\ cW1hZ2m`2r_5vZ7zYAzXCzWEzVHzUJzULzVKzWJzXIzYIzZHz_\ Gz`FzaFz`Gz_HzZIzYJzXKzWLzVLzXMzZNz_OzaPzcQzdQzbUz\ `XzZ_zYbzWfzUizSlzRozQjzPfzOazNYzMTzLPzLLzz_zzbzzf\ zzizzlzzpzzszzvzzrzznzzjzzfzzczz_zzWzzSzzOzzLzzHzz\ Dzz9zz6zzAzzDzzGzzJzzMzzPzzSzzVzzYzz`zlczofzriztlz\ uizvgzwezxczy`zzZzzXzzVzzTzzSzzRzzROzQQzQSzPVzOXzO\ ZzNazNczMezMfzNgzNhzOhzOizPjzPjzQkmQloRlqRmsQmuPnw\ PnzOozOozNpzNpzMqzMqzLrzLrzKrzKqzJqzIqzIqzHqzHqzGq\ zGpzFpzEpzEpzDpzDpzCpzCnzDlzDjzEhzEfzFezFczFazG_zG\ YzHWzHVzHWzKWzMWzOWzRWzTWzVWzYWz_WzaWzdWzfWzhWzjYz\ hZzf_zd`zbaz`bz_czYdzWezU } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 17-09-09 (Troubling Triumph [7])
by Jim Muth 16 Sep '09

16 Sep '09

FOTD -- September 17, 2009 (Rating 7) Fractal visionaries and enthusiasts: The name "Troubling Triumph" refers to my success in finding today's scene, which is interesting enough but has its problems. To start, it's a rather pleasant though slightly gloomy scene in the parent fractal that arises when Z^4 is mixed with twice as much Z^3. But look closely. The central quadratic minibrot lacks the usual 2,4,8... symmetry. In fact, the outer symmetry seems to be 6,12,... while within this range there is little symmetry at all. The whole affair is indeed a bit troubling, thus the name. The rating of a 7 continues the unbroken string of similar ratings. The little mathematical problem does not detract from the image, and with its blazingly fast calculation time of 23 seconds there is no reason to miss its curiosities. Those with not quite enough curiosity to set up and run the included parameter file may still see the image by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing it there. I was undecided whether to tackle science, religion, politics or the paranormal in my philosophical outburst today. On all these topics I have strong views, most of which are not very popular. So I waited for FL to say something that would get me started on one of them. When the day passed without a comment, I decided to write nothing. The clouds slowly thickened here at Fractal Central on Wednes- day, but the temperature reached 72F 22C and there was just enough sun at the right time of day to satisfy the fractal cats, who took turns on the shelf in the sunny southwest window. My day was appropriately busy. The next FOTD will be posted in 24 hours, with or without the accumulated wisdom of the better part of a lifetime. Until then, take care, and I wonder why different people accumulate such contradictory wisdom during their lives. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Troubling_Triumph { ; time=0:00:23.16-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.35203885984/-0.00077531473/322693.7/\ 1/-75/0 params=1/4/2/3/0/0/0/0 float=y maxiter=1500 inside=255 logmap=45 periodicity=10 colors=000d0Lc0Ma0N_0OY0PW0QU0SR1UO2WL3YI4_F5aA6c4\ 7e88cB7ZE5QI4LL2GO1BR06YUJdwWWkPgjbO_JGOC8C656E45C\ 34A338237125113001emaZdVSXPLPJEKC7G6mzzZkgQ_XHOM8C\ BrqQhhL__HRRDII8994m`rfWk`RdVNYPIRIDKC9D646dtfZl`U\ eWPZQKSLFLGAEA575BzL9oH7eE5VA3L71A3szJkqGchDW_AOR8\ GI5892RMyNJqKGiGDaDBVA8N65F327FI2CF1AC1791560230AM\ 08J07G06D05B0380250120JzkEj_9VO4FCrigjb`bWVVQPNJIF\ DC7669LF7HC6EA4A7375132NoZIdSDVL9KE4A7ejmX`cPSUGIK\ 89AtLCjHAaE8SA6J74932SEDLA9E76733qCfjA`c9WX7QR6LK4\ GD3A615JfeEWV9LL4AA4Vf3Q_2MU2HO1DI18C046TV0OQ0KM0G\ H0CD0880440rc1RK0GCmDAdA8X86P54G228`ZAVU8QP7LK5FF4\ AA2551cHpUCbK8QA4Dm2zP1V62Z51T41N31H20B105AHS7CL58\ E247QhmK_cFRUAIK59AvPfbGSJ8EpbHxGsU8S5OnUDgOAZI7QC\ 5H628mSyNEJF9C746h`X`URUOMMIGFCB765Gp5AZ35H1TWNOQJ\ JLFEGB9A7453xUvkOj_IZOCNC6BwmAof8h`7`V6UP5MI3FC2Pu\ WBtICnJDhJEbJFXJGRJHLJzzz } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 16-09-09 (Conquest of Infinity [7])
by Jim Muth 15 Sep '09

15 Sep '09

FOTD -- September 16, 2009 (Rating 7) Fractal visionaries and enthusiasts: Back in my wonder years I sometimes wondered how long it would take a space ship to reach infinity if it traveled at infinite speed. Sometime later I realized that the speed of light is in effect infinite speed, since at light velocity the spatial direction in which an object is moving contracts to zero, and the trip, however long from our viewpoint, is accomplished instantly. I have yet to decide how long it would take to reach infinity at the speed of light, but I now suspect the question is a wrong one, based on a wrong assumption. One thing certain however is that from a photon's point of view, the photon does not exist at all. However great the distance it travels from our point of view, in the photon's own world it is absorbed the same moment it is emitted. With a magnitude of over 2*10^(13), today's image is as close to infinity as one is likely to come with the MandAutoCritInZ formula and the Fractint program. The magnitude inspired the name "Conquest of Infinity". Luckily, the mathtolerance entry makes such an extreme magnitude reachable. There is a minibrot at the center, but it is far beyond resolution and I'm not sure of what order it is. The parent fractal has Z^2, Z^3, and Z^6 minibrots in the vicinity of today's image, so who knows what lies unseen in the depths. The rating of a 7 is above average. We have had many ratings of 7 recently, so many in fact that it is starting to become boring. The calculation time of 2-1/4 minutes is reasonable for those with some time to spare. Those with no spare time on their hands may escape the task of calculating the included parameter file and enjoy the image by viewing it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The next several FOTD's will explore some of the fractal craziness in the area of the parent fractal in which today's image lies. It makes no sense at all to see an order-6 minibrot in a fractal created by combining Z^4 with 2 parts of Z^3, but take my word, in today's parent fractal it does happen. Well, I guess anything is possible in the world of fractals. Sunny skies and a temperature of 79F 26C made Tuesday a near- perfect day here at Fractal Central. The fractal cats agreed, and if it had been a bit cooler, they would have spent the afternoon on the sunniest shelf in the southwest window. My day was average. With only a little luck, tomorrow will be the same. The next FOTD will be posted in 24 hours. Until then, take care, and all too often one man's wisdom is another man's nonsense. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ConquestOfInfinity { ; time=0:02:18.74-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.3517738391872782/-0.0010203750647082\ /2.23271e+013/1/-177.5/0 params=1/4/2/3/0/0/0/0 float=y maxiter=1600 inside=0 periodicity=10 mathtolerance=0.05/1 colors=00054G228`ZAVL8QJ7LI5FF4AA2551cHpUCbK8QA4Dm\ 2zP1V62Z51T41N31H20B105AHS7CL58E247QhmK_cFRUAIK59A\ zPfzGSc8EpbHxGsU8S5OnUDgOAZI7QC5H628mSyNEJF9C746h`\ X`URUOMMIGFCB765Gp5AZ35H1TWNOQJJLFEGB9A7c5czUzkOj_\ IZOCNC6BwmAof8h`7`V6UP5MI3FC2PumztICnmzhJEbmzXJGRJ\ HLJjEoiHjiJfhLbhNZgPVgRRcSN_TKWUGSVDMPKGKRAFY4Ad88\ _B7VE5QI4LL2GO1BR06YUJdwWWkPr4bO_JGOC8C656E45C34A3\ 38237125113001zm0zdVzXPzPJzGCz86gwrZkgQ_XHOM8CBrzQ\ hsL_fHRXDII8994m`rfWk`RdVNYPIRIDKC9D646dtfZl`UeWPZ\ QKSLFLGAEA575BzL9oH7eE5VA3L71A3szJkqGchDW_AOR8GI58\ 92RMyNJqKGiGDaDBVA8N65F327FI2CF1AC1791560230AM08J0\ 7G06D05B0380250120JzkEj_9VO4FCrigjb`bWVVQPNJIFDC76\ 69LF7HC6EA4A7375132NoZIdSDVL9KE4A7ejmX`cPSUGIK89At\ LCjHAaE8SA6J74932SEDLA9E76733zCksA`c9WX7QR6LK4GD3A\ 615JfeEWV9LL4AA4Vf3Q_2MU2HO1DI18C046TV0OQ0KM0GH0CD\ 0880440rc1RK0GCmDAdA8X86P } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 15-09-09 (Coming Together [7])
by Jim Muth 14 Sep '09

14 Sep '09

FOTD -- September 15, 2009 (Rating 7) Fractal visionaries and enthusiasts: A rather busy day on Monday here at Fractal Central means a short discussion and no philosophy. But today's image means a moment of fun, and the incredibly brief calculation time of 46 seconds means the fun will come with minimum effort. The image lies in the parent fractal that exists when the Z^2 Mandelbrot set is about half-way through the process of morphing into the Z^(4.5) Mandeloid. I will not try to describe the par- ent fractal, though I will comment that today's image is located in the infinitely divided network of filaments just east of one of the two main minibrots near the negative X-axis. The name "Coming Together" can mean whatever the viewer would like it to. The rating of a 7 means that the image is just enough above average to make it interesting. The 3/4 minute calculation time may be avoided by surfing out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and perusing the finished image there. Monday was a fair enough day here at Fractal Central, though a few too many clouds were overhead. The fractal cats approved of the temperature of 77F 25C but wanted more sun on the shelf by the window. My day was peaceful but rather busy. The next FOTD will be posted in 24 hours. Until then, take care, and keep asking the questions. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Coming_Together { ; time=0:00:46.35-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=NewDivideBrot function=recip inside=0 center-mag=-2.649698550476496/+0.1051131773869893/\ 1.197514e+013/1/-35/0 params=4.5/1.5 float=y maxiter=3600 periodicity=10 mathtolerance=0.05/1 colors=000muLoZeqDyySMpAch7d`5dU3dZDUcNKgWA_CadMTi\ VLndDlcetvhssZsqProFckuklVSASZKMeUGlcAZSrR`e`eTiiH\ rsR0izNSCY_9hf7Gsgei9qJOrUHrcB4l4Hm5Um5fm5FT6T_5ef\ 5DO`RXQdeFZRIB_oQd_diK6O9V`7L9fUKXaUOjcEUDm`NafWRl\ dGlPinYWpeIKNva`WKthapPgdEkgBoj8JXkSa``eQiiF2HGKSC\ ab8nR6pZ5qf5q15_MXfWNldEsRXcrMkoD2GtKSbabMUp7bo6jn\ 5ry`n0rfN4jW5nd51h1IJd`ZNGhuTjcelMOgn54wMKdbZNYP8d\ Y7ke6mJOoRJpZEqf9oQwpWiqaWrgIMZi2BXGLQTVJedCwuktqQ\ crrhpamnLAqBPo9cn78yHKvEWsBgp8qpurocrnMItMSrH`pDin\ 9R00dP3qlhrmVrmI7y6Jv5Vs5fp5uIRtQLsYGreASnd`mTAAcA\ AbAAaF3_0FU000h0VnCApV7XLGbTDg_Amf7pQ6qW5qa5rg5SvC\ `s9ip7Ib7I61SH2`S3ib4mgkoi`pjQqlF1dEFgBSi9ek7eLQiT\ Kl_FofA3dYqoorncrnSrmGdMJhTFk_Cof8fwFjsBnp8zDRzTJz\ gC98BLJ9WO8gX6czzNufbqOpbqqf`rjLb0OhHHmYBXlE5bKKZ_\ afKHa5Ue5fi5U4pfRT7tmVpRpJWqZIUH1uuATKAYB_VPQA8ZMJ\ RXTKgcCsjLrlDodIaOPeZOijM } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 14-09-09 (Goofy Pop-Eyes [7])
by Jim Muth 14 Sep '09

14 Sep '09

FOTD -- September 14, 2009 (Rating 7) Fractal visionaries and enthusiasts: Due to an unexpectedly busy though not too unpleasant day on Sunday, today's discussion will be brief, with no philosophical wisdom -- at least not until the next FOTD. The image lies in the parent fractal that is created when Z^4 is mixed with 0.8 part of Z^5 on each iteration before C is added. The parent fractal is a wide open rectangluar bay with a kind of East Valley on its west side. Today's image lies rather deep in this valley, on its southern side. I named the image "Goofy Pop-Eyes" when I saw the eight disconnected pairs of typical East-Valley goofy eyes surrounding the blazingly blue central minibrot. The rating of a 7 means I kind of like the scene. The image's calculation time of 1 minute is brief enough to make the task of actually calculating it almost enjoyable. For total enjoyment, visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the image there. Perfect weather on Sunday here in the Fractal Central area brought out the antiquing urge in FL. After a minute of mild resistance from me, we headed down to Harrisburg to look at the stuff someone else no longer wanted. Actually, I must be getting soft, since I rather enjoyed it. The fractal cats gave us a good scolding when we returned in the evening. Anyway, the next FOTD will be posted in around 10 hours. Until then, take care, and wait with bated but not abated breath. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Goofy_Pop-Eyes { ; time=0:01:01.11-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=-1.292977015146073/-0.00017451099266728\ /1.986418e+012/1/113/0 params=1/4/0.8/5/0/0/0/0 float=y maxiter=1400 inside=255 periodicity=10 mathtolerance=0.05/1 colors=000RXPIUS9RV1PY5OX9OWCOVGNUJNTNNSRNRUMQYMPF\ 7mG7jH7gI7dJ7aK7ZK7WL8TM8QN8NO8KP8HQ8EQ8CO7BM6BL6A\ J5AH59G49E39C38B28927717617D46K66R95XB5cD4jG4qI3wK\ 3vI2vH2vF2uE2uC1uB1t91t81t60s50s30s20s10r24r28q2Bq\ 3Fq3Ip3Mp4Po4To4Wo5_n5bn5fn5il8jkBkjDliGlhImgLnfNn\ eQodTpcVpbYqa_r`br_dsZgtYitffhocYxaNsbNnbNibNdbN_b\ NVcNQcNLcNGcNBcN7cN8iI8oD8t9CsDGsGKrKOrNSqRWqU_qXc\ p`gpckogoojromsmksljtjhtigteduecudcvcavb`va_w_YwZX\ xXVxWUxVTrTQlSNfQK`PHVNEPMCNODMPDLQDKSDJTEIUEHWEGX\ EFYFE_FD`FCaFBYF9WE8UD6SC5QB3OA2N93PD9UHFZLKcPPhTU\ mWZrYcv_hz`mzbwzdAheBfgCciDajEZlEXm7Pq1Hu3Oi5VZ7`O\ 9gDAk29j58h87dB6aE5YH4VK3RN2PQ1MT1KVFPfTTqUVoUWnUX\ mUYkVZjV_iV`gVafWbeWccWdbWeaXf_XgZXhYXiX_jYajZdjZf\ j_ij`kj`njapjbsjbujcwjcrebmaahX`cT_ZPZUKYPGXKCXMBZ\ OB`QAaSAcUAdW9fX9gZ8i`8jb8ld7mf7og7pfAmeCkeEhdGfcJ\ ccLabNZbPXaSU`US`WP_YNczp } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 13-09-09 (Scoured Out [6])
by Jim Muth 12 Sep '09

12 Sep '09

FOTD -- September 13, 2009 (Rating 6) Fractal visionaries and enthusiasts: There is no philosophy today, but I am posting this FOTD to the philofractal list anyway, since there will be lots of philosophy in the upcoming FOTD discussions. Today's image is a semi-evaporated one lying in the parent fractal that is created when 5.5 negative parts of Z^(-2.2) are combined with 2.2 negative parts of Z^(-5.5) and (1/C) is added. I livened up the image by rendering it with the outside set to 'tdis' and the inside set to 'bof61'. The image is quite busy, with splashes of brilliant colors all over the screen. In fact, the colors are a bit excessive, which probably cost the image a whole rating point. The parent fractal is a rather interesting one, though quite difficult to describe in words. Basically, it impresses me as a near-symmetrical arrow pointed southeast. Today's image is located on the edge of the main bay. The name "Scoured Out" makes about as much sense as the song 'Stairway to Heaven'. I can give no logical reason for choosing it. The rating of a 6 however is an honest opinion of what I think of it. The calculation time of 2-1/2 minutes is acceptable. The trip to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is also quite pleasant. Heavy clouds with occasional showers marred Saturday here at Fractal Central. Despite the lack of sun, the temperature of 70F 21C was quite satisfactory to the fractal cats. My day was close to average. The next FOTD will be posted in 24 hours. Until then, take care, and when life hands you a lemon, sweeten it with a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Scoured_Out { ; time=0:02:32.62-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+1.0619032858539/-0.859580233968/9e+008\ /1/-85/0 params=-5.5/-2.2/-2.2/-5.5/0/500/0/0 maxiter=1900 inside=bof61 outside=tdis periodicity=10 colors=000zzzeRBiT8lV6mX5nY5oZ5p_5p`5qa5rb5sc5td5t\ e5uf5vg5wh5xi5xj5rg8ldBgbEa_HXXKRVNMSQGPTBNW5KZ0I`\ 1JY2JW3JU4JR5JP6JN7JL7KI8KG9KEAKCBK9CK7DK5DK3FJ4GJ\ 5HJ6IJ7JJ8KI8LI9MIAOIBPICQHCRHDSHETHFUHGVHGTFEYDFb\ BGg9GfHHfPHfXHecHekHesHezH`tNXnSTiXPcbLYgHTlOSgURb\ _QYePUkOPqNKwNGnPLeQQXRUOSZGTbMV`RW_XXZaYYg_Wl`Vra\ UwbT6deFZXOTOXNFdH7cLEbPKbSQaWW`_b`bh_fn_itUgrPeqJ\ coEan9`mcuRbsWbq`apeani`mn`ks`jwZlpXniVpbTqXRnYPkY\ NhZLeZJbZQVfWOmaHtdGugFvjEwmDwpCxsByvBy_DYEE6WNUlW\ pgaqbfqYkrTprQjdOdRLZDJT0FYCBaN7fY3jh0nsKtubyvcsod\ mhdhaebVeYO_bTUgXPk`JpdEthDscDrZCqUCqPCpKBoFBnABn5\ NjFYfPibZtZhbQXLHM48B9DDDIFHNHLSIPXKTaMXeNVcMUaLS_\ KRYJWSCTUGQWJNYMKZQI`TFbWCc_9eb6ge3jk4hh5fe5dc6c`7\ aZ7_W8ZU8XR9VOAUMASJBQHCPECNCDL9DK7HI8KH9NGARFBUDC\ XCD`BEcAFf9G71H95KB8NDBPEESGHVIKXKO_LRbNUdPXgR_jTf\ mSdlSblRakR_kQZjVLIZNGaPD } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 12-09-09 (More Void Bubbles [7])
by Jim Muth 11 Sep '09

11 Sep '09

FOTD -- September 12, 2009 (Rating 7) Fractal visionaries and enthusiasts: The parent fractal of today's image combines Z^(2.5) with half as much Z^(5) and adds C. This parent is another letter 'V' lying on its right side. Today's image lies in a curious tiny blip on the negative X-axis at the point of the 'V'. The features in this area appear as near-circular holes surroun- ded by strings of smaller such holes apparently to infinity. The deeper the location, the longer the strings and the more holes on them. Minibrots lie at the mid-points of the filaments connecting the holes. The tiny imperfectly-resolved dot at the center of today's image is one of these minibrots. Most of the 'artistic' effect, if any, was achieved by rendering the scene with the outside set to 'tdis' and the inside set to 'bof60'. The brilliant yellow spots are actually the open holes. Being moderately pleased with the final result, I rated the image at a 7. I named it "More Void Bubbles" because of the similarity to the image of September 10. The calculation time of a little over 36 seconds should incon- venience no one but the super-hurried. And for those few, salvation is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted for instant happiness. Steady rain fell all day Friday here at Fractal Central, with a temperature of 59F 15C, which was just a little too chilly for comfort. The fractal cats set up shop near the hall radiator, waiting for the heat to appear. It never did. My day as a little busier than the usual Friday. The next FOTD will be posted in 24 hours. Until then, take care, and if every- thing we think and feel is caused by activity in the brain, then who or what is in charge of our behavior? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= More_Void_Bubbles { ; time=0:00:36.41-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.4048589980240619/+0.0214316450281102\ /1.04344e+013/1/-115/0 params=1/2.5/0.5/5/0/0/0/0 float=y maxiter=1500 inside=bof60 outside=tdis periodicity=10 mathtolerance=0.05/1 colors=000VOOVeNfPLq9JmBIiCHeDGaEFYGEUHDQICMJBJKAI\ JFHJJGIOFISEHXEH`zwzzvQzvMzuzzuDzu9zqmzmDZiFYeGXaI\ WYKVULXVNZWP`WRbXTdYUfYWhZYj__l_an`bpadraftbhubimf\ gehcbcZ_ZUKUPGRK8OFEEAF80AF06J39M6CO9FRCHTFKWINYLP\ _OSbRVdU000_K_ZN`YQaXTbWWcVZdUaeTdfSggRjhOiiLhiJgi\ GfiDeiAdi8ci9ad9``9ZX9YTAWOAVKATGASCAR8CSDDTHFTLGU\ PIVTJVXLW`MXdNXhLWiJWjIWjGWkFWkDWlBWmAWm8Wn7WnAYkD\ ZiG`gJaeMccPdaSe_VgYYhW`jUckSfmQinOloMmpNmqOmrOmrP\ msPmtQmuQmuRmvRmwSmwSicMfKGc0BWBLOMUGWbPR_YMYfHVrf\ suxkslfr`apPX67kI9fTAadCXtFfrEapDXQxFBw2W_G8yaNhZa\ TWKVHVPLeJPpqYoXVQLgXJcbH_iFW51VH4UT7UdAT`UHhLNfgo\ i_ikScmKYAvxOfmaSbivPl_RSPhcJ`8tyJipUZhdO`C`UBkZAv\ b7ga4UaoZCpd9qi6ro3rt1mUUh4vk7llR_mAb2hDJYJ_NOSVE_\ PJgJOdzKgmNjaPmPRPDObDRlJGxC9uDGrDNbRRgMSkHTRHmYGg\ cFbiEYHAETBJdCOZZsdRjjKa1N4IJDZGLhxejlal`ZnPWKz4_a\ Hbu0KSLVNOeIRn65RBRT8QU5Q } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 11-09-09 (Negative Attitude [6])
by Jim Muth 10 Sep '09

10 Sep '09

FOTD -- September 11, 2009 (Rating 6) Fractal visionaries and enthusiasts: Today's name came to me Thursday afternoon when FL commented that I should try to develop a more positive attitude. When I heard this I glanced at the screen and saw today's image -- about as dark and gloomy as a fractal can get. To give the image a single highlight, I colored the inside of the central minibrot a brilliant white, declared it FOTD for Sep 11, and named it "Negative Attitude". The image was created when I mixed Z^3 with 1/2 part of Z^6 and added C. The parent fractal is shaped rather like a letter 'V' lying on its right side. Today's image is located on the edge of a valley on the eastern side of the northern arm of the V-shaped main bay. Other than the unusually somber coloring, the image is a pretty ordinary thing. Considering all this, I could rate it no higher than a 6. The calculation time of 1-5/6 minutes is within reason, though anyone in a big rush will find it a bit slow. To ease all problems I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> As for negative attitudes, I have discovered over too many years that a good realistic, depressing negative outlook, especially in politics, is far more likely to be correct than a feel-good but dreamy positive outlook. Rain was forecast for Thursday here at Fractal Central, but the day actually turned into one of the best of the year, with deep blue skies, puffy clouds and a temperature of 73F 23C. The sunlight in the fractal cats' window was nearly blinding. They took turns stretching out, closing their eyes and enjoying it. My day was close to average. The next FOTD will be posted in a near average time of 24 hours. Until then, take care, and those with a negative outlook are rarely disappointed. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Negative_Attitude { ; time=0:01:50.88-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.6752499395090378/+0.446406321396262/\ 926968.8/1/102.5/0 params=0.5/6/1/3/0/0/0/0 float=y maxiter=1500 inside=255 logmap=150 periodicity=10 colors=000CEwEDwFCvHCvIBvKBvLAvNAvO9uQ8uR8uS7uT7uU\ 6uU4sU6qT8oS9mRBkQCiPEgOGeNIcMKaLM`KN`JPXIRYHTZGV_\ FX`HZcKaeNchQejTgmWioZkramtdovfnuhmthmsglsflrfkqej\ pdjpdiocinbhnbgmagl`fk`fk_ejZdiZdhYchXcgXbfWafVaeV\ `dU`cT_cTZbSZaRYaRY`QX_PWZPWZOVYNVXNUWMTWLTVLSUKSU\ JRTJQSIQRHPRHPQGOPFPQGOPHOPHOPINOINOJNOJNOKMNKMNLM\ NMLMMLMNLMNLMOKLOKLPKLPKLQJKRJKRJKSIJSIJTIJTIJUHIU\ HIVHIWGHWGHXGHXGHYFGYFGZFG_GHZFGYFGYFFXFFWFFWEEVEE\ UEDUEDTEDSDCSDCRDBQDBQDBPDAOCAOC9NC9MC9MC8LB8KB7KB\ 7JB7IB6IB6HA5GA5GA5FA4EA4E93D93C93C92B92A80B91B92B\ 92B93B94B94B95B95B96B97B97BA8BA8BA9BAABAABABBACBAC\ BADBADBAEBBFBBFBBGBBGBBHBBIBBIBBJBBKBBKBBLBCLBCMBC\ NBCNBCOBCOBCPBCQBCQBCRBCRCBSCBSDBSDBSEBSEBSFASFASG\ ASGASHASHASIASI9SJ9SJ9TK9TK9TL9TL8TM8TM8TN8TN8TO8T\ O8TP7TP7TQ7TQ7TR7UR7US6US6UT6UT6UU6UU6UV6UV5UW5UW5\ UX5UX5UY5UW2TX4UY5UZ7Uzzz } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 10-09-09 (Bubbles in the Void [7])
by Jim Muth 09 Sep '09

09 Sep '09

FOTD -- September 10, 2009 (Rating 7) Fractal visionaries and enthusiasts: A very busy day on Wednesday means a brief discussion. The fractal image lies in the parent fractal that is created when negative Z^(1.5) is mixed with negative Z^(-5.5) and straight C is added. This parent fractal is a somewhat distorted Mandelbrot set rotated 180 degrees, with a disk surrounded by area of interest off to its west. Today's image lies in one of these interesting areas. Most of the worth in today's image was achieved by rendering it with the outside set to 'tdis'. But even then, I could rate it no higher than a 7. The name "Bubbles in the Void" refers to the appearance of the image. The calculation time of a superluminal 23 seconds means that the image will finish before it is started. This will give the fractalist an early view of what will appear on the screen and give him a chance to decide not to do the calculation. Hmmm....something seems wrong here, but regardless, another simple way to view the image is to view it in finished form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I had intended to write some political philosophy here, but luckily I counted to 10 and decided to remain quiet. But I just couldn't resist putting a brief comment at the end. Heavy clouds but no rain kept Wednesday boringly dreary here at Fractal Central. The temperature of 75F 24C was the only thing not boring. The fractal cats had quite a bit of excitement however when two beat-up tomcats met and got into a shouting fight in the yard next door. When the loser slinked away in defeat, the victor sprayed the area generously. I hope the rain comes soon. (Don't ask why.) But even if it doesn't rain the next FOTD will be posted in 24 hours. Until then, take care, and anything that seems too good to be true probably is -- including presidents. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Bubbles_in_theVoid { ; time=0:00:23.94-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident center-mag=+1.095446005963/+0.763733641913/8393119\ /1/-2.5/0 params=-1/1.5/-1/-5.5/0/0/0/0 float=y maxiter=1800 inside=0 outside=tdis periodicity=10 colors=000J`QKdPgiT`bUVWUOPVIIVBBW54W96ZC8`GAcJCeN\ EhQGjVHf_IbcIZRYfFlnPhsOggOgWNgKNg9Lh7Ki5Jj3Ik2Th9\ ffFqcLzaRwWViRYfMaWHdFChCEkAG`C8QEAFGCKIGOKLTMPXOR\ aLSeJTiLUhNUhPUhQUhSWhUYhW`h_chfhhmmmrrrvvvzzzOoqN\ koMhmLekKbiJZgIWeHTcGQbSUWcYPn`JodHpgFqjDrmCpkAoj8\ ni6lg4kf2je1nlBrsLuzVjiK_TAPD0LJ5HOAETFAYK6bP3gTCa\ QKXNSSK`NHhIEpDBx88nDEdHJVMPLQUCUZAX_8Z_6a_5c_9ZRC\ VJGQBJM3QRDXVNcZWjceqgoxkxpUugRiZOZQMOHJD8H2UbCnxL\ osIonGojDoeBoa8oX6oT4cdUSpsXiq`coeYniSlnMkrGivAhp9\ aj8Wd7P_7JbPRefZgwe_UmT0ttJuoIqjHnfGkaGgYFdTEaPEZ_\ 9Wi5UpHRwTPmMZcFgU8pK1yOBoRLfUUYYcO`mFcv6bpAakEafI\ ``L`WP_RTqJdlKahL_dLY_MWWMUSNSX3gSDZONQGP4HR8ITBJV\ EKXHLZK9NFESIIWLM_NQcQVhTZlVbpYft_VjOGOpP_4M`8JaCH\ bGEcKCdO9eS7fVSTnUQlVOjWMhXKfYIdZGb_E`SAV`CZiDbvBQ\ tCWsD`qEfpFknGqyIQsHfmGvjKogNhdRaaUVZXOW`HTcAbbnXd\ RRf3OaAMYGKTNHKUIPTITSJXR } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 09-09-09 (Hexagonal Pentagram [8])
by Jim Muth 08 Sep '09

08 Sep '09

FOTD -- September 09, 2009 (Rating 8) Fractal visionaries and enthusiasts: Philosophy fans check the philofractal version. Today's image rates an honorable 8, a welcome change indeed. The parent fractal is an oversized Mandelbrot set caught morphing into a Z^6 Mandeloid. The scene of today's image is located near the shore line of the northern period-3 bud, which has become quite ragged. The contrast between the 5 lobes of the central minibrot and the hexagon surrounding it is quite striking. It inspired the name "Hexagonal Pentagram". The calculation time of a mere 36 seconds will cause the impatient heart to leap for joy. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the already-calculated image will bring instant bliss. Lots of clouds but little rain marked the conditions here at Fractal Central on back-to-work Tuesday, while the temperature of 79F 26C could hardly be improved upon. The fractal cats would have preferred a bit more sun and a lot more treats. My day was about average. The next FOTD, hopefully above average, will be posted in 24 hours. Until then, take care, and what would an alien visitor think if he landed on earth and saw a few of those late night 'adult' cartoons. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= HexagonalPentagram { ; time=0:00:36.46-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip float=y center-mag=-0.4482506806503804/+2.629349679422971/\ 7.197278e+012/1/-108.5/0 params=6/3 maxiter=1500 inside=0 logmap=114 periodicity=10 mathtolerance=/1 colors=000A0IA0KA0MA3OA6Q33S76UA9WDCYMF_QKaUPcZUec\ ZghchmhmrmrvrvzvzzzzzzzzzzzzzzzzzzzrkUogQlcMh_HeWD\ bS9_O5XK1YM4YN7YPAYQDYRGYTJYUMYVPVWRTXTRYVOZWM_YK`\ _HadFboDczAdz8ez6ezFXzOPzXHze9zm1Cj6HgAMdEQaJVZN_W\ RcTVhQ_mNcqKgvHkzMbxRUwWLu`Ctd4s`GhYRZUaORlEOw4mt8\ zrCzoGSmKTjNUhRVfVWcZXabYZeZXi_Um`Sq`QtXPqUPoROlOO\ jLOhd`Q_bOWcNSdMOfKJgJFhIBjG7kF3lE4kD5kC6kB6kB7kA8\ j98j89j8Aj7Aj6Bi5Ci5Ci4Di3Ei2Ei2He8JbDL_JNWOPTUSQZ\ UMdWJiYGo_DtZFmYHgXI`WKVVMOUNITPBTQ5g5CbBGZGKVLORQ\ RNVVJ_ZFdbBieCccDZaET_FOYGIWHDVJETKERMFQNFOPFMQGLR\ GJTGHUHGWHEXHCZIB_I9`I8YNBVSESXHPaKMfNJkQGpTDuWBzY\ EvWHrVKoUNkSQgRSdQefRshStfWueZvdawbdxagy`jz_mzPdzE\ Wz3Nz8OzDOzIOzNOzSOzXOz`OzaRzaTzbVzbXzc_zcazdczdez\ dgzddzdazdZzdXzdUzdRzdOzdMzdJzdGzdEzj7zXFzJNz6VzX3\ zR2zL2zF2zMEzSPzY_zSZzNYzIYzDXz8Wz3Wz8YzDZzI_zM`zR\ azWbz`czddzNazM`zL_zKYzJX } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 08-09-09 (Doubled Troubles [6])
by Jim Muth 07 Sep '09

07 Sep '09

FOTD -- September 08, 2009 (Rating 6) Fractal visionaries and enthusiasts: O.T. philosophical stuff on the philofractal version. Today's image is more a mathematical curiosity than a work of fractal art. It is a scene on the negative stem of the fractal that results when the Mandelbrot set starts to take on Z^13 characteristics. Most of the minibrots in the image have 12 lobes like proper Z^13 minibrots should. The oval-shaped mini- brot in the center of the image however has 25 lobes, which is definitely not what should appear in a Mandeloid of order-13. I suspect this minibrot is a blending of two normal minibrots, though I can't quite figure out where the 25 lobes come from. 12 lobes plus 12 lobes equals 24, not 25. Regardless, the image with its interconnected network of spidery filaments has enough interest to rate a 6. The name "Doubled Troubles" refers to the central minibrot with the wrong number of lobes. Unlike yesterday's slow-poke image, today's calculates in a mere 16 seconds, which doesn't leave time to go to the kitchen and pour a drink before it finishes. The finished product is avail- able for instant viewing satisfaction on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The spell of fine weather here at Fractal Central came to an end on Monday as heavy clouds moved in. No rain fell, but the fractal cats did not approve of the drabness. The temperature of 75F 24C did little to relieve their let-down. My day was average. The next FOTD will appear in 24 hours. Until next time, take care, and who can be sure that truth even exists. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Doubled_Troubles { ; time=0:00:16.33-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip float=y center-mag=-11.2582359658/0/35243/1/-90/0 params=13/6.5 maxiter=275 inside=0 periodicity=10 colors=000XxIcyCjy6py0qv4rs8rpCsmGtkKthOueSvbWv__w\ YcxVgxSkyPoyNr5wxVNXZOUbOScUNcZJdcFdhBgMFh0Je1Lb1L\ Y2LU2KP3KK3KF4KB4KHCKMJKRQKWXI`gEerAzz0kjKkUXlcjmm\ zn`aoPHmxzhwzzvzzurzthzsczrZvrUrqKmq8hqBcqEZpHUpKz\ pNzpQzmPzkOziOzfNzdMzbMzLdz3wz8uzCszGqzLozPmzTkzXi\ zUjzSkzQlzOmzLnzJozHpzFqzKkzOfzSazXXz`SzdNzcO2zz3z\ z4zz5zz6zz6zz9zzCzzEzzHzzJzzLzzNzzOzzQzzSzzTzzUzzV\ zzWzzXzzYzzZzzZzzYzzZzzZzzZzzZzzZzzZzzZzzZzzZzzZzz\ ZzzezzSzzmzz3zz5zz6zz7zz9zzAzzBzzDzznzzrzkqzlpzloz\ mozmdzeVzZLzSBzLJzPQzSYzWdzZ_zYVzYRzYMzYIzYDzY9zY4\ zY0zY3zW6zV9zTCzSFzRIzPLzOOzMRzLTzKZzQdzWizaozguzm\ zzrvzqrzpnzojznfzmbzlZzlVzkRzjNziJzhFzgCzgOzd_zbkz\ `vzZwzgxzoxzwpzvhzv`zvUzuMzuEzu7zu8zt9ztAztBztCztD\ ztEztFztGztHztIztKztMztOztQztSztUztWztYzt_ztazjbza\ dzTezJgzAhz1gz4gz6gz8gzAgzDgzFgzHgzJgzMgzOgzQgzSgz\ VgzXgzZgz`Xz_Nz_Dz_KzURzO } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 07-09-09 (Cause and Effect [4])
by Jim Muth 06 Sep '09

06 Sep '09

FOTD -- September 07, 2009 (Rating 4) Fractal visionaries and enthusiasts: Today's fractal lies in the parent fractal that comes about when various portions of Z^(-1.414) and Z^(-4.414) are mixed together and (1/C) is added. I rated it at a lowly 4 because even after all the work involved in finding it, I ended up disappointed. The name "Cause and Effect" implies that I was pondering some abstruse philosophical conundrum while the fractal cooked. Worst of all, the calculation time of 18 minutes is about 1100 times as long as yesterday's, yet the resulting image is only 1/10 as good. Luckily, all the frustration may be avoided by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the completed image there. Lots of sun and a temperature of 81F 27C made Sunday a day to be enjoyed here at Fractal Central. The fractal cats tried lying on their window shelf, but it was still too warm to enjoy the increasing sun there. My day was average, which means boring, but is the way I like it. The next FOTD will be posted in 24 hours. Take care, and religion tells us the universe began when God said 'let there be light'. Science tell us there was a big bang. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cause_and_Effect { ; time=0:18:11.31-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip inside=0 center-mag=-0.19386319223/-1.76480211712/230000/1/\ 120/0 params=-4.4/-1.414/-1.4/-4.414/0/0/0/0 float=y maxiter=14500 logmap=-1600 periodicity=10 colors=000AWIFZOLaUQd_Wge`jkelpamjZneVo_SpVOqPLrKI\ rFLpGNoHPmIRlJTkKViKXhLZgM`eNbdOdbOfaPh`QjZRlYSnXS\ oWUpVWqVYrU_sUatTbuTdvSfwShxRjyRktQfpQblQZhQVdPR`P\ NXPJTPFWOEYOD_ODaOCcOBeOBgOAjO9lO9nO8pO7rO7tO6vO5x\ O5vS9uVCtZGsaJreMqhQplTooXns_mvblqdkmejifiehhaihYj\ j_ck`YlaSnbMocGpdAsdNvd_ydlxeixffwgcwhawiZvjWvkUvl\ RumOunLuoJtpGtqDtqBupEuoGunIvmKvlMvkPvjRwiTwhVwgXw\ f_xeaxdcxcexbgvaduaasaZr`Xp`Uo`Rm`Ol_Mj_Ji_Gg_DfZB\ dZ8cZ5bZ3`Y5ZX7YX9WWBVVDTVERUGQTIOTKNSMLROKRPMLJOF\ EQ99NFBLKDJPFHVGF_ICdKAjL8oN6tP4yQ7wR9vRBuREsRGrRI\ qRLoRNnRPmSSkSUjSWiSZgS`fS`k_`k_XjYUhXQgVMfTIeREcP\ AbN6aL3`K6ZN9XQBVTETWGSZJQaLOdOMgQLjTJmVHpYFs_EuYJ\ qXNmVSiUWeT_aOdVJhPElI9pC4t67aNAJc9Ie9Ig9Ih9Ij9Ik9\ Im9In9Ip9Ir9Is9Iu9Iv9Ix9Iy8Ti8bV8lF8v07q36l66h95cC\ 5_F4VI3QL3MO2HR2DT7GSCJSGMSLPSPSRUVRYYRb`RfcQkfQoi\ QtlQxnQthPpbO4YC4WC4UC4TC } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 06-09-09 (Insense Outsense [8])
by Jim Muth 06 Sep '09

06 Sep '09

FOTD -- September 06, 2009 (Rating 8) Fractal visionaries and enthusiasts: As I suspected might happen, FL was seized by the antiquing bug on Saturday and talked me into a trip to an antique emporium down in Annville. The trip was not a total loss; we found just the carpet we were looking for to add to those already in the FC hallway. The new carpet has gained the approval of the fractal cats, who checked it, marked it, then stretched out on it. With little time to do a fractal search, I turned to the war- horse Mandelbrot set and found the fastest fractal image of all time -- one that calculates in nine-tenths of one second on the rejuvenated P4-2000mhz machine. I gave today's image a rating of an 8, even though it is nothing more than a typical minibrot on a filament extending from the period-8 bud on the northeast shore-line of the main bay of the Mandelbrot set. The name "Insense Outsense" can mean anything the fractalist wishes it to. To me it means nothing more than the sound it makes when spoken. The magnitude is an extreme 3*(10^12), but the image still renders almost perfectly using standard math. I included the mathtolerance entry to assure that the program does not flip into arbitrary precision math mode, which would increase the calculation time from one second to one hour. The parameter file is so fast that the image is finished before the video mode can switch to super VGA, causing the fractalist to miss the fun of seeing it generate. So why not enjoy a conso- lation prize of a virtual trip by surfing out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Perfect weather made Saturday most enjoyable here in the Fractal Central area. The fractal cats mostly approved of the new carpet, though at one point I did hear some foul language from Nicholas. My day was good enough; I survived the trip to Annville. But tomorrow should be even better. The next FOTD will be posted in 12 or so hours. Until then, take care, and relax. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Insense-Outsense { ; time=0:00:00.91-SF5 on P4-2000 reset=2004 type=mandel center-mag=+0.3704568047918\ 252/+0.1102991974787538/3.113184e+012/1/74.75/0 params=0/0 float=y maxiter=1000 inside=0 logmap=130 periodicity=10 mathtolerance=0.05/1 colors=000D30E40F50G60H70I80JA0KD0LG0NJ0PM0QP0SS0U\ V0VY0X`0Zb0_d0Yc8WaFU_MSYTQW_OUfMSmKTtOYoRcjVjfYra\ `wYcveeuljthnsdrr`vqXzqTtkPlfLc`HWWDNQ9FL5FJ6EI7FH\ 8FF9FEAGDBGBCHADH9EH7FI6GI5HI4HF9JDDKBIL9MM6QO4VP2\ ZQ0bR6VNCOJIGFN9BWOnVKrUGvUDyWCxXBwYBvZAu_Ata9sb9r\ c8qd8pe7og7nh6mi6lj5kk5jj9fiCchF`hJYgMVfPSeTPeWMdZ\ JcbGbeDbhAdeBebBf`BgYBhWCiTCkQCnOCrLDvJDzGDzEDzCBz\ A9z98zA9zBATCBVDCWEDXFDZGE_HF`IGbJHcKHdLIfMJgNKhOL\ iOLnQMrSNvUOzWOXON4GNELMOPMXUMfYLpbLyfLlYQ`PUPHYD8\ a10eB9WLINVRDdZ4_a8VcCQeGLgKGiOBkRDlUElXFlZGlaIldJ\ lfKliLllNlnOlqPltQlvRioSfiTcbT`XQMYN8ZMBXLDVKFTJHR\ JJPMKROLTQMUTNWVOYXPZ_Q`aQacRcfSehTfjUhmVjoWkqXmsX\ nsYksYhsZfsZcs_as_Zs`Xs`Us`RsaPsaMsbKsbHscFscCscAq\ bErcIseLtgPuiSvkWwnZxqbytfzwizzmzzpzztzzwzzqzzrzzr\ zzrzzrzzrzzrzzrzzrzzrzzrzzrzzdzz_zzWzzVzzUzzUzzTzz\ SzzSzzRzzQzzQzzPzzOzzOzzN } END PARAMETER FILE=========================================

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FOTD 05-09-09 (Half a Valley Down [6])
by Jim Muth 04 Sep '09

04 Sep '09

FOTD -- September 05, 2009 (Rating 6) Fractal visionaries and enthusiasts: The philofractal version of this FOTD is much longer. Today's image shows a minibrot of order 1.5. It lies rather deep in the Seahorse Valley of the Z^(1.5)+C Mandeloid as it appears 55 levels up the logarithmic ladder when no function is applied. I named the image "Half a Valley Down", a name that has at least a bit of something to do with its location in its parent. The minibrot impresses me as being just a little better than the average minibrot of order 1.5. All things considered, I rated the image at a 6. At first glance, there appears to be some- thing important just beyond the right edge of the frame. When I checked there however I found nothing but an area of bottomless pits with no minibrots at their centers. The calculation time of 6-1/3 minutes is rather slow for an image that rates a mere 6. I recommend going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the completed image there. Doing this will eliminate the hassle of running the parameter file. Friday was totally perfect here at Fractal Central, with blue skies, light winds, and a temperature of 81F 27C. The fractal cats took advantage of the sun, which is now coming in their window at a more favorable angle. My day was near average. With a 3-day holiday week-end coming up, I can't guarantee a FOTD on every day, but we'll see how it goes. The next FOTD is scheduled in 24 hours. Until then, or whenever, take care, and believe in reality. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Half_a_Valley_Down { ; time=0:06:20.82-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.02344014694273223/+0.742969732713732\ 10/361282.8/1/-20/0 params=1.5/0/55/0 float=y maxiter=12000 inside=0 periodicity=10 colors=000pSJpSIpTGpTFiULcURYUXSUbLUhFUn9Ut3Uy6Tu9\ TrCSnFSkIRgLRdOQ`RQYUPUXPRZPOeS`lVlrYxn_wjavgbvcdu\ _ftXgtTisPkrMlrLdpKXoJPnIHlH9kG1jHeqHhjHkdHnYHqSHt\ MFsOErPDrQBqS9aU9aU7`W6`X5_Y3Z_2Za1Zb0Zd3_d6`d9aeC\ bfFdgHehKfiNgjQikTjlWkmYln_njapgcrdesagsYitVkuSmvP\ nvMltPjrRhpUfnWdlZbj``hcZfedcdiadnZdsXdmSahNZcJWZE\ TU9QP5NW6Ua7`Z6XW6UT6QQ6NN6JK6GH6CF69G8CGAFGCHGDKG\ FMGHPGIRHGSHFSIESIDTICTJATJ9TJ8UK7UK6UK5UKAOKFIKKC\ KP6KU1RW6XYAc_FgaJkdRogZsjevmhzkkzhmzclzZlzUlzPlzK\ lzHlzFlvClrAlm7lh5lc7kZ9kUBjPDjKFiGGiHJ_ILQJOGJQ6K\ VBL_FMdJNiOOnSPsWQx_OnZMdYKVYILXHCXKBTNBQQBNTAJWAG\ ZADa99d96g93iKBjVIleQmpXjlWhiWffWdbWa_W_XWYUWWQWUN\ WRKWPGWNDWLAWJ7WL9VNBUODTQFSSHRTJQVLQXNPYPO_RNaTMb\ VLdXKeZKc_Nb`PaaR`bU_cWZdYYe`XfbWgdVhgUiiTikPchMZf\ JUcGOaDJZAEX79VUFaPL_LQZHWYD`W9fV5kU1pT3mR5jP7gN8d\ LAaJCZHDXFFUDHRBJO9KL7pRL } 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 04-09-09 (Not Something Else [No Rating])
by Jim Muth 03 Sep '09

03 Sep '09

FOTD -- September 04, 2009 (No Rating) Fractal visionaries and enthusiasts: I spent more time than usual writing the philofractal version of today's discussion, so the actual fractal part is necessarily brief. Check the philofractal list or the FOTD web site for the long version. Today's image lies in a bit of left-over debris rather deep in the Seahorse Valley of an oversized almost-Mandelbrot set. It shows an unpretentious quintic Mandeloid, with very ordinary surroundings. The many 5-petaled things scattered throughout the image are other smaller quintic Mandeloids very similar to the one at the center of the frame. Check them if you must, but don't expect any surprises. I named the image "Not Something Else". Who knows why. After putting so little effort into the image, I could hardly post a rating, though it impresses me as being worth around a 6. The calculation time of 2-2/3 minutes is mercifully brief. The trip to the FOTD web site also is brief. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Absolutely perfect weather prevailed here at Fractal Central on Thursday. The fractal cats fully enjoyed the temperature of 79F 26C, but did not spend too much time lying in the strong sunlight. My day was about average, which seemed like a holiday after the hectic day here at FC on Wednesday. The next FOTD will be posted in 24 hours. Until then, take care, and live until you pass on. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Not_Something_Else { ; time=0:02:42.42-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip passes=1 center-mag=-3.787641619241377/+0.3663265529188874/\ 1.794017e+007/1/72.5/0 params=5/5 float=y maxiter=5000 inside=0 logmap=165 periodicity=10 colors=000An0Am0Al0Ak0Aj0Di3Fg6Ge8HcBIaDK_FLYIMWKN\ UMRVOVWPYXQaYRdYThZUk_Vo`WpVVr`XseZtj`uobvtdxzgwye\ vycvyauy_tyZtxXsxVsxTrxRqxQqxOpwMpwKowJnwHnwFmwDmv\ BlvAkv8kv6jv4jv3_nCQgKG_S6T_9U`CUaFUaIUbLVcOVcRVdU\ VeYXfXVeXUdXTcXSbXRaXQ`WP_WOZWNYWMXWLWWKWVIVVHUVGT\ VFSVERVDQUCPUBOUANU9MU8LV5JU7LT9MSBORDPQFRQHSPJUOL\ VNNXMPYMR_LT`KVbJXcIZeI`fHbhGdiFfkEhlEjmGijIihKhfM\ hdOgbQg`SfZUfXWfVYeT_eRadPcdNecLgcJhcHdZK`VMXROTNR\ QITMEVIAYE6_90bB2aD4`F5_G7ZI9YKAXLCWNEVPFUQHTSJSUK\ SWMRXOQZPP`ROaTNcUMeWLfYKhZJj`IkaIi_KgYLfXNdVOcUQa\ SR`RSZPUYOVWMXVLYTJ_SI`QGaPFcNDdMCfKAgG9jJ9hL9fO9d\ Q9bT9`V9ZY9X_9Vb9Td9Rg9Pr0Ei9NaHWUQdLXmMYlMZkM_kM_\ jM`jMaiMbiMbhMchMdgMegMefMfeMgeMhdMhdMicMjcMkbMkbM\ laMmaMn`LodMn`NnYNnVOnSPnPPnLQnIRnFRnCSn9Sn6Tj9TfC\ TcFT_IUWLUTOUPRUMUVIXVE_VBbV7eU3hV4gV5gV6gV7gW8fW9\ fWAfWBfWCfXDeXEeXFeXGeYHd } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 02-09-09 (Seventh Instar [6])
by Jim Muth 02 Sep '09

02 Sep '09

FOTD -- September 02, 2009 (Rating 6) Fractal visionaries and enthusiasts: I'm sorry to let down the philosophy fans waiting with bated breath to read my ghost story and doubt that I saw an actual ghost, but there is simply too much work piled up to write a proper story. Tomorrow will once again be quite busy, so the ghost adventure will probably not be posted until Sep 4. Meanwhile we have a fractal as a consolation prize. Today's image was created when I combined various negative portions of Z^(-1.04) and Z^(-5.5) then added (1/C). The parent fractal is a grossly oversized continent, lying in an infinite ocean, with a bulb on its eastern shore line. Today's image is located deep in this bulb, though the bulb is so large that the actual magnitude of the image is a modest 616. I named the image "Seventh Instar" for no apparent reason. I rated it at a 6 because I don't consider it worth any more. The calculation time of under 4 minutes will pass so fast that it will barely be noticeable. Those who can still notice the time may find relief on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed image is posted for speedy gratification. Absolutely perfect though rather chilly conditions prevailed here at Fractal Central on Tuesday, with a near cloudless blue sky and temperature of 70F 21C. The fractal cats would have enjoyed the afternoon sun on their shelf, if they had not been so occupied with their catnip toys. My day was very busy. Tomorrow is expected to be very busy again, so do not be sur- prised if the FOTD is late or abbreviated. Until whenever, take care, and when a person views one of those optical-illusion line drawings of a cube that appears to turn inside-out and back again, in their minds they are actually rotating the cube in 4-D space around the plane through the center of the cube. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seventh_Instar { ; time=0:03:51.73-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=-146.4881370706049/+859.5083389189768/\ 615.9855/1/-102.5/0 params=-4/-1.04/-1/-5.5/0/0/0/0 maxiter=5700 inside=0 logmap=-700 periodicity=10 colors=000qsipriprioqhpphnqjppjmqljqmgrodsqasrZttW\ uvTuwPuuUssZqrcomhmhkkcniZmfUmcPl`KkYFkVAjS7iP7hM7\ hJ7gG7fD7fF7cHD`JIYRNVYTSeYPlbNm_MmYLmWKmUJmSImQGm\ OFmMEmKDmICmGBmEAmCElDHkEKkFNjGQjHTiIWhJZhKagLdgMg\ fNjfNggQdhTaiVZjYWk`TlbRmeOnhLojIpmFqpCrr9su7swBtq\ EtlHufLuaOvXRvRVwMYwG`xBcx6_u8XsAUqCRoEOmGLkIIhKFf\ MCdO9bQ6`S3ZTBPqAIv9BzBHrCMjDSbEXWlekjfhifezzbzz_z\ zXzzVzzHzz3zz4zz4zz5zz5zz5zz6zz6zz6zzBzzGzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzgzzbzzYzzTz\ zOzzJzzEzz9zz4zzBzzIzzKzzMzzOzzQzzSzzUzvWzvWziWzXW\ zKUzTTz`RzhQzpSznTzmUzkVzjWzhXzgVzcTz`RzXPzUNzRLzN\ JzKHzHIzOJzUKz_LzfMzlNzrMzkLzeKz_JzTIzNHzHHzBEzMBz\ X8zf7zX7zO7zFHzHQzJWzH`zGfzFkzDqzCvzBgzR`zLUzGNzBH\ z6zzmtzfnz`hzUbzOXzHRzBMz5QzFTzPXzZ_zhKzgPziUzjZzk\ czmhznmzoqzpmzqizrezsbzsWzsQzsKzsOzqSzpWzn_zmczldz\ jezifzhazgXzgTzgOzfJzfFzf } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 01-09-09 (High Contrast [6])
by Jim Muth 31 Aug '09

31 Aug '09

FOTD -- September 01, 2009 (Rating 6) Fractal visionaries and enthusiasts: Check the philofractal version for a much longer discussion. Perhaps today's image should have been named "High Contrast" rather than "High Energy", but a name is a name, and that's what I named it. The parent fractal was created by combining various negative portions of Z^(-1.1) with Z^(-6.6) then adding (1/C). As expected, this parent is a grossly oversized thing with a fan, several large bays, and lots of fancy rings in the suburbs. Today's image lies in one of these suburban rings. To get the high-contrast effect I ran the image through a graphics program and increased the contrast almost to the limit. A few minor tweaks gave the final result, which despite the color work, still rates only a 6. The calculation time of 2-3/4 minutes will pass like a cruise ship. Why not avoid the voyage by viewing the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Unusually chilly weather prevailed here at Fractal Central on Monday, with enough clouds to keep the day from being sunny and a temperature of 70F 21C. The fractal cats ignored the weather, choosing to get into trouble instead. My day was active enough. The next FOTD will be posted in 24 hours, give or take a few. Until then, take care, and fractals can be hauntingly beautiful. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= High_Energy { ; time=0:02:44.26-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-20.74327502908762/-29.09300598549294/\ 3.744615e+009/1/-77.5/0 params=-4.1/-1.1/-0.6/-6.6\ /0/0/0/0 float=y maxiter=1750 inside=0 outside=tdis periodicity=10 mathtolerance=0.05/1 colors=00000Y00f00f00f00f00f00f00f00f00f00f00f00f0\ 0f00f00f00f00f00Y00Y00Y00Y00Y00Y00Y00Y00Y00Y00Y00Y\ 00Y00Y00Y00Y00Y00Y00Y00Y00Y00Y00Y00Y00Y00Y00Y00Y00\ Q00Q00Q00Q00Q00Q00Q00Q00Q00Q00Q00Q00Q00Q00Q00Q00Q0\ 0Q00Q00Q00Q00Q00Q00U00Z00c00h00m00h00c00Z00U00Q00I\ 00I00800800800000000000000000000000000000000000000\ 800800800I00I00Q00Q00Q00Y00Y00Y00f00f00p00pzczzczz\ hzzmzzrzzvzzzzzzzzzzzzzzzzzzz0zz0zz0zz0zz0Iz0Qz0Yz\ 0Yz0fz8pz8xzIxzQzzQzzzzUzzUzzUzzUzzUzzUzzUzzUzzUzz\ UzzU0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz00z00z00z0zz0zz00z00z0zz00z00z00z00z00z00z00z\ 00z00z00z00z00z00z00z00z00z00z00z00z00z00z00z00z00\ z00z00z00z00z00z0Yz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zz0zz8zzIzzIzzz00z00z00z00z0\ 0z00z00z00x08p0If0QY0Yx0z } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 31-08-09 (A King's Scepter [7])
by Jim Muth 30 Aug '09

30 Aug '09

FOTD -- August 31, 2008 (Rating 7) Fractal visionaries and enthusiasts: The philofractal version of this discussion is longer. Today's image is a simple scene rather deep in Scepter Valley. I named it "A King's Scepter" and rated it at a 7. Just like Seahorse Valley to its east, Scepter Valley is filled with 'peanut holes' in its depths. This type of image can be hard to color attractively, but with today's image the 'tdis' outside option works reasonably well. The image calculates in 10-1/3 minutes on the P4-2000mhz machine, mostly due to the extreme maxiter of 15,000,000. But on the P200mhz unit it would take about 3 hours to complete. If time is a problem, solve the difficulty by going to the FOTD web site and viewing the finished image there. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A picture perfect day prevailed Sunday here at Fractal Central, but my sister reported light rain back at Old Fractal Central. The new fractal cats approved of the sun and temperature of 77F 25C. My day was slow enough to be enjoyable. The next FOTD will be posted in 24 hours. Until next time, take care, and look for the unexplained. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_King's_Scepter { ; time=0:10:19.83-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.2500000363126\ 57/+0.00007448147432569/1.402647e+011/1/-5/0 params=0/0 float=y maxiter=15000000 inside=0 outside=real periodicity=10 mathtolerance=0.05/1 colors=000lUFmTFmSGmRHmQImPJnOJnNKnMLnLMvPOrNNnLMk\ JLgHLcFK`EJXCITAIQ8HM6GJ5GK6IL6KM7LN7NN7OO8QP8RQ9T\ R9VR9WSAYTAZUB`UBaVBcWCeXCfYDhYDiZDk_El`EnUq2`Eo_G\ lZHiYIfXJcXK`WLYVMVUNSTOPkGbAcBTPNk0ik6ckBZkGTkLOk\ QIkVDk_7kd2fe3af3Yf3Tg4Og4Kh4Fh5Ai56i57h68g79f8Ae9\ AeABdBCcCDbCDbDEaEF`FG_GHZHHZIIYIJXJKWKKWLLVMMUNNT\ OlYm_V`NTOGdy7O7BRCETGIVKLXPOZTS`XVcaZeeagidinhkrk\ mvnozonyomxolwpkwpjvpiuqhuqgtqfsrerrdrrcqsbpsaps`o\ t_ntZmtYmuXluWkuVkvUjvTivTiuVhuWhtXhtYgtZgs_gs`fsa\ frbfrcerdeqeeqfdpgdphdpicojcokcolbnmbnnborenpcnobm\ m`ml_mjYliXlhVlfUkeSkcRjbPjaOj_NiZLiXKiWIhUHhTFgSE\ gQCgPBfN9fM8hM4gL6fL7fL8eL9dKAdKBcKCbKDbJEaJFaJG`J\ I_JJ_IKZILYIMYINXHOWHPWHQVHRWGSVHSUISUJSTKSTLSSLSS\ MSRNSROSQPSQPSPQSPRSOSSOTSNTSNUSMVSMWSLXSJYQLXSMXT\ OWUPWVRVWSVXUVYVUZXU_YT`_Ta`SbbSccSdeRefRfhQgiQhjQ\ ifTjbWkZZlVamRdnNgoBnnFko } END PARAMETER FILE=========================================

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FOTD 30-08-09 (Mocha-Mocha_Midget [6])
by Jim Muth 29 Aug '09

29 Aug '09

FOTD -- August 30, 2009 (Rating 6) Fractal visionaries and enthusiasts: Check the philofractal version for credulity. The unlikely mixture of Z^(0.8) and Z^(100) plus (1/C) created an unlikely parent fractal in the shape of a giant disk edged by buds of various shapes and surrounded by the trapped emptiness of infinity. Today's scene is located in the center of this unlikely parent. I named the image "Mocha-Mocha Midget" because of the coffee- colored background. Then, seeing nothing unusual in it, I rated it at a 6. The calculation time of under 15 seconds means lots of free time for those overworked computers. A visit to the FOTD web site means lots of fun. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday began cloudy and muggy here at Fractal Central, but by noon the sun broke through and the temperature rose to 86F 30C. All was not yet well however, for at 5pm a brief but very heavy rain squall passed over, dropping the temperature to 72F 22C and getting the fractal cats' attention. The sun re-appeared even before the rain had ended and the day ended picture-perfect. My day was all right. The next FOTD will be posted in 24 hours. Until then, take care and wouldn't it be fun is the aliens actually *were* phantoms and we caught one of them. Then we would have proof of both aliens and ghosts. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mocha-Mocha_Midget { ; time=0:00:14.67-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip center-mag=42.2529/-12.0857/32.86356/1/-133.3/0 params=1/0.8/1/100/0/0/0/0 float=y maxiter=1000 inside=0 logmap=14 periodicity=10 colors=000jYRiXQhWPaTOVQNONKHKKBIKKEHTHK`EJiBIr8Hz\ 5GwBFuGErMDpRCmWBkaAhf9fk9bmE_oIXqNUrRSpNQnKPlGNkD\ Mi9Kg6Jf3Ia8IYDHTIHPNHLRIKVIJYII`IHcIGgIFjIEmIDpGE\ qEErDErBFs9Ft8FtOQsc_sYXnTViNSdIQ_MQZQQYUQXYQXaQWe\ RViSUmTUpUZrVbtWfvXjxYnzZrx_qw`puaotborcnqdmoelnfl\ egZXhLPi8NjALkCKlEImFGnHFoJDpLCqMErQGsTItWKuULvTMw\ ROxQPyOQzNPzPOzQNzRNzSTzRZzQdzQjzPpzOvzOozSzzVzzYz\ z`zzdzzgzzjzzmzznzznzznzznzznzznzznzznzzlzzjzzhzzf\ zzdzzbzz`zzczzfzzizzlzzozzrzzuzzwzzozzhzUazZVzcOzh\ SzmWzqZzvbzzeztZzoTziNzdHzdkz_hzWfzRdzNazI_zEYzAWz\ D_zGbzJezMhzPkzRnzRmzRlzRlzRkzRkzRjzRjzJlzCnzDozEo\ zFpzFpzGqzHqzIrzIrzvGzkNz`UzQ`zSVzUPzWJzYDz_7zkAzk\ Azl9zl9zl8zm8zm7zm7zn6zn6zn6zl5zj5zi5zg5zf5zd5zc4z\ a4z`4zZ4zY4zW4zV3zT3zS3zQ3zO3zN3zL3zK2zI2zH2zF2zE2\ zC2zB1z91z81z61z51z31z21zsgzqezpdznczmbzlazj`zi_zg\ ZzfYzeXzcVzbUz`Tz_SzYhzY_ } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 29-08-09 (Various Distortions [No Rating])
by Jim Muth 28 Aug '09

28 Aug '09

FOTD -- August 29, 2009 (No Rating) Fractal visionaries and enthusiasts: Check the philofractal list for a longer discussion. Today's image is more a fractal study than any kind of art work. But as a combination of Z^2 and Z^(-2) it is still worth a look. The image is named "Various Distortions". I gave it this name when I saw in it the three types of distortion that can afflict Mandeloids. These distortions surely have sound mathematical causes, but other than the non-critical type of distortion, I have no idea what these causes might be. The first type of distortion appears in the dark Mandeloid fragments vaguely showing in the background in the northeast and southeast parts of the fractal. This distortion appears when the starting point of Z is set to a non-critical value. This particular distortion can be readily seen by calculating the type=mandel Mandelbrot set and setting the parameters to something between zero and one. The distortion simply cuts off part of the set. The second type of distortion is clearly visible in the two prominent Mandeloids on the X-axis. In the Mandeloid on the left, the main period-2 bud is too large and the higher-order buds are bunched toward East Valley, while in the Mandeloid on the right, the main bud is too small and the higher-order buds are spread out toward the main bud. I have no idea of the mathematical cause. The last type of distortion is visible in the two smaller asymmetrical Mandeloids at the top and bottom of the image. In this case the entire system of buds is skewed to one side or the other. In the buds in the image, this skewing is not too severe, but it sometimes becomes so severe that the main period-2 bud is impossible to find without checking the actual orbits of the points. Once again I have no idea of the cause. Since the image is more a mathematical study than a work of art, I could give it no rating. But with a calculation time of under 15 seconds, at least on my recently rehabilitated middle-aged 2000mhz machine, there is no reason for anyone to miss seeing the distortion. Of course, the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is still more fun than calculation. Heavy clouds and periods of rain spoiled Friday here at Fractal Central. The temperature of 70F 21C was irrelevant. The fractal cats checked the outside several times, but when they saw too much rain and no sign of the end of the world. they went back to sleep. My day was rather busy but not frantically so. The next FOTD is scheduled to be posted in 24 hours. If an unexpected antiquing expedition comes up, the FOTD might be delayed however. Until next time, take care, and prepare. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= VariousDistortions { ; time=0:00:14.88-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.861346/0/0.814578 params=0.1/-2/0.55\ /2/0/0/0/0 float=y maxiter=350 inside=0 logmap=yes symmetry=xaxis periodicity=10 colors=000wkCri0mg3he6cc9ZbCU_BPXAKU9FR9ANH5JO1FV1\ Ba07h03z9DzINzQXzZfzfpzamzXjzSgzNdzIazDZz8Wz4UzCQz\ KNzSJz_GzgDz_AzS8zL6zD4z62zWSzMBzNAzNAzNAzNAzNAzNA\ zNAzNAzNAzNAzNAzNAzNAzXSzehncimajl_jkYkjWliUlhSmgR\ mfPneNodLocJpbHqaFq`Dr_CrZFs_Ht_Ju_Lu_Nv_Qw_Sw_Ux_\ Wy_Yy_iwOuvDtrFsoHrlJqiLpfNobPn_RnXSmUUlRWkNYjK_iH\ ahEchBdiEejGekIelLemNemPenSfoUfpWfqZfr`frbfodble_j\ fXghUeiRbjO`lLYmIWnFTpCRq9Or6Ms3Pp4Rn5Tk6Vi7Xf8_d9\ aaAc_BeXCgVDjSElQFnNGpLHrIItGJvPXxYjzexzguzhrziozj\ lzkjzlgzmdznazoZzpXzqUzrRzsOztLzuJzvLDwzFxzGyzIzzJ\ zzLzzMzzOzzPzzRzzSzzUzzVzzWzzTzzQzzOzzLzzJzzGzzDzz\ Bzz8zz6zz9zzBzzDzzFzzHzzJzzLzzNzzPzzRzzTzzVzzTzzRz\ zQzzOzzNzzLzzKzzIzzHzzFzzEzzCzzBzkEzeGz`IzWKzRMzMH\ zKCzI7zG2zE7zFBzGFzHJzIOzJSzKWzL_zMczIfzEizAlz6oz2\ gz3_z4Sz5Kz6Cz79z67z65z53z51z5vzNqzOlzPgzQbzRYzSTz\ TOzUJzVEzW9zX5zYCzZWzUSzP } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 28-08-09 (Spots on a Window [7])
by Jim Muth 27 Aug '09

27 Aug '09

FOTD -- August 28, 2009 (Rating 7) Fractal visionaries and enthusiasts: Sorry! No philofractal version today. I had no time for philosophy. Due to a work rush, today's discussion is very brief. The image is located in the same parent fractal as yesterday's image, though its character is quite a bit different. Some but not all of the difference was achieved by rendering the image with the outside set to 'tdis'. When all was said and done, I named the image "Spots on a Window" and rated it at a 7. The fast calculation time of 1-1/2 minutes will make the task of calculation a minor pleasure. Another pleasure will be to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and gaze in awestruck wonder at the finished image posted there. Heavy clouds with occasional light rain and a temperature of 68F 20C marred Thursday here at Fractal Central. The fractal cats' day was marred by too few treats. The next FOTD will be posted in 24 hours. Until then, take care, and do what you will. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Spots_on_a_Window { ; time=0:01:31.68-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip center-mag=-0.7552993857561324/-2.623422967775008/\ 1.915784e+012/1/61.6/0 params=-1.5/-1.5/-0.5/-5.5/\ 0/0/0/0 float=y maxiter=1000 inside=0 outside=tdis logmap=59 periodicity=10 mathtolerance=0.05/1 colors=000b5dd6Zf7Sh8Mi8Gg9PfAXdAecBmbBuaGs`Mq_RpY\ XnXalWgjZMgYShXXhWbiVgigyG`rViiGejOakVYlbOMPS__5JR\ AOVETYIY`NbcRgf8OhBSiEViHYiK`iNciQfiTiiXjYWk`WkbVl\ eVlgqO7e`RPyBzzPQsSKbVDVY7M`1Eb5FZ8GVBHREHNHIJKJFN\ KBQK7deXzzzovtmsskorilrgiqeepcboa_ovLWcPUcSTdWSZZR\ TbQNePHhOFf_EdkySprRqlRrfRs_RtURuORvIRwJUsJXoJ_kKb\ gKecKh_KkXJmTJoPIqLIsILpGNmEPkCRhATf8Vc6Xa5abGecRi\ damelddoXdrPduIiiBmY5qM3aO2MQ5SL8YGAcCDi7Fo3InBLnI\ NmP`lnQmWTlbDxdJtfPphfWTc`Y`daYhe8fpCgoFhnIimMjlbZ\ RgYOlYMqXJuXHoTJiQKcNLYJMSGNMDOOLUPTZR`cShiUpnVwsZ\ iobXkeKgjR_oXStcKyiDrkGklJdmLYnORoQKpTEqVXcInR6cOI\ TMTQOSNPSKQRHRRESQBTQ8UQGSWOR`WQfcOkkNqrMvgTwX_wMe\ xBlx1rx9lvHftPasXWqdRpcRnbRlaRj`Rh_RfZRdVjsSknPljM\ meKnaNhcPceRZfTUhVPjXKknxXhyYcyZZy_Ty`OyaJya9gO0RA\ 1WF1_J2cO2gS6U_AGgE2oZTsrrvrT9HwvJluLbtNStPIsQ8sSF\ pUMmVTjX_hYfe_mb`t`Z3q`4j } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 27-08-09 (End of the World [6])
by Jim Muth 27 Aug '09

27 Aug '09

FOTD -- August 27, 2009 (Rating 6) Fractal visionaries and enthusiasts: There is no philofractal version of today's FOTD. Today's image lies in the fractal that results when various negative portions of Z^(-1.5) and Z^(-5.5) are combined and (1/C) is added. I named it "End of the World" and rated it at a 6. The name came about while I was watching one of those watered- down 'science' shows on one of the pop-science channels and the commercial break came. Believe it or not, one of the ads was from a group selling lottery tickets to escape the end of the world, which according to the Mayans and supposedly confirmed by science, is coming on December 21, 2012. I didn't catch all the details, but I suppose that the group is preparing survival chambers which will hold only a limited number of people, and when the end comes, only a lucky few winners will gain admit- tance to the survival chambers or space ships or what ever. Oh well, I'm not going to do anything. It's only the end of the world. I thought it was another serious something to worry about. I'd best get back to worrying about the asteroid or the volcano or the swine flu or the solar storm or the climate change or the . . . wait a minute . . . I thought the world was supposed to have ended almost 10 years ago at midnight December 31, 1999, when Y2K struck and all the computers went crash and civilization collapsed. The calculation time of today's image of a measly 2-5/6 minutes is just the slightest slow. So why not whiz out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. BTW, I cleaned all contacts and reseated every card in the 2000mhz fractal machine, and it's once again running like new. A rather nondescript summer day passed unappreciated here at Fractal Central on Wednesday. The partly cloudy but hazy skies were OK, as was the temperature of 86F 30C. The fractal cats were more interested in chasing each other up and down the hallway. My day was busy. The next FOTD will be posted in about 6 hours. Until then, take care, and be first in line. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= End_of_the_World { ; time=0:02:51.04-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.6399078173036166/+0.5867437930194448\ /4.255127e+009/1/22.5/0 params=-1.5/-1.5/-0.5/-5.5\ /0/0/0/0 float=y maxiter=1800 inside=0 logmap=280 periodicity=10 mathtolerance=0.05/1 colors=0009NJ6LH8NJAOLCPNEROFSQHTSJUULWVNXXOYZQZ`S\ `aUacWbeXcfZec`gabhZdjXfkUgmSioPkpNmrKosIquFrvDoqM\ mmUkhaidjg_reWzX_vObrGenFbmE_mEYmDVmDSmCQlCNlBKlBI\ lAFlACm9Cm9Bm8Am8Bm9CmADmAEmAFmAGm9Hm8Im7Jm6Km5Lm8\ MhBNfDOdEPbFQaHR`IS_JTZLUYMVXNWWPWVQWURWUSWVWXTZXS\ aXReXQhXPkXOmZRn_To`VpaXqb_rcatecufevghwhjxilxjnvg\ lsekrejn`ikZhiWgfUfcSeaPdZNcXLbYMaZM`_N_`N_aNZbOYc\ OXgDOgCLfAJf9Ge7De6Ad48d35c12c00Y23S46M69H7BOALVDV\ aGdhJnnMwkJuhHsfFqcDoaBnZ9lW7jU5hR3fP1eQ4dQ6cQ8cRA\ bRCaREaSG`SI`SK_TMZTOZTQYUSXUUXUWWUYWRZVP_VN`VLaVJ\ bVHcUFdUDeUBfU9gU7hU8eW9cYAa_B_aCYcCWeDUgESiFPkGNm\ GLoHJqImsJFuKmwKBxMAvOAtQ9sS9qU8pW8nY7m_7ka6jc6he6\ gg7ci8`j9XlAUmBQoBNpCJrDGsECuF9vF6sI9qLBoODmQFkTHi\ WKgYMe`ObcQ`eSZhVXkXVmZTp`RsbPudzv`NwXzxTLyPzzLJzH\ zzDHz9zz6JzAzzEPzHzzLVzPzzS`zWzz_fzbizfzzjnzmzzjfz\ gzzd_zbzz_SzXzzULzSzzPDzM } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 26-08-09 (Heavenly Vision [7])
by Jim Muth 25 Aug '09

25 Aug '09

FOTD -- August 26, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image mixes negative Z^(-2.3) with 0.4 negative part of Z^(-6.4), then adds (1/C), which turns the naturally inside-out parent fractal rightside-out. This parent is a shapeless thing with a large bay on its southern side. This bay has Mandeloid buds along its shore line, with filaments extending inland from these buds and bits and pieces of scrap material scattered about the filaments. Today's scene lies inside one of these pieces of scrap material. I'm not quite sure what to make of the image, though I think I see quite a few disembodied elephant trunks in it. This means that an East Valley cannot be too far away. In a moment of high enlightenment I named the image "Heavenly Vision". I guess all the light blue shades inspired the name. The rating of a 7 is boringly average, but like an average super- nova, it can still be quite interesting to see from close range. The calculation time of 53 seconds will pass in a flash. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will be just as fast, and the full philofractal discussion is posted there. Tuesday began with a fog bank hanging over the river, but by 9am the fog lifted to reveal a blue sky that lead to a near perfect summer day here at Fractal Central, with wall-to-wall sunshine, low humidity and a temperature of 84F 29C. The fractal cats enjoyed the conditions, but they did not enjoy a beat-up stray tomcat that prowled the yard for a while in the morning. My day was busy enough to keep boredom away yet still allow time for a FOTD. The next FOTD will be posted in 24 hours. Until then, take care, and maybe its all just a dream. But if so, who or what is doing the dreaming. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Heavenly_Vision { ; time=0:00:53.40-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+0.461851890412/-1.467279726811/2223760\ /1/-3.5/0 params=-1/-2.3/-0.4/-6.4/0/-90/0/0 maxiter=1500 inside=0 logmap=85 periodicity=10 colors=000KKUKLWKMXKNZKO_KP`KQcJReISgGTjFUlEVnCWqB\ XsAYuD_vF`wIaxKbyNczPdzSezUfzXgzZhzaizcjzfkzhlzkmz\ mnzprzrvztzzuzyuvwuruumquimuhivfeveavcYvbUz`Qz_MzZ\ IzbNzeVohacliSoqMrxNoyNmyNjyOhyOeyOcyPayPZyPXyQUzQ\ SzQPzRNzRLzRIzSGzSDzSBzS9zPLtMWnJfhHqbLpfPoiSnmWmp\ ZlsdejiZboSUtLMoMQjNTeOX`O_WPbRQfMQiHRmCSp8SsCRoGR\ kKRhORdSQ`WQY_QUcQQgPNkPJoPFsPCqQEpRGoSInSKlTMkUNj\ UPiVRgWTfXVeXXdYYbZ_aZa`_c_`eYagXahWbjVclTcnSdpRer\ QesRgrRiqRkpRloRnnRpmRqlRskRujRvjPskOplNnlMkmLhmKf\ nJcnI`oHZoFWpETqDRqCOrBLrAJs9Gs8Dt7Bt8Bs8Br9Bq9Bp9\ BoABnABmBBlBBkBBjCCiCChDCgDDfEDeEDdFDcFEbFEaGK`GK_\ HK_HKZIUzIUzIUzJUzJUzKUzKUzLUzLUzLcQFc3Ic7LcAOcDRc\ HUcKXcN_cRbcUecXhc`kccncfjcggcgcmz`mzYmzUrzRvzOzzK\ zzHzzEzzAzz7zz4zz3zz3zz3zz3zz3zz2zz2zz2zz2zz2zz1zz\ 1zz1zp1zp1zp1zp5zq9zqDzqHzrLzrPzrTzrWzmYzh_zi`ziaz\ jbzjczkdzkezkfzefz_TzcTzc } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 24-08-09 (Ring Around the Posie [4])
by Jim Muth 25 Aug '09

25 Aug '09

FOTD -- August 24, 2009 (Rating 4) Fractal visionaries and enthusiasts: Check the philofractal version of this discussion for a philosophical outburst. Have we ever seen a fractal similar to today's? The answer is neither yes nor no, but how many times. Today's image shows a minibrot on a filament, one of the easiest kind to find. It was so easy to find in fact that I could rate the image no higher than a miserable 4. The parent fractal is a humongous thing about 1000 times the size of the Mandelbrot set. It is shaped like a distorted M-set with rings on three sides. To see this parent, set the magnitude to 0.001, the center to 0,0 the rotation to zero, and reset the logmap to zero also. Today's image is located in the East Valley area of a larger minibrot on the filament leading to the northeast ring. The name "Ring Around the Posie" refers to the rings in the image. Such rings are a universal feature in most double- negative fractals. I have no idea what a 'posie' might be, or even if it's a real word. The calculation time of 5 minutes means that a modicum of patience will be needed to calculate the image. The impatient may have their impatience relieved by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Lots of clouds and oppressive humidity prevailed here at Fractal Central on Saturday. The temperature of 81F 27C felt more like 104F 40C. The fractal cats, not worried about humidity, seemed quite comfortable as they lounged most all day on their shelf by the window. Sunday was sunny and less humid. My Saturday was good enough. Sunday was better. But that is no reason that tomorrow should not be better yet. The next FOTD will appear in around 24 hours. Until then, take care, and be subjectively objective. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= RingAroundThePosie { ; time=0:05:04.61-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip center-mag=+268.2218482282329/+86.61052102191096/\ 8612658/1/-145/0 params=-3/-1.3/-0.3/-3.3/0/0/0/0 float=y maxiter=3600 inside=0 logmap=-436 periodicity=10 colors=000Ok9PkDQkIRlMSlQTlVUlZVmbWmgXmkXmoUikSehQ\ aeNYbLV_JRXGNUEJRCGO9CL78I54F31CS84UH7cPAmXCreFvmI\ zuKrrLmpMcnMUlNNjONhONfPNdQNbQN`RNZRNXSNVTNTTNRUNP\ VNNVNLWNJWRIVUHUXGU_FTbFTfESiDRlCRoBQrBQqCOqDMqEKq\ FIqGGpcEpcCpcApc8pc6rcCtcIvZOwUUvRXuPZtN`tLbsKdrIf\ rGhqEkpCmoBoo9qn7sm5um4wk8tjBqiEnhHkfKheNedQbcT_aW\ X`ZU_aRZdOXaQV_STYURWWPUXOSZMQ`KObIMcGJeEHgDFiBDk9\ Bl79n57p35r23s48q5Do6Hm7Ml8Qj9VhBZgCceDgcElbFp`GuZ\ HyYOvXUsX_pWemWkjWiiYhiZgi`fiaeibdidciebifaih`ii_i\ jZhlYhmXhnWhpVhqUhrThtShuRhvQhxPhyOhzMfsLglJheIiZG\ jSFkLDlECm7Bn9AoAApC9qD9rF8sG7tH7uJ6vK6wM5xN5yO6zQ\ 7zR8zS9zTAzVBzWCzXDzYEzZFz`GzaGzbHzcIzdJzfKzgLzhMz\ iNzjOzlPzmQznRzoRzpUzmWzjYzg_zdbzadzZfzXhzUkzRmzOo\ zLqzIszGqzJozLmzNlzPjzRhzTfzVezXczZaz``zbZzdXzfVzh\ UzjSzlQznOzpNzrLztJzvIzxJzhJzUJzFKzELzEMzENzENzEOz\ EPzEQzERzESzESzETzFNz4Nz4 } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 22-08-09 (Egg-zactly Eastern [6])
by Jim Muth 25 Aug '09

25 Aug '09

FOTD -- August 22, 2009 (Rating 6) Fractal visionaries and enthusiasts: For a discussion about aliens from space, check the philofractal version of this FOTD. As far as fractals go, today's image is quite simple. It simply subtracts Z^7 from Z^8 and adds C. At first glance, the parent fractal resembles the Z^8+C Mandeloid, with some irregularities at its eastern end. A second glance shows the first glance was correct. Today's image lies rather deep in the valley on the positive X-axis, which is basically an east valley, and just about the only part of the parent fractal with true quadratic minibrots. The name "Egg-zactly Eastern" refers to the location of the scene in its parent and hints that calculating fractals is an egg-head activity. The rating of a 6 implies that I consider the image average. The calculation time of 11-3/4 minutes will drag. I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Morning clouds here at Fractal Central on Friday were followed by a period of moderate rain at midday and a partly cloudy afternoon, which, with a temperature of 81F 27C, was quite pleasant. The fractal cats were happy; I was appropriately busy; the next FOTD will be posted in 24 hours. Until then, take care, and keep looking up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Egg-zactly_Eastern { ; time=0:11:46.46-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+1.001517485529658/-0.00009139358870301\ /4.087e+009/1/170/0 params=1/8/-1/7/0/0/0/0 float=y maxiter=4000 inside=0 logmap=712 periodicity=10 colors=000_f_Zg_Yh_Yi_XjZWkZVlZe2td4sd6rc8qcApbCob\ EnaGmaIlaKl`Mk`Oj_Qi_RhZTgZVfYXeYZeY`dXbcXdbWiaWp`\ fv_arV_nVZjVXgVWcVU_WTWWRTWQPWOLWNHWMEWLHZKKaKNdJP\ fJSiIblOgrLapIXnFSlEPkDNjSAsW71SG9OPGKzNGxU8tbBqaD\ n`Fk_HjZJhYMfXOdWQcVSaUU_TXYSZXR`VQbTPdEjdL_dSPzcD\ r`EdYFaVGYSGVQHRNIOKIKHJHFzDCvA9r66m10h34c47Z6AU7D\ P9GKAJFCMADP7FS5GV3FU5FT7FT8FSAFRCFRDFQFEPHEPIEOKE\ NMENNEMPELRELSFJRFIQFHPFGOGENGDMGCLGBKGAJH8IH7HH6G\ H5FH1BH4EH7HHAKHDNHGQHJTHMWHPZHSaHVdHYiH`lHcoHfqKh\ rHjrClrEmrFdlHWfIN`JFVDCL79C263_Vg`Sd`QaaN_aLXbIUb\ GScDPcBMaD5bBDc9Kd7Rf4ce5Ye6Sc6md7Gc8Am4cc85aB8ZEB\ XHDULGSOKPRPNUULYZI`cGchDfmBjr8mv6pz4sz5oz5lz5iS6e\ N6bH6_B6X65W63W52W51W52X63Y74Y85Z96ZA7_B8_C9`DAaEB\ aFCbGDbHEcIFcJGdKGdKHeLIfMJfNKgOLhPViZMjQNkROlSPmT\ QnURoVSpWTqXUrYUsZUteUudUvdUwdZxccychzcmzcrzbvzbzz\ bzzbzzazzazzazz`zz`zz`zz` } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 25-08-09 (Deep-Blue Blues [No Rating])
by Jim Muth 24 Aug '09

24 Aug '09

FOTD -- August 25, 2009 (No Rating) Fractal visionaries and enthusiasts: Check the philofractal list for a longer discussion. Today's image came about when 0.3 part of Z^5 was combined with Z^2 before C was added. The indescribable parent fractal is little more than a jumble of Mandeloid parts, some critical, some not. Today's image is located near a larger minibrot in an area with East Valley tendencies in one of the more critical appearing parts of its parent. The image has East Valley hints, though no true elephants or pop-eyes are apparent. I named the image "Deep-Blue Blues" because I kind of got carried away with the blues in the image. Since I lost control of the coloring, I could give the image no rating, though a rating around 6.5 would be pretty close. The calculation time of 1-1/2 minutes will cause no one any inconvenience. And those with absolutely no time to spare may view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Blue skies, puffy clouds, lots of sun, lower humidity and a temperature of 81F 27C made Monday near ideal here at Fractal Central. The fractal cats appreciated the afternoon sun that came in the window where they watch the world. My day was average. The next FOTD will be posted in 24 hours. Until then, take care, and be one of them. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Deep-Blue_Blues { ; time=0:01:30.78-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.8097582757255464/-0.3657870943551191\ /1.4693e+012/1/5/0 params=1/2/0.3/5/0/0/0/0 float=y maxiter=1500 inside=0 logmap=91 periodicity=10 mathtolerance=0.05/1 colors=000`8wY2yZ8x_Ew`Kv`QvaWubatbgtYbqUYoQUmLPkH\ LiDGg9Ce44H000aUfcUceUmjavnizrqzvxzoszhozbjwWfuQbv\ ZjafrSnzIjrOfjTbcYZWbVPgRHlOAqKJjGSdC_Y8hS4qL0yF3p\ K5hO7`SATWCL_EDcG5gL7dQ8bV9`_BZdCXiDVmETkKSjQRhWQg\ aQegPdmOcrOZoZUljPjuUgpYelache`diZ`mXXqVTnTQlSOiRL\ gPJdOGbNEaPKaRQ`SW`U`_Vf_XldpgaokZmoWK_TMYTOWTQUTS\ XTVYTY_Q`cNcjKfsHnjEtnCzkFskIlhL`dNTbS8YMFQHMICSBO\ TK_UTkVawWjrRimNhhIgcEfZAfjfdmbcoZbqVbtRavNaxJ`zF`\ pEUfEOYEIOECFE6ACD6AKABJDCIGCHJDGMEFPEEUIHYLKaONeR\ QiUTmXWq_YjWWdTVYPTSMSLJRFFP8CO29Nu4bp9ZlDWgIScMP_\ QMVVIRZFNbCKcEHdGEeIBfJEeOHeSKeWMe_PecSegUekThhTje\ SlbSn`RqYRsVQuSQwQ3`s2ao2bl2ch2ce5ac7`b9_aBZ`DY_FX\ ZNS`VNbaJdiEfq9hx5isCenIaiOYdUU__QbCGYGITJKONMJQOE\ TQ9XS4_U0bW2fS3iP5lM6oI8rF9uCAx9Bq6Ck3Ce0HfALgKPhU\ UicYjmajvdnfgrRiuCcjBZ_BUPBPEBK3BP8FTDIYHMaMPeQS_F\ JU5BKAGBFL2JQlYniSpfLscFu } frm:MandAutoCritInZ {; 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)+(p4)), 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] FOTD 22-08-09 (Egg-zactly Eastern [6])
by Jim Muth 22 Aug '09

22 Aug '09

At 09:34 PM 8/21/09 -0700, you wrote: >Phlofractal? I thought that this had died, and I have missed it. I tried >several times to find it with no success. I signed on and sent a couple >of test messages. They were not bounced, but I never saw any signs of >activity. How do I get there? To subscribe to the philofractal list send an e-mail to philofractal-subscribe(a)lists.fractalus.com BTW, due to an antiquing journey there will be no FOTD for August 23. Jim M.

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FOTD 21-08-09 (Something Somewhere [5])
by Jim Muth 20 Aug '09

20 Aug '09

FOTD -- August 21, 2009 (Rating 5) Fractal visionaries and enthusiasts: The time has come to start sharing some of the opinions and philosophy I have been pondering for several years. So those who remember the lively discussions on the old philofractal list may soon find themselves back in the good old days. But this time nothing will be sacred, especially politics and religion, so stay tuned for some action in the days and weeks to come. If the philofractal list is still in business, I'll post the opinionated philosophy there, if not I'll find some other forum. Here is today's image. Take it or leave it. It's a scene in the fractal that results when Z^(-0.12) is combined with Z^(2) and (1/C) is added. The scene is obviously located on a filament. The coloring could be a lot better. The name "Something Somewhere" is true of all fractals. I rated the image at a 5 because I feel this is all it deserves. The colors are bad and since the image is not animated, it just sits there looking at you and doing nothing. But the calcula- tion time of 1-1/2 minutes is short enough to make it all worth while. As always, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The temperature of 84F 29C was not too bad, but the humidity ruled here at Fractal Central on Thursday. A light midday shower just made things worse. The fractal cats are not bothered by humidity, so they suffered no discomfort. My day was busy -- enough said. The next FOTD will be posted in 24 hours. Until then, take care, and all the world loves an internet troll with good stuff to say. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SomethingSomewhere { ; time=0:01:31.61-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.5350217127618986/-0.3948405689023601\ /7.323998e+010 params=1/-0.12/1/2/0/0/0/0 float=y maxiter=500 inside=0 logmap=80 periodicity=10 colors=000QRmSUmWYm_amcemgimkmmoqmsrlorhjp_elR`hId\ cRg__jWgmSpmSsc_OUZ_KXQAPH298ESEQaJamPlrUenPZfKTYF\ MQAFH5990UQrKIRAB0EF4HI8LLCOPGSSKVVNWYRX_VYaZYcbZe\ f_gj`in`kqZemY_jXUfWPcXTfYXiZ`l_do`hraluaowdhrfamh\ VhjOclHZsIHyJ0sI4mI8gIC_VATg8QhAOhBMhDJiEHiGFiHPjN\ YkTgkYplcylhjOGcPNXQUQR`JSgCSmFXeHaZKeRMjKPoCRs51k\ AbHcY9LT13U9AUGGUNMUUSU`YUgcOmZJsUEyQGrPHkOJezKZzL\ SzNMzOFzP9zLAzHAzEAzABz7Bz3Bz0Bz1Ez2Gz3Jz3Lz4Nz5Qz\ 6Sz6Uz8Vz9VzAWzCWzDXzEXzDSzCNzBIzGOzLUzz_Yzefzjozf\ lzbjzZgzVezRczN`zJZzFXzGSzGOzGKzHFzHBzH7zH3zIlzEbz\ BUz7Lz4Cz13z6jz9izBhzEhzGgzJfzLfzQgzzgzzgzz8zzRzzZ\ zzUzzQzzEzz3zz6zz9zzCzzFzzIzzKzzL_zNSzOKzQDzRzzWzz\ _zzczzgzzkzzgzzdzz_zzWzzSzzOzzKdzG_zIWzKRzMNzOIzQE\ zS9zU5zVHzvxzMtzQpzUlzYhzadze`ziYzlazidzggzekzbnz`\ qzZtzXczQOzK8zEEzFJzFOzFTzFZzGczGhzGmzG`zLPzQDzV1z\ _AzTJzNizkazhUzeNzbFz_7zX } frm:MandAutoCritInZ {; 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)+(p4)), 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] Fractal animations on YouTube
by JackOfTradeZ＠comcast.net 19 Aug '09

19 Aug '09

. The zoom was kinda dull, but the 3D one is awesome. Wish I could do that in fractint ... There are MANY fractals on youtube - just do a search. Here are some more good ones <g>: http://www.youtube.com/FractAlkemist Cheers .

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FOTD 20-08-09 (A Second Look [4])
by Jim Muth 19 Aug '09

19 Aug '09

FOTD -- August 20, 2009 (Rating 4) Fractal visionaries and enthusiasts: Today's image rates a 4. Normally, a fractal with such a low rating would never qualify as a FOTD. But for some reason I kind of liked what I found when I made a slight zoom into yesterday's image. I could rate the image no higher than a 4 because it actually is a repeat, but those who enjoy variations on a theme may find a bit of pleasure in the hastily colored image. The name "A Second Look" says it all. The brief calculation time of 2 minutes means little time will be wasted in taking a second look. Perhaps the best way of taking that second look is to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another muggy day with a temperature of 90F 32C here at Fractal Central on Wednesday was put to rest when a gust of cool air arrived from the north at 5pm, dropping the temperature to 75F 24C. The threatening cloud that accompanied the gust passed over harmlessly. The fractal cats approved. As might be expected, my day was very busy. But whether I'm busy or not, the next FOTD will be posted in 24 hours. Until then, take care, and live lively. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Second_Look { ; time=0:02:09.26-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident center-mag=+0.582575936368227/+0.8363401268104876/\ 4.716808e+010/1/22.5/0 params=0.5/3/-1/2/0/0/0/0 float=y maxiter=4200 inside=0 logmap=35 periodicity=10 mathtolerance=0.05/1 colors=000WTkZWh`Zec`bfc_hfXkiUmkSaXNQJIE5ED7LC9SB\ BZADe9Fl8Hs7IyCUoRWeV_XdaNhcEgcHfaKhYMhUPfQShMUkIX\ mFZkKVjORhTNgXKfaGdeCcj8bn5kKIiSDg_9eg4co0el5fiAgg\ FhdKjaPk_UlXZmVbnX`oY_pZYq_Xr`WsaUtbTucSpYQkTPfONb\ JMeMKgPJiRIkUHmXGoZFqaEscDtZKuUQuPWvKavGgnIigKj_Ml\ TOmLQoESpFSpFSpFSpFSpFSqFTqFTqFTqFTqGTqGUqGUqGUqGU\ qGUqGVqGVqGVqHVqHVrHVrHVrHWrHWrHWrHWrHWrHXrIXrIXrI\ XrIXrIYrIYrIYrIYrIYsJYsJZsJZsJZsJZsJZsJ_sJ_sJ_sK_s\ K_sKZsKYsKXsUWscVsiUskTskTvlUrmVonVloWipXfqXcrY`rY\ YsZUt_Ru_Ov`LwaIxaFybCyc9xh8wm8vr7vv7uz6tz6tz5sz5r\ z4qz4qz3pz3oz2oz2pz5pz8pzApzDqzGqzIqzLqzNozQnzSmzV\ kzXjzZizagzcfzfezhczjbzmazo`zqVzlQzgLzcFzZAzU5zQ8z\ SAzUCzWEzYGz_IzaKzcNzePzgRziTzkVzmXzoZzq`zjbzdczYe\ zSgzLhzFTzyTzyTzyUzyUzyUzyUzyUzyUzyUzyUzy1zS2zT2zT\ 2zU3zU3zU3zV4zV4zV4zW4zW5zW5zX5zX6zX6zY6zY6zY7zZ7z\ Z7zZ8z_TzZ_zSfzLbzNZzPWzQ } frm:MandAutoCritInZ {; 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)+(p4)), 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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not bad at all...
by Guy Marson 19 Aug '09

19 Aug '09

Hi fractinters, some fratal animations (a/m/o) on You Tube: http://www.youtube.com/watch?v=FkJ2d2krDok&feature=fvsr http://www.youtube.com/watch?v=GZ0MAx-30C0&feature=related gm ##################################################################################### Scanned by MailMarshal - Marshal's comprehensive email content security solution. #####################################################################################

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FOTD 19-08-09 (Pales by Comparison [6])
by Jim Muth 18 Aug '09

18 Aug '09

FOTD -- August 19, 2009 (Rating 6) Fractal visionaries and enthusiasts: I notice that I forgot to include the formula in yesterday's FOTD parameter file. But it should have been no problem since I have posted the MandAutoCritInZ formula hundreds of times. A question has arisen about the calculation time of the FOTD images. The time listed in the parameter file is the time I estimate the images would have taken to calculate on the Dell P4-2000mhz unit, the up-and-down machine that is currently in down mode. All FOTD images are presently being calculated on the ancient nameless 11-year-old Pentium-200mhz machine, which still runs like new. (Not much to say for Dell hardware.) I simply edit the calculation time, cutting it by 75 percent to convert the time. Yes, the 2000mhz unit runs only 4 times as fast as the 200mhz machine. (That is except for the type=mandel and type=julia, where it runs 20 times as fast.) Today's image lies on the northwest shore line of the egg-shaped Mandeloid that results when Z^2 is subtracted from 0.5 part of Z^3 before C is added. To add a bit of interest I rendered the image with the outside set to 'tdis'. Then I named it "Pales by Comparison". The name came about when I had to tone down the too-intense warm reds. The listed calculation time of 3-1/4 minutes is actually 1/4 of the actual 13-minute calculation time on the Pentium 200mhz machine. The rating of a 6 is average. So why not forget all this calculation confusion by viewing the completely-calculated image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Stifling 93F 34C heat and 75-percent humidity prevailed here at Fractal Central on Tuesday until it was broken up at 5pm by a cooling thunder-shower that dropped the temperature to a far more reasonable 73F 23C. The evening was then quite pleasant. The fractal cats would have been happier if the cool-down had come earlier, but they hung in there bravely and were finally rewarded. My day was busy. The next FOTD will be posted in 24 hours. Until then, take care, and never give up the search. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= PalesBy_Comparison { ; time=0:03:14.85-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.582575936368227/+0.8363401268104876/\ 9.677674e+009/1/-20/0 params=0.5/3/-1/2/0/0/0/0 float=y maxiter=4200 inside=0 outside=tdis logmap=35 periodicity=10 colors=000u_Ov`LwaIxaFyaCxa9v_8tY8rW7qT7oR6mP6lN5j\ K5hI4gG4gD3fB3e92e72fD5fJ8fPAkVDq`GqfIqlLqrNosQnsS\ msVktXjtZitagucfufeuhcvjbvmavo`vqVwlQwgLwcFxZAxU5x\ Q8wSAvUCuWEtYGs_IraKrcNqePpgRoiTnkVmmXloZlq`kjbjdc\ iYehSggLhgFToyTpyTpyUpyUpyUpyUqyUqyUqyUqyUqy1`S2aT\ 2aT2aU3aU3aU3bV4bV4bV4bW4bW5bW5cX5cX6cX6cY6cY6cY7d\ Z7dZ7dZ8d_ThZ_oSfuLblNZdPWXQSPSOHUL9VGFkbXOym1nh2d\ d3V_4LW5ITPFQgCNz8cy5txGhoNekUch``efZbgNXhCSh1NlB_\ oLlZAjJ0iF7aBEUAIQ9LN9PK8SH8VE7SC7QB6N96L86J7GPBPV\ FY_IfeMojPbYUQLYVMWZNUbNSfOQkPOoPMsQKwQJpMKjJLcFLY\ CMR8NL5NP6UT7`U7YV7VV7RW7OW7LSESOLZLRdHYkEcqDXpDQp\ EQpEQpEQpERpERpERpERpERpESpFSpFSpFSpFSpFSqFTqFTqFT\ qFTqGTqGUqGUqGUqGUqGUqGVqGVqGVqHVqHVrUpxHVrHWrHWrH\ WrHWrHWrHXrIXrIXrIXrIXrIYrIYrIYrIYrIYsJYsJZsJZsJZs\ JZsJZsJ_sJ_sJ_sK_sK_sK`sK`sK`slThkTlkTokTskTvlUrmV\ onVloWipXfqXcrY`rYYsZUt_R } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 18-08-09 (Mixed Messages [5.5])
by Jim Muth 17 Aug '09

17 Aug '09

FOTD -- August 18, 2009 (Rating 5.5) Fractal visionaries and enthusiasts: Today's image lies in the fractal that results when 5.5 negative parts of Z^(-1.5) are combined with 2.5 negative parts of Z^(-5.1) and (1/C) is added. The portions are rather whimsical, as is today's image, which I named "Mixed Messages" for no logical reason. The rating of a 5.5 indicates that I do not consider the image to be of the top rank, but I still feel it is worth the brief 1-2/3 minutes required to calculate it from scratch. As for more details about the image, there is little to be said. It's an image that speaks for itself, and even then it has little to say. Perhaps the best way to see the image and avoid the math is to surf out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Hot sun and a temperature of 93F 34C on Monday reminded us that we're still in the middle of summer here at Fractal Central. The fractal cats reminded us that they would like it a little cooler by stretching out in the doorway to the bathroom, making us step over them. My day was appropriately busy. The next FOTD will be posted in 24 hours or so. Until then, take care, and don't be too disap- pointed in the political situation. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mixed_Messages { ; time=0:01:41.94-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip center-mag=+0.030179776/-1.406157231/36996.88/1/\ 107.5/0 params=-5.5/-1.5/-2.5/-5.1/0/0/0/0 float=y maxiter=1500 inside=0 periodicity=10 colors=000XMXXNWURURUSOYQL`OIcMQaRX`Wc_`kZerYjyXos\ WpnWpiWpcVqZVqUVqVWnWXkXYiYYfZZd__a``Za`XbaUcbSdcP\ ecNfZVgVahRhiNohOkgOhfOeeObdO_cOWbOTaOQ`ON_OKaQQbR\ VcS_dUeeVjfWogXtk_nnbhqebthXwkSuiQshOqgMofKmeIkdGi\ cEgbCeaAc`8a_6_Z4YY2WX1XW1YV1ZU1ZT1_S1`R1aQ0bP0bO0\ cN0dM0eL0fJkeKheKeeKbeK_eKXeKVeKSeKPeLMeLJeLGeLEG5\ HG5HG5HG5HG5HG5HG5HG5HG5HG5HG5HG5HG5HW2Oe0Vh5RkANm\ FKpKGsPCuU9xZ5zb2oTYZXgI`q2dz9dtGdoNdiUdd`d_Y`VWXR\ UUNSQJQMFOJBVXG`jLftQiqPkiPmeOoYOrVNpPNvJMmEMuKQsQ\ TpWWnaZkgaimdgsgGyUMuRSrPYoNckLihJoeHtbFpdKlfPhhTd\ iY`kaXmfTnjXih`dgc`fc`fc_ec_ec_dc_cc_ccZbcZbcZacZ`\ cZ`dY_dY_dYZdYZdXYdXXdXXdXWMoKPmNRlPTkRWiTYhW_gYbe\ _ddafcdiafk`hm_jpYmrXotWqvVsqYpm`nibleejahhYjfUmdQ\ pbMr`IuZEwXohZliWijUfkRclP`mMYnKVoHToFRlGPjGNgGLeG\ JbHH`HFYHDWHBTI9RI7OI6MI9JMBHPEESGCVI9YL7`N4cP2fQ4\ eR6dS8cSAbTCaUE`VG_VIZWKY } END PARAMETER FILE=========================================

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FOTD 17-08-09 (Pebbles in the Night [7])
by Jim Muth 16 Aug '09

16 Aug '09

FOTD -- August 17, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the fractal that comes about when 4.4 negative parts of Z^(-1.4) are combined with 0.4 negative part of Z^(-4.4) and (1/C) is added. To make things more interest- ing, the scene was half-evaporated by increasing the bailout radius to 850. Then, to add still more interest, the final image was rendered with the outside set to 'tdis' and the inside set to 'fmod' with a proximity of 0.2, which makes it quite difficult to tell the inside from the outside parts. The final result rates a nominal 7, which might be a bit liberal. The name "Pebbles in the Night" refers to the smaller bits and pieces in the image, which, with a little imagination, might be seen as pebbles lying on some forgotten beach. I would prefer the calculation time of 7 minutes to have been shorter, but that's how it goes sometimes. If 7 minutes is too long to wait, why not visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. Midsummer heat continued here at Fractal central on Sunday as the temperature reached 91F 33C. The fractal cats spent the day doing nothing, while asking for more cool air. My day was slow, leaving lots of time for contemplation, which I did quite well. The next FOTD will be posted in 24 hours. Until then, take care, and be happy in your sleep. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= PebblesIn_TheNight { ; time=0:07:05.28-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.5882197682228385/-1.557107074318487/\ 4.726208e+007/1/-137.5/0 params=-4.4/-1.4/-0.4/\ -4.4/0/750/0/0 float=y maxiter=1500 inside=fmod proximity=0.2 outside=tdis periodicity=10 colors=500XZFUZERYEOYDMXDJXCGWCCXBEWCFWCHWCIWCKWCL\ WDNWDOWDQWDRWDSWEUWEVWEXWEYWE_WF`WFbWFcWFeWFfWGgWG\ iWGjWGlWGmWHoWHpWHrWHsWHtWHsYIsZIr_Ir`IqaJqcJqdJpe\ JpfKogKoiKnjKnkKnlLmmLmoLlpLlqMkrMksMkuMjvNjwNixNi\ yNizNjxPjvQjuRjsSjqTkpUknVklWkkXkiYlgZlf_ld`lbalab\ m_cmYdmXemVfmUgkWejXdhZcg_beaadb`cd_aeZ`gYZhXYjWXk\ VYlUYlTZlSZlRZlQ_lP_lO_lO`mN`mM`mLamKamJamIbmHbmHb\ nGcnFcnEcnDdnCdnBdnAenAeo9eo8fo7fo6fo5go4go3go3dm4\ bl5`j6Zi7Wg8Uf9SdAQcARaER_HRZKRXNSWQSUTSSXSR_TPbTO\ eTMhTLkVNhXOfYQc_RaaTZbUXiNYpGZ_IaJJcKKaLL`MM_MNZN\ OYOPWPQVPRUQSTRTSSUQSVPTWOUXNUXMVYKWZJX_IX`HYaGZbE\ _cD_dC`eBafAbg8bh7ci6dj5dj4af5_c5Y`5WY6UV6SS6QP7OM\ 7MJ7KG7JF9IEAHDBGCCGBDFAEE9FD8GD8HC7JB6KA5L94M93N8\ 2O71P60Q60R73T75U77V79W7BX7DY7GZ7I_7K`7Ma7Ob7Qc7Sd\ 7Ve7Xf7Zg7`h7bi7dj7gk7il7km7mn7oo7qp7sq8pr8nr8lr8i\ s8gs8eslaHiaHf`Gd`Ga_GZ_F } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 16-08-09 (Great Balls of Fire [6.5])
by Jim Muth 15 Aug '09

15 Aug '09

FOTD -- August 16, 2009 (Rating 6.5) Fractal visionaries and enthusiasts: Saturday was another busy day here at Fractal Central, which explains but does not excuse the briefness of the discussion. Today we have another average FOTD fractal. But a rating of an average 6.5 does not mean totally without value. The parent fractal came to be when (1/Z) was subtracted from 0.5 part of Z^(-2) and (1/C) was added. This parent consists of three main bays, two with Mandeloid shore lines and one with a smooth shore line. Today's scene lies in a valley between one of the Mandeloid-edged bays and the smooth-edged bay. Most of the effect was created by rendering the image with the inside set to 'bof61' and the outside set to 'tdis'. The image consists of about 50-50 outside-inside stuff. The rating of a 6.5 could easily have been a 7 if I had given more effort to the coloring. The calculation time of a slow 7 minutes is a bit more than the effort is worth, so I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Summer came on strong here at Fractal Central on Saturday, as the temperature reached 90F 32C, with high humidity and a lack of a breeze making the heat seem even more oppressive. The fractal cats passed the day stretched on the cool tile floor in the bathroom. My day was quite active, but things should be back to normal within a day. The next FOTD will be posted in 24 hours. Until then, take care, and why is it considered spiritual for a person to talk to God in prayer, but crazy for that person to hear God talk to him. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Great_Balls_O_Fire { ; time=0:06:57.72-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip center-mag=-2.57093955/-2.08933182/55493/1/-135/0 params=-1/-1/0.5/-2/0/0/0/0 float=y maxiter=1500 inside=bof61 outside=tdis periodicity=10 colors=000lazjbchbzfcdeddcedafe_feYgeWhfUifSifQjgO\ kgNlgLmhJmhHnhFoiDpiBpi9qj7rj5sj2tl4sj6sh7rg9reAqd\ CqbDp`Fp_GoYIoXKnVLnUNmSOmQQlPRlNTkMUkKWjIXjHZiF`i\ EahCchBdg9fg7gf6if4je3le1me0cg9ViHLjQClY1nc3me5mf6\ mh8li9ljBllCkmEkoFkpHjqIjsKjtLivNiwOixNguMfrMepLdm\ KbkKahJ`fJ_cIZaHXZHWXGVUFTfFScERaEQ_DPYCOWCNUBMSAL\ QAKO9JM9JKAJ1AJ1BJ1BJ1CK2CK2DL2DL2EM2EM3FN3FN3GO3G\ O4HP4HP4IP4IQ4JQ5JR5KR5KS5LS6LT6MT6MU6NU6NV7OV7OW7\ PW7PW7NU9MSBLRDKPFJOHIMJHKLGJNFHPEGRDETCCVBBXA9Z98\ `86b74d63f51h40i62h73h84h95hA6hC8hD9gEAgFBgGCgIEgJ\ FgKGfLHfMIfOKfPLfQMfRNeSOeUQeVReWSeXTe_VgYUeXTcWSb\ US`TR_SQYRQXPPVOOTNNSLNQKMPJLNJJOILMHNLHOKGQJGSIFT\ HFVFEWEEYDD_CD`BCbACc9C_8CW8CS8CO8CK8CG8AA7CC8DD8E\ E8FF8HH8II8JJ9KK9MM9NN9OO9PP9RRASSATTAUUAVVAXXAYYB\ ZZB__BaaBbbBccBddCffCggChhCiiCii9jjCkkEllGlgemnKnd\ jopOoazp_zvYztZzr_zp_zn`z } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 15-08-09 (It Averages Out [5])
by Jim Muth 14 Aug '09

14 Aug '09

FOTD -- August 15, 2009 (Rating 5) Fractal visionaries and enthusiasts: There was no FOTD for August 14, and this FOTD is very brief. My alibi is that I have been very busy! Subtract Z^2.5 from Z^1.5 and you get a Mandeloid rotated 180 degrees and split apart on both its east and west sides. Today's image is located in one of the branches of its parent's West Valley, which has East Valley characteristics. I named the image "It Averages Out" because the two exponents of Z, 1.5 and 2.5, average out to 2. The rating of a 5 means I am not too impressed with the image. The calculation time of 1-1/4 minutes is within reason, but viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is even more reasonable. Thursday proved to be rather pleasant here at Fractal Central, with lots of sun, some puffy clouds, and a temperature of 82F 28C. The fractal cats must have enjoyed things, for they slept over 3 hours without stirring. Friday was a repeat, with a temperature of 84F 29C. My day was quite busy on Thursday. This is normal. It was incredibly busy on Friday, and this is not normal. If the next FOTD is late, you'll know the rush is not yet under control. Until whenever, take care, and give your garden gnomes all the water and sunlight they need to thrive. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= It_Averages_Out { ; time=0:01:15.10-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident center-mag=+0.09245420142930875/-0.165441019141986\ /2.1427e+011/1/-112.5/0 params=-1/2.5/1/1.5/0/0/0/0 float=y maxiter=1000 inside=0 logmap=119 periodicity=10 mathtolerance=0.05/1 colors=0004F75I65L65P56S46V37Y27`17c1rbFvn`zzvxvtv\ ssuorslprhopenoalmZkkWjjShhPggLfeIddEcbBba8acDceId\ gNeiSfjWgl`hneipjjroksslptjmthjugguedvdavbZwaWw_Tx\ ZQxXNyWKyUHzTEzRBzQCxOCwMCuLCtJDrHDqGDoEDnDElBEk9E\ i8Eh6Eg5Ff5Ff5Ff5Ff5Ff5Ff5Ff5Ge5Ge5Ge5Ge5Ge5Ge5Gf5\ Kh8PiAUkCZlEcoHhpJmrLpsNsvUvwcwxmyyzzzzL1bO3dQ4eT5\ fV6hX7i_8ja9kcBmfCnhDojEqmFroGsqHtnGokFkhEgeDcbCZ_\ BVXARU9NR8IO7EL6AJ66M85O95RA5TB5WC5YD5`E4bF4eG4gH4\ jI4lJ4nRDoZLm_Kk`Ji`IgaHeaGcbFacE_cDYdCWdBRfFMhIHj\ LClO7nR3oU5pS6pQ7pO8pM9qKAqJBqHCqFErDFrBGrAHr8Is6J\ s4Ks2Ls1Lr1Lq1Mp1Mo1Mn1Nm1Nl1Nk1Sl4Wl6_l9clBhlEllG\ plJtlLxlNtWJuZKvaKwdKxgLyjLE1fL8bSF_ZMXeTUl_RzfOz8\ KdCLzFLzILzLLzPLzSLzVLqYLsaLudLwgLyjLzzWzzTzzQzaNz\ zZzzWXzTz_QpzNNzDQzETzFWzFZzGazGdzHfzHizIlzJozJrzK\ uzKxzLHzXPzVXzTczRkzPszNrzOtzNuzNvzMwzMxzLyzLPzbWz\ _azXgzUnzRtzO6z33zA3z94z8 } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD -- August 12, 2009
by Roger Alexander 14 Aug '09

14 Aug '09

The design is really enhanced by great coloring. Roger A. _________________________________________________________________ Send and receive email from all of your webmail accounts. http://go.microsoft.com/?linkid=9671356

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FOTD 13-08-09 (The Glory of Numbers [8])
by Jim Muth 12 Aug '09

12 Aug '09

FOTD -- August 13, 2009 (Rating 8) Fractal visionaries and enthusiasts: So there actually is a minibrot at the center of yesterday's so-called dry valley. I'm not surprised. But it takes a version of Fractint more capable than the classic DOS version or at least a much faster machine to reach it within a day. I'll be buying a new computer in a couple months, which will be reason to check some of the more windows-friendly versions of the program, but this is still a few months in the future. Meanwhile, today's image was created with the ancient DOS version. The minibrot in today's image is one of the fanciest midgets of the year. I named it "The Glory of Numbers" accordingly. The parent fractal is little more than a scattering of not- necessarily-critical bits and pieces of Mandelbrot stuff, plus some near-perfect mini M-sets here and there. Today's scene is located in the East Valley of one of these small M-sets. The rating of an 8 means that I think the image is pretty good as minibrot images go. The calculation of under 2 minutes will use only a small part of the time granted to each of us. The trip to the FOTD web site is not only magical, it also serves the practical function of eliminating the need for calculation. The finished image is posted there for instant viewing satisfaction. <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies and a temperature of 84F 29C made Wednesday a rather muggy day here at Fractal Central. Storm clouds that gathered threateningly late in the afternoon passed off harmless- ly. The fractal cats slept through most of it, but came to life when a stray tomcat wandered through the yard. My day was about average, which is normal. The next FOTD will be posted in 24 hours. Until then, take care, and since no one agreed with my sure way of saving the earth, I guess we're not as concerned with global warming as the media puts on. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheGloryOfNumbers { ; time=0:01:48.51-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident center-mag=+0.4433279054904762/+0.2777639686142115\ /5.640635e+007/1/-25/0 params=1/2/0.1/8/0/0/0/0 float=y maxiter=1500 inside=0 periodicity=10 colors=000ZVG_TG`SGaQGbPGcOGdMGeLGqZUpYToXSnWRnVQm\ UPlTPlSOkRNjRMiQLiPKhOKgNJgMIfLHeKGGPeLO`PNXTMTYLO\ aKKMzhOzePycRuaSr_UnYVkWWgUYdSZ`Q`YOaUMcRKdNIPhFUa\ GYWGaQGnVYmUXmTWlTVlSUkRTkRSjQRjQQiPPiOOhONhNMgNLg\ MKfLJfLIeKH18G59G8AGBBGECGHDGKEGOFGRGGUHGXIG_JGbKG\ HDDJEEKEELEEMFENFEPFEQGERGFSGFTHFVHFWHFXIFYIFZIG`J\ GaJGbJGcKGdKGZH__IY`IW`IUaJSbJQbJPcJNdKLdKJOOcNPdM\ QeLRfKSgJTiIUkHVmGWoFXqCYsAZuBYvBXwBWxCVyCVzCXzHZz\ M`zRbzWdz`hzekzinzyxzwtzuqzslzqhvobrmZmkVmiSmhPmfO\ mdOmbOm`OlZOkXOiVOgTOfRNdPMbNL_LKXJJVHISFIRDIPCIOG\ HNJHNMGMQGMdLHTLLWLK_KIbKHbEUcFScFRcGQcGPdHOdHNdIM\ dILeJKeJJeKIeKH5f79d8Cb9F`AIZALXBOVCRTDURDXPE_NFbL\ GzzWzzVvzUrzTmwSitSirRioQhmPhjPhgOgeNgcMg`MgZLfXKf\ VJfSJeQIeOHeMGfn8jSMgOJ4D78E8BF9FFAIGBMHCPHCTIDWJE\ _JFbKGezseymergekaedXeYReRLLpGMnGNmGOkGPjGQiGRgGSf\ GSeGTcGUbGV`GW_GXZGYXGZWG } frm:MandAutoCritInZ {; 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)+(p4)), 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] FOTD 12-08-09 (A Good Dry Valley [7])
by Brian Prentice 12 Aug '09

12 Aug '09

Jim, As you suspected your fractal for 8/12/09 does indeed have a minibrot at its center. Here is a monocrome picture of it: http://linuxenvy.com/bprentice/Fractals/Jim%20Muth/08_12_09.png Brian Prentice

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It's my turn...
by John W. 11 Aug '09

11 Aug '09

I've chuckled on many previous occasions, when fellow-fractaleers were unable to access Paul's site to view the lataest FOTD with minimal effort. O.K. O.K. So what's the magic charm which will get me past August 4th? (I've tried using the middle finger on F5... no dice). John W.

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FOTD 12-08-09 (A Good Dry Valley [7])
by Jim Muth 11 Aug '09

11 Aug '09

FOTD -- August 12, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image is another 7-rated one. It's becoming boring, but that's what I've been coming up with lately. The scene lies in the East Valley of the cut-off minibrot on the right side of yesterday's image. I named the image "A Good Dry Valley". The name implies that it is one of the best dry valleys I have yet found -- unusually rich in interesting elements. I give the name 'dry valley' to areas of two-way symmetry that look as though they lead to minibrots, but die out before getting there. Actually, I am not sure that today's dry valley is truly dry. I have taken it to the limit of resolution and discovered that it did not yet run dry, so a minibrot might indeed lie at its center. One of these days I might check deeper with arbitrary math, though it will not be today or tomorrow. The rating of a 7 means I consider the image to be of average worth. The calculation time of 5 minutes is barely justified by the result. If justice is what you want, go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and give the world its comeuppance there. The heat was a bit more reasonable here at Fractal Central on Tuesday, when the temperature reached only 88F 31C. But it was still enough to keep the fractal cats stretched in the coolest place they could find. My day was about average. The next FOTD will be posted in 24 hours, give or take a few. Until then, take care, and it would be really simple to save the earth. All we would need to do would be bring about a world- wide depression. As the economies ground to a halt, and the factories shut down, imagine how much fuel we would save and how much less carbon dioxide we would put into the atmosphere. If we actually cared about the environment as much as the media implies, we should be willing to make a few small sacrifices. And if we all do the right thing, global warming might actually start to slow down in 100 years or so. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Good_Dry_Valley { ; time=0:04:58.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip center-mag=-349.3239689251149/+0.0850910315003183/\ 1.129942e+009/1/127.4/0 params=2.5/200 float=y maxiter=7200 inside=0 logmap=756 periodicity=10 colors=000K2_L3YL4WL5UM6SM6QM7OM8NN9LNAJNAHOBFOCDO\ DBODANFEMHHLJKLLNKMRJOUJQXIS_HUcHWfGXiFYlFZoG`mGbm\ GcmKfmPhoUjqZlscougqwisxkuymwzoxzqyzswzuwzwxzxyzzz\ zXG6YF8ZGA`HCbHEdHGfIIiJKkJMnKOqOQtPSxZUzcWzhYzmVz\ qTztRzzPzzOzzNzvMzsLzrKzqJvqJrhGm`DhTBcK8ZC5U43Z64\ c74c84c94cA4cB4cC4cD4cE5cF5cG5cH5cI5cJ5cK5cL5LO6JQ\ 7HS8FU9DXABZB9`C7bC8aD8`E8_F9ZF9YG9XHAWHAWIAVJBUJB\ TKBSLCRLCQMCPNCPNEOSFNXGN`HMeIMiKLfMLdOLbQL`SLZULX\ WLVYLT_LRaLPcLNeLLgLJfKLfKMfJNfJPfIQfIRfHTfHUfGVfG\ WeIUdKScMQcOObQMaSK`UI`WG_YEZ_CYaAYb9aZKdWVgSejPoi\ NniLmhKlhIkgHjgFifEhfCgeBfe9ed8dd6cd5bf8dgAehDfiFg\ jIikKjlNkmPlnRmoTkoVjpWipYgpZfq`eqbdrcbrearf`sh_sj\ YtkXtmWtnVnmQhlMckIYjESiANh6Lf8Je9IcAGbBF`CD_DCZEA\ XF8WG7UH5TI4RJ2QK1PL4NN6LP8JRAHSCFUEDWGBXI9ZK7`M5a\ O3cQ1eS0fT2dU3bU4`V5ZV6XW7VW8TX9RXAPYBNYCLZDJZEHWK\ KTPNRUQOZTLdWJiZGnaK5gK3c } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 11-08-09 (Going Out of Sight [7])
by Jim Muth 10 Aug '09

10 Aug '09

FOTD -- August 11, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image exists in a parent fractal that resembles a Mandelbrot set about 200 times its normal size. The actual scene is at the edge of the infinitely-divided negative X-axis of the parent, in the East Valley of the large minibrot on its main stem. The image shows a minibrot of about average quality, which is well enough. But just to the right of this minibrot lies a second minibrot, this one with subtle variations. Its large bud is cut off at Seahorse Valley, while notable differences exist in its surrounding pattern. The visible part of this second minibrot resembles a fractal that lies very near the escape radius of its parent. In this case however, it is not the escape radius, but rather a discon- tinuity that the minibrot lies very close to. Regardless, the effect is the same. I named the image "Going Out of Sight", which is what the second minibrot is doing. I rated the image at a 7, which is FOTD average. The calculation time of just over one minute will pass in a flash for those who have no time to spare. It will also pass in a flash for those with all the time in the world, how- ever much time that might be. Taking all this into consideration, I recommend avoiding the task of measuring the amount of time in the world by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Monday was marked by hot weather here at Fractal Central. The hot sun and temperature of 91F 33F kept activity at a minimum, at least among the fractal cats, who spent the day under the cool air. I spent the day doing the work, while FL repaired some of the damage done to her garden by Sunday's storm. Unfortunately, the flattened sunflowers look like goners. If all goes well, the next FOTD will be posted in 24 hours. It will probably be posted even if a few minor things do go wrong. Until then, take care, and do well. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Going_Out_of_Sight { ; time=0:01:04.87-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip center-mag=-349.323801403/+0.085115707/3873.97/1/\ -175/0 params=2.5/200 float=y maxiter=1800 inside=0 periodicity=10 colors=000TFNcGXnHfyHo9oJdvNirLmnJqjIib`jZWkVSlROm\ OJnKFoGBoD7nKLmRYlYkkcxyHTtIXoI`kIdfJhbJlYJpUJsC`J\ pt6njBmaFkSJjJNiQCiW1aOGVHUOAgH3uH5nH6hH7bH9XHARHB\ LJANLAPN9QP9SR8US8VY6Vb5Vh3Vm2Vf9Q_GLTNHMUCF`79g3B\ gCCgLEgTFgaGgiLDmMJmNKmOLmPMmQNmROmSPmTQmURmVSmWTm\ XUmYVmZWm`XgbXadYWeYQgZKiZEk_8l_3kb4jd4jf5ih5zm6zp\ 6zs7zw7zz4AJGYcQZkUWgQSaMNVIBPF8JB5C7263nu1PT09gY4\ MHPkaKcVGWPCOJ8GC486ILfFI`DFWBDQ9AL67G45A225TcNLUH\ EKB7A5p4ru3dp2Rp1DuKWlHRmEMcBIc8DU59U24UlWPcQKWLFO\ GAGA585KTfGOZDJSAEL69E347eHzZPmSPmLPmE54722j6Wv1xm\ 0oe0fX0YP0QG0H808VHfQE_MCUH9OD7I84C426ai7Wb6RW5LQ4\ GJ3AD25614rd3gW2XO1MG0B8T9rO7hJ6_E4R93I419JNvGJmDG\ eADX89P56G238A7P86L75I64F53C329216103Iy89V4XZgSU`N\ PVIKPEFI9AC4568kZ6aS4SL3JE197UjwKVcAFK2nL1aF1PA0C5\ aYWXTSSPONLKJHGECC988444KgJG_FDTCAM96E6373LveHlZEb\ SioLonPumThcMWVGJM97D3IED } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 10-08-09 (Crossover In Sight [No Rating])
by Jim Muth 09 Aug '09

09 Aug '09

FOTD -- August 10, 2009 (No Rating) Fractal visionaries and enthusiasts: With so many things going wrong on Sunday, it's a wonder that today's FOTD image was posted at all. My main alibi is the weather, which caused a power outage in the evening. The center of attraction in the very hasty image is a quintic minibrot surrounded by an unbalanced field of not-particularly- attractive elements. The coloring is barely adequate, with nothing of note to comment on. I named the image "Crossover In Sight" because the scene is located in an area where two broad valleys appear to cross. One glance will reveal why I gave it no rating. The calculation time of 10-1/2 minutes makes the image not worth the time spent calculating it. To avoid disappointment I recommend viewing the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather on Saturday was near perfect here at Fractal Central, with mostly sunny skies and a temperature of 81F 27C. But Sunday was a different story. The day began with heavy rain, then turned very muggy around noon, when the sun suddenly burst through and the temperature soared to 88F 31C. At 4pm however the western sky grew almost as dark as night, followed in a couple minutes by a violent thunder-storm, which caused a six-hour power outage and made the already late FOTD even later. We survived the storm with minimum damage, though FL's garden took a beating. The fractal cats took most of it in stride but cringed at the loudest thunder claps. If all goes well the next FOTD will be posted soon. But from the way things are going, I'm making no definite promises. Until next time, whenever that is, take care, and be cool. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Crossover_In_Sight { ; time=0:10:38.61-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip center-mag=-1.6217008186111/+0.03820895763581716/\ 1.290596e+008/1/-157.5/0 params=5/1 float=y maxiter=6250 inside=0 logmap=-342 periodicity=10 colors=000qaZsfbqbYq`TqZPqXLqXJqWGqUDqTBqS9qS7qS5q\ R4qR4oP4mP4mP4kP4kO5iO6iO6gO7gN7eN7cM8cN9aMAaMA_MB\ _NDYMDYMEXMFXMGQJFLHFHGFEEDAA977677688767855935A14\ C11943C74DA5ED7FG8GJ8IM9KP9MSANVAPYAR`FUcKbfPeiUhi\ Zhichifhiihgghdcha`h_ZhXWhUThRQhOOhLLhJJhHHhGGhDGd\ BHb9J`ALZFNXKQUPVSU_TZdUchUhiSmjRhkQcjPZiPUgPGgPJe\ PNePQcQUcSTaQUaPU_NW_LXYK_ZJe`KgcKiaJi`Ii_HiYGiWFi\ VEiUDiTDiRCiQBiQAiO9iM9iL8iK8iJ7iI7iH6iF6iF5kE5mC3\ oE6qG9sJEuNKuRQuSTuTYuVbuVfuXguYfuYeu_eu_tuatubtub\ tudtudtuftugtugtuituituituftuctu`tuYtuVtuStuPtuOtu\ NtuNtuNtuNtuNtuNtuNtuNtuNtuNtuNtuNtuNtuOtuPtuRtuSt\ uTtuVtuXtuYtu_tuatubtudtuftugtuituituituituituitui\ tuituituituituituituituituituituituituituituituitu\ ituituituituituituituituituituituituituituituituit\ uituituituituituituituituituituituituituituituitui\ tuituituituituituituituit } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 08-08-09 (The Good Old Days [Rating Green])
by Jim Muth 08 Aug '09

08 Aug '09

FOTD -- August 08, 2009 (Rating Green) Fractal visionaries and enthusiasts: Alert! There is a minor crisis here at FC. When I turned on my fractal-dedicated Dell P4-2000mhz unit this morning, it beeped 1...3...2 and did nothing more. The 1...3...2 is obviously some kind of code indicating what the problem might be, but I have been unable to find what the code means. Meanwhile, the FOTD is once again being created on my 14-year-old P200mhz unit, which for all its years still works perfectly. So as not to create confusion, I have edited the calculation time to what it would have been on the P4-2000mhz machine. The computer problem is why this FOTD is late. As for today's FOTD image, it is 100-percent natural, with abso- lutely no artificial stuff. It is also organic. In addition, for every person who views the image, a stalk of corn will be planted, which will help feed a starving child somewhere. But view the image NOW. Don't let this opportunity to reverse the environmental decline slip by. The ice caps are melting, the polar bears are dying, the coastal cities are flooding, children are starving everywhere. Only you can save the earth. But wait! If you view the image in the next 10 minutes, two stalks of corn will be planted, and will save the earth in half the time. The image lies in the parent fractal that results when 8.8 parts of Z^(1.11) are subtracted from 8 parts of Z^(1.1) and straight C is added. This parent fractal closely resembles the fractals that result when formulas such as (-Z)^1.25+C are calculated, but instead of minibrots of the same low order, the parent holds perfect quadratic minibrots. Today's image shows one of these minibrots, this one buried very deep in the chaos on the southern shore line of the parent, which is actually the northern shore line when the parent is rotated 180 degrees to its true orientation. I named the image "The Good Old days" and rated it at a rating of 'green'. The rating shows that fractals are good for the environment, since even though they are infinite in number, they do no environmental damage at all. The calculation time of 3 minutes and 30 seconds is one quarter of the actual 14 minutes and 09 seconds the image took to calcu- late on the P-200 machine. My advice is to avoid time confusion by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Near perfect conditions prevailed here at Fractal Central on Friday, with ample sun and a temperature of 81F 27C. The fractal cats enjoyed it, but I was too busy to do so. Despite all the adversity however, a fractal did appear, and another one will appear in 20 hours or so. Until then, take care, and does anyone know what that 1...3...2 signal from the sick Dell P4-2000mhz machine means? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Good_Old_Days { ; time=0:03:30.00-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.717978244060236/-3.465927070574558/\ 4.1068e+012/1/41.5/0 params=8/1.1/-8.8/1.11/0/0/0/0 float=y maxiter=2100 inside=0 logmap=264 periodicity=10 mathtolerance=0.05/1 colors=000KK2LJ3MI4OG4PF5QE6RD7TB8UA9V9AW8AYAD_CFa\ EHbGJdIGfJIgLKiNMkPOlRQnSSpUUqWWsXYtY_tZYsYVnXTjTM\ fRFdN8aK2WI1QH1LG1GF5CE5AD5AD4BE4BF4CG8CH8DH8DI7EJ\ 7EK7MJ9THB_GDfEFmCHtBJqIHoPFlWEjbKgiUepccwmZvwVvzR\ vzNzzIzzEzzAvz6uu2sm7pcBmUFhKJeHNaIRZJVVKZSKbQIfPH\ jNGnMErKDvJCwKGwLKwMNwNRwOUwPYxQ`xRdxSgxTkxUnxVrxV\ uvWrtWpsWnqXlpXjnXglXekYciYahY_fYXdZVcZTaZR`ZPjfUs\ mZoj`kgbgedcbf__hWYjSVlOSnKQpGNrDLtwIuvQguXUtdGtk3\ lkAekHYkORkVJkaCkgFmiHokKpmMroPsqRusTvuKflBSc2DV6C\ Y9B_CAbF9dI8gL7iO6kMCmKHnIMoGRqFWrD`sBeu9jv7ow6txA\ qvEouImtLksPhrTfqWdo_bnc_mfYljWknUjqSiYm2Ti8PeEKaK\ GZQBVW7Ra3Of6dV9uJHoCOj6VaA`TEfLIlCMr4QuCFxK4tL8qL\ BmMzjMzgNzcNz`zzYzzzzzRzzOzzzzzzzzEzzDzzzzzDzzCzzz\ zzCzzBzzzzz9zz9zzzzz7zz6zzzzz5zN4zM3zL3zK2zJ1zI0zH\ 0zG6zJBzMGzPLzSQzVVzYjzkyzypzuhzr_zoSzlJziBzf3zc7z\ aAz`Ez_HzZLzXOzWSzVVzUZzT } frm:MandAutoCritInZ {; 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)+(p4)), 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] Fractint Digest, Vol 78, Issue 7
by JackOfTradeZ＠comcast.net 08 Aug '09

08 Aug '09

. C'mon people - keep it nice. Aren't there enough wars in the world already? .

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Re: [Fractint] very large images in fractint
by JackOfTradeZ＠comcast.net 08 Aug '09

08 Aug '09

. Load your pet image, hit "B" key to get to PAR screne, look near bottom for: "the following is for generating images in pieces" It is intuitive, play with it. There is no limit (I think) to size, just how many pieces you can generate and if it is not too deep and takes too much time. Also it is described in the DOC file. .

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Disk Video mode of 12,000 x 12,000 pixels tried
by Hal Lane 08 Aug '09

08 Aug '09

The Benoit Mandelbrot Fractal Art Contest 2009 rules: http://www.fractalartcontests.com/2009/rules.php say: "Some images may be selected for printing at even larger size (12000 pixels in the largest dimension) so entrants would do well to be aware of the size requirements." To test Fractint's current large image abilities I created a Disk Video mode of 12,000 x 12,000 pixels for my DOS 20.0 Fractint by adding a line to my FRACTINT.CFG file and used it to create Fractint's default Mandelbrot set. Amazingly, it took only a minute and 30 seconds to calculate the 144 million pixels using my 2.2 GHz AMD processor. Encoding the .GIF format file while saving it seemed to take about a minute. Fractint chose to write directly to my hard disk using a 54 KB 'Fractint cache size.' The resulting .GIF image was a well-formed 4.4 MB file -- with a *lot* of detail in it. (But not as much as in a typical zoom.) I was able to easily pan and scroll around in the 12,000 x 12,000 .GIF image using my image viewing program, CompuPic. The image aspect ratio was stretched slightly vertically since I specified a 'square' output image instead of the usual 4 x 3 aspect ratio (that would be 12,000 x 8,000 pixels here). I also created a 12,000 x 8,000 pixel image which had the expected aspect ratio and shape of the Mandelbrot set. - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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Stitching together images for the Fractal contest
by Hal Lane 08 Aug '09

08 Aug '09

Maryetta Campbell mentions two apps that don't appear to join images together horizontally and vertically as needed for the current Fractal contest: http://www.321slideshow.com/gif-joiner.htm Web page says: output format: AVI http://www.amath.washington.edu/~jsk/giffo.html Web page says: produce an animation What's needed is software for "putting together multiple raster images (stitching)." Fractint can create ultra large images in at least two ways. Fractint for Windows beta 5 --------------------------- One of the default output sizes for images in Fractint for Windows beta 5 (*not* WinFract) is 8192 x 8192. I have successfully created images of that size. It can likely create even larger sizes without problems, since it uses Windows-style memory management. Use its configuration file to specify the desired image resolution of a new "Disk Video" mode. A description of the Fractint for Windows beta and the program are available here: http://legalizeadulthood.wordpress.com/2007/04/13/fractint-for-windows-beta- 5/#more-7 or, if the above URL gets cut into pieces: http://tinyurl.com/n4ynl5 A couple of the comments posted on the above web page say that the program is faster than the DOS version running under Windows. That said, remember that it is a beta. There are a number of comments and responses about the beta version to and from the author of Fractint for Windows on the Fractint Developer's List: http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractdev or http://tinyurl.com/lf9sgk Fractint for DOS "X and Y Multiples" ------------------------------------ The Fractint 20.0 for DOS docs say this about the stitching capabilities of the program when using the "b" command: ======================================================================== "X Multiples - How many divisions of final image in the x direction Y Multiples - How many divisions of final image in the y direction Video mode - Fractint video mode for each piece (e.g. "F3") The last item defaults to the current video mode. If either X Multiples or Y Multiples are greater than 1, then multiple numbered PAR entries for the pieces are added to the PAR file, and a MAKEMIG.BAT file is created that builds all of the component pieces and then stitches them together into a "multi-image" GIF. The current limitations of the "divide and conquer" algorithm are 36 or fewer X and Y multiples (so you are limited to "only" 36x36=1296 component images), and a final resolution limit in both the X and Y directions of 65,535 (a limitation of "only" four billion pixels or so). The final image generated by MAKEMIG is a "multi-image" GIF file called FRACTMIG.GIF. In case you have other software that can't handle multi-image GIF files, MAKEMIG includes a final (but commented out) call to SIMPLGIF, a companion program that reads a GIF file that may contain little tricks like multiple images and creates a simple GIF from it. Fair warning: SIMPLGIF needs room to build a composite image while it works, and it does that using a temporary disk file equal to the size of the final image - and a 64Kx64K GIF image requires a 4GB temporary disk file! This is how a particular "named group of parameters" in a .PAR file is invoked as is used in the file MAKEFIG.BAT: @FILENAME Causes Fractint to read "filename" for parameters. When it finishes, it resumes reading its own command line -- i.e., "FRACTINT MAXITER=250 @MYFILE PASSES=1" is legal. This option is only valid on the DOS command line, as Fractint is not clever enough to deal with multiple indirection. @FILENAME/GROUPNAME Like @FILENAME, but reads a named group of parameters from a parameter file." ======================================================================== I used the "b" command in Fractint and specified 3 'X' multiples and 2 'Y' multiples. I did this just after running Jim Muth's Fractal of the Day for Aug 3, 2009 by creating a file named: F090803.PAR and invoking it inside Fractint by using the key sequence: "@", "F6". F090803.PAR contained his image's parameter spec and the formula needed for the image. The "b" command created the file MAKEMIG.BAT and added six parameter 'sets' (image creation specs) (named groups of parameters) to the bottom of my existing F090803.PAR and named them: The_Worm_Turns3X2_00 The_Worm_Turns3X2_01 The_Worm_Turns3X2_10 . . . The_Worm_Turns3X2_21 (See the portion of the file F090803.PAR I put below.) ------------------------------------------------------------- It appears that Fractint does the heavy lifting when it executes the "b" command. It: - Creates the MAKEMIG.BAT file - Adds six parameter 'sets' to the existing .PAR file And when the MAKEMIG.BAT file is run in a DOS command window: - The pieces of the image are created (you see Fractint open and run) - Six temporary files named: frmig_00.gif, frmig_01.gif, etc. are written and eventually deleted. - Fractint stitches the six images together when the following command is executed in the .BAT file: FRACTINT MAKEMIG=3/2 (It writes out an image file named: FRACTMIG.GIF.) - I manually entered the following command in a command window: SIMPLGIF FRACTMIG.GIF SIMPLGIF.GIF to create the final output SIMPLGIF.GIF file. (SIMPLGIF.EXE is provided with the Fractint 20.0 distribution.) Alternatively, you could remove the "Rem " and "in case you need it" from the line provided in the MAKEMIG.BAT file. ------------------------------------------------------------- MAKEMIG.BAT: Note: "MIG" in MAKEMIG stands for "Multi-Image Gif." Fractint created this MAKEMIG.BAT file: ======================================= Fractint batch=yes overwrite=yes @C:\Program Files\_ Graphics\Fractint for Windows\pars\F090803.PAR/The_Worm_Turns3x2_00 If Errorlevel 2 goto oops Fractint batch=yes overwrite=yes @C:\Program Files\_ Graphics\Fractint for Windows\pars\F090803.PAR/The_Worm_Turns3x2_01 If Errorlevel 2 goto oops Fractint batch=yes overwrite=yes @C:\Program Files\_ Graphics\Fractint for Windows\pars\F090803.PAR/The_Worm_Turns3x2_10 If Errorlevel 2 goto oops Fractint batch=yes overwrite=yes @C:\Program Files\_ Graphics\Fractint for Windows\pars\F090803.PAR/The_Worm_Turns3x2_11 If Errorlevel 2 goto oops Fractint batch=yes overwrite=yes @C:\Program Files\_ Graphics\Fractint for Windows\pars\F090803.PAR/The_Worm_Turns3x2_20 If Errorlevel 2 goto oops Fractint batch=yes overwrite=yes @C:\Program Files\_ Graphics\Fractint for Windows\pars\F090803.PAR/The_Worm_Turns3x2_21 If Errorlevel 2 goto oops Fractint makemig=3/2 Rem Simplgif fractmig.gif simplgif.gif in case you need it :oops I modified my MAKEMIG.BAT file as follows: (Note that the "3x2" has been deleted. I comment on this later.) Fractint batch=yes overwrite=yes @F090803.PAR/The_Worm_Turns_00 If Errorlevel 2 goto oops Fractint batch=yes overwrite=yes @F090803.PAR/The_Worm_Turns_01 If Errorlevel 2 goto oops Fractint batch=yes overwrite=yes @F090803.PAR/The_Worm_Turns_10 If Errorlevel 2 goto oops Fractint batch=yes overwrite=yes @F090803.PAR/The_Worm_Turns_11 If Errorlevel 2 goto oops Fractint batch=yes overwrite=yes @F090803.PAR/The_Worm_Turns_20 If Errorlevel 2 goto oops Fractint batch=yes overwrite=yes @F090803.PAR/The_Worm_Turns_21 If Errorlevel 2 goto oops Fractint makemig=3/2 Rem Simplgif fractmig.gif simplgif.gif in case you need it :oops F090803.PAR (excerpt) ===================== . . . frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)/(z^(aa)+bb)+c |z| < 1000000 } The_Worm_Turns_00{ ; Hal Lane Aug 06, 2009 time=0:00:22 ; F090803.PAR is Jim Muth's orig file. ; 3 'X' multiples ; 2 'Y' multiples Video = F5 (640x480) ; Fractint Version 2099 Patchlevel 8 reset=2099 type=formula formulafile=F090803.PAR formulaname=dividejulibrot center-mag=4.57011/0.278067/3.603758/1.5 params=89.980000000000004/0/89.980000000000004/0/-0.770\ 00000000000002/0/0/0/1.05/1.5 float=y maxiter=600 inside=0 logmap=25 periodicity=10 sound=off colors=000I6I<6>PKP<4>UUU<3>mmmzzzzzzzzzmmmmmmcccUUUPRo\ MDUBIB<2>ZG8c32<2>hNAmR0kS6iTCkQ9mNC<3>mZOmaRrdUre_rgbq\ ddpb`q`YrYUtWQwUNzRL<3>zFDzDBzHPzLazOnzHZzAKzF5zF8<3>za\ HzgKzmMzmOzmZzmZzmd<2>zmXzhLzcKzZKzeK<2>zZH<3>zhgzjnzlt\ <3>zRhzLezGbzB`zNkzYvzWizVYzMOzDFvPIr_KmVRZQYcLd<3>KUoM\ Wl<3>QEQK9UO5YS1bb0fl0z<3>NlzrzzjwzeszUqzPmzQkzN`zKRzHG\ uF6pJ9kNCk<2>XJz2oz9izFczFpz<3>FTzFOzJSz<3>WczZfzWez<3>\ ObzLdzJez5sz<3>TUzZNzcHz<3>SPzhaz<3>JOzDKz1Bz<3>PWzVaz`\ fzfkzf8zkpz<4>SkzOjzHlz<3>RdzTbzW`zYZzScz_Xz<3>RnzOMz<2\ >OUzJ1z<3>PezKyz<3>WfzZbzaYzYYz<2>dUztRz<3>aUzXVzTVzOWz\ 70z<3>OfzsBzUvzSpzQjzhqzWhz<2>BZz0_z video=F5 savename=frmig_00 } The_Worm_Turns_01{ ; Hal Lane Aug 06, 2009 time=0:00:22 ; F090803.PAR is Jim Muth's orig file. ; 3 'X' multiples ; 2 'Y' multiples Video = F5 (640x480) ; Fractint Version 2099 Patchlevel 8 reset=2099 type=formula formulafile=F090803.PAR formulaname=dividejulibrot center-mag=4.57011/-0.278067/3.603758/1.5 params=89.980000000000004/0/89.980000000000004/0/-0.770\ 00000000000002/0/0/0/1.05/1.5 float=y maxiter=600 inside=0 logmap=25 periodicity=10 sound=off colors=000I6I<6>PKP<4>UUU<3>mmmzzzzzzzzzmmmmmmcccUUUPRo\ MDUBIB<2>ZG8c32<2>hNAmR0kS6iTCkQ9mNC<3>mZOmaRrdUre_rgbq\ ddpb`q`YrYUtWQwUNzRL<3>zFDzDBzHPzLazOnzHZzAKzF5zF8<3>za\ HzgKzmMzmOzmZzmZzmd<2>zmXzhLzcKzZKzeK<2>zZH<3>zhgzjnzlt\ <3>zRhzLezGbzB`zNkzYvzWizVYzMOzDFvPIr_KmVRZQYcLd<3>KUoM\ Wl<3>QEQK9UO5YS1bb0fl0z<3>NlzrzzjwzeszUqzPmzQkzN`zKRzHG\ uF6pJ9kNCk<2>XJz2oz9izFczFpz<3>FTzFOzJSz<3>WczZfzWez<3>\ ObzLdzJez5sz<3>TUzZNzcHz<3>SPzhaz<3>JOzDKz1Bz<3>PWzVaz`\ fzfkzf8zkpz<4>SkzOjzHlz<3>RdzTbzW`zYZzScz_Xz<3>RnzOMz<2\ >OUzJ1z<3>PezKyz<3>WfzZbzaYzYYz<2>dUztRz<3>aUzXVzTVzOWz\ 70z<3>OfzsBzUvzSpzQjzhqzWhz<2>BZz0_z video=F5 savename=frmig_01 } The_Worm_Turns_10{ ... } The_Worm_Turns_11{ ... } The_Worm_Turns_20{ ... } The_Worm_Turns_21{ ... } When I ran the MAKEMIG.BAT file in a DOS command window and Fractint had problems, Fractint wrote the file STOPMSG.TXT with error messages in it. Fractint was kind enough to *append* errors from additional execution attempts to the *end* of STOPMSG.TXT Note that I chose to have three F5 (640 x 480) images in the X direction and only two in the Y direction. This stretched the aspect ratio of my final image in X. For the final image to have the same aspect ratio as the original video mode specified when you issue the "b" command, use the same number of images in both the X and Y directions. Note that the six named groups of parameters *names* were too long after the "_00", "_01", etc. were appended: The_Worm_Turns3X2_10{ ... } It looks like a length of about 18 characters is Fractint's limit, so the original base name of the image needs to be a max of 15 chars: The_Worm_Turns{ ... } then gets modified to: The_Worm_Turns_10{ ... } Then everything works correctly. Fractint opens and runs seven times. You see the six sub-images being created and then Fractint inserts them into a single file. I ran the program SIMPLGIF.EXE on this single file to create the final image. I happened to use the "Multiple-Image Gif" feature of Fractint for Windows beta 5 to create my stitched-together image. The DOS 20.0 version has this same capability. - Hal Lane ######################### # hallane(a)earthlink.net <mailto:hallane@earthlink.net> # #########################

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Corrections to: Stitching together images for...
by Hal Lane 08 Aug '09

08 Aug '09

I see now that Fractint v 20.0 can natively create large images directly in Disk Video mode. From the docs: "New 32767 x 32767 (32K) pixel limit. Removed the 2048 pixel limit for the size of fractals. You can now define disk video modes larger than 2048 x 2048." You define new Disk Video mode resolutions in the file: FRACTINT.CFG. Note that the format of this file is slightly different in Fractint for Windows beta 5. See "6.2 "Disk-Video" Modes" and "6.3 Customized Video Modes" in the docs. Basically, you duplicate an existing Disk Video mode line in FRACTINT.CFG. Then modify the new line to the resolution image you want Fractint to create. You won't see the image while it is being created, so you need to have composed it to exactly how you want it to appear before invoking your new Disk Video mode. Also, two corrections to the message I just posted: "This is how a particular "named group of parameters" in a .PAR file is invoked as is used in the file MAKEFIG.BAT:" should be: "This is how a particular "named group of parameters" in a .PAR file is invoked as is used in the file MAKEMIG.BAT:" and "It looks like a length of about 18 characters is Fractint's limit, so the original base name of the image needs to be a max of 15 chars:" should be: "It looks like a length of about 18 characters is Fractint's limit, so the original base name of the "named parameter group" needs to be a max of 15 chars:" - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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Benoit Mandelbrot Fractal Art Contest 2009
by Damien Jones 08 Aug '09

08 Aug '09

Good evening listfolk, I would like to inform you that the Benoit Mandelbrot Fractal Art Contest 2009 is open and accepting submissions. This is a contest to select images for exhibition at ICM in 2010. The submissions period closes October 10, 2009. For complete information, please visit the contest web site: http://www.fractalartcontests.com/2009/ Thank you for your attention. Damien Jones

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Re: [Fractint] What Numbers Do
by Roger Alexander 08 Aug '09

08 Aug '09

To Jim Muth -> What Numbers Do, Aug-04-09: Very eye catching! Best Regards Max _________________________________________________________________ Stay in the loop and chat with friends, right from your inbox! http://go.microsoft.com/?linkid=9671354

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Re: [Fractint] Benoit Mandelbrot Fractal Art Contest 2009
by Brian Prentice 08 Aug '09

08 Aug '09

Jones, I have read the following link: http://orbittrap.blogspot.com/2009/08/has-2009-benoit-mandelbrot-fractal-ar… and consider it to be a well written, thoughtful and valid criticism. The fact that you chose to answer it with an unjustified virulent and spiteful attack rather than address the issues raised is further evidence of your ugly and despicable personality. Brian Prentice

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FOTD 07-08-09 (Around the Corner [No Rating])
by Jim Muth 07 Aug '09

07 Aug '09

FOTD -- August 07, 2009 (No Rating) Fractal visionaries and enthusiasts: Thursday was the busiest day in several months here at F.C., and Friday promises to be a repeat. I have no time for a discussion of today's image, which I leave to speak for itself. But I will go so far as to reveal that it is a spiral. The name "Around the Corner" means nothing. The lack of a rating means I don't think it deserves one. The calculation time of 4-1/4 minutes may be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday turned into a perfect day here at Fractal Central, with blue skies, puffy clouds and a temperature of 79F 26C. The fractal cats spent the day on their best behavior. My day was very busy. The next FOTD is likely to be late, but it will eventually appear. Until then, take care, and think infinite. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Around_the_Corner { ; time=0:04:14.77-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.687160502161487/+0.1669954825400754/\ 67758.4/1/102.5/0 params=1e-040/-100/0.5/2/0/0/0/0 float=y maxiter=3600 logmap=94 periodicity=10 colors=000DswEqvEovEmvEkuEiuEftFdtFbsF`sFZsFXrFVrG\ TqGRqGPpGNpGKpGIoGGoHEnHDnHCmHBmHAmH9lI8lI7kI5kI4j\ I3jI2jJ1iJ0iJ0hJ0hJ0gJ0gJ0gI0hI0hH0hH0hH5hG4hG3hG2\ hF1iF0iF0iE0iE1iE2iD3iD4iD5iC6jC7jC7jB7jB7jB7jA8jA\ 8jA8j98k98k98k88k88k88k78k78k67m78k89i99gAAfABdBBb\ CCaDC_EDYEEWFEVGFTHFRHGQIHOJHMKIKLIJLJHMKFNKEOLCPL\ APM8QN7RN5SO3TP0SO2SO4RO5RO7QO8QOAPNBPNDONEONGONHN\ NJNNLMMMMMOLMPLMRKMSKMUJLVJLXJLYIL_ILaHLbHLdGKcGKb\ FKaFK`EK_EKZEKY2eI5cH7aHA_HCYHEWHHUHJSGMQGOPGQQGTR\ GWSGXTGXUGXVHXWIXXJXYKXZJY_IY`HYaGZbFVeARh6Lk0Nj2P\ j4Ri6Ti8VhAXhCYgD_gFafHcfJeeLgeNidPjdQlcSncUpbWrbY\ ta_wcbua`s`_q_ZoZXmYWkXViWUgVSfURdSQbRO`QNZPMXOLVN\ JTMIRLHOIEQKGSMITOKVPMWROYTQZUS`WTaYVcZXd`Zfb`hcbi\ edkgelhgnjiolkqmmrootqqvssurrvqqwrrxssyttzuuzvvzww\ zxxzyyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 06-08-09 (Transformation Site [5.5])
by Jim Muth 06 Aug '09

06 Aug '09

FOTD -- August 06, 2009 (Rating 5.5) Fractal visionaries and enthusiasts: There is a big problem in quantum mechanics called the measurement problem. Basically, the problem is how anything at all can be measured accurately. Since the quantum world is a world of uncertainties, and the 'real' world is made of quantum stuff, how then can objects in the 'real' world have attributes such as position and momentum, which can both be accurately measured at the same time. There is an equally big problem in fractal exploration. Since the number of fractals is infinite, and most fractals are infinitely complex, how many undiscovered quadratic minibrots are out there, waiting to be discovered. And what are the chances that any particular minibrot will ever be calculated and brought to life by some computer. And then there is today's image -- an image with hardly any problems at all. It is a scene in a tiny valley at the east edge of the parent fractal that results when Z^10 is subtracted from Z^11 and C is added -- hardly important enough to create any problems. I named the image "Transformation Site", a phrase that sounds like it has a hidden meaning. Then I rated it at a 5.5, which is just a bit below FOTD average quality. The calculation time of 2-3/4 minutes means that little time will have been wasted if the image is disappointing. But don't worry about calculation. View the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Hazy sun and a temperature of 86F 29C made Wednesday a typical midsummer day here at Fractal Central. The fractal cats slept through most of it, while FL and I finished the day's work. The next FOTD fractal, for all it is worth, will be posted in 24 hours. Until then, take care, and is the total number of minibrots in all the fractals greater or less than the number of electrons and neutrinos in the multiverse? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TransformationSite { ; time=0:02:42.55-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+1.0018437624534/-0.0001074821397/8.484\ 326e+008/1/10/0 params=-1/10/1/11/0/0/0/0 float=y maxiter=1500 inside=0 logmap=121 periodicity=10 colors=0009Qe9SeAUeAWeGYZL_TQ`MVaG_XAYUEWRHVOKTLOS\ JRQGUPDYNA`M8cOBhPEmQHrRKwPIuNHoLGmKElIDjGCgFAdD9a\ B8ZA6W85T64Q53PJGSXSdjdgzzjzokrdkoZklTliNlfHlcBm`5\ mW0kT9fQI_NRTJZMGgFCp89x2EwAIvHNuPRuWTqTVmRXjPZfM`\ cKbeId_FfVDhRBjM8lJ6nF4pC2iGPbKkgGjkDipAit7hx4hxBf\ xHmxNdxTbxZaxd`xjZxpYxvXsujotwavdOxMAy3Eu2Hr2Ko2Ol\ 1Ri1Uf1Yc0``0cY0e_1fa2gc3hd4if5jh6ki7lk7mm8nn9opAp\ rBqsCruDswEtxEpuHmsJjqMgoOdlRajTZhWWfYSc_PabM_dJYg\ GViDTlARn7PpBOlFNhJMdNM`RLXVKTZKQbJMfIIjIEnHArG6vG\ 3rH7nIAkIDgJGcJK`KNXKQULTQLXMM_JMbFNeCNhPBKUBPYBUa\ BZeBciBhmBmqBruBwqEsnHpjKmgNjcQg`SdXV`UYYQ`VNcSJfP\ GhMMjSSkYXmcbnigoniqokspmuqowrqxromnmcknbinahnago`\ eo_dqUQo_cpZapZ`pY_qXYqXXqWWrVUrVTrUSU16Z7BcDFhJJm\ PNrl3rj5ri6rh8rg9rfBreCrdDrcFraGr`Ir_JrZKrYMrXNrWP\ rVQJkkVedf_Y2zP7wQBtQFrQJoQNmQRjQVhRZeRbcRf`RjZRnW\ RDsTRjSdaRvi2ug6ue97le8ne } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 05-08-09 (Just Doodling [No Rating])
by Jim Muth 04 Aug '09

04 Aug '09

FOTD -- August 05, 2009 (No Rating) Fractal visionaries and enthusiasts: With no time to do a proper fractal search on Tuesday, I disengaged my brain (which took little effort) and struck some random keys without thinking. The fractal that resulted is little more than a fractal doodle, which is why I named it "Just Doodling". One look at the finished product will reveal why I gave the image no rating. The calculation time of 8 minutes uses up more time than the image is worth. The solution to all these minor problems is to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a high temperature of 88F 31C and equally high humidity, the weather at Fractal Central on Tuesday felt more like Houston than Central Pennsylvania. The fractal cats didn't seem to care. They spent most of the day watching a stray cat that hung around the area most of the afternoon. As stated above, my Tuesday was very busy. Unfortunately, the FOTD suffered. But the next FOTD is due to appear in 22 hours more or less, and who knows -- it might even be better. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Just_Doodling { ; time=0:08:01.98-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=t center-mag=-2.368\ 0503783/0/8000/1/-90/0 params=-2/6/0.01341100004/-8 float=y maxiter=1600 inside=0 periodicity=10 colors=000UBKWCKXDKYEKZFL_GM`HMaINbJOcKPaLP`MQZNRX\ NRWOSUOTSPURPUPQVNQWMRWKRXISYFTXHSYJRYLQYNPYPOZRNZ\ TMZVMZXL_ZK_`J_bI_dH`fG`hF`jFdlEhnDmpCrrBvtAzv9zx8\ zz7zy8zx8zw8zw8zv9zu9vu9rt9ms9hrAcrAZqAVpARpAQoBPn\ BOmBNmBMlBLkCKkCJjCIiCHk8EiCHgFJfILdMNcPPaSR`WTZZV\ YaXWeZVh`TkbSndUobVoaXo`Yp_ZpZ`pYaqXcqWdqVeqUgrThr\ SjrRksQlsPnsOotNqtMrtLstKqqMpoNnmOmjPkhQjfRhcSgaTe\ _UdXVKAZKAYKAZKA_KA`KA`KAbKAcK9dL8cM7fN6gN1gM4hL7i\ KAjJDjIGkHJlHLmGOmFRnEUoDXpC_pBbqBdrAgs9js8nt7qv6u\ x3zz6wx8twApuCmsFiqHfoJcmL`lOYjQViSSgTReUQfVPfVPfW\ OfWNfXNfYMfYLfZLfZKf_Kf`Jg`IgaIgaHgbGgcGgcFgdEgdEg\ eDgg4heDgdLfcTea`d`hc_pbZxa_t`_q__nZ_kZ`gY`dX`aW`Z\ WaYTbXRcWOdVMdUJeTHfSEgRChQ9hQ7iQ9jQAjQCkQDkQFlQGl\ QImQJnQKnQMoQNoQPpQQpQSqQTqQUnPTlOTjNThMSeMScLSaKR\ _JRYIRVIQTHQRGQPFQMFPKEPIDPGCOEBOBBO9AN79N58N16O38\ N59MAALFAKIAKLAKOAKQAKSAK } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 04-08-09 (What Numbers Do [8])
by Jim Muth 04 Aug '09

04 Aug '09

FOTD -- August 04, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's skeletal scene returns us to yesterday's image, but have no fear. It is far from a boring repeat. The image is actually a modest blow-up of a scene in the 'tree' at the eastern edge of yesterday's image. I named the image "What Numbers Do". While studying it, I began wondering how mere abstract numbers could possibly create such a scene. But that's what makes a fractal a fractal. The image rates an eight. I gave it this rating because I think it deserves such a rating. The calculation time of just over four minutes may be reduced to almost nothing by surfing out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image posted there. A near perfect day passed un-noticed here at Fractal Central on Monday. The temperature of 82F 28C was made even more enjoyable by the lower humidity, while the electronically-intensified blue skies and puffy cumulus clouds lent a perfect backdrop to any outdoor activity. But my day was spent indoors, and the fractal cats seemed more interested in the worn-out catnip rat than the sunny window. The next FOTD will be posted in 24 hours. Until then, take care, and is it an oxymoron to have faith in science? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= What_Numbers_Do { ; time=0:04:16.01-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideJulibrot passes=1 center-mag=+5.51760082/0/345/1/-90/0 params=89.98/0/89.98/0/-0.77/0/0/0/1.05/1.5 float=y maxiter=750 inside=0 logmap=370 periodicity=10 colors=000zzzmvzUpznjzUqzihzUdzrazUZzm_zI6IJ8JKAKL\ CLMEMNGNOIOPKPQMQRORSQSTSTzUUzZZzcczhhzmmzzzzzzzzz\ zmmmmmcccUUUPRoMDUBIBJHARH9ZG8c32eA5fG7hNAmR0kS6iT\ CkQ9mNCmQFmTImWLmZOmaRrdUre_rgbqddpb`q`YrYUtWQwUNz\ RLzOJzLHzIFzFDzDBzHPzLazOnzHZzAKzF5zF8zKAzQDzWFzaH\ zgKzmMzmOzmZzmZzmdzmazmZzmXzhLzcKzZKzeKzbJz`IzZHza\ OzcVze`zhgzjnzltzfqzanzWkzRhzLezGbzB`zNkzYvzWizVYz\ MOzDFvPIr_KmVRZQYcLdZOgUQjPSlKUoMWlNRfON`PIVQEQK9U\ O5YS1bb0fl0zeDz_PzT`zNlzrzzjwzeszUqzPmzQkzN`zKRzHG\ uF6pJ9kNCkQEpUHuXJz2oz9izFczFpzFjzFdzFZzFTzFOzJSzM\ UzPYzT`zcmzcmzcmzcmzcmzcmzObzLdzJez5szBlzHfzN_zTUz\ ZNzcHz`JzYLzVNzSPzhazaYzWVzQRzJOzDKz1Bz7HzDMzJRzPW\ zVaz`fzfkzf8zkpzgozcnz_mzWlzSkzOjzHlzKjzMhzPfzRdzT\ bzW`zYZzScz_XzXazVezTjzRnzOMzOPzORzOUzJ1zLCzMMzOWz\ PezKyzNtzQozTkzWfzZbzaYzYYz`WzbVzdUztRzoSzjTzfTzaU\ zXVzTVzOWz70zCBzGMzKWzOfz } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 03-08-09 (The Worm Turns [6])
by Jim Muth 02 Aug '09

02 Aug '09

FOTD -- August 03, 2009 (Rating 6) Fractal visionaries and enthusiasts: Don't be shocked if today's image seems strangely familiar. It's merely a near-repeat of yesterday's image, with only a little tweaking of the same color palette and an 0.02-degree double rotation from the Julia orientation. The name "The Worm Turns" refers to the tiny departure from the true Julia direction. The rating of a 6 is generous for a near-repeat. The result is a bit more interesting than yesterday's image, though still far below top-FOTD quality. But why all this obsession with quality, whatever fractal quality might be? Fractals are for enjoyment. And today's image can be enjoyed to the fullest only 56 seconds after the included parameter file starts running. Another way to see the image is to view it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday started with light rain here at Fractal Central, but by mid-afternoon the sun appeared and the temperature reached 82F 28C, making the rest of the day quite pleasant. The fractal cats forgot their fractal roots when they got into a spat over the one remaining catnip rat. The next FOTD, not another repeat, will be posted in 24 hours. Until then, take care, and the asteroid that will eventually strike earth is already on the way. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Worm_Turns { ; time=0:00:56.37-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideJulibrot center-mag=4.94067/0/1.8 params=89.98/0/89.98/0/-0.77/0/0/0/1.05/1.5 float=y maxiter=600 inside=0 logmap=25 periodicity=10 colors=000I6IJ8JKAKLCLMEMNGNOIOPKPQMQRORSQSTSTUUUZ\ ZZccchhhmmmzzzzzzzzzmmmmmmcccUUUPRoMDUBIBJHARH9ZG8\ c32eA5fG7hNAmR0kS6iTCkQ9mNCmQFmTImWLmZOmaRrdUre_rg\ bqddpb`q`YrYUtWQwUNzRLzOJzLHzIFzFDzDBzHPzLazOnzHZz\ AKzF5zF8zKAzQDzWFzaHzgKzmMzmOzmZzmZzmdzmazmZzmXzhL\ zcKzZKzeKzbJz`IzZHzaOzcVze`zhgzjnzltzfqzanzWkzRhzL\ ezGbzB`zNkzYvzWizVYzMOzDFvPIr_KmVRZQYcLdZOgUQjPSlK\ UoMWlNRfON`PIVQEQK9UO5YS1bb0fl0zeDz_PzT`zNlzrzzjwz\ eszUqzPmzQkzN`zKRzHGuF6pJ9kNCkQEpUHuXJz2oz9izFczFp\ zFjzFdzFZzFTzFOzJSzMVzPYzT`zWczZfzWezUdzSczQbzObzL\ dzJez5szBlzHfzN_zTUzZNzcHz`JzYLzVNzSPzhazaYzWVzQRz\ JOzDKz1Bz7HzDMzJRzPWzVaz`fzfkzf8zkpzgozcnz_mzWlzSk\ zOjzHlzKjzMhzPfzRdzTbzW`zYZzScz_XzXazVezTjzRnzOMzO\ PzORzOUzJ1zLCzMMzOWzPezKyzNtzQozTkzWfzZbzaYzYYz`Wz\ bVzdUztRzoSzjTzfTzaUzXVzTVzOWz70zCBzGMzKWzOfzsBzUv\ zSpzQjzhqzWhzPdzIazBZz0_z } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 02-08-09 (A Deep Dark Forest [No Rating])
by Jim Muth 02 Aug '09

02 Aug '09

FOTD -- August 02, 2009 (No Rating) Fractal visionaries and enthusiasts: As I expected, I had to make a trip to Old Fractal Central on Saturday, and did not get back to new FC until noon Sunday, when the FOTD was already late and there was far too little time for a proper fractal search. In a rush, I found today's image and named it "A Deep Dark Forest". The image is actually a tiny part of a Julia set. Curiously, the entire Julia set consists of an infinite string of similar but gradually changing elements. The name refers to the blue, egg-shaped things surrounding the central element in the frame, which are actually fractal trees that have not quite fully formed. A large number of trees makes a forest, thus the name. I never rate such hastily found images, and today is no exception, though if I were to rate it, I would probably give a rating of a 6.5, mostly for the coloring. The calculation time of 1-3/4 minutes may be cut in half either by setting the symmetry of the image to X-axis or by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But before going to the web site, give Paul a fair chance to calculate and post the image. The weather was quite muggy at Old Fractal Central on Saturday, where the temperature reached 86F 30C and the one remaining old fractal cat, Thomas, spent the afternoon stretched on the stones in front of the fireplace. I hear things were pretty much the same back here at New Fractal Central, where the two new fractal cats, Nicholas and Cassie, spent the afternoon stretched under the cool air. If all goes well, the next FOTD will be posted in around 9 hours, but there is no guarantee, so don't hold your breath waiting for it. Until whenever, take care, and philosophize. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Deep_Dark_Forest { ; time=0:01:46.80-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideJulibrot center-mag=+16.94930143\ 560947/0/1.83592e+011/1 params=90/0/90/0/-0.77/0/0\ /0/1.05/1.5 float=y maxiter=6400 inside=0 logmap=174 periodicity=10 mathtolerance=0.05/1 colors=000MEMNGNOIOPKPQMQRORSQSTSTUUUZZZccchhhmmmz\ zzmmmccc```YYYVVVSSSPRoMDUBIBJHARH9ZG8c32eA5fG7hNA\ mR0kS6iTCkQ9mNCmQFmTImWLmZOmaRrdUre_rgbqddpb`q`YrY\ UtWQwUNzRLzOJzLHzIFzFDzDBzHPzLazOnfHZRAKBF5CF8DKAE\ QDFWFGaHHgKImMIrOzzZzzZmzdcvaUrZKmXvhLmcKdZKXeKWbJ\ W`IWZHQaOLcVGe`Bhg6jn1ltAfqJanRWk_RhgLepGbxB`ZNkAY\ vVWioVYTMO7DFDPII_KCVR6QY0Ld5Og9QjESlIUoMWqNRpONoP\ InQEnR9mS5lS1lb0kl0zeDz_PzT`zNlzHxzJuzLrzNpzPmzQkz\ N`zKRzHGzF6zJ9zNCzQEzUHzXJz2oz9izFczFpzFjzFdzFZzFT\ zFOzJSzMVzPYzT`zWczZfzWezUdzSczQbzObzLdzJez5szBlzH\ fzN_zTUzZNzcHz`JzYLzVNzSPzhazaYzWVzQRzJOzDKz1Bz7Hz\ DMzJRzPWzVaz`fzfkzf8zkpzgozcnz_mzWlzSkzOjzHlzKjzMh\ zPfzRdzTbzW`zYZzScz_XzXazVezTjzRnzOMzOPzORzOUzJ1zL\ CzMMzOWzPezKyzNtzQozTkzWfzZbzaYzYYz`WzbVzdUztRzoSz\ jTzfTzaUzXVzTVzOWz70zCBzGMzKWzOfzsBzUvzSpzQjzhqzWh\ zPdzIazBZz0_z4Wz8TzCQzGNz } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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Re: [Fractint] Diode Animation?
by JackOfTradeZ＠comcast.net 02 Aug '09

02 Aug '09

. Well, I finally got it to work with tweax; it is one of the most interesting images I have seen, like with all the dots. However, there are no parameters to tweak so I can't do a morph animation, or as I was hoping, something that would model electricity thru a diode or something. Zooming in gets you nowhere fast; zooming out is ok for a few orders, then it STOPS at about E-005. You cant back out further - keep getting the same image. (I have seen this before. Strange) .

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Re: [Fractint] Diode Fractal
by JackOfTradeZ＠comcast.net 02 Aug '09

02 Aug '09

. No PAR or FRM is seen, and no attachments. Maybe it is problem on my end? I am using comcast web client email. .

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FOTD 01-08-09 (Brontosaurus [7])
by Jim Muth 31 Jul '09

31 Jul '09

FOTD -- August 01, 2009 (Rating 7) Fractal visionaries and enthusiasts: For today's fractal I mixed Z^2 with half as much Z^4 and added straight C. This combination creates another parent fractal shaped like a boomerang. Today's image is located on the outer edge of the boomerang, near the point where it is curved. The image rates a 7, mostly because I kind of like the soft pastel coloring. The name "Brontosaurus" has no connection with the image. In fact, I believe the brontosaurus is no longer considered a single species of dinosaur, since so many dinosaurs of the same general type existed. The already brief calculation time of 1-1/2 minutes may be eliminated entirely by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Clouds and rain spoiled Friday here at Fractal Central. The temperature of 75F 24C would have been near perfect if the day had been dry. As it was, the fractal cats had to content them- selves with raindrops on the window. I'm thinking of giving them a screened porch by next summer so they can enjoy the great outdoors without having to be constantly watched. We'll see how it goes. Except for the weather, things went quite well on Friday, with the real work finished by 2pm. But there might be a trip to Old Fractal Central coming up on Saturday, so if the FOTD for August 2 is late, you will know what happened. Until whenever, take care, and live life. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Brontosaurus { ; time=0:01:35.50-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.5013003260653149/+0.012863632787256/\ 5.466798e+010/1/110/0 params=1/2/0.5/4/0/0/0/0 float=y maxiter=1500 inside=bof60 outside=tdis periodicity=10 mathtolerance=0.05/1 colors=000FFXIAeK5mN9hPDcRHZTLUVPPXTKZWGaVLcUQfTVh\ T_kSdmRioRnrTqtUsvWuxXwzYyE4YL8RRCKYFEcJ7iM1dLA`KI\ XJRTIZPHgLGoHFwIGsJHoKHkLIgMJcNJ_OKWOKSSNUVQVYTXaW\ YdZ_ga`jdakhfkkjknnkrrkuvkxzimygbxfSwdHvc7uZDuVJuR\ PuMVuI`uEeuN`r000dRlmMinPeoSboV_OpiTjgXee`_cdVbhP`\ lKZpEXt9WsIUsRSrZRrgProOiZNaIMU1L`UYWTTSTONTJJSFES\ AAS56S15P65NB4KG4IL3GQ3DV2B_29cVxxYus`snbqjeoehm`j\ kXelffhifdkg`ngXphTrhPuiLwiHyjJdjLLjN1iO7hODhPJgPO\ fPUfQ_eQeeQjZJRTC8YIDaNHUOSMPaEQk6RuNd3KL9I1EN4MS7\ UWAaSIbPPcLWdIbeFifOdjX_neWrnRvwNysLypJymHyjFydHo_\ JfVLYPNOKPFFR6OWPW`gcdy_eoWfeSgXNhUIiSEjQ9kO5lMKUc\ ZCuRVsKmqhH8ZSAPbBFmC6xDFqLNjTWc`cXhlQptJxpKnmLegP\ baT`WXZQ`XKdVGgRDiNAlK6nG3qC0s9CjZObxXZyeVynRywNyk\ Tn_ZcOcTLgQJjNdV7gSBjQEmNHpLKrJNmPVhVac_hZeoUjvY`n\ aRgeH`eGXeFUeEReDOeCLeBIeAFeAChCHjELlGPXUeeGmm2tl2\ kk2bj2Vi2Mh2EmDKqNP9QGCLP } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 31-07-09 (Spiral Straightness [7])
by Jim Muth 30 Jul '09

30 Jul '09

FOTD -- July 31, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the fractal that results when Z^3 is mixed with half as much Z^6 and straight C is added. The parent fractal resembles nothing as much as an over-decorated boomerang with a Mandeloid attached to its center. Though at first glance, the area where today's image is located would seem to be a Seahorse Valley, it actually is an East Valley, with the image located on the wrong side of the north branch of this valley. As is true of so many out-of-the-ordinary images, today's image is filled with holes. I named it "Spiral Straightness" when I was struck by the way the tight spirals suddenly resolve into eight elements with almost no spiral effect. The rating of an FOTD-average 7 indicates a continuation of the sameness that seems to be creeping into the FOTD images. But it's still an interesting image to see, even if the calculation time of 8-1/3 minutes is rather slow. Of course, the calculation may be avoided altogether by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Things were going well enough on Thursday until I waxed philo- sophical and began pondering the things that might go awry with teleportation. I imagined that the Enterprise's teleport device got stuck in an endless loop and before the error was corrected, created several copies of the same person on the planet's sur- face. This would be possible because teleport machines teleport only a field pattern and not an actual stream of individual atoms, which would probably be quantum impossible. If this duplication were to happen, the question would arise as to which teleported body, if any, held the continuation of the individual's stream of consciousness. Of course, each presum- ably conscious copy would claim to be the same person, but it is obviously impossible for the same person to be in several places at the same time. I surmised that this paradox most likely is a sign that teleportation is impossible, and booted Fractint. Lots of sun and a seasonably warm temperature of 86F 30C made Thursday a pleasant but unexceptionable day here at Fractal Central. The fractal cats yawned, stretched and went back to sleep. Except for the philosophical diversion, my day was average. The next FOTD will be posted in 24 hours. Until then, take care, and live in harmony with yourself. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SpiralStraightness { ; time=0:08:22.02-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.4156458287859106/+0.003206070095215/\ 1.188422e+011/1/-37.5/0 params=1/3/0.5/6/0/0/0/0 float=y maxiter=12000 inside=0 logmap=1964 periodicity=10 mathtolerance=0.05/1 colors=000DaPD`QE_REZSFYTFYUGXVGWXHVYHVZIU_IT`JSaJ\ RbKRcKQdLPeLOfIV2JU5JU8JTBJTEJSGKSJKRMKRPKQSKQULPX\ LP_LObLOe9MuBNsCNrDNqENoFNnGOmHOlIOjJOiKOhBjgk`diY\ cgUadR`bO_`LYYIXWFWUCVYGWaJXeMYiPZjS_kV_kY_k`_dc_Y\ eZKgYSdcZaheZmdWldUkdSjdQidOhcMgcKfcIecFdcDcbBbb9a\ b7`b5_b3Zb1Zc3_c5`c6ad8bd9cdBdeDeeEeeGffHgfJhfLigM\ jgOkgPkcTb`XUX_LUcCRf4Pe9OeDMdHLdLKdQIcUHcYFbaEbfD\ bjBanAar9avA`rB`oC`lD`hE`eF`bG`ZH_WI_TJ_PK_ML_JM_F\ N_CO_9NaBNcCNeDNfENhFNjGNlHMmJMoKMqLMsMMtNMvOMxPMy\ QRg_WRhVRhTQhSQgQPgPPgNOgMOgIr2Jn7JkBJhFKeJKbNK_SL\ XWLU_LRcgFbaIdWKexeJlaHaYGQUEFQD4MC8OFBQIESLHUNKWQ\ NYTQ_VTaYWc`Zebagedihgkjjmmmoppqrssuvuxyvzruvltres\ n_rjTqgNpcGo_AnW4nT8jVBgXEcYI`_LXzOUzNSzMRzMQzLPzL\ Oz7mz8mz9mz9mzAmzBmzBmzCmzDmzcZzcZzcczchzcmvcrrcvm\ czkzzjzzizzizzhzzgzzSzzUzzWzzYzz_zz`zzbzzdzzfzzjzz\ izzhzzgzzGzzJzzLzzMzzNzzO } frm:MandAutoCritInZ {; 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)+(p4)), 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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30-07-09 (Magic Can Be Real [6])
by Jim Muth 29 Jul '09

29 Jul '09

FOTD -- July 30, 2009 (Rating 6) Fractal visionaries and enthusiasts: I named today's image "Magic Can Be Real". I have forgotten the reason, but one thing certain is that 100 years ago, fractals themselves would have been considered magic. Of course, stage magic is real enough, but all of it is based on natural laws and is not really magic in the supernatural sense. Today's magic fractal came to pass when I combined 1/2 part of Z^(5.5) with Z^(3.5) and added C. The parent fractal is shaped rather like a north-south oriented lozenge with a Mandeloid hanging from its lower end. A small oval bay lies between the lozenge and the Mandeloid. Today's image is located in the east branch of the valley separating this small bay from the lozenge. The rating of a 6 is all I could do for the image, which really could have benefited from additional work on the colors. The calculation time of 6 minutes is a bit longer than the image is worth. Better value may be found however on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted for peace and contentment. The temperature of 79F 26C was pleasant enough, but the clouds and occasional light rain kept a damper on outdoor activities here in the Fractal Central area on Wednesday. The fractal cats checked the weather once or twice, then Cassie found the empty laundry basket and spent the rest of the afternoon curled in it. When Nicholas saw he would not have the basket, he leaped to the top of the secretary, where he stretched out for the afternoon. My day was spent getting the work out of the way. The next FOTD will be posted in 24 hours. Until then, take care, and we're rational people. We know that real magic of the supernatural kind does not exist . . . or do we? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Magic_Can_Be_Real { ; time=0:06:12.83-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.2005630573/-1.0418614259/12201.01/1/\ -175/0 params=1/3.5/0.5/5.5/0/0/0/0 float=y maxiter=6400 inside=0 logmap=344 periodicity=10 colors=0008pzUgyVdxWbwX`uYZsZXq_Vo`TmaRkbQicQgdQee\ QcfQagQ_hQYiQWjQUkQSlQQmQOnQNoQMpSLqUKrWJsYItYKp_I\ k`GfaEabCXcASd8Ne6Kg4Jf5Jf5Jf5Je5Ie5Ie5Ie5Id5Hd5Hd\ 5Hc5Hc5Hc5Gc5Gb5Gb5Gb5Fa5Fa5Fa5Fa5E`5E`5E`5E_5E_5D\ _5D_5DZ5DZ5CZ5CZ5CY5CY5CY5BX5BX5BX5BX5AW5AW5AW5AV5\ 9V59V59V59U59U58U58T58T58T57T57S57S57S57S58T68T68T\ 69T79U79U79U7AU8AU8AV8BV8BV9BV9BV9CW9CWACWADWADWAD\ XBDXBEXBEXBEXCFYCFYCFYCFYDGYDGZDGZDHZEHZEHZEH_EI_F\ I_FI_FJaDI_FIYGIXIIVJIULISMHQOHPPHNRHMSHKUHJVGHXGF\ YGE_GC`GBbG9cF7eF6fF4hF3iF1kE0nF0lF1kF2jF3hF4gF4fF\ 5dF6cF7bF8`F9_F9ZFAXFBWGCVGDUGESGERRFQTGOVHNXIMZJK\ `JJbKIdLGfMFhNEjNDlOEnPEpQErRFtRFvSFxTGzUGzUGzVHzW\ HzXHzXIzYIzZIz_Jz_Jz`JzaKxbKubOtcQtdSteUteWtfYtg_t\ hathctjetkgtmiuokvrmwtoxwqyxszzuzzwzzxzzyzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandAutoCritInZ {; 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)+(p4)), 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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29-07-09 (Nothing In Sight [?])
by Jim Muth 28 Jul '09

28 Jul '09

FOTD -- July 29, 2009 (Rating ?) Fractal visionaries and enthusiasts: Today's image shows nothing. Take my word for it, there is nothing in the image. If you doubt this, reset the inside to 'numb' and rerun the parameter file. True, there is nothing in the image, but like in quantum physics, where a vacuum can be filled with quite a lot of something, the nothing in today's image is filled with invisible energies, and an active inside fill will make the energy of the nothing visible. The 'bof60' inside fill did the job in today's image, where nothing fills the screen. The nothing appears to be a skeletal Mandeloid, which fades into even less than nothing as it approaches its East Valley. There is a curious thin broken line extending southeast from where the East Valley of the large Mandeloid should be. This line probably holds interesting patches of nothing also, but I have not yet checked it. Since it is rather hard to give a rating to nothing, I rated the image at a question mark. The name "Nothing In Sight" describes the image perfectly. The calculation time of 4-1/2 minutes is brief enough to make running the included parameter file worth the effort, especially since nothing will be visible when the calculation is completed. Another way to see nothing is to visit the FOTD web site where the finished image is posted. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where you might be surprised at how attractive nothing can be. Typical midsummer weather prevailed here at Fractal Central on Tuesday, which means heat, haze, humidity and a continuing threat of showers. The fractal cats gave up activity when the temperature reached 88F 31C and spent the day under the cool air vent. My day was busy enough to keep me distracted from the hot weather but not so busy as to seem hurried. The next FOTD will be posted in 24 hours. Until then, take care, and prepare. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Nothing_In_Sight { ; time=0:04:37.32-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip passes=1 center-mag=1.3263/4.64017/13.7457/1/-147.5/0 params=-0.5/50 float=y maxiter=1500 inside=bof60 logmap=yes periodicity=10 colors=000zzzzxxzwwzuvystxqqwnnvklviiufftcdt`asZ_r\ WXrTUqQSpOPoLMnIKmFHlFEkDFjCGiBHhAIg2Jf6Ke9LdAMcBN\ bCOaDP`EQ_FRZGSYHTXIUWJVVKWUKXTKYSKZRKZQK_PK_OK_NK\ _MK`LK`KK`KK`JKaJKaJKaJKaJKbJKbJKbJKbIKcIKcIKcIKcI\ KdIKdIKdIKdIKeIKeHKeHKeHKfHKfHKfHKfHKgHKgHKgHKgHKh\ GKhGKhGKhGKiGKiGKiGKiGKjGKjGKjFKjGKjGKjHKjHKjIKjIK\ jIKjJKjJKjKKjKKjKKjLKjLKjMKjMKjMKjNKjMKjOKjOKjOKjP\ KjPKjQKjQKjRKjRKjRKjSKjSKjTKjTKjTKjUKjUKjVKjVKjVKj\ WKjWKjXKjXKjXKjYKjYKjZKjZKj_Kj_Kj_Kj`Kj`KjaKkaKlaK\ mbKmbKmcKmcKmcKmdKmdKmeKmeKmeKmdKmdKmdKmdKmcKmcKmc\ KmcKmcKmbKmbKmbKmbKmaKmaKmaKmaKmaKm`Km`Km`Km`Km`Km\ _Km_Km_Km_KmZKmZKmZKmZKmZKmYKmYKmYKmYKmXKmXKmXKmXK\ mXKmWKmWKmWKmWKmWKmVKmVKmVKmVKmUKmUKmUKmUJKUJJTJJT\ JITIITIHSIHSIGSIGSIFSIFRIERIERIDRIDSFERIDRKCRMCROB\ QQAQSAQU9QW8PZ8P`7Pb6Pd6Of5Oh4Oj4Ol3WjbLr0Mp1No2On\ 3Pl4Qk5Rj6Ri7Sg8Tf9UeAVdB } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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28-07-09 (Terraces of Desire [7])
by Jim Muth 27 Jul '09

27 Jul '09

FOTD -- July 28, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image is more a creation of program gimmicks than a fractal discovery, but even so, the final result earns an honest and average 7. The parent fractal came about when I combined equal parts of Z^3 and Z^5 before adding straight C. It is a double-bayed thing oriented north-south and resembling a peanut. Today's image is located in a wedge-shaped bar in a double bud on the southwest shore line of the southern bay of the parent. When rendered in the normal equal-iteration manner, today's image is most boring, but when the inside is set to 'fmod' and the outside to 'tdis' the scene comes to life. Most of the effect is due to the critical setting of the 'fmod' proximity factor. The terraced effect was achieved by the outside setting of 'tdis'. The name "Terraces of Desire" is a kind of joke. It hints at the junky romance novels known in the trade as bodice rippers, which FL sometimes picks up when nothing better to read is available. (I must be sure she doesn't manage to read this discussion.) The rating of a 7 is good enough to make the calculation time of 26 seconds worth the effort. Even less effort will be expended if the finished image is viewed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Typical warm summer weather prevailed here at Fractal Central on Monday, with a temperature of 86F 30C. A few small showers were in the area around noon time but none fell at FC. The fractal cats seemed content with the conditions, and spent most of the day sleeping, though a bit of a row broke out when Nicholas tried to chase Cassie from her sleeping spot on the living room ottoman. Nicholas ended up shaking off a scratched ear; Cassie ended up with the ottoman. My day was fair enough. The next FOTD will likely be posted in 24 hours. Until then, take care, and let me know when men get to Mars. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Terraces_of_Desire { ; time=0:00:26.14-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=+0.488820481/-0.874460107/29089/1/47/0 params=1/3/1/5/0/0/0/0 maxiter=1500 inside=fmod proximity=0.00229 outside=tdis periodicity=10 colors=000isDgsDfrCdrCcrBarB_qA`oCamEbkHdhJefMfdOg\ bRi_TjYWkWYlU`nRboPe6UoBPgGK_LFTORVvbWmnYevZSuXRqV\ QmTOiRNePMaNKYLJUKIQIGMGFIEEECCAAB68A27E3AH4DK5GO6\ JR7MU8PY9S`AVcBYgC`jDcmDepMjrVnPdsWe`bfJhg1WY6X`EY\ bLZdS_fZ`he`hd_hc_hb_h`Zh_ZgZZgYYgXUdGYgWXgVXgUXfT\ WfSWfQWfPVfOVfNVeMUeLUeKUeJTeITeHdRKbTJaVJ_XIZZIX`\ HWbHUdGLdeMebNe_OeYPeVPeTQeQReNSeLTeIwzYtxWrwVpuUn\ tTlsSjqQhpPfnOdmNblM`jKZiJXgIVfH4Eo8IiCMdFQ_JUVMYQ\ QaLi`yfasdbmbbg`cbZdXXdRVeLEZHF_GG_GG_GH_GH`GI`GI`\ GJ`GJaGKaGKaGLaGLbGMbGMbGNbGNcGOcGOcGPcGPdGQtOItUA\ t_2tdHjXW`PiSIjUKjWMjYOk_QkaSkbTjjTirTizTerSajSYbR\ VVRRNQNFQK8QQ6NV5K`3He2Ej1Bb7IWCPPIWINbBShFTgIUfMV\ fPWeTXdWYd_Zcb_ca`da`da`ea`e``f``f``g``gKeN3j36hA9\ gGCfMFeTIdZQbrOctNevMfwz6Yy7UvCSrHQnMOkRMgWKcaHc`G\ dZFeYEfWDgVBhTAiS9iQ8jP7kN5lM4mK3nJ2oH0SC1XL4aU7gb\ AlkDrrGrsGqtFqvFpxEpzEggh } frm:MandAutoCritInZ {; 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)+(p4)), 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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27-07-09 (Time for Thinking [7])
by Jim Muth 27 Jul '09

27 Jul '09

FOTD -- July 27, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that results when equal parts of Z^4 and Z^6 are mixed and C is added. This parent fractal looks somewhat like a butterfly with a head on the negative X-axis shaped like a Mandelbrot bud. With thick arms converging on its mouth, this bud appears to be non-critical, but curious double-bays along the edges of these arms are filled with spider-like minibrots. Today's image shows one of these minibrots made all the better by rendering it with the inside set to 'bof61'. After all the work, I rated the image at an average 7. It's kind of fun to look at, with a bit of an art-deco feeling. I named it "Time for Thinking" for some reason that I have forgot- ten. The words probably just popped into my head. (An armchair psychologist could probably work up a complete psychoanalysis based on the names I give the FOTD's that just pop into my head.) Luckily for those with time issues, today's image calculates in only 1-1/6 minutes, about the time it takes to make a New-York style egg cream. (An egg cream consists of chocolate syrup, milk and seltzer water mixed in just the right amounts. The amounts are critical. It's kind of a chocolate ice-cream soda without the ice cream.) Those who prefer to avoid calculation may view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Lots of clouds and humidity with some sun and a temperature of 84F 29C made Sunday a perfect day for warm weather activity here at Fractal Central. The fractal cats believe in warm weather inactivity however, so they did little but eat and sleep. My day was correspondingly inactive. If I get the ambition, the next FOTD will be posted in around 12 hours. Until then, take care, and then do it again. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Time_for_Thinking { ; time=0:01:10.02-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.73229701362/+0.00870137264/385017.8/\ 1/82.5/0 params=1/4/1/6/0/0/0/0 float=y maxiter=950 inside=bof61 periodicity=10 colors=000XTBVVCSWDPYEN_FK`GHbHFdICeJ9gK7hL9dOAaRB\ YTCVWERZFO`GKcHHfJDhKAkL6nM3pN5nO7lP9kQBiRDgSFfTHd\ UJbVLaWN_XOZTNXQNWNMUKMTGLRDLQAKO7KN4KM7JKAJJDJIGI\ HJIGMIEPHDSHCVHBYHAZGDZFFZFHZEJZEKZDKZDKZCKZBKZBKZ\ AKZAKZ9IZ9GY8ET8CO7AI7AG6AI6AK6AM5AO5AQ5AS4AU4AW4A\ Y3A_3Aa3Ac8AeCAgGAiKAjOAlSKnWKp_PrcKsgUriUtkcvlcwn\ mvpmzqszqwTP8TQ6RU9Q_CPeFOjINmLMqOKrNIsMGtLEsKCvJA\ vI8tH6rG4rF2rE5rU8rmAuzCuwDutEunFujHugIudJuaKuZLuW\ KrUKoTJmRJjQIgPIeNHbMH`KGYJGVIFTGFQFFOEINFLMGNMGQL\ HSLHVKIXKI_JJaJJcLKdMKfOLgPLiRLjSMlUMmVNoXNpYNr_Os\ `OtaOqfRokUmoWktZix`ksblodmkfnghobipZkrVmsRotMpuIr\ vEtwAvx6wsBsnGojKlePh`UdXYaZ`c`bebdgdfieijgklimnko\ plrqntspvurxwszxtrntketcXuXNuPEuI5sJ8qKApLCnMElNGk\ OIiPKgQMfQOdNMbKKaHI_EGYCEX9CV6AT38S16R28R39Q4AQ5B\ Q6CP7DP7EP8GO9HOAIOBJNCKNDLNDMcHaWLfOPkGTp8Xu0_z4`\ x8`vBatFarIapMbnQblTcjXch } frm:MandAutoCritInZ {; 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)+(p4)), 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] Water Lilies
by JackOfTradeZ＠comcast.net 27 Jul '09

27 Jul '09

. They look alive! I wonder what the "biomorph" tweak will do. I'm gonna see if I can get them to "move" .... .

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Re: [Fractint] Star Nursery
by JackOfTradeZ＠comcast.net 27 Jul '09

27 Jul '09

. Yeah - looks a little like that famous Hubble picture, or maybe an ice-volcano plume on a far-out planet with a rich starry sky background. I ate it a good 9. .

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26-07-09 (Flight of the Bird [7])
by Jim Muth 26 Jul '09

26 Jul '09

FOTD -- July 26, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image is late, just as I warned might happen. FL and I decided to have a fun afternoon on Saturday, and, not wanting to carry along the laptop, (I never do), I had to forget the frac- tal search. But when we returnrd to FC late in the afternoon, I had good luck with the search for the day's fractal. Good luck is always necessary because one of the greatest problems in the continuing FOTD is how to avoid giving the impression that the images all look the same -- just another minibrot with just so much more fractal variety around it. Today's image was found in the East Valley of the parent that results when 1.1 part of plain Z is combined with Z^11 and plain C is added, and it actually does appear at least a little different from what has gone before. But to be honest I must mention that the parent fractal is a Mandelbrot set with 10 east valleys, which are on its west-southwest side. Today's scene is located in the break between valleys 5 and 6. I named the image "Flight of the Bird", leaving it to the viewer to supply the exact identity of the 'bird'. I rated the image at a 7 -- FOTD average. The calculation time of 44 seconds is almost breathtakingly fast, so if shortness of breath becomes a problem, the finished image is or soon will be available for instant pleasure on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The image will bring some pleasure, but it will not answer the question of why there is something instead of nothing. A warm muggy day on Saturday with a temperature of 84F 29C was given variety by a short but sharp shower at 6pm. The fractal cats do not worry about rain, so they slept through the event. My day was relaxing. If all goes well, the next FOTD will likely be posted in about 8 hours. If not, the wait will be longer. Until whenever, take care and worry not. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Flight_of_the_Bird { ; time=0:00:44.10-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.1254246947312831/-0.038926514109924/\ 6.77158e+011/1/10/0 params=1/11/1.1/1/0/0/0/0 float=y maxiter=800 inside=0 logmap=74 periodicity=10 mathtolerance=0.05/1 colors=00003B04C05D06E07F08G09H0AI3BK5CM7DO8FQBPVD\ V`F`zHpzIzzRpz_dzoBEY8MH5U03aTT`XUa`VbdWcgXckYdoZe\ c_i0`mHSgYJanAXlDBiMLfUVcac`imYqvXroWrhVsaVsVUtOTt\ HSuASu4Wq8_mCbiGffJibNmZRpWUDuQLpWSk`_fefajj_hnZfq\ YduXbxWasUboScjQdfOeaMfYKgUJhWFcXC_Y8WZ5S_2OZ5MZ8L\ YBKYEJYHIXKHXNGXQFPctQeoQgkRifRkbXgfacif_mkWppSsqQ\ jqObqMVqKNvRdzXu_iU9u3X_cUbbSeaPhaNk`Kn`Iq_FtZcMZZ\ NSUPK`BQS19dMb`OZXQVSSROUNKWJFYFfMbdNZbOW`QSZROXSL\ VTHTVDQaf6sggMeeOddPcbRcaSb_UaZV`XX`WY_U_ZT`YRbYQc\ XOeWMgVfLcdM`aNY_OVXPTVQQSRNQRKOSHLTFJUCGV9EW6BX3d\ Nb_Q_VSXQVULXRG_OXdZLyRgOafSXeVTdZOcaKbeFahB_l6hNe\ hQehTehVehYeg`djJelGfnDgpAhr7ijTXmaNojDrs3gNefQeeT\ edVecYeb`eabe_eeZheYjeXmeVRdTTZzzTzzNzzHzzIzzJzzKz\ zOzzRVzVRzYNz`IzdEzgAzjBzgCzeDzzEzzEzzBzz9zz7zz5zz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzztzzqzzozzlzzjzzgzzezz\ SzzEzzLzzSzzZzzdzzUzz`zzg } frm:MandAutoCritInZ {; 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)+(p4)), 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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25-07-09 (Northeast Bride [No Rating])
by Jim Muth 24 Jul '09

24 Jul '09

FOTD -- July 25, 2009 (No Rating) Fractal visionaries and enthusiasts: Friday turned unexpectedly busy here at Fractal Central, leaving almost no time for a proper fractal, much less a new type of fractal. What we have is an almost-Julia set with a bridge across its center. This bridge is a side view of the north branch of the valley leading to the period-4 bud on the north- east shore line of the main bay of the Mandelbrot set. The wedge-shaped valley has become a stripe with parallel sides because, regardless of where the Z-points are initialized in the Mandelbrot set, they eventually settle into the same orbits. I have no time for the technical details so just take my word for it. The image is a harmless one -- a Julia outline with a blue stripe running diagonally across the center. The area north and east of the stripe has many spirals, all spiralling clockwise, while the area south and west has only vague hints of spirals, and these are spiralling counter-clockwise. Checking the orbits will show that the northeast half of the area inside the Julia outline lies inside the period-4 bud; the southwest half lies on the outside. Some of the orbits are quite interesting. I leave it to the individual fractalist to find these orbits. I named the image "Northeast Bride". I had intended to type the word 'bridge' but typed 'bride' instead. I kind of liked the error, so I decided to let it remain. As for a rating, forget it. How many who have remained with the list all these years are really thrilled by seeing such trite images? At least the calculation time is reasonable. Who can complain about a calculation time of under 2-1/2 minutes? And if there are any who do complain, relief may be found on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is or soon will be posted. Hazy sun but otherwise pleasant weather prevailed here at Fractal Central on Friday. An afternoon threat of rain proved to be a false alarm. The fractal cats approved of the dryness and temperature of 82F 28C. My day was very busy, even with FL helping. There is a 50- percent chance that the next FOTD will be posted in 24 hours. The other 50 percent is that we decide to take the day off. Until whenever, take care, and something very important is happening unseen just beneath the surface. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Northeast_Bride { ; time=0:02:26.10-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=t center-mag=-0.00921296/0.0053159/1.11/1/-105/0 params=90/90/92/89/0.241/0.512/0/0 float=y maxiter=25000 inside=0 logmap=-3 periodicity=10 colors=000UV9UVCUWEUWGVWIWWLWWNXXPYXRYXUZXW_XY_X_`\ VY`UXaSWaRVaPUbOTbMScLRcJQcIPdGOdFNdHMgIJiKHkMFmOD\ pQBrS9bazbazbazbazbbzbbzbbzbczbczbczbdzbdzbdzbdzbe\ zbezbezafzafzafzagzagzagzahzahzahzahzaizaizaizajza\ jzajzakzakzakzakzalzalzalzamzamzamzanzanzanzaozaoz\ aozaoz`pz`pz`pz`qz`qz`qz`rz`rz`rz`rz`sz`sz`sz`tz`t\ z`tz`uz`uz`uz`vz`vz`vz`vz`wz`wz`wz`xz`xz`xz`yzayzb\ yzczzdzzezzfzzgzzhzzizzjzzkzzlzzmzzmzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzznzzozzpzzqz\ zrzzszztzzuzzvzzwzzxzzyzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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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24-07-09 (Star Nursery [8])
by Jim Muth 23 Jul '09

23 Jul '09

FOTD -- July 24, 2009 (Rating 8) Fractal visionaries and enthusiasts: Something in today's image reminds me of a cosmic dust cloud, which is also a star nursery. And that's what I named it. The parent fractal is nothing -- the blank screen that results when the (1/Z)+C fractal starts to morph into the Z^2+C fractal. But the blankness turned interesting when I tried the 'bof60' inside fill on it. It turned interesting enough, in fact, that the resulting image earns an 8. If I had more time to work on the colors, I might have brought the image up to a rating of 9. The result of calculating the included parameter file is worth the 8 minutes or so it takes to do the calculation. And if 8 minutes is too long to wait, the finished image is available for immediate viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds, high humidity and showers of rain kept Thursday from being acceptable to the fractal cats of Fractal Central. The temperature of 82F 28C was fair enough, but the cats demand sun. My day was unusually busy. When I fell behind however, FL stepped in to bail me out. The next FOTD will be posted in 24 hours. Until then, take care, and don't ask 'what'. These questions are too easy. Ask 'why'. These questions are far more difficult but far more satisfying. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Star_Nursery { ; time=0:08:09.33-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideJulibrot passes=1 center-mag=1.6021/13.942/5.9192/1.1171/-17.1932875\ 494030064/-6.00330107850168204 params=86/0/86/0/\ -0.77/0/0/0/-1/1 float=y maxiter=1500 inside=bof60 logmap=yes periodicity=10 colors=000zzzmszcfzUXmKShKNcK5AK0AK0AK4AP7JUCGYGDa\ KBcNJePPgQSiRVkRYmR`mRdmRemRemRfmRfmRgmQgmPfmNdmKb\ kJ`iIYgHVfGTeFSfDSh1Tj6WlBYnG`pIbrLetOgvRjxUlyXnvZ\ _sQLpI6mHCkGHhFMfERdDWaC`_BeYAjaDddG_gJVjMQmOLpRGs\ UBvX6yZ1tV3oR4kO6fK7aG8YDAT9BO5CK2EF0FB0GJ5`REuPCt\ NAtL8tJ6tH4tG3tccih_ZmWOrTEgYEYbENgEDkEHjIKiLNhORg\ SUfVXeY_d`ccdfbgiajl`mp_qsZtvYwyYztXypXxlXwhXvcXu_\ XtWWsSWrNWqJWpFWoBWn7WnAVlDUkFUjITiKThNSfPSeSRdVQc\ XQb_P`aP_dOZfOYiNXkNW`FUQ8SF0Q40P90NE1MI5LN9JRDIWG\ H_KGdOEhSDmWCqZBr_Fr_Is_Ls_Pt_St_Vt_Yu`TvaPvbLwbHx\ cCxd8ye4ye0nZ7dSDVLKLEQB8WDAVFBVGCVIDUJEULFUMGTOIT\ PJTRKSSLSUMSVNRXORYPR`MTcJVeHWhEYkB_m9`p6br4co5`l6\ Yi7Vg8Sd9Pa9MZAJXBGUCDRDAOE7ME5LE9KEDJEHIELHEPGETF\ EXEE`DEdCEhJMkPUnWaqaisaUkaFda0Y_1ZZ2_Y3_X4`W5aV5a\ U6bT7bS8cR9dQ9dPAeOBfNCfMDgLDgJCgICgHBgFBgEAgCAgB9\ gA9g88g78g57g47g13j37g5Ad } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

1 0

23-07-09 (Water Lilies [6])
by Jim Muth 22 Jul '09

22 Jul '09

FOTD -- July 23, 2009 (Rating 6) Fractal visionaries and enthusiasts: Today's image is another venture into the multi-dimensional world created by the DivideJulibrot formula. Apparently I have already posted two previous versions of this formula, which are all slightly different, but hopefully will produce the same images from the same parameters. Even now however, I see a way to make the formula a bit faster, so I cannot guarantee that the version included in today's parameter file will be the final version. I named the image "Water Lilies" when it reminded me of water lily leaves floating on a quiet tropical pond. Actually, the image is very closely related to the fractal trees I occasion- ally post. The rating of a 6 indicates that I am not totally satisfied with the colors, but find them good enough to meet FOTD minimum standards. One thing that cannot be questioned however is the calculation time of 31 seconds. Such lightning speed can hardly be exceeded. Web surfers may view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday's weather proved to be routine here at Fractal Central. The hazy sun, temperature of 81F 27C and moderate humidity was neither good nor bad. The fractal cat Nicholas was bad however. Leaping onto the kitchen counter without looking, he spilled a carton of half-and-half. To atone for his misdeed he began lapping up the spilled cream, while Cassie cleaned the cream that dripped onto the floor. The day was otherwise uneventful. The next FOTD will be posted in 24 hours. Until then, take care, and where are all these indispensable wireless electronic devices coming from? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Water_Lilies { ; time=0:00:31.86-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideJulibrot passes=1 center-mag=-1.72942/0/12.8 params=90/0/84/0/-0.893\ 279/0/0/0/1.5/1.5 float=y maxiter=1500 inside=0 logmap=50 symmetry=xaxis periodicity=10 colors=000kU9iS6gP7cM7_I8WA8S59O19N8INFQMLZMSfMYnW\ d`ekNor9jq8eq8`q7zv7zp7vp6ro6mo5ho5eo5bm7_k8Xi9SgA\ NeBKcCNaDP`ESZGVXH_VIcTJeRKhPLjNMlMNmLNnLNnLNoLNpL\ NpLNpLNpLNoLNnLNnLNoLNnNImPEmRAlPBkNCjLDjJEiIFhGGh\ EzgCzfAzf9zgBMhCPiDRjEUkFWlGzmHzmFznCzmDzpGzmJz9Mz\ ANzCPzEQzGSzITzKVzMWzOYzQZzS`zUazWczYdz_fzahz`UzZU\ zYUzWUzUUzTUzRUzQUzOUzMUzLUzJUzHUzHUzGUzGUzFUzEUzE\ UzDUzCUzCUzBUzAUzAUz9Uz8UvPOreDmv2ir7fnCcjH_fMXbRU\ ZUQVUNRUKNUGJUDFU9JUgKUgMUhOXiPRjRLkTFlRFSPG6RH8TJ\ BVLEXNHZOK`QNbSPdUSfVVhXYdTX_OWVJVQEUL9SM9UN9WP9YQ\ 8_S8aT8cV7ebFgjOjrXmK3JP3QV3X`3de3kk3rq4zp4zn5zm5y\ k6yj7xh7xg8we9wd9wbAvaAv_BuZCuXCtWDtUEsSIoQMkNQfLV\ bJZYGbUEfPCkL9oG7sC4x7BrDIlKPfQW`XbVciPipJpwCwuCws\ CwpDwnDvkEviEvfEudFuaFu_GuXGtVHtTHtQHsOIsLIsJJsGJr\ EJrBKr9Kq6Lq4Lq1Mp4Mp8LpCKqGJqKJrOIrSHsVGsZFsbFtfE\ tjDunCurBvrCsrDprEmrGjjXC } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

1 0

20-07-09 (Julia from the Side [8])
by Jim Muth 22 Jul '09

22 Jul '09

FOTD -- July 20, 2009 (Rating 8) Fractal visionaries and enthusiasts: Possible new formula alert! Today's curious image must take a back seat to an event that happened on this day 40 years ago, when a man first set foot on the moon. Yes, I know the exact date was July 21 in parts of the world, but why quibble? Back then, I was still in my wonder years, perhaps a bit wiser than a few years earlier, but I certainly had not yet realized the power of politics, nor had I reached my present state of cold cynicism. I thought I was lucky enough to have been born at the right time to see mankind actually begin the exploration of the solar system, just like in those stories I was reading and in the shows I was watching on TV. But something went wrong. After a few more dramatic journeys to the moon, the manned exploration of outer space (low earth orbit is not outer space) came to an abrupt end. Instead of expanding our exploration to the planets, we settled on developing a reusable shuttle that could do little more than enter low earth orbit. To ease the disappointment, we were told of all the scientific wonders that the shuttle program would bring, but so far, except for the Hubble telescope when it was finally brought into focus, the scientific wonders have been conspicuous only by their absence. Of course, the shuttle program gave us the international space station, a white elephant if ever there was one. It might bring some minor benefits eventually, though if so, I have yet to hear of them. And I now hear that once the shuttle program ends in a year or so, the space station will be considered junk, and unless Russia wants to take it over, it may be sent to burn up in the atmosphere over the ocean. It now looks like the space station was dreamed up only to justify the expense of the shuttle program by giving it something to do. What a waste of money! True, the dreamers are talking of men going back to the moon and even to Mars in a decade or two. Anyone who thinks this will happen should pay attention to the news. Where will the money come from? The current administration, which is very liberal with spending, can't even find the money for critically-needed health care reform, medicare and social-security, etc. Given the present dire economic conditions, what would voters think of spending trillions of additional dollars on a space exploration program? The answer is, 'don't even think of it'. I was not born too early to see mankind explore and colonize space, the sorry truth is that it will never happen, not in our lifetimes nor in the lifetimes of our descendants. An organiza- tion of space explorers exploring the galaxy in space ships is a fantasy. It always was a fantasy and always will be a fantasy. Some ideas are even more bizarre. Some say we could reach inter- stellar space by leaving our bodies behind like un-necessary baggage and making the trip with only our minds, which would need no life-support system, nor even a ship. It's too bad that this is also a fantasy. Would we ever spend money and effort trying to separate our minds from our bodies (astral projection) when science tells us that our minds are a function of our brains? And even if it were possible, how could astral explorers prove what they had discovered without people on earth wondering if the discoveries were mere fantasies of the explorers' minds? The things I say are negative and not at all hopeful, but they are fact. And one thing we must never lose is the courage to face the truth even when it is harsh and not what we want to hear. My one glimmer of hope is that some rational thinker will point out an error in my reasoning. Since no one is likely to do this, let's turn our attention to fractals, which don't really exist but can be explored anyway. I named today's image "Julia from the Side" because it's an almost-Julia set of an image created by the DivideBrot series of formulas, with a mixture of Z^101 and Z^2. The DivideJulibrot formula included in the parameter file might be posted for the first time in this FOTD. I'm not sure. The image is just different and curious enough to earn a rating of an 8. And the calculation time of an incredibly short 1-1/2 minutes only helps the rating. But as always, the most enjoyable way to see the finished image is to view it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The near-perfect summer weather continued here at Fractal Cen- tral on Sunday, laying to rest any lingering fears about man- made climate change, AKA global warming, at least in this area, though I hear that the fears of warming are rising along with the temperature in Alaska. The high temperature of 81F 27C and blue sky filled with puffy white clouds made Sunday in the FC area seem like a holiday on one of the Hawaiian islands. Never having been to Hawaii, the fractal cats had no comment. My day was fair enough. FL was happy with the antique treasure she found in Benton yesterday -- a victorian lamp shade with lots of fringes. Unless we reach the stars within 24 hours, the next FOTD will be posted then. Until the next time, take care, and nothing negative I might say about space exploration will change the fact that I am certain that precognition does exist. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= JuliaFromTheSide { ; time=0:01:29.37-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideJulibrot passes=1 center-mag=0/0\ /0.5883363/1/-37.5/0 params=89.9999/0/89.9999/0/\ -2.3155315/0/0/0/101/1.5 float=y maxiter=1500 inside=0 symmetry=none periodicity=0 colors=0000Hh3Hf6HdFHbGIbIJaLK`OLaTMcZPceWblbbpibt\ oawq`zs_ztZqaddJjfKigKhhKhjKgkKglKfnKeoKepKdrKdsKc\ tKcsTYraSqiMprGpzBrsGtlKufPw_TyTXzNazGezAiy9kv9mr9\ oo8qk8sh8ud7wa7yY7zV7zPAlJCXDEHCIIBMJAQKAUL9YM8aN7\ eO7hO8eT8cX9aa9ZeAXjAVnATrCVsEWtGYtIZuK_uMavObwQdw\ SexUfxWhyYiz_kzalzbmz`jyZhwXfuWdsUbqS`oRZmPXkNUiMS\ gKQeIOcHMaFK_DIYCGXGHVJITNJSQJQUKPXLN_LMcMKfNIjOHm\ OFqPEtQCwQBvPEvPHvPKuONuOQuOTuOWtNZtNatNdsMgsMjsMm\ sMorNkqNhqNepNaoNZoNWpMVpMVpLUpLUqKUqKTqJTqJSrISrI\ SrHRrHRrHRpKWnN_lPcjSghVkfXod_scawqadlgggmibskYymT\ zoZtudizbgw`ftZepYdmWciUbfSabR`_P_XNZTLYQKXMIWJGVF\ EUCDT9FP8HM8JJ8LG7ND7PA7RBBTBEVBIXCLZCP`CSbDWdDZfD\ bhEejEilElnFppFsrFvqJsqMpqPnqSkpVhpYfp`cpc`pfZqf_q\ f_qf`rf`rf`rfarfasfbsfbsfbsfctfctfdtfdtfdrjiqmnpqs\ otwnpvnmvmjvmgvmdvlaulZukVukSukPujMtjJtiGtiDtiAtjD\ vkGwlIxmLynNznQzoSzpVzqXz } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

2 1

22-07-09 (In Deep Trouble [5])
by Jim Muth 21 Jul '09

21 Jul '09

FOTD -- July 22, 2009 (Rating 5) Fractal visionaries and enthusiasts: Today's image shows a scene in a tiny remote valley deep in East Valley of the Mandelbrot set, at a level where unexpected things start to appear. The area is extremely difficult to color, and I managed only a barely adequate job. With no logmap in effect, the image becomes total chaos and basically worthless. The 'tdis' option does a reasonable coloring job, but slows down the calculation by a factor of near 100. The other outside options are useless. The coloring difficulty lies in the extreme iteration range, which ranges from a low count around 80,000 to a maxiter of 2,500,000. After several failed attempts, I set the logmap to an unlikely -3 to get the barely adequate effect in today's image. Though the scene lies in East Valley, no elephants or pop-eyed aliens are in sight. But the area is quite rich in minibrots, the largest of which, a rather twisted one, lies at the center of the image. The name "In Deep Trouble" refers to the image, not to any lingering unpleasantness here at FC. The rating of a 5 includes a 1-point penalty for the less-than-stellar coloring. The calculation time of 21 minutes is rather slow, and on some machines will run into several hours, so I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I sent the finished image on ahead, so it should be waiting. Things got pretty much back to normal here at FC on Tuesday, at least among the humans. The fractal cats were cranky for some reason, perhaps over the lack of sun and rather chilly tempera- ture of 73F 23C. The next FOTD will be posted in 24 hours, give or take a few. Until then, take care and be pragmatic. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= In_Deep_Trouble { ; time=0:21:05.64-SF5 on P4-2000 reset=2004 type=mandel passes=1 periodicity=10 center-mag=+0.2500121338008163/-0.0000000770449661\ /8.49238e+011/1/112.5/0 params=0/0 float=y inside=0 maxiter=2500000 logmap=-3 mathtolerance=0.05/1 colors=000Gt6Ft1zQGzNMzHPzNRzWWz`XzeYzk_vobpiaic_b\ _ZUUUNKMJDLE6N80N20N00P00R6CX9N`EYbIigPypVzpazofzp\ nzqszsuzoyzklzqRzr4wy0rz0ktC_`PPPRLCgH0y90Bz2Gz2Jz\ 1Lz1PU0TPcWU0UPcUU0UPcUU0UPcUU0UPccUcUPcPJE00U30`G\ 0gT3nb8tnHzzPzzYzzfzzozzyzzzzozzfzzYzzPzzHzz9zzHzz\ RvsZbbXWWgDJt02p02k03g44b63X94RA3NC2ID1EE0CI3BN49R\ 57X64`60e61e74g86g8BiBCiBEkBGkBJn9Kn9Mp9Np9RrATrAW\ tBZv9Vt8Rr6Mn5Ik2Eg2Ae04`02Z00X00R00P00L00I00E00I0\ 0PE6USIdkXnzkzzPDv6ir0zu0zy0zz9qzKizV`z`azd`zfXziU\ zlRznNyqMtvLrzJpzIozHnzGizBfr6eb1bQ0gPMtF`z2uzLqze\ oznnnnnnnjpoerpdtq`vtXyuVzuQzyMzzLzzGzzCzzAzz6zz1z\ z8zzHzzOzzYzzbzzlzzszzzzzzzzzzxzzszzqzzpzznzzrzzzz\ zzzzzzzzzzzzrzznzzfzz`zzUzzOzzIzzOzzUzzZzudvpipoog\ ggfaicXp_RvTJzUIvYJp_KiaJbgM`nQ_tRXzVWzWRzVMzXGzX7\ rYCR`L0kO0kO0nP3nR5pS8rVArVDtWGtYIvZLy`Ly_LyYLyVLy\ ULySLvOLvNLvLJvIIvGHtBGt8 } END PARAMETER FILE=========================================

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Re: [Fractint] Fastest Fractint Setup
by Vortex Swirling 21 Jul '09

21 Jul '09

Comments in line. > Vortex Swirling wrote:/ > > > > I have been wondering what makes for > > a fast Fractint setup nowadays?/ > > A real fast PC running straight DOS. :-) > > But I use two machines for the rendering of Jim's FOTDs: > Â• A 10-year old P3 running Win-98. > Â• An 7-year old P4 running Win-XP. Out of necessity, I built a new machine a few months ago. The processor is an Intel I7 920 2.66Ghz. It has 4 physical cores and 8 logical cores. > /> > > What I would like for the group to do > > is pick one of the FOTD's which is > > computationally intensive. Then those > > who'd like to participate generate said > > fractal and report times with a system > > description./ > > The recent "Seahorse Valley-12" has a rather lengthy calc-time. We > already know how long it took on Jim's machine. I tried this on both setups. On the DosBox setup (with cycles=max) it was taking north of 3 hours so I evoked the mercy rule and just stopped it. This was at 320x240. On Ubuntu 64 running xfractint 20.04.9 I completed in around 18 minutes. It would probably have been a bit faster but I kept messing around during the run. The screen size was the default of 800x600 so this is higher than Jim's 640x480. I check the Performance Monitor which running this and it was indeed using all 8 processors. Well that settles it, I will use xfractint. xfractint needs a little work but, if set up right it works. I can't seem to walk around directories without crashing so I make sure that the pars and formula I am working with are in the pars and formulas directories. The -geometry parameter doesn't seem to work and it is difficult to resize the screen and know what its going to be. I can't change maps. I can't do disk video. Sound doesn't work. Color cycling is not possible the way xfractint is written. However, it might be possible to load the gif in a seperate OpenGL application and, given the map as a parameter, be able to do the color cycle. The OpenGL application, "Antiprism", where I have done programming work can do it. (I didn't code the color cycling but the code for it was open source and free to be added in). > Too bad FractInt will not run on my double QuadCore 64-bit 16-MB RAM > machine. Up until a couple of months ago, it rated the highest in speed > doing similar fractal rendering tests in two other email lists. > / > > > > Also any tweaks or suggested improvements > > in system setup are welcome./ > > I can make a few when it comes to the Windows OS. There are so many > things that get established a certain way with the default settings. > And they really slow machines down. After months, I am still running Vista 64 with most of the defaults. This are so fast I haven't had to change anything. If it were to shave a minute off xfractint's time I probably wouldn't find it worth it. If it halved the time it would be different story. Roger

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21-07-09 (Fractal Telescope [No Rating])
by Jim Muth 20 Jul '09

20 Jul '09

FOTD -- July 21, 2009 (No Rating) Fractal visionaries and enthusiasts: Despite my questionable mood, there is a fractal for today. Its name is "Fractal Telescope" and it's pretty much the same as yesterday's fractal. If you enjoyed yesterday's image, you'll enjoy today's also; if yesterday's image left you bored, you'll be bored again today. But today's image calculates in only 10 seconds, so regardless of how you feel, little time will be wasted. If in doubt, view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Monday got off to a bad start here at Fractal Central when FL asked why I wrote such a negative discussion for yesterday's FOTD and suggested that I should learn to think in a more 'positive' manner. (She does read most of the FOTD discussions.) I told her that I assumed we would never again explore deep space because we lack the resources -- it's that simple. And being testy, as I always am during the early hours, I launched into a lecture about the overblown value of 'positive thinking'. 'All the positive thinking in the world will not get men to the other planets.' I added. Then, still annoyed by the original comment, a great old sci-fi movie, "The Day the Earth Stood Still", came to mind. In the movie, a visitor from an advanced race of space aliens tells us either to get our act together and stop fighting, or face total destruction. I speculated whether there might be a lot more truth in the old movie than we first imagined. I thought of some kooky conspiracy theories floating around. One of them is about a 'Galactic Federation', of the advanced races in the galaxy, which is closely monitoring mankind's behavior. When they saw us successfully reach the moon, they became alarmed and feared we might soon spread our violence to the other planets of the solar system and eventually the stars. To protect themselves from our violence, they secretly ordered our government to end the moon landings at once and abandon all future plans for manned deep-space exploration. This is why the Apollo program was terminated prematurely. The aliens then restricted our manned space efforts to low earth orbit, where we could do no harm, and kindly permitted us to develop the space shuttle to give us something to keep us occupied. We would not be permitted to return men to the moon or send men to the other planets until we learned how to live in peace among ourselves. Then, almost believing my own words, I said we have failed miserably, and as a result the aliens have ordered us to destroy the space station, which was to have been our stepping stone to the stars. 'But hope is in sight,' I added. The aliens will soon appear openly and reveal the truth about life throughout the galaxy, which we now are aware of only as the various beliefs of the religions. Hopefully, when we know the details about things now considered supernatural and are given proof that these things actually exist, we will have no further reason to fight about our different religious beliefs. Soon after that, we will all start to love one another, everyone will be equal, no one will be in need, etc. etc. etc., and we will be permitted to join the Galactic Federation and, as inhabitants of the galaxy, travel to the stars. At this time, FL told me to come to my senses, and I told her that she was now the one thinking negatively. She got offended, went into a sulk and sulked for most of the day. Due to much higher humidity, the seasonal temperature of 81F 27C here at Fractal Central on Monday felt more unpleasant than the same temperature on Sunday, when the air was dry. The fractal cats' inner thermometers must have registered the humidity, for they spent the afternoon stretched to almost their full lengths of about one meter. With FL sulking, my day was unusually quiet but not all that unpleasant. The work was out of the way by mid-afternoon, and I spent the rest of the day watching reruns of the moon landing. Unless a man lands on the moon before tomorrow around this same time, the next FOTD will appear on schedule. Until then, take care, and do I really believe in an alien conspiracy to confine mankind to the planet earth? That's for the wise to know and the others to guess. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fractal_Telescope { ; time=0:00:10.06-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideJulibrot passes=1 center-mag=0/0\ /0.591666/1/-31.5/0 params=89.99/0/89.99/0/-1.9119\ 5247/0.64047271/0/0/101/1.5 float=y maxiter=255 inside=0 periodicity=10 colors=000_9RS8TJ7VB6X35ZBAbJEfRJjZNnfSrnWvv_zzz_z\ zKzvKzsKypKxnKwlKujKshKqfKodKmbKk`KiYKgWKeUKcRKaPK\ _MKoYZqYcsYhuXmvXrwWzxWzyWzzVzzVzzUzzUzzUzzDzzDzzD\ ziDTgCUeBUcAUa9U_8UZ7UY6VX5VZ4V`3Va2Vc1Ve0Vf0Vh0Sj\ 0Ok0Lm0Io2Fp4Cr6As8AqAApCAoEAnGBmIClKDkMFjOHiQIhQJ\ gQKfRLfRLeRMdSNcSObSPaTQ`TR`TR_TSZUTYUUYUVXUWWVXVV\ YUVZTW_SW`RWaQXbPXcPXcOYdNYeMYfLZgKZhiDPhAPRn4Qj4Q\ f4Qc4P_4PX4PU4PV4RSYUVg5__Fe`Oe`Xdaedahb_k`YnZWqXV\ tVTwTRzSQLU_NWYPYXR_VTaUVcSXeRZgQ_aN_XK`SH`ME6tf4u\ kC0XKpIaHBaC8dGBfJEiNHkQJmTMpXPr_StbUqPSoCQr9Ku6Fx\ 3AvDLuMWsVfrcppdhNl9KnFHoLEpQCrW9s`od`neTmeLleEmgJ\ niNokSolWpn_qpdrrhrslskascSibS_bSQaSHaSSTTbKUmBVx2\ Ww6_wAbvEevIhuMkuPnnWqgbs`hvU0xNuzHXoC8d8Ma4_Z1lWA\ n`JpeSrj`snVsqPstKswLsvh0SMruMquNqtNqtOpsPpsPorQor\ QoqRnqSnpSmpTmoTmoUlnUlnVkmWkmWklXjlXjkYikZijZij_h\ i_hi`gh`ghaggbfgJmCNiEReH } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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More diode
by John W. 20 Jul '09

20 Jul '09

There's a LOT more to this par than I first thought, including these gaudy spirals which are spectacular, (I thought), when color-cycled. John W. } Indiode { reset=2004 type=formula formulafile=indiode.par formulaname=lndiogh corners=0.162666075843/0.162711833171/-0.00140221356379/-0.0013678955678\ 4 float=y maxiter=512 logmap=yes periodicity=0 colors=00000j0j0jj0j00j0j0jjkkkkrkdmwW000W0WW000WW0W0WWFNF<4>rNFzNFFVF<4\ >rVFzVFFbF<4>rbFzbFFjF<4>rjFzjFFrF<4>rrFzrFFzF<4>rzFzzFFFN<4>rFNzFNFNN<4\ >rNNzNNFVN<4>rVNzVNFbN<4>rbNzbNFjN<4>rjNzjNFrN<4>rrNzrNFzN<4>rzNzzNFFV<4\ >rFVzFVFNV<4>rNVzNVFVV<4>rVVzVVFbV<4>rbVzbVFjV<4>rjVzjVFrV<4>rrVzrVFzV<4\ >rzVzzVFFb<4>rFbzFbFNb<4>rNbzNbFVb<4>rVbzVbFbb<4>rbbzbbFjb<4>rjbzjbFrb<4\ >rrbzrbFzb<4>rzbzzbFFj<4>rFjzFjFNj<4>rNjzNjFVj<4>rVjzVjFbj<4>rbjzbjFjj<4\ >rjjzjjFrj<4>rrjzywccdWWWz000z0zz000zz0z0zzzzz } frm:LnDioGH{ Pd = 0.0000000000001 Gm = 0.00000000000094 Ids = 0.00000000252 Rs = 0.968 n = 1.752 Vt = 0.025 u = Gm*n*Rs*Vt+n*Vt Pt = n*Vt vr = Ids*Rs x = 0.1 x = x-((u*x*log(x)+vr*x*x-(Pixel+vr)*x)/(vr*x+u)) z = 0-(Pt*log(x)-Pixel)/Rs: u = z x = x-((u*x*log(x)+vr*x*x-(Pixel+vr)*x)/(vr*x+u)) z = 0-(Pt*log(x)-Pixel)/Rs |u-z| > Pd }

2 1

New life
by John W. 19 Jul '09

19 Jul '09

Nice to see new fractals here. First "Diode" and now the rather fiery "BH_CubicMan" Thanks guys. John W.

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FOTD 19-07-09 (Clandestine Action [No Rating])
by Jim Muth 18 Jul '09

18 Jul '09

FOTD -- July 19, 2009 (No Rating) Fractal visionaries and enthusiasts: I might have expected FL to be bitten by the antiquing bug on Saturday, and so she was. We spent the entire afternoon at an antique emporium an hour away. Luckily, we got back to FC in time for me to find a barely adequate fractal. Today's image lies in the East Valley of a larger minibrot in the Z^(1.5)+C Mandeloid as it appears 100 levels up the logarith- mic ladder when no function is applied. The typical East Valley elements are there -- at least bits of them are there. Do not try to investigate the minibrot at the center. With the magnitude of the entire image already at a galactic 2*(10^12), the tiny dot at the center is well beyond resolution. The name I gave the image, "Clandestine Action", must have some connection to the image, though at the moment the connection eludes me. Rather than embarrass myself by rating the image at a lowly 4, I gave it no rating at all. The calculation time of just over 4 minutes is within reason, but an even more convenient way to see the image is to view it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A near perfect day prevailed here in the Fractal Central area on Saturday, with enough sun and a temperature of a un-summerlike 73F 23C. Only a few too many clouds prevented the day from being absolutely perfect. The fractal cats were cranky after being left alone for the entire afternoon, but cheered up when their treat was served. The next FOTD will be posted in 24 hours. Until then, take care, and think positive in a negative manner. Or is it the other way around? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Clandestine_Action { ; time=0:04:03.31-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.05486496989607698/-1.832864340918919\ /2.453859e+012/1/-30/0 params=1.5/0/100/0 float=y maxiter=2400 inside=0 logmap=366 periodicity=10 mathtolerance=0.05/1 colors=000JGZKHYKIYLJXMKXMLWNMWONVOOVPPZQQcQRhRSmS\ TrSUvcWzoZzmhzzz00EI4FH7GGAHFDIEGJEJKDMKCPLBSMBVNA\ YO9`P8cP8bM9aKAaIA`GB_EC_CCZADY8EY6EXAFWDGVGGUJHTM\ ISPIRSJRVJQZKPaLOdLNgMMjNLmNKpOKsORmWYgbdbikXpqSwX\ hwCmwJjsPdoW_kaUgUQdKMQKHCEIGJJJOKMULPZMScNVfMShMP\ jLMlLJnLGpKDrKAtK7sN9rPBqRDpTFoVHoXInZKm`MlcOkeQkg\ RjiTikVhmXgoZgq_OpO5pC8lGBiJDfMGcPJ_SLXVOUYRR`TOcU\ NeVMfWLgXKhYJiZIj_Hk`Gl`FmeNfjV`naUsiOwjInaJeNJgMN\ iLRkKVmJYoIapIerHitGlvFpxEtyEwwDvuCutCurBtqBtoAsnA\ skCpiDngFleGibIg`JeZKcXM`VNZSPXQQUOSSMTQKUOIVRGWTE\ XVCYXAYZ8Za6_c4`e2ap1az9WzHQzTWzd`Izz3zz7zmAzmDrhG\ miJhiMcjQZkTUkWPlZKmaFmdBjeIizOczVdzabig`jnZktXlzY\ gzYbrYYnZTmZPlZKj_Fi_Ah_6f`8daAcbCacE`dGZdHYeJWfLU\ gNThPRhQQiSOjUNkWLlYKmZMn`NobOpcRqeUrfXshZtjculcvn\ cwpmxrmytmzvmzxmzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 18-07-09 (Knotted Trunk [5])
by Jim Muth 17 Jul '09

17 Jul '09

FOTD -- July 18, 2009 (Rating 5) Fractal visionaries and enthusiasts: Today's image returns us to the elephant menagerie. While wandering aimlessly through the zoo, I stumbled upon the strange elephant in todays image, which is one in a series of similar elephants lined up along the shore line of East Valley of a minibrot on the main filament of the fractal that results when the formula Z^(1.1892)+C is calculated 4 levels up the logarith- mic ladder. BTW, 1.1892 is the 4th root of 2. The elephant in the image, as well as the unseen ones on either side of it, has its trunk apparently tied in a knot, or at least a spiral. Actually, it takes quite a bit of imagination to see an elephant in the image at all. The most striking feature is the sawtooth pattern that pervades the scene, and the almost too intense colors. The name "Knotted Trunk" refers to the trunk of the unfortunate elephant in today's image. The rating of a very mediocre 5 indicates that I don't give a croak about the trunk. But the calculation time of 30 minutes is indeed a problem. The image is hardly worth the wait, so I recommend viewing the already finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> While stuck in a traffic backup today, FL found herself next to a car playing a Hip Hop 'song' at ear-splitting volume. A white woman was driving the car and FL was shocked at the violence and anger expressed in the shouted words. When FL returned to FC, she asked me how such unpleasant 'music' could be so popular. How, she asked, can people stay so angry that they enjoy listening to such stuff all day. Not wanting to get into a philosophical discussion, I went to the book shelf in my workroom, picked up the book "Patterns in the Void" by Sten Odenwald, and told FL to read the epilogue, which describes the rational but hopeless view of the world that I feel is largely responsible for the festering anger and depression that makes such violent music not only acceptable but actually fulfilling. But the last time I noticed, she had not opened the book. Clouds and light rain spoiled the day on Friday here at Fractal Central. The fractal cats enjoyed the much cooler temperature of 72F 22C. My day was average. The next FOTD will be posted in 24 hours. Until then, take care, and I hear that the aliens are softening us up so we'll be unable to resist when they arrive in force to carry us off as slaves. But then, why would an alien race so technologically advanced as to be able to navigate interstellar space need something as primitive as slave labor to do their menial tasks? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Knotted_Trunk { ; time=0:30:06.87-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandelbrotBC3 function=floor passes=t center-mag=-6.050216876515906/+7.990641684923723/\ 2289070/1/-140/0 params=1.1892/0/4/500 float=y maxiter=15000 inside=255 logmap=457 periodicity=10 colors=000Acw7cw4cw2cw5ev7fv9huBiuEjuGltImtKosNpsP\ qsRsrTtrVur`omejiYmkQomJqoOmZTiIYe1Xc3Xb5W`6W_8VYA\ VXBUVDUUEUTGTRITQJSOLSNNRLORKQRJRQKPQLOQLMPMLPMKPN\ IPNHOOGOOEOPDOPC_VBj_BudBvbCvaDw`Ew_FwZFxYGxXHyWIy\ VJyUJtb9ok0E`yD_vDZtDYqDYoCXmCWjCVhCVfBUcBTaBSZBSX\ ARVAQSAPQAPOEQQHQSLQUORWSRYVR_YR`aSbdSdhSfkThoTjrT\ luTmrUjpVgnWdlWajXZhYWfYTdZQa_N__KY`HWaEUaBSb8Qc5O\ c3Vf6`i9flCmoFsrIytKvqLtnMrkMohNmeNkbOh`OfYPdVPaSQ\ _PQYMRWKRXPVXUZYZbYbfZgjZlnZpr_nq`mp`loakoajnbirbk\ vcnzchzdesddqeciebic`ja_k_ZlYYlkcpxitwgrvepvcnuamu\ _ktYitWgsVfsTdrRbrP`qN_qLYpJWpHUoGToERnCPnANm8Mm6K\ l4Il3Hk5Gk6Gj7Gj8Gj9GiAFiBFdPFiCFhDFhEFhFFgGEgHEfI\ EfJEfKEeLDeMDeNDdODdPDWvEXtDXsDYqDYpDYnDZmDZkD_jD_\ iD_gD`fD`dDacDaaDa`Db_DbYDcXDcVDcUDdSDdRDtaAu`Bw_B\ w_CxZEyZGzYIzYKzXMzXOzWQzWRzVSzWTzYUz_VzaWzcXzdYze\ Zzf_zgazhczihzjmzkrzlzKFK } 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 17-07-09 (Just Getting Started [7])
by Jim Muth 16 Jul '09

16 Jul '09

FOTD -- July 17, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's scene doesn't make it as a work of fractal art, (Since when have the FOTD images ever been art?), nor does it bring an insight into some obscure mathematical conundrum. It simply shows some elephants pieces gathering into finished elephants. Now don't expect full-blown elephants to appear when you run the parameter file. The elephants in today's image are little more than their disembodied trunks. But the rest of the ponderous beasts are there, at least in spirit, faithfully mounting guard over their shrunken Z^(1.5)+C buds. The parent fractal is the Z^(1.5)+C Mandeloid as it appears 24 levels up the complex logarithmic hyper-spiral. Today's scene is located in a rudimentary East Valley that lies on the X-axis. I rated the image, for those who care, at a 7, which is FOTD average. The name "Just Getting Started" refers to the elephants, which are just now getting their act together. The calculation time of 1-1/6 minutes will pass in a jiffy. The time might seem a bit longer for those desperately impatient to see the image. These desperate few may view the image already calculated on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Summer finally arrived here at Fractal Central on Thursday as the temperature rose to 91F 33C and the sun sizzled down. The fractal cats paid no heed to the hot weather, spending the day in front of the living room fan. My day was as quiet as might be hoped but busy enough to keep financial worries at bay. The next FOTD will be posted in 24 hours. Until then, take care, and why are there trillions of trillions of stars in the universe yet only one of each one of us? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= JustGettingStarted { ; time=0:01:10.14-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandelbrotBC3 function=floor center-mag=+0.165500928/-0.005217105/1112.595/1/\ 28.8/0 params=1.5/0/24/0 float=y maxiter=4500 inside=0 logmap=34 periodicity=10 colors=000CCCAFE8HH6JK4LN2NP6PQARQDTRHWRLZSO`SScTV\ eTZhUbjUelVimVlnVjoWhpWfqXdqXbqY`pYZoZXnZVm_Tl_Rk`\ Pj`Oi`QhbSgcTfeVefXdhYci_bk`ala`jb_hcagccededegbfi\ afk_gmYhoXiqVipUjoSkoRlnPjlOghMcdKZ_IVVHRRFMMDIJCD\ HA9F85D7CBEJDLQHRWMYbRdiVjp_qvcwwazw_zwYzxWzxUzxSz\ xQzyOzyMzyKzzIzzGvzErzDmxGhwJcvMZtPUsSVrUWlYVg`Ubc\ TYgTTjSOmRJpRKmTLjVLgXMdZMa`NZaNWcOTeOQgPNiPLjPMgP\ MdPMaPM_PNXPNUPNSPNPPOMPOKPOHPOEPOCRMDTLDVJEXIEYGF\ _FFaDGcCGdAHf9Hh7Ij6Ik5IQWR5uZ7rX8oV9lTAiRBgPCdNDa\ MEZKFXIGUGHREIOCJMBGLHEKMCKRAJW8I`6Ie4Hj2Ho7NmBSkF\ XiKagOfeSkcWpbWpbXpbXpaYoaYoaZoaZo`_o``n``n_an_an_\ bm_bmZcmZcmZdmYijVelYelYflYflXglXgkXhkWhkWikW7iz8j\ z9jzAjzBjzCjzDjzEjzFjzGjzHjzIjzJjzKjzKjzLjzMjzNjzO\ jzPjzQjzUjzZkzckzhkzmkzrkzvkzzkzzkzzkzzkzzkzzkzzkz\ zkzzkzzkzzkzzkzzkzzkzzfzzgzzgzzgzzgzzgzzhzzhzzhzzh\ zzhzzhzzizzizzizzizz_zzYz } 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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Re: [Fractint] Diode
by JackOfTradeZ＠comcast.net 15 Jul '09

15 Jul '09

Brings back memories - I'm an electronix tinkerer from way back, nothing recent though, just computers etc. "" Why attempt this ; because a better , more interesting insight might be obtained . Has anyone on this list delved into this ?"" If anyone can code the diode equation into something the fractint formula parser can understand, and make a "diode" fractal, and it loox cool enuf, I will try to animate it. It seems that many natural phenomenon, (like chemistry, my profession), can be modelled to some extent with fractals, often leading to interesting and unexpected results. stay amazed!

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FOTD 16-07-09 (A Million to Two [?])
by Jim Muth 15 Jul '09

15 Jul '09

FOTD -- July 16, 2009 (Rating ?) Fractal visionaries and enthusiasts: Today's scene shows East Valley of the Mandelbrot set mixing with the true East Valley of the Z^(990000)+C Mandeloid. Some very unusual things are going on in the vicinity, and today's image is just the beginning. I'll probably have another FOTD along these lines in the near future. With a calculation time of 1-2/15 minutes, the image is a fast one, so little more need be said about it. The order-990000 and quadratic elements are quite apparent. The next step is to see the scene in person, and the best way to do this is to run the included parameter file or view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I could not decide on a rating, so I rated the image at a question mark. The name "A Million to Two" means nothing beyond its sound. Wednesday turned out to be an average mid-July day here at Fractal Central, with partly cloudy skies and a temperature of 84F 29C. The fractal cats' behavior was also average. Since my day was average as well, little remains to be said, except that the next FOTD will appear in 24 hours. Until then, take care, and watch those alternate realities. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Million_to_Two { ; time=0:01:08.00-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip passes=1 center-mag=+0.999992197912849/-0.00005552426384695\ /1.380431e+008 params=990000/3.993 float=y maxiter=15000 inside=0 periodicity=10 colors=000jPijTeiYaiaYifUijQioMisIjpMkmPljTmgWnd_o\ abpZeqWirTlsQptNsuLvtGjsB_r6PkBTdGXYL_RQcKVfD_j7cm\ 5Uj4Kg3Ad8DfDGgIJhMMjRPkWSl`VndYoi`pncrsfswitvkovl\ jvmevn`vpWvqRvrMvsHvtCwvLxwTyyazzizymzzszzxzzzzyxz\ yrzxrzvszutvuurrsmoqimohjmghkfeiecgd`ecZdlNKjOUiPc\ C0uTDqVuSZmYaebeYhhhShZbCPCrAmnGmkLm8vfImhRej_Yl2E\ ZOKfOKKC25L8HTES`KbSCwAMW5UsvSzqRulQqFmDNgNUaW7kS8\ lR8mQ8nP8oO8oNApKBpHDpEEpCGp9Hp6Jp3Kp1Mn6OmBQkFRjK\ ThOVgTWfXV_WUUVTOUTITPFXMD_JBcG9fC6i94m62p30scz_cx\ ZcuYcrXcoWclVcjUchTcfScdRcbQc`PcZOcWNcUMcSLcQKcOJb\ MIaKH`IG_GFZEEYCDWACUCFSBHQBKODMMEOKGRIITHKWHMYHN_\ GPXGQVFRTFSRFTPEUNEVLDXJDYHDZFC_DC`BBa9Bb7Bc5Fc7Jd\ 9NdBRdDVeFZeHbeKffMjfOnfQrgSvgUzgWvfSrfOneLjeHfdEb\ dAZd7PXOFPd6Iu5Kq5Ln4Nj4Og4Pd3R`3SY3TV7VTBWSFXRIYQ\ MZPQ_OUaNXbM`cLddKheJkfIigHhgGfhFehEciDbiDaiC_jBZj\ AXk9Wk8Vk8cR_k6zjBujGqjKm } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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Re: [Fractint] F Diode
by JackOfTradeZ＠comcast.net 15 Jul '09

15 Jul '09

' ""After an extended search on the internet and considerable testing I'm now able to provide you with a preliminary model and fractint formula for a diode"" Please do - I will check it out. But I am confused. I remember from my electronics days (a long time ago) a diode is a semiconductor crystal which lets current flow one way but not the other, so it converts AC into a pulsing DC current. How does this relate to fractals?? .

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FOTD 15-07-09 (High-Order Radicals [No Rating])
by Jim Muth 14 Jul '09

14 Jul '09

FOTD -- July 15, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image is a scene very deep in the true East Valley of the Z^(1-million)+C Mandeloid. I chose the 'true' East Valley, which is the one on the positive X-axis, because this Mandeloid has 999,999 identical East Valleys, and the one on the X-axis is the easiest to explore. I was surprised to find such well-defined buds in the area, and I even found several sets of alien pop-eyes, but no matter how hard I searched, I could find no elephants. With 999,999 of them guarding every bud, it is little surprise they are so hard to pick out. As for minibrots, the entire image is a mass of them. In fact, in the more intricately detailed areas, the minibrots occupy more area than the normal 'outside' stuff. But because of their distortion, the minibrots are hard to recognize. The choice of an exponent of 1-million was totally arbitrary. Any exponent greater than 10,000 or so would have given a near identical image. This is one case where they all really do look the same. Since this kind of stuff is hardly new, I gave the image no rating. The name "High-Order Radicals" refers to the bud complexes. The calculation time of 12-1/3 minutes may be cut in half with only a tiny loss of detail by rendering the image with the passes set to 't' instead of '1'. But do not use passes=g. It guesses wrong far too often and really chews up the image. There is no guess work involved however in the trip out to the FOTD web site to view the finished image. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Think of absolutely perfect weather -- blue skies with a few decorative cumulus clouds, a temperature of 79F 26C, unlimited visibility, low humidity, gentle breezes, and you have pictured the weather in the Fractal Central area on Tuesday. The local youngsters, idealistic, naive, and apparently misled by the media hype, have been warning of an unbearably hot summer due to man-made climate change. But they are now starting to admit they were wrong. And the same local media that forecast an unbearable summer is now starting to call this year 'the year without a summer'. The clamor for legislation to fight climate change, whatever kind of legislation could possibly do that, is thankfully fading rapidly. The fractal cats don't worry about things like flooded coastal cities and palm trees in Nova Scotia. But they do worry about stray cats prowling the area and their next treats of tuna. Luckily, no cats were prowling around F.C. on Tuesday, and the treats appeared on schedule. My day was average, as are most days here at F.C. The next FOTD will be posted in 24 hours. Until then, take care, and what ever happened to Kamenoi Ostrov? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= High-OrderRadicals { ; time=0:12:20.39-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotN passes=1 center-mag=+0.999\ 9851854051747/-0.000000000003291/2.83e+012/1/-47.5\ /0 params=1000000/0/0/0/0/0 float=y maxiter=10000 inside=0 logmap=156 periodicity=10 mathtolerance=/1 colors=000m4Uk4Wi5Yg5_e5ac6ca5e_4gY4iW3kX3na2qf2tk\ 1wp1zm1vj1sg1pd1ma1jZ1gW1dT1aQ1ZN1WK1TH1QE1NC1KE3J\ G4JI6JJ7IL8INAIPBIQCHSEHUFHWGHXIGZJG`KGbMGcNFeOFgQ\ FiRFjSElUEnVEqYDoWEnUEmSElQEkPFjNFiLFhJFgIGfGGeEGd\ CGcBHb9Ha7H`5H_4Ha6Ib7Id9IeAJfCJhDJiFJkGKlHKmJKoKL\ pMLrNLsPLtQMvSMwTMxUMuYNraOoePliQimRfqScuT`xUauWbr\ YboZcl`dibdfcecef`gfYhgVjhSlhPmfOldOlbNlaNl_MlYMlX\ LlVLlTKlSKlQJlOJlMIlLIlJHlHHlGGlEGlCFlBFl9El7El2Cm\ 6El9FkCHjGIiJKhMLgQNfTOeWQd_RcbTbeUaiW`lX_oZZqWdr_\ ZrbUseOsiJtlDto8tr3qp4on5mm5kk6ii7gh7ef8ce9ac9_aAY\ `BVZBTYCRWDPUDNTELRFJQFHOGFMHDLHBJIz9KzIIzQHzYFzfE\ znCzu8zvBzvDzvFzvIzvKzvMzvPzvRzvTzvWzwYzw_zwbzwdzw\ fzwizwkzwmvwprwrmwthuscssZrsUpsPosKmsFksBjsBhsBgsA\ gsAisAksAms9os9qs9ss8vs8ws8ys8zs7zs7zs7zs6zs6zs6zs\ 6zs5zs5zs5zs5zs7zt9ztBztDztFzuGzuIzuKzuMzvOzvPzvRz\ vTzvVzwXzwYzw_zwazxczxezx } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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Fastest Fractint Setup
by Vortex Swirling 13 Jul '09

13 Jul '09

Hi All, I have been wondering what makes for a fast Fractint setup nowadays? I have two setups for Fractint under Vista 64. One is using DosBox. The other is xfractint running under Ubuntu 64 under VirtualBox. Both have their quirks, however each generates the various FOTD fractals correctly. They are just way slower than I'd expect them to be considering the hardware I have. What I would like for the group to do is pick one of the FOTD's which is computationally intensive. Then those who'd like to participate generate said fractal and report times with a system description. Also any tweaks or suggested improvements in system setup are welcome. Roger

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FOTD 14-07-09 (One Long Shoreline [8])
by Jim Muth 13 Jul '09

13 Jul '09

FOTD -- July 14, 2009 (Rating 8) Fractal visionaries and enthusiasts: What does today's image have to do with East Valley? It has everything to do. There are 12 east valleys in the image. The tip of the 12 spikes at the top of the scene are actually 12 of the 10-million east valleys spaced evenly around the edge of an order 10,000,001 minibrot. On my screen the spikes at the top of the image are about 3cm apart. Since there are 10-million spikes around the perimeter of this minibrot, its circumference must be 30-million centime- ters, which gives a diameter of about 10-million cm. Since there are 100,000 centimeters in one kilometer, the diameter of the entire minibrot at the scale of the image must be about 100 kilometers or 63 miles. No wonder the tiny bit of the minibrot that fits on the screen appears to have a straight edge. It's the same reason that the surface of the earth appears flat. Another curiosity is the detail inside the 12 spikes. At first glance, this detail appears to be identical in every spike, but actually it changes slightly in each spike. What an interesting trip it would be to circle the entire minibrot and watch the detail in the 10-million spikes gradually cycle through its series of changes. The elements at the top of the frame are made of order-10000001 stuff, which changes very slowly. The elements at the bottom of the frame are quadratic stuff however, and down here the changes come fast. And yes, there are countless smaller near-circular minibrots in the image. The most obvious one lies in the lower right quadrant. I named the image "One Long Shoreline" after the 300-kilometer shoreline of the minibrot whose edge appears at the top of today's image. I rated the image at an 8 because that's what I think it's worth. The calculation time of 4-1/2 minutes is well within reason. But if you decide to calculate the image, don't become concerned when nothing shows up for a minute or so. The top several lines are blank black. As always, the finished image is posted for immediate and total gratification on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Picture perfect weather prevailed here at Fractal Central all day Monday, while the fractal cats, Nicholas and Cassie, took it easy. (For the exact conditions, picture an absolutely perfect day at your favorite spot on earth.) At one point, Nicholas, apparently having forgotten the talk he had with the doctor when he was a kitten, got a bit frisky and started yelling like a lovesick tomcat. A quick serving of half-and-half settled him down and reminded him of what the doctor had told him. My day was un-eventful. With only a modicum of luck, tomorrow will be the same. The next FOTD will be posted in 24 hours. Until then, take care, and wouldn't life be dull if rational- thinking skeptics were right when they claim the paranormal does not exist? (Of course, this in no way implies that I think the skeptics are wrong. I *know* they are wrong, even though they are convinced they are right!) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= One_Long_Shoreline { ; time=0:04:30.40-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip passes=1 center-mag=-43.09731830432293/+56.66689961740695/\ 2.21687e+010/1/110.34/0 params=10000001/100 float=y maxiter=4000 inside=0 logmap=157 periodicity=10 colors=000`I4_H6YG8XFBVEDUDFSCGQBINAKLALIANGAQDARB\ AT7BV6DW5FY5I_5Lb5Ld5Nf5Og5Oj5Pm5Rn5So5Tn5Rn5Pl5Pk\ 5Ok6Ni7LgBLfDJdGIdIGbKGaNE_PD_SDYUBWV9VY7T_7Tb6Rd4\ Qf2Pi2Nk1Nn1Lp1Kq1It1Iv1Gy1Fz1Dz1Bz1Bz19z18z16z14z\ 16z16z18z18z19z19z19z1Bz2Bz6Dz9DzDFzGFzJFzNGyPGySI\ wSIwPKvNKvJKvGKtD4t90s60s20q10q42p78pBDnDInGLlJQlN\ VkP_kTbiWgiYlg`qgdtfgyfjzdkzblzdmzdnzdozdpzfqzfrzf\ szftyfuxgvvgwtgxqgxogxnixkixiixgixfixbkxakx_kxYkxV\ kxTlxRnxPpxNqxLsxKtxGvxFwxDyxBzx8zx6zx4zx1zx0zx0zx\ 0zx0zx0zx0zx0zx0zx0zx0zx0zx0zx0zx0zx0wx0px0gx0_x0Y\ x6WwFWvNVvVUtbSrkQplPpiNobSmV_lNglFpj0wi0zg0zg0ze0\ wd0rb0mb0h`0c_0ZY0UY0PW0KU0FU0AT09R09S0BS0DS0DS0ES\ 0GS0GS0IS9ISPKQbLOmLMmNKmPImPGmQEkPDkNDkLBkKBkK9kK\ 9kK7kKDbKDbKDbKDbKDbKDbKDbKDbKDVKDVKDVKDVKDVKDVKDV\ KDVKDVKDVKDVKDVKDVKDVKDVKDVKDVKDVKDVKDVKDVKDVKDVKD\ VKDVKDVKDVKDVKDVKDVKDVKDV } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 13-07-09 (She Sells Sea-shells [7])
by Jim Muth 12 Jul '09

12 Jul '09

FOTD -- July 13, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's scene is located in the 30-pointed star in the rump of the period-30 elephant on the south shore line of East Valley of a parent fractal about halfway between a quadratic and cubic Mandeloid. Something about it reminds me of small shells lying in the sand at the surf line of a beach, so I named it "She Sells Sea-Shells", which is a well-known tongue twister. There is not much to be said about the image, which rates an FOTD-average 7. The calculation time of 6 minutes is also boringly close to average. The solution to this boredom is to surf to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. Shortly after I posted the FOTD for July 12 on Saturday, all hell broke loose here at Fractal Central in central Pennsylvania as a whopper of a thunder-storm moved in with a tornado warning included. The fractal cats sought shelter from the crashing thunder in the most secure closet, while I watched the action from the front porch. It took 5 hours before things finally calmed down. Luckily, no tornado developed. The only damage was the usual fallen tree limbs, flooded streets, houses struck by lightning, power outages and flattened flowers in FL's garden. Sunday was absolutely perfect, with not a cloud in the sky, low humidity and temperature of 81F 27C. The next FOTD will be posted in 24 hours. Until then, take care, and where does dark matter go when the lights go on? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SheSellsSea-Shells { ; time=0:06:04.26-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip passes=1 center-mag=+0.87205078572003780/-0.004897985853331\ 83/691947.4/1/-155/0 params=3/2.75 float=y maxiter=6400 inside=0 logmap=540 periodicity=10 colors=000BvXBsXBoXBlXBhXBeXBaXBZXAVXASXAOXALXAHXA\ EXAAXA7X55TA4XF4`K3cP3gU2kZ2nc1rh1vl1yi5wg8udCsbFq\ _IpYMnVPlTTjQWhOZgLbeJecGiaEl_7pWCoZHo`LobQndUnfZn\ ibnkgmmkmopmqtmsunnunjvofvobvpZwpVwqRwqNrjRmcUhYYc\ R`ZKdUEgP7kK1nI8iHFdFM_ETVC_QBeLFfOIgRMgUPhWSiZWia\ Zjdajf_hdZgcXfbWdaUc`Tb_RaZQ_YOZXNYWLWUKVTIUSHTRFR\ QEQPCPOBNN9MM8LL8LG7KK7JO7IS5IW7HV8HVAHUBGUCGUEGTF\ FTHFTIFSJFSLESMEROERPDRQDQSDQTCQVCPWCP`9RXCPTEOPHN\ LJLHMKHNKDOJGPLIQNLRPNSRPTTSUVUVXXVZZW``Ybc_dkafqe\ hzljzplvjktfkkbkjZkiXjiUjhSjhQjgOjfMifLieJieIidHhc\ GhcFhbEhbChaBg`Ag`9g_8g_7gaAecCcdEafH_hLYiOWkRUmUS\ nXQpZOr`MsbLrcMqdNqdOpePoeQofRnfSngTmhUlhVliWkiXjj\ YjjZik_il`hlagmbgmcfndjmbfndcof_pgXqiTrjQslMtmJuoF\ vpCwr9wsCtrFqrInrLkrOhrRfrUcrX`r_arbcreerhgrciq_kq\ VmpRopNqoIsoEun9wn5xm1ym2zj3zh3ze4zc4z`5zZ6zW6zU7z\ R7zPgz8bzCXzGSzKMzOHzSCzW } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 12-07-09 (Egde of the Valley [6])
by Jim Muth 11 Jul '09

11 Jul '09

FOTD -- July 12, 2009 (Rating 6) Fractal visionaries and enthusiasts: Yesterday's image is found deep in the interior of the East Valley of a large minibrot in a double-negative-Z fractal. Today's image is found near the edge of the valley at about the same depth as yesterday's. Many of the same types of elements are in the image, though the overall effect is much richer. A good part of the richness comes from the coloring, which I suspect is a bit too gaudy, and holds the rating to a less-than-overwhelming 6. The coloring was particularly difficult with this image. Regardless of what I tried, the colors turned out either too busy or too flat. The name "Edge of the Valley" refers to the fact that today's image is located on the edge of its parent valley. At first glance, those ubiquitous elephants are nowhere to be seen in today's image, though a closer, but slow, investigation will probably turn up some elephant parts and maybe an entire elephant or two. Perhaps the greatest problem with the image is its inconvenient- ly long calculation time of 37 minutes. Go ahead and run the included parameter file if you wish, no harm will be done. But by far the most convenient way to view the image is to surf out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished product there. Saturday brought clouds, humidity, and eventually, sprinkles of rain to Fractal Central. The humidity made the temperature of 82F 28C feel more like 90F 32C. The fractal cats, being comfort- loving creatures, enjoyed themselves stretched out under the cool air vent in the computer room. Meanwhile, my day was average, with another average day expected on Sunday. The next FOTD, a near glorious scene in some remote East Valley, will be posted in 24 hours. Until then, take care, and if it makes you feel good, believe it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Edge_of_the_Valley { ; time=0:37:12.28-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+3.254239745259663/+0.9577720814431667/\ 3.7405e+009/1/-75/0 params=-4.5/-1.35/-1.1/-7.2/0/\ 0/0/0 float=y maxiter=64000 inside=0 periodicity=10 colors=4400CJ4BI4AH49C3694784885985A75B76C76D66E67\ F67G58H58I58J49K49L49M3AN3AO3BP2BQ2BR2CS1CT1BS0CT1\ CU1DU1DV1DV1EW2EX2FX2FY2FY2GZ3G_3H_3H`3H`3Ia4Ib4Jb\ 4Jc4Jc4Jc4Kb7Kb9LbBLbDLbFMbHMbJNbLNbNNbPObRObTPbVP\ bXQ_`PbZPdYPfWOhVOjUOlSNnRNpPNrOMtNMvLMxKMzJNxINwI\ NvINuINsHNrHNqHNpHNnGNmGNlGNkGNjGNhFNgFNfFNeFNcEUj\ DTjESjGQjHPjJOjKNjMMjOLjPJjRIjSHkUGlVFmX2nT8oWEjYK\ e`Q`bWVeaQggLjpCqnEnlGlkIjiKhgMefOcdPacR_aSX_UVZWT\ XYRX_NWaPWcQWeSVgTViVVgWVeYUdZUa`U_aTYeTXgTXiUWlTX\ rTXrTXpTXrSXmSYhSYcSYcRYcRYbRYbRZaRZ`QZ_QZZQZYQ_XP\ _WP_VPYUPWUPUUQSURQUSOUTMTUKSVIRWGQZEQbEReDRfDRgDR\ hDRiFQjHPkJOlLOmNNnPMoRLpTLqVKrXJsZIt`IubHvdGxgHwf\ GweFweFwdEvdDvcDvcCvbBubBuaAuaAu`9u_8t_8tZ7tZ6tY6s\ Y5sX4sX4sW3qU1rV2rW2sW3sX3sY4tY4tZ5t_5u_6u`6u`6r_8\ pZAmYBkXDgXFcWG_VIWUKSULOTNKSPIRQGQSEPUCOVANU8MT6L\ S4KR2JQ0IP0HO0GN0FM0EL0DK } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 11-07-09 (Eastern Outpost [7])
by Jim Muth 10 Jul '09

10 Jul '09

FOTD -- July 11, 2009 (Rating 7) Fractal visionaries and enthusiasts: In keeping with the East Valley theme of July, today's scene lies deep in the East Valley of a large minibrot at the eastern edge of the 'fan' of the parent fractal that results when various portions of Z^(-1.35) and Z^(-7.2) are combined and (1/C) is added. As promised, no elephants appear in the scene, though various elephant parts are scattered about, and the alien pop-eyes are also in evidence. I named the image "Eastern Outpost" for no apparent reason. The rating of a 7 is unexceptional, but still better than the parade of discombobulated pachyderms that just finished passing. The calculation time of just under 13 minutes is admittedly slow. Most of the slowness is due to the fact that the scene lies so deep in its parent valley, where the iteration count is unusually high. But why not escape the burden of running the included parameter file by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a high temperature of 86F 30C, Friday was a bit too warm and muggy for total comfort here at Fractal Central. And in addition, the crystal blue skies of the past few days turned a hazy gray. The fractal cats didn't mind it a bit however. The intruding tomcat appears to have gone off to prowl elsewhere. My day was unusually busy, busy enough in fact that things started to get out of control. But the panic was nipped in the bud, and in the end everything was as it should have been. The next FOTD will be posted in 24 hours. Until then, take care, and if you work at it hard enough, you too could become a professional skeptic. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Eastern_Outpost { ; time=0:12:56.54-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+3.254236186523234/+0.9577664576000631/\ 2.3288e+007/1/55/0 params=-4.5/-1.35/-1.1/-7.2/0/\ 0/0/0 float=y maxiter=16000 inside=0 periodicity=10 colors=44047q4Bo4Fo4Jl4Ol4Si4Wi4`g4dg4ie4ne5sb7z`5\ xb5sb5ne5ie5dg5`g5Wg5Si5Fe5Jl5Fi4Bl47m44o44p44q4Hr\ 44t4It4Ku4Ku5Mu4Mu4Ov4Pv4Sv4Sw4Uw4Uw4Wx4Wx4Yx4Yy4_\ y4`z4cz4dz4gz4hz94SF4IM4AS42440Z40zSizUbzWWzZPz`Iz\ bCzd6zg0zi0zl0zg0zl0zp0zs0zx8zzGzzNvzWpzelzogzubzu\ `zu`zu`zq`vo`niZgeZbbZWYZQUZMSZFNW9IW5GW4CW48W46U4\ 2U40U40U40U40U40`40d4CiJSndelg`liYllWilSinPipNgpIg\ sGgvEdvAdx8dz6bz2bz0bz0bz0g`EiBYg4ul4qn4bp4Ps4Cv52\ x90zF0zJ0zO0zQ0vS0pS0lU0gW0bW0ZZ0UZ0Q`0Mb0Hb0Dd49d\ 85gC4iG4iL4lP4dScWclRiz4tz4uz4tz4lx4bl4Wb4NU4GM48B\ 424404404404404404404404F44bW4ZP7WLDUGJSCOQ8UM2`J0\ gH0nF0sD0z90z70z50z40z40z40z40z40z40v40p40i40d40Z4\ 0U44`50Q46F4P54i94gB4gD4eF4eH4bJ4bO4`Q4`S4YU4YW4WZ\ 4Wb4Wd4Ug4Ui5Sl9SnBPsFPvHNxJNzOLzQLzSLzMAzH2zB0z70\ z40z40z40z40z40z40z40z40z70x90sD0pH0lJ0gO0bQ2`U6WZ\ AS`E44u44u44u44u44t44t44q } frm:MandAutoCritInZ {; 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)+(p4)), 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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FOTD 10-07-09 (Elephant Transition [No Rating])
by Jim Muth 09 Jul '09

09 Jul '09

FOTD -- July 10, 2009 (No Rating) Fractal visionaries and enthusiasts: Elephants, elephants, elephants! We certainly have seen enough elephants so far this month. But today's image will be the last one to feature these over-familiar fractal elephants. The image shows a normal elephant morphing into a pair of alien pop-eyes. The normal elephant is at the lower left corner of the frame. Extending upward and to the right from the normal elephant lies a series of steps between a normal elephant and the tiny set of 'Greetings Earthlings' alien pop-eyes at the upper right edge. It can be seen that the spiral elephant trunk becomes one eye, while the deep basin on the elephant's rump becomes the other eye. The very minor mystery has been solved and we can move onward to more artistic things in the days to come. The name "Elephant Transition" refers to the transition from elephant to alien eyes. Of course, I could give no rating to an image that I find pretty boring myself. But all is not lost, for the parameter file runs in a blazing 50 seconds. Those who do not like blazes may access the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An absolutely perfect day passed unappreciated by the fractal cats here at Fractal Central on Thursday. The kodachrome (digitally intensified) blue skies and temperature of 81F 27C kept the humans happy, but the cats were more concerned with an unwanted stray tomcat that spent half the afternoon yelling somewhere nearby. When the stray wandered on, he left his aromatic calling card, and this further disturbed the fractal duo. My day was perfectly average, which means perfectly boring, and what's wrong with that. The work was finished on time and FL offered no (accidental?) philosophical bait to get me pondering. The next FOTD, from an East Valley but with a guarantee of no elephants, will be posted in 24 hours, or maybe not for 36 hours if a certain rush job comes in. Until whenever, take care, and they say we live on the surface of a multidimensional ocean. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ElephantTransition { ; time=0:00:50.51-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 center-mag=-0.127123/-0.601833/9.67109/1/99.4/0 params=89.9/0/89.9/90/0.252/0/0/0/2/0 float=y maxiter=4200 inside=0 logmap=54 periodicity=10 colors=000ZczZdzZex_fw`gvahubitcjsdkrelqfmrgoqgpqf\ orforeoremrdlrdkrcjrchsbhsbhsahsags`gs`gs`gsS_fKSV\ CKI4C66B97BC9AFAAIB9JD9LE8NG8PH7RI7TK6WL6ZN5aO5dP4\ fR4iS3lU2oV2rW2tU4rS5pR6nP7lN9kMAiKBgICeHEdFFbDG`C\ HZAJY8KX7LW5MV4NV5PY5RZ5T_5V`6Xa6Zb6`c6bd7de7ff7hg\ 7jh8li8nj8pk8rl8tmArkCpjEnhFlgHjeJidLgbMeaOc_QaZS_\ XTZWS_VS`UR`URaTRbSQbSQcRPdQPdQPePOfOOfOOgNNhMNhMM\ iLMjKQjKUkJZlIclIhiQmcXrZdvVkzQszMzzSnzaUze8zi9zmA\ zqBzlFzhJzdMz`QvXTrSXnO`jKcjGgjCjgEcdGYaIR_KL`NIaQ\ GaTEbWCbZAca8cc6ab9`bBZaDYaFWaHV`JT`Lc`Nc_Pc_RcZTc\ ZVcZYcYbcYhccmdcrhcvmczmczmczmczmczmczmczmczmYzmYz\ mZzh_zh_wh`uh`sh`rg`pf`oeamdalcajHahHagHbeHbdHbbHb\ aHb_HcYHcXYZ`TaYOdVJgTMeSOcRQbQS`PU_OWYNYXM_VLaTKc\ SJeQIgPHiNGkMFmKEoIDqHCsFBuEAwC9yB9wDAvEAuGBtHBsJC\ qKCpMDoNDnOEmQElRFjTFiUGhWGgXHfYHe_Ic`IbbJacJ`eK_f\ KZgKYdQYbWX_aXYgWVmWTszzz } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 09-07-09 (Elliptic Elephants [No Rating])
by Jim Muth 08 Jul '09

08 Jul '09

FOTD -- July 09, 2009 (No Rating) Fractal visionaries and enthusiasts: Can we bear one more elephant? Why not? In fact, we have two more elephants. They are located in the Elliptic direction, and there is not much to be said about them other than to note that they are little more than empty shells of elephants. The spirals on the elephants' rumps have 30 converging arms. The elephant parade continues beyond the right edge of the frame, the elephants growing ever more vague as they progress. I could not bring myself to rate the image, and the name is a mere description. The calculation time of just under 6 minutes may be cut to almost nothing by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tomorrow's image will have no elephants in it, but it will certainly have something unexpected. So check back then to see the unexpected. FL is famous for asking casual questions that get my philosophi- cal energies on the move. On Wednesday afternoon she asked me, if I had been God, what would I have done differently when I made the world. I told her I would answer the question when we have a few weeks with nothing else to do. A perfect day was spoiled by just a few too many clouds here at Fractal Central on Wednesday. The high temperature of 77F 25C and humidity of 50 percent were in the middle of the comfort range. The fractal cats must have a somewhat warmer comfort range however, for they stayed curled up most all day. My day was quite busy, which explains but does not excuse the hasty FOTD. The next FOTD, hopefully not so hasty, will be posted in 24 hours. Until then, take care, and stay out of trouble by not asking theological questions. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Elliptic_Elephants { ; time=0:05:52.90-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=t float=y center-mag=-0.00085060982005127/-0.837474988123020\ 10/7545.193/0.08195/93.4882993053210924/-87.654270\ 0908922683 params=90/90/0/0/0.26090366/-0.00195958\ /0/0/2/0 maxiter=27500 inside=0 logmap=29 periodicity=10 colors=000wzMxzLwzKuzKszJqzIozHlzHizGfzGczG`zFYzHW\ zKUzNSyQRxTQxWPxZPyaPycPyePxgPxjPxmPwpPwsPwvPwwPvw\ PvvPvsPuqPuoPumPtkPtiPtgPtePscPscPsaPr`Pr`Pr`Pq_Pq\ _Pq_Pq_Pp_PpZPpZPoZPoZPoYPnYPnYPnYPnYPnYPnYPnYPnYP\ lVPiSPfQPcNP`KPYHPVFPSCPP9PM7UM8ZK8cJ9hH9mGAmEAmDB\ rBBv89zABzBCzCDvDErFFmGGhHHcIIaKJ_LKYMLWNMUPNSQOQR\ POSQMURKVSIWUGXVEZWC_XA`YAaZAc_9d`9ea9fb9hc9id8je8\ kf8mg8nh8oi8pj9oi9niAmiAliAkiBjiBiiBhiCgiCfjCekDdl\ DcmDbnEaoE`pE_qFZrFYsFXtGXuGXvHXwHXxH`yIYzI_zIazJg\ zJazJ`zKVzKUzKOzLNzLHzLGzMFzMEzMDzNCzNBuK5pM8pNApP\ CpNApOCuPDuQEuRFzRGzSHzTIzUJzULzVMzWNzXOzYPzYQzZRz\ _Sz`Uz`VzaWzbXzcYzdZzd_ze`zfbzgczgdzhezifzjgzkhzki\ zlkzmlznmznnzoozppzqqzrszquzqwzqwzpwzpwzpwzowzowzo\ wznwznwznwzmwzmwzmwzlwzlwzlwzkwzkwzkwzjwzjwzjwziwz\ iwziwzhwzhwzhwzgwzgwzgwzfwzfwzfwzewzewzewzdwzdwzdw\ zcwzcwzcwzbwzbwzbwzawzawz } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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Re: [Fractint] Fractint Digest, Vol 77, Issue 3
by marcusadriana 07 Jul '09

07 Jul '09

I made my first fractals in 1985 in a MSX, in a Basic interpreter in a green screen. I had no drive or 5 1/4 disk to write on, so I had to write it everytime and then clic "run" and I was happy after many, many minutes.You should see my face when I first connected the computer to a color TV screen!!! Marcus Rezende

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FOTD 08-07-09 (Parabolic Elephants [7])
by Jim Muth 07 Jul '09

07 Jul '09

FOTD -- July 08, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image is sliced in the direction I have named Parabolic. With the real(Z) axis perpendicular to the screen in our 3-space, and the Mandelbrot aspect on the screen, we are looking down from above. And what do we see? . . . more fractal elephants! The elephants are everywhere when the period-30 East Valley elephant complex is viewed in this direction, but they are well hidden. I had to do quite a bit of stretching and skewing to make them recognizable. The baby elephant in the upper left corner is almost, should I say . . . cute. It actually appears to be leaping into the air, something I doubt an everyday elephant could do. And what about those elephants at the right edge of the frame? They seem to be falling into an abyss. They really are fractal elephants, but since when do elephants behave like this? Also, where are the double-spiral things that look like big eyes with a big bulbous nose between? They are everywhere in every East Valley. Actually, they are closely related to the fractal elephants, though the connection will have to wait until another day. Tomorrow's FOTD will show some Elliptic elephants. They are there in the Elliptic planes also. The rating of a 7 that I gave today's image might be a bit liberal. And the calculation time of under 6 minutes may be eliminated entirely by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Typical early July weather prevailed here at Fractal Central on Tuesday. The temperature of 84F 29C and partly cloudy skies were right on the normal mark. The fractal cats slept through most of it. My day was rather busy but still under control. The next FOTD will be posted in 24 hours. Until then, take care, and fly like an elephant. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ParabolicElephants { ; time=0:05:50.97-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=t maxiter=27500 center-mag=-0.00059573625921465/-0.446555463085238\ 70/1341.626/0.2304/90/-86.8491299926404423 params=0/90/0/0/0.26090366/-0.00195958/0/0/2/0 float=y inside=0 logmap=29 periodicity=10 colors=000wzMxzLwzKuzKszJqzIozHlzHizGfzGczG`zFYzHW\ zKUzNSyQRxTQxWPxZPyaPycPyePxgPxjPxmPwpPwsPwvPwwPvw\ PvvPvsPuqPuoPumPtkPtiPtgPtePscPscPsaPr`Pr`Pr`Pq_Pq\ _Pq_Pq_Pp_PpZPpZPoZPoZPoYPnYPnYPnYPnYPnYPnYPnYPnYP\ lVPiSPfQPcNP`KPYHPVFPSCPP9PM7UM8ZK8cJ9hH9mGAmEAmDB\ rBBv89zABzBCzCDvDErFFmGGhHHcIIaKJ_LKYMLWNMUPNSQOQR\ POSQMURKVSIWUGXVEZWC_XA`YAaZAc_9d`9ea9fb9hc9id8je8\ kf8mg8nh8oi8pj9oi9niAmiAliAkiBjiBiiBhiCgiCfjCekDdl\ DcmDbnEaoE`pE_qFZrFYsFXtGXuGXvHXwHXxH`yIYzI_zIazJg\ zJazJ`zKVzKUzKOzLNzLHzLGzMFzMEzMDzNCzNBuK5pM8pNApP\ CpNApOCuPDuQEuRFzRGzSHzTIzUJzULzVMzWNzXOzYPzYQzZRz\ _Sz`Uz`VzaWzbXzcYzdZzd_ze`zfbzgczgdzhezifzjgzkhzki\ zlkzmlznmznnzoozppzqqzrszquzqwzqwzpwzpwzpwzowzowzo\ wznwznwznwzmwzmwzmwzlwzlwzlwzkwzkwzkwzjwzjwzjwziwz\ iwziwzhwzhwzhwzgwzgwzgwzfwzfwzfwzewzewzewzdwzdwzdw\ zcwzcwzcwzbwzbwzbwzawzawz } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 07-07-09 (Elephantettes [7])
by Jim Muth 06 Jul '09

06 Jul '09

FOTD -- July 07, 2009 (Rating 7) Fractal visionaries and enthusiasts: In today's image we shift the direction of our gaze to the Rectangular orientation and see what goes on at the period-30 elephant complex when seen from this angle. Some fairly normal elephants are still there, such as those scrunched at the right edge of the image, but what caught my attention are the bits and pieces of elephants at the center. I named the image "Elephantettes", an oxymoron if ever there was one. But the front halves of elephants, their trunks curling out left and right, actually do appear a bit delicate. The double-half-elephant effect is due to the angle of the slice and the curved shape of the things being sliced. Elephants are actually four-dimensional shapes that curve and twist through four-dimensional space. It would take a five-dimensional viewer to actually see the entire 4-D elephant shapes, though a 4-D viewer could intuit the entire shapes. The improved color palette makes the image worthy of a rating, and the rating I chose is a 7. The calculation time of five minutes is bearable for all but the most impatient. The most impatient may avoid calculation altogether by enjoying the fin- ished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A perfectly average early July day prevailed here at Fractal Central on Monday. The mostly sunny skies and temperature of 82F 28C were just what the fractal cats ordered. Their only complaint was that they never get to go outside like the old fractal cats used to do back at old fractal central. (Actually, the old and the new fractal cats never met.) My day was comfortably busy. The next FOTD will be posted in 24 hours. Until then, take care, and I believe only what I see, and I'm not sure I believe most of that. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Elephantettes { ; time=0:05:18.62-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=t periodicity=10 center-mag=-0.0019407218694615/-0.4731591677497216\ /2371/0.001754/90/0 params=90/90/0/90/0.260821781/\ 0/0/0/2/0 float=y maxiter=27500 inside=0 logmap=25 colors=000wzMxzLwzKuzKszJqzIozHlzHizGfzGczG`zFYzHW\ zKUzNSyQRxTQxWPxZPyaPycPyePxgPxjPxmPwpPwsPwvPwwPvw\ PvvPvsPuqPuoPumPtkPtiPtgPtePscPscPsaPr`Pr`Pr`Pq_Pq\ _Pq_Pq_Pp_PpZPpZPoZPoZPoYPnYPnYPnYPnYPnYPnYPnYPnYP\ lVPiSPfQPcNP`KPYHPVFPSCPP9PM7NM8MK8LJ9KH9IGAHEAGDB\ FBBF89EABEBCECDEDEEFFDGGDHHDIIDKJDLKCMLCNMCPNCQOCR\ PBSQBURBVSBWUBXVAZWA_XA`YAaZAc_9d`9ea9fb9hc9id8je8\ kf8mg8nh8oi8pj9oi9niAmiAliAkiBjiBiiBhiCgiCfjCekDdl\ DcmDbnEaoE`pE_qFZrFYsFXtGXuGXvHXwHXxH`yIYzI_zIazJg\ zJazJ`zKVzKUzKOzLNzLHzLGzMFzMEzMDzNCzNBuK5pM8pNApP\ CpNApOCuPDuQEuRFzRGzSHzTIzUJzULzVMzWNzXOzYPzYQzZRz\ _Sz`Uz`VzaWzbXzcYzdZzd_ze`zfbzgczgdzhezifzjgzkhzki\ zlkzmlznmznnzoozppzqqzrszquzqwzqwzpwzpwzpwzowzowzo\ wznwznwznwzmwzmwzmwzlwzlwzlwzkwzkwzkwzjwzjwzjwziwz\ iwziwzhwzhwzhwzgwzgwzgwzfwzfwzfwzewzewzewzdwzdwzdw\ zcwzcwzcwzbwzbwzbwzawzawz } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 06-07-09 (Oblate Elephant [No Rating])
by Jim Muth 05 Jul '09

05 Jul '09

FOTD -- July 06, 2009 (No Rating) Fractal visionaries and enthusiasts: On July 3 we viewed an East Valley elephant from the normal position directly in front of the screen. On July 4 we viewed the same area from the direction of the past and saw a different aspect of the elephant complex. Today we rotate the Julibrot so that in our 3-D space the real(Z) axis is perpendicular to the screen, and view the same East Valley area from the left side of the screen, which gives what I call the Oblate view. The area we see lies invisibly about two feet in front of the screen, and is stretched about 120 times in the vertical direction to make the elephants recognizable. Well, they're still the same period-30 elephants, but now they appear as gossamer, ethereal things with barely any substance, so fragile that light passes right through them. And they are changing shape before our eyes. The one on the left is over- weight, while the one on the right is actually anemic. The elephants are still standing guard over their appointed bud, but we now see the hypercylindrical bud sideways, sliced in a direction that appears to stretch it to infinity. The horizon- tal black strip is the bud; the bluish stripe near the bottom of the frame is the valley leading to the bud. We have found that there are many elephants guarding each East Valley bud, lurking both behind and in front of the screen while we are viewing the buds. The Mandelbrot elephants have minibrots in the area of their shoulders, while the Julia elephants have Julia sets. But the oblate elephants have only dry valleys that lead nowhere, and a scattering of 30-pointed stars. There are many more varieties of elephants to become acquainted with, and in tomorrow's FOTD we'll see what the Rectangular elephants have to offer. Today's parameter file runs in 4 minutes, but a bit of time may be saved by checking the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another perfect day passed uneventfully here at Fractal Central on Sunday. The near cloudless skies and temperature of 81F 27C were just what the doctor ordered. (Don't ask which doctor.) After a Saturday evening of exploding firecrackers, the fractal cats had a peaceful day of recovery. My day was kept busy by chasing the japanese beetles from FL's raspberries. Unless something unexpected happens, the next fractal elephants will be posted in 24 hours. Until then, take care, and fight the threat of global warming hysteria. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Oblate_Elephants { ; time=0:03:59.92-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=t center-mag=+0.2921149279660176/-0.001977650433172/\ 2484.439/0.007941/0/85.7426211542968275 params=0/0/90/0/0.260821781/0/0/0/2/0 float=y maxiter=27500 inside=0 logmap=25 periodicity=10 colors=000s9qr6rq3ro3rm5ok7mi9kgBidDgaFdZHbWJ`SLZP\ NXMPUJRSGTQDVOAXM2ZF5`I7bS9dUBeWDeVFeWKeXQeTWeS`dO\ bcKdbIcaJb_KaYL`WN_UOZSPYQQXORWMTVKSUISTGSSESRCSQA\ SQERPKRPPRPUROYRO`ROcQOfQNiQUlQZoQeoNhnPdnQZnRUnTP\ lUOkVOiXOgYOeZOc`ObaP`bPZdPXePVfPThQSiQQjQOlQMmQKn\ ULsQJoMHkIGgEEhACm74r6Bv6Hz6Oz6Uz6Yz5`z6az7az7Xv8S\ r9Nm9IhADcB8Z83UB4OD5QF6UI7YK7aM8eP9iRAmTBqVBuUDrT\ EoSGlRHjRJgQKdPLaON_NOXNQUMRRLTPKUMJVJJXGIYEH_BG`8\ Ga6I`9J_AKZFLYHMXKNWNOWPfeUadNLmXLgaLafLWkIX`GXRzX\ HzP8zI0zD5z9Az5EzqLzeczVvzTwSRxHPy6NyNNqcNitNalLgd\ JmXHsPGyQHjRIWSJHSK3QLEPMPNN_MOjWYldfmnoowxpsmmqb`\ pSzj8zXgz`Oz`hzYfzWezUdzqdzhcz_czFJzMUzltzakzprzcj\ zFvz1EzANzJWzrIzkOzdTzYZzv4z1WzuLzfEzaNzXWzh9zbKzX\ Uza0zXKzSPzUhzy1zFYzM`zHizLgzPezYizVfzt_zl`zeazZbz\ LgzNfzPezRdzdzz_rzWjzY8zMXzP`zsNzfAzr_zdazHKzo`zcb\ zlOz5FzBMzHSzNYz8yzFqzMjz } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 05-07-09 (Julia Elephant [No Rating])
by Jim Muth 05 Jul '09

05 Jul '09

FOTD -- July 05, 2009 (No Rating) Fractal visionaries and enthusiasts: East Valley elephants are multi-dimensional things the entirety of which mere human minds will never fully comprehend. But unlike Mandelbrot minibrots, their elephant aspect appears in all slices of the Julibrot. We have already seen the Mandelbrot aspect of the period-30 elephant on the south shore line of East Valley. Today we see the Julia aspect of the same elephant. This version of the creature also has a 30-pointed star on its rump, but instead of placidly plodding along, it appears to be raising its trunk, perhaps in celebration of some victory known only to itself. And this elephant is not guarding a Mandelbrot bud. Such buds are impossible in pure Julia images. It is standing guard over a delicate Julia set of the minibrot on the shoulder of its Mandelbrot brother. Not surprisingly, another Julia set is found on this Julia elephant's shoulder, where the Mandelbrot version has its large minibrot. There are identical copies of this same elephant arranged symmetrically around its parent Julia set, as well as larger and not as well developed elephants and elephant parts. But all the Julia elephants have the same periodicity of 30. This is not surprising, since they all are related to the same Mandelbrot elephant. As for the direction of today's view, if the direction of the Mandelbrot view is taken as being directed from the viewer toward the front of the screen, then time must be considered the fourth dimension and today's Julia view must be taken as directed from the past toward the future. I know this sounds like nonsense, but the fourth dimension makes nonsense of common sense all the time. I named the image "Julia Elephant", which of course it is. I gave the image no rating. After all, how unusual can a typical Julia set of East Valley be when it calculates in 2-1/2 seconds, far too brief a time for enjoyment? That 3 seconds can be turned into a minute or so however if the image is viewed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Viewing the image this way will make the fun last a little longer. Conditions were almost too good here at Fractal Central on Saturday, July 4, which is Independence Day in the U.S. With heat, humidity and evening thunder-showers usually expected, we had crystal clear skies decorated with puffy white clouds, and a temperature of 70F 21C. The fireworks went off uninterrupted. The fractal cats disliked the noise however, and stayed near cover until things calmed down. My day was otherwise unevent- ful. The next FOTD will be posted in the near future. I'll say nothing more about the exact timing. Until whenever, take care, and I think I'll make an egg-cream. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Elephant { ; time=0:00:02.29-SF5 on P4-2000 reset=2004 type=julia center-mag=0.122253/0.018399\ 5/15.63/1/55/0 params=0.2609391/-0.00184566 float=y maxiter=27500 inside=255 logmap=29 periodicity=10 colors=000s9qp6qo3pn3om5nk7mi9kgBidDgaFdZHbWJ`SLZP\ NXMPUORSQTQSVOUXMWZMYZO_ZQaZScZReZQgZPiZOhZNgZMfZL\ eZKdZIcZJbZKaYL`XN_VOZTPYRQXPRWMTVKSUISTGSSESRCSQA\ SQERPKRPPRPUROYRO`ROcQOfQNiQUlQZoQeoNhnPdnQZnRUnTP\ lUOkVOiXOgYOeZOc`ObaP`bPZdPXePVfPThQSiQQjQOlQMmQKn\ ULsQJoMHkIGgEEhACm74r6Bv6Hz6Oz6Uz6Yz5`z6az7az7Xv8S\ r9Nm9IhADcB8Z83UB4OD5QF6UI7YK7aM8eP9iRAmTBqVBuUDrT\ EoSGlRHjRJgQKdPLaON_NOXNQUMRRLTPKUMJVJJXGIYEH_BG`8\ Ga6I`9J_AKZFLYHMXKNWNOWPfeUadNLmXLgaLafLWkIX`GXRzX\ HzP8zI0zD5z9Az5EzqLzeczVvzTwSRxHPy6NyNNqcNitNalLgd\ JmXHsPGyQHjRIWSJHSK3QLEPMPNN_MOjWYldfmnoowxpsmmqb`\ pSzj8zXgz`Oz`hzYfzWezUdzqdzhcz_czFJzMUzltzakzprzcj\ zFvz1EzANzJWzrIzkOzdTzYZzv4z1WzuLzfEzaNzXWzh9zbKzX\ Uza0zXKzSPzUhzy1zFYzM`zHizLgzPezYizVfzt_zl`zeazZbz\ LgzNfzPezRdzdzz_rzWjzY8zMXzP`zsNzfAzr_zdazHKzo`zcb\ zlOz5FzBMzHSzNYz8yzFqzzzz } END PARAMETER FILE=========================================

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Re: [Fractint] Compuserve
by JackOfTradeZ＠comcast.net 05 Jul '09

05 Jul '09

. Compuserve was my first online adventure when I got my 1st PC, a screamin-demon pentium-75 with an incredible 16 Meg RAM and a totally awesome 1 Gig HD, in 1995, complete with windows 3.11 (ouch!). I loved it, especially dialing in and hearing that wet-dream voice say "welcome to wincim"! I liked the graphics and programming forums and the chats; this is also where I got into fractals and fractint. After AOL took over and totally bastardized it (I always HATED AOL!) I quit; from then on I had my own ISP and server and didnt need it anymore anyway. All good things come to an end, I have fond memories and nostalgia. RIP Compuserve! .

3 2

CompuServe Requiem
by Lee H. Skinner 04 Jul '09

04 Jul '09

The original CompuServe service, first offered in 1979, was shut down this past week by its current owner, AOL. The service, which provided its users with addresses such as 73402,3633 and was the first major online service, had seen the number of users dwindle in recent years. At its height, the service boasted about having over half a million users simultaneously on line. Many innovations we now take for granted, from online travel (Eaasy Sabre), online shopping, online stock quotations, and global weather forecasts, just to name a few, were standard fare on CompuServe in the 1980s. CompuServe users will be able to use their existing CompuServe Classic (as the service was renamed) addresses at no charge via a new e-mail system, but the software that the service was built on, along with all the features supported by that software, from forums for virtually every topic and profession known to man to members’ Ourworld Web pages, has been shut down. Indeed, the current version of the service’s client software, CompuServe for Windows NT 4.0.2, dates back to 1999.

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FOTD 04-07-09 (The Elephant [No Rating])
by Jim Muth 04 Jul '09

04 Jul '09

FOTD -- July 04, 2009 (No Rating) Fractal visionaries and enthusiasts: East Valley is sometimes called Elephant Valley. The reason is because, with just a little imagination, the fractal features there can be seen to resemble elephants. I have often mentioned elephants in the FOTD discussions, but until now I have only been talking about them, and not actually showing one in its full glory. Well, in today's image this oversight has been corrected. As the name "The Elephant" indicates, today's image shows an East Valley elephant standing guard over its bud, as all fractal elephants must do. This particular elephant is the period-30 one on the southern shore line of East Valley. The periodicity is determined by the number of filaments leading into the 'star' with the small red ring around it on the elephant's rump at the far end of the filament leading from the bud. The elephant's trunk is quite obvious, though material elephant trunks do not terminate in an endless spiral. One of the big floppy ears elephants are famous for is quite obvious also, as is its ponderous rump, which is marked by the 30-pointed star. Like all fractal elephants, this one has a large minibrot on its shoulder, with lesser minibrots around its mouth and belly. The poor pachyderm appears to have a problem with its front legs however. Its front legs, like those of a tyranosaur, are so small as to be virtually useless. I doubt that those tiny legs could ever reach its mouth to stuff in some tasty vegetation. Many other elephants are scattered about the scene. Every smaller bud has an elephant standing guard over it, though the individual elephants become less recognizable as the buds get smaller, until they blend into a general elephant haze over the tiny buds along the main shoreline. As we go deeper into East Valley, the elephants appear pretty much the same, but they move closer together as the fractal elements get pinched off, until their trunks rather inelegantly touch the rumps of the elephants in front of them. As we move out of the valley, the elephants' bodies gradually lose solidity and turn into mere fractal filaments. When we reach the very last elephant, the period-2 one, the only thing left is its trunk, which has become perfectly straight and is now the nega- tive stem. Elephants are four-dimensional creatures that exist in all six perpendicular planes of the Julibrot, as well as the oblique slices. But they have subtle differences in each of the planes as well as the in-between slices. In the next FOTD, I will check the appearance of elephants in the Julia orientation. After that, who knows. I could give today's image no rating. After all, East Valley elephants are things the tyro fractalist finds during his first hour with his first fractal program. But there is still much to be said about the endangered fractal creatures that are rumored to communicate with subsonic sounds, so stay tuned to this channel for the latest dope. With a calculation time of a sizzling 3 seconds, today's image is one of the all-time fastest, but it's still more fun to see the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday turned out fair enough here at Fractal Central, the only flaw being a brief shower in the afternoon. Otherwise it was partly cloudy with a temperature of 79F 26C, all of which was fully appreciated by the fractal cats. My day was unusually busy, which explains but does not excuse the lateness of this FOTD. The next FOTD, once again late, will be posted in 24 hours, maybe sooner. Until then, take care, and if you still think global warming is a threat that calls for prompt and panicky government legislation, notice this summer's weather, something the legislators are apparently not doing. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Elephant { ; time=0:00:03.40-SF5 on P4-2000 reset=2004 type=mandel center-mag=+0.2609036571578\ 1090/-0.00195958268028537/2610.432/1/18/0 params=0/0 float=y maxiter=27500 inside=0 logmap=29 symmetry=none periodicity=10 colors=000s9qr6rq3ro3rm5ok7mi9kgBidDgaFdZHbWJ`SLZP\ NXMPUJRSGTQDVOAXM2ZF5`I7bS9dUBeWDeVFeWKeXQeTWeS`dO\ bcKdbIcaJb_KaYL`WN_UOZSPYQQXORWMTVKSUISTGSSESRCSQA\ SQERPKRPPRPUROYRO`ROcQOfQNiQUlQZoQeoNhnPdnQZnRUnTP\ lUOkVOiXOgYOeZOc`ObaP`bPZdPXePVfPThQSiQQjQOlQMmQKn\ ULsQJoMHkIGgEEhACm74r6Bv6Hz6Oz6Uz6Yz5`z6az7az7Xv8S\ r9Nm9IhADcB8Z83UB4OD5QF6UI7YK7aM8eP9iRAmTBqVBuUDrT\ EoSGlRHjRJgQKdPLaON_NOXNQUMRRLTPKUMJVJJXGIYEH_BG`8\ Ga6I`9J_AKZFLYHMXKNWNOWPfeUadNLmXLgaLafLWkIX`GXRzX\ HzP8zI0zD5z9Az5EzqLzeczVvzTwSRxHPy6NyNNqcNitNalLgd\ JmXHsPGyQHjRIWSJHSK3QLEPMPNN_MOjWYldfmnoowxpsmmqb`\ pSzj8zXgz`Oz`hzYfzWezUdzqdzhcz_czFJzMUzltzakzprzcj\ zFvz1EzANzJWzrIzkOzdTzYZzv4z1WzuLzfEzaNzXWzh9zbKzX\ Uza0zXKzSPzUhzy1zFYzM`zHizLgzPezYizVfzt_zl`zeazZbz\ LgzNfzPezRdzdzz_rzWjzY8zMXzP`zsNzfAzr_zdazHKzo`zcb\ zlOz5FzBMzHSzNYz8yzFqzMjz } END PARAMETER FILE=========================================

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FOTD 03-07-09 (Fast and Slow [No Rating])
by Jim Muth 02 Jul '09

02 Jul '09

FOTD -- July 03, 2009 (No Rating) Fractal visionaries and enthusiasts: There are two versions of today's scene, calculated by two different formulas, one sliced in the Mandelbrot direction, the other sliced in the almost-Julia direction, give or take a fraction of one second of arc. The fast Mandelbrot version takes under 3 minutes to calculate, the slow Julia version takes 4-1/2 hours. Since the images are virtually identical, I advise running the fast version and taking my word that the slow version appears identical. The slow version is the topic of this discussion however. In three-dimensional space two planes must intersect in a line, and lie at a certain single unique angle to each other. In four- dimensional space two planes intersect in only a single point and lie at two independent angles to each other. When the two angles are equal, every point in one plane in a circle around the point of intersection is at the same distance from the other plane. It makes no sense to a 3-D programmed mind, which visualizes a conic section, but that's the way it is. Today's fast image intersects the Julia plane at a double angle of 90,90 degrees. The slow image intersects the Julia plane at a double angle of a tiny fraction (about 1/50th) of one second of arc from the actual Julia direction, yet the change from Mandelbrot to Julia features has not yet appeared. The change will appear in the next 0.000001 degree of double rotation however. Some pretty abstract thinking is needed to figure out what's happening here. (It's beyond me!) All this abstraction prevents me from rating the image, though the calculation time of the fast version of under 3 minutes makes it relatively simple to see the image. Masochists who want to assure themselves that both images are virtually identical may start the slow version and wait half a day or so. The best way to see and compare both versions is to view them on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies and a temperature of 82F 28C made Thursday near ideal here at Fractal Central. The fractal cats enjoyed things as much as they could, while my day was average. The next FOTD is due to be be posted in 24 hours, but we expect a big rush job on Friday, so don't be surprised if the FOTD is late. Until whenever, take care, and keep searching. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fast_Version { ; time=0:02:50.81-SF5 on P4-2000 reset=2004 type=mandel center-mag=+0.2500000999954\ 752/-0.00000000004996773/8.672315e+011/1/-165/0 params=0/0 float=y maxiter=500000 inside=0 symmetry=xaxis periodicity=0 mathtolerance=0.05/1 colors=000EpADq9Cs8d4ge5fe6ef8ef9dfAcgBbgCahEahF`h\ G_iHZiIYjKYjLXkMWkNVkOUlQUlRTmSSmTRjMLlQOmURoXUp`X\ rcZsgaujdvngzujxsiwqiuoitmhrkhqjhohhnfgldgkbgiagh_\ ffYfeWfcUfbSe`Re_PeYNeXLdVJdUIdSGdREcPCcOAcSeAPPPN\ 9cO8eP8fQ8gR8hS8iS8jT8kU8lV8nW8oW8pX8qY8rZ8s_8t2Mx\ JFv_8uo0xp1vp1tp1rp1pp1np1lp1jp1hp1fp2dp2bp2`p2Zp2\ Xp2Vp2Tp2Rp2Pp3Np3Lp3Jp3Hp3Fp3Dp3Bp39p37o13p35p47p\ 68p7Ap8BpADpBEpDGpEHpFJpHKpIMpJNpLPpMRpOSpPUpQVpSX\ pTYpV_pW`pXbpZcp_evXnsZjp`fnbbkdZifVjeUkeUldUldTmc\ TncTnbSobSpaSpaRq`Rr`RyXOuZQr`RnbSkcUheVdgWahYZjZV\ l_SmaOobLqcIreEtfBvg6zg8whAuhBriDpiEmjGkjIhkJfkLcl\ MalOZmQXmRUnTSnTPqUQnVQlWQjXQgYReZRc_R``RZaSXbSVcS\ SdSQeTOfTLgTJhTHmUIkTGiTFhTEfSDdSCcSBaRA_R9cU9`S8Z\ R8XQ8VO8TN8RM8PL8NJ7LI7JH7HG7FE7DD7BC78769979B79C8\ AE8AF8AH9BI9BKABLACNACOBCQBDRCDTCDUCEWDEXDEZEF_EFa\ EFbFGdFGeGGgGGhGGjEFlDEnC } Slow_Version { ; time=4:31:16.93-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 center-mag=-0.002030815\ 15044265/-0.0022062339955831/15067.5/1/-105/0 params=89.999999/0/89.999999/60/0.2500001/0/0/0/2/\ 0 float=y maxiter=500000 inside=0 symmetry=xaxis periodicity=0 mathtolerance=0.05/1 colors=000d4ge5fe6ef8ef9dfAcgBbgCahEahF`hG_iHZiIYj\ KYjLXkMWkNVkOUlQUlRTmSSmTRjMLlQOmURoXUp`XrcZsgaujd\ vngzujxsiwqiuoitmhrkhqjhohhnfgldgkbgiagh_ffYfeWfcU\ fbSe`Re_PeYNeXLdVJdUIdSGdREcPCcOAcSeAPPPN9cO8eP8fQ\ 8gR8hS8iS8jT8kU8lV8nW8oW8pX8qY8rZ8s_8t2MxJFv_8uo0x\ p1vp1tp1rp1pp1np1lp1jp1hp1fp2dp2bp2`p2Zp2Xp2Vp2Tp2\ Rp2Pp3Np3Lp3Jp3Hp3Fp3Dp3Bp39p37o13p35p47p68p7Ap8Bp\ ADpBEpDGpEHpFJpHKpIMpJNpLPpMRpOSpPUpQVpSXpTYpV_pW`\ pXbpZcp_evXnsZjp`fnbbkdZifVjeUkeUldUldTmcTncTnbSob\ SpaSpaRq`Rr`RyXOuZQr`RnbSkcUheVdgWahYZjZVl_SmaOobL\ qcIreEtfBvg6zg8whAuhBriDpiEmjGkjIhkJfkLclMalOZmQXm\ RUnTSnTPqUQnVQlWQjXQgYReZRc_R``RZaSXbSVcSSdSQeTOfT\ LgTJhTHmUIkTGiTFhTEfSDdSCcSBaRA_R9cU9`S8ZR8XQ8VO8T\ N8RM8PL8NJ7LI7JH7HG7FE7DD7BC78769979B79C8AE8AF8AH9\ BI9BKABLACNACOBCQBDRCDTCDUCEWDEXDEZEF_EFaEFbFGdFGe\ GGgGGhGGjEFlDEnCEpADq9Cs8 } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 02-07-09 (One Skinny Trunk [No Rating])
by Jim Muth 02 Jul '09

02 Jul '09

FOTD -- July 02, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image shows the grossly enlarged Mandelbrot aspect of a scene very deep in East Valley, framed by the Julia set of East Valley. The angle of the slice is one-millionth of one degree from the true Julia direction. This is the angle of one centi- meter as seen from a distance of over 570 kilometers. But as tomorrow's image will show, all the Mandelbrot features are still there, and undistorted as well. I named the image "One Skinny Trunk", even though the skinny thing running diagonally from lower left to upper right is not an elephant trunk, but the entire width of East Valley at the C point of 25.00001. Since the image trick is a virtual repeat of one I did with Seahorse Valley, I could give the image no rating. If you think the calculation time of 24 minutes is slow, wait until you see the calculation time of tomorrow's image. But don't fret. Both images will be available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Fairly warm but otherwise pleasant weather prevailed here at Fractal Central on Wednesday, with partly cloudy skies and a temperature of 84F 29C. A light thunder-shower moved in well after dark, which passed pretty much un-noticed by the fractal cats, who spent the day watching for stray cats. During a hurried lunch I asked FL why she spends so much time watching those silly latin TV novellas. She commented that people with common sense ignore the silly questions I sometimes ask. Then I told her that this shows the stupidity of people with common sense. When she asked if I think she has common sense, I took a long sip of coffee. The day was so busy that I was forced to post the FOTD 12 hours late. This means the next FOTD is due in 12 hours. It's a very slow one, so be prepared. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= One_Skinny_Trunk { ; time=0:24:23.10-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=t periodicity=0 center-mag=0/0/1.147423/1/90/0 params=89.999999/0/\ 89.999999/60/0.2500001/0/0/0/2/0 float=y maxiter=60000 inside=0 logmap=-3 symmetry=xaxis colors=000UDcXFe_KgbPieUkmcmmmmEmmDmmCmmCmmBmmBmmA\ mm9mm9lW8nW8pWBnYEm_HlaKkbNidPhfSggVfiYdk`clbbneap\ h_qkZsnYupXvmWskVpiUnfTkdShbRf`QcYPaWOZUNWRMUPLRNK\ OLJMIIJ8C7GHHEGEBFB9E97D6QqwOnsNlpMimLgiJdfIbcH__G\ YXEVUDTRCQNBOK9LH8JD7GA6E7zgnudjqbgm`ciY`eWYaUUYSR\ TPOPNKLLHHIEDGA9E7At`9pY9mV8iT8fQ8bO7_L7WJ6TG6PE6M\ B5I95F6ym0yh5xcAxZFwXKwVPvTUvRZuPcuNctLctKcFGCBF98\ D6GMRFLPEKNDJLCIJBIIAHGAGE9FC8FB7E96D75C5UurRplPkg\ MgbKbYHZTFUOCPJALE7G9v27s36p46m46j56g56d66a65Z75W7\ 5T85Q95N95KA4HA4EB4BB48C4zXnnSdbOWSKMGGDRVXOTUMRRK\ POINLGLIDJFBHC9F97D6oFplEliEifEfcEc`E`YDYVDVSDSPDP\ MDMJCJGCGDCDACA7C7E5xC7lA8a8AQ6BF5Q25O35M35K35I45G\ 45E4vV0dO2NI3lEviDsgDpeDncDkaDh_DfYDcWDaUDZSDWPCUN\ CRLCOJCMHCJFCHDCEBCB9C97C6iCyfCtcCp`ClYChVCdSC`PCX\ MCSJCOGCKDCGACC7C8eQhaOcYN_ULWRKSNJOJHKGGGCEC8D8`6\ 0Z71Y71W71V81T81S82Q82P92 } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 01-07-09 (Algae on a Pond [6])
by Jim Muth 30 Jun '09

30 Jun '09

FOTD -- July 01, 2009 (Rating 6) Fractal visionaries and enthusiasts: June was the month of seahorses; July will be the month of Elephants. This means that the theme of July will be East Valley -- not only the familiar East Valley of the Mandelbrot set, but any valley of any minibrot that I suspect has East Valley characteristics. We start the East-Valley adventure today with an attractive and blazingly fast minibrot deep in the East Valley of the large minibrot on the main spike of the M-set. It is very typical of the features found in East Valley areas. I named the image "Algae on a Pond" because the colors remind me of the algae on the surface of a pond, where many years ago I used to sit and watch the dragon flies, butterflies, occasional frogs and various and sundry other things. The pond has long since been filled in, but the memories remain. The rating was held to a 6 because such images are quite familiar to every explorer of the Mandelbrot set. The upcoming East valley images however will be far less familiar, and will include some downright bizarre scenes. As I said earlier, today's image is blazingly fast. It calcu- lates in only 12 seconds. Those who would rather avoid playing with fire may view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Variable clouds, showers and a temperature of 77F 25C marked Tuesday here at Fractal Central. The fractal cats marked time while they waited for their afternoon treats to be served. The next FOTD will be posted in 24 hours. Until then, take care, and keep in step with progress. (It sounds good but means nothing.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Algae_on_a_Pond { ; time=0:00:12.90-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.7499995409\ 75928/0/2e+012/1 params=0/0 float=y maxiter=60000 bailout=6 inside=0 symmetry=xaxis periodicity=10 mathtolerance=0.05/1 colors=000yhQzhOzhLzhIzhGwkPunYrpfpsonuwlqsknoiklh\ hhfdeeaacZZbWVaSR_POZMKXJHWFDUCAT96S63T57T5AU5DU5G\ U5JV4LV4NV4PW4SW4UX3XX3_X3bYKeYQhbUkiVllZlqcmqhmtk\ msndnlXijPdhH`fA_bE__GZYIZVKYTMYQOXOQXLSWJUWGWWEYU\ F_SGaQHbOHdMIeKJgIJhGKjELlCMmAMo8Np6Or4Os3Lc3IO3F9\ 5IA6LA7OB9QBATBBWCDYCE`DFcDGeDEaGDYJCUMBQPAMR90L80\ W70Y61_52a53c54e55g5Ai5FkAJmFOoKSqPXsUauZewcjzhnzm\ qzruzvxzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzQeWWfSafOggKzgGzgCzeBzcBzaB`_BWYASXANVAJTAER9AP\ 95N91M95LC8KFBKIEJLHJOKIRNHUQHXTG_WGbZFeaFh`Ic_L_u\ PwvJvwDux7tx1tnGldUeVhZMvSQpRUjQYePa_OeUNhPMHQANSF\ TTJ1Wz6VuAVpEVkIVfMUaQUXUUSOfhSa`VYUDumKkdRbWKDfMG\ cOI`QLYSNVUQSWSPEyiIrdMl_QeWU_RCs0Hm5LhAQcEUZJ90LG\ 8MMFMSNNf_YdYVbXT`WRZVP00KyystsmonhkibfcYaZSktbhnZ\ eiWbcT_ZQfTqdUjbUd`UZZUTizC1yS6uRAqQEmQIiPMeOQaOUU\ NzMNzZNz0NrFbkKXdPSSIsUMh } END PARAMETER FILE=========================================

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FOTD 30-06-09 (Seahorse Valley-30 [8])
by Jim Muth 29 Jun '09

29 Jun '09

FOTD -- June 30, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a puzzle. Everyone knows that Mandelbrot-type minibrots are impossible in Julia sets, so how do we explain the obvious midget M-set in today's image, the parent of which is a Julia set. To see this Julia set, reduce the magnitude to 0.5 and recalculate the image. The Seahorse-Valley Julia set that soon fills the screen is obvious. Well, two things need to be explained. To begin, the minibrot is somewhat warped. Its two period-3 buds as well as its main stem are missing. And in addition, the parent Julia set is not quite a Julia set. It is double-rotated 1/1000 of one degree from the true Julia orientation. This rotation is extremely small -- the width of one centimeter as seen from a distance of over 1/2 kilometer -- but it is enough to reveal the Mandelbrot shape of the minibrot. To see the minibrot magically turn into the Julia set of the center of the main Mandelbrot bay, change real(p1) and real(p2) to 90. Yes, 1/1000 of one degree can make this much of a difference. Other things of interest are the four partially-filled peanut holes and the breakdown of the 2,4,8... series of elements surrounding the minibrot. This breakdown is no surprise, since it often appears in warped minibrots such as the minibrot in today's image. The unusual texture of the image was achieved by rendering it with the outside set to 'summ'. I rated the image at an 8. I think it has enough interest to earn such a rating. The calculation time of just over 9 minutes is rather slow, but nothing to get excited about, especially since the image may be viewed on the FOTD web site without the need to calculate it. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Picture perfect weather prevailed here at Fractal Central on Monday -- at least the fractal cats thought so. They thoroughly enjoyed the blue skies, puffy white clouds, low humidity and temperature of 84F 29C. >From indoors I half enjoyed the outside conditions. Meanwhile, FL, having asked a question on Sunday that I had no immediate answer for, enjoyed an afternoon in her garden, keeping a sharp lookout for japanese beetles in the roses. The next FOTD, the first of a new month, will be posted in 24 hours. I wonder what the new theme, if any, will be. Until then, take care, and the pleasantly cool summer we're having this year should quiet those greenie fanatics clamoring about the imaginary perils of equally imaginary man-made global warming . . . at least until it gets hot again. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-30 { ; time=0:09:05.19-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=1 center-mag=-0.000394521/0.010564/31.23732/1/72.5/0 params=89.999/0/89.999/0/-0.7500830511589915/0.007\ 7264749796986/0/0/2/0 float=y maxiter=15000 inside=0 outside=summ periodicity=10 colors=000mO2zP5mP6la8mPAzPCmPDzPEmOKaMNYLSVKWSJ`P\ IfMHkKGpJLlJQiJVgJZcJcaJh`KnXKsVKxTQwXUv`Zvbctfhsi\ lslprpsssxsutprqlonhmkfjhbgeZebXb_T`YQYUNWRKTOGRME\ QPHTTKWWMY_Q`bSbfVeiYhm`kqcntfpxiszkuznxzluvksrjqn\ hpigmgflbdiYbhVagYihbskdzlczhczebzbazZ`zW`zSZzP_zL\ YzIYzESs8Mk2Gc0JgBLkOMn`OzzPezPzzPezQezzzzQzzQezRe\ zzvzRezRtSSuzSezSezSezzzzTxJzyIzzHTzGTzESzDTzDRzCQ\ zCOzBOzBNzALz9Lz8Kz8Jz7Iz7Hy6Fy6Fy6It8KpAMkCOgFQbH\ SYJTVLWRNYNP_KRXMQWNQTPPSQPQROQSOOVNNWNLYMK_MIaLHb\ LEeJDfKEeLGeMHeNIcOJcPKcQLbRObTPbUQaVRaWSaXT`YU`ZW\ `_X_`Y`aZ`b`````_b`Yc`WfaTg`RcfS_kUWqVTvVStUSsUSrT\ SqTSpSSpSSnSSmSRlQRlQRkPRiPRhORgORfOQeMQcMQbLQbLQa\ KQ`KQ_KQYJQXIPWHQVHPTGPTGPSGPRFPQFPPEPOEPNCPMCPLCP\ KBPJBPIAPHAPG9PF9PE9PD8PC8PC7zC8PA5P85m97P64P54m65\ P33bHHzHHaGG`EEmGG_EE_DDmEEmDDmDDzzDmCCzCCzzCmBBzB\ BzzAmAAzAAm88zz1zY0zQ0zz1 } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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Re: [Fractint] Seahorse Valley-27, 28
by JackOfTradeZ＠comcast.net 28 Jun '09

28 Jun '09

. Re: Re: Seahorse Valley-27, 28, Are those bands real or "artifacts"? They look like some julias I did animations a few years back, I thought it looked cool but someone pointed out they were software artifacts. Who cares. It looks cool. <g> .

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FOTD 29-06-09 (Seahorse Valley-29 [8])
by Jim Muth 28 Jun '09

28 Jun '09

FOTD -- June 29, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's image was rendered with the outside set to 'summ', which gives the image most of its effect. The scene lies deep in the Seahorse Valley of a minibrot lying deep in the Seahorse Valley of the large minibrot on the negative stem of the Mandelbrot set. Few words are required; the image speaks for itself. And yes, there is a much smaller minibrot at the center of the mini-Julia set at the center of the image. Anyone curious about its appearance should turn on the arbitrary math routine by entering the command <mathtolerance=0.05/0> and start diving. But don't expect to see the minibrot until this time tomorrow. The rating of an 8 might be a bit overdone. Sometimes I think the colors are a bit too intense. The calculation time of 1-1/2 minutes is true on the P4-2000mhz machine. On the old P200 it takes 25 minutes. But calculation time becomes meaningless if the image is viewed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> FL has a way of asking questions that demand full engagement of the thinking apparatus. While watching the rain on Sunday, she innocently asked whether I think suicidal terrorists go to heaven or hell. In our eyes they are evil murderers. There is no doubt of it. In their eyes they are heroic martyrs, doing the work of god. They have no doubt of it. Do they go to heaven for killing innocent people, or do they go to hell for doing what they sincerely believe is the will of god? And the question cannot be evaded by invoking Atheism and claiming the question is meaningless. I'll surely have more to say about this philosophical/theological puzzle in an upcoming discussion. Thick clouds and occasional light rain spoiled fractal Sunday here at Fractal Central. The fractal cats ignored the outside temperature of 75F 19C and concentrated on the indoor condi- tions, which were close to ideal. Nicholas enjoyed a bit of cheddar cheese in a puddle of half-and-half creamer. Cassie enjoyed her seafood treat. My day was close to normal. FL was a bit down because she had wanted to work in her garden and the forecast of a sunny day was a bust. The next FOTD, the last one of the Seahorse-Valley series, will be posted in 24 hours. If all goes well, the month will go out with a bang; if not, it will go out with a whimper. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-29 { ; time=0:01:32.77-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.7685\ 27712489421/+0.00052196884344596/5.65e+012/1/-12.5\ /0 params=0/0 float=y maxiter=500000 bailout=6 inside=255 outside=summ logmap=29878 periodicity=10 mathtolerance=0.05/1 colors=000KAALAAMAANAAOAAPAAQAARAAYAATAAUAAVAAlAAX\ AAUADQ66Y9CdCHlFMsIRzKWEa_FcZFeZFgZFiYFkYFmYFoXFqX\ GsXGuWGwWGxWGzVGzVzzVzzUzzVzzWzzWzcXzcXzcYzcYzcZzc\ _zc_zc`zU`z0az0azUbzUbzUczUdzUdzUezUezUfzafzagzagz\ ahzaizaizajzajzakzakzalzalzalzbczcVzeLzdMzcMzcNzbN\ zbNzaOz`Oz`Oz_Pz_PzZPzYQvYQrXQmXRhWRcVRZVSUUSPUSKT\ TFSTDSTDRUDRUDQUDPVDPVDOVDOWDNWDMWDMXDLzDLzDKzDJmD\ JcDIUDIZDHZDG_DG_DF_DF`DE`DE`EGaFHaFIbGJbGKcHLcHMc\ INdIPdJQeJReKSfKTfLUfMVgMWgNXhNZhO_hO`iPaiPbjQcjQd\ kRekRgkShlSilTjmUkmUlmVmnVnnWooWqoXrpXspYtpYuqZvqZ\ wr_xr`zs_yrZyqZxqYxpYxpXwoXwnWvnWvmVvmVulUulTtkTtj\ StjSsiRsiRrhQrhQrgPqfPqfOpeNpeNpdModMocLnbLnbKnaKm\ aJm`Jm`zzphzZLrYMrXNZWNkVOjUOjTPjTQiSQiRRiQRhPShOT\ hNTgMUgLUgLSfKReJPdIOcHMbGLaGK`FI_EHZDFYCEXBCWABV9\ 9U88T77S77U87W87Y87_87a97b97d97f97hA7jA7lA7mA8oG9q\ LAsQAtVCrUDpTEnSFlSVQTWPS } END PARAMETER FILE=========================================

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FOTD 28-06-09 (Seahorse Valley-28 [7])
by Jim Muth 28 Jun '09

28 Jun '09

FOTD -- June 28, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's strange new view of Seahorse Valley shows the valley as it appears in perspective. The center of the image is the point at (C=-0.76+0i),(Z=-0.5+0i), which is a point of convergence of many thick filaments. I assume the large open area at the top of the frame, which has a periodicity of 2, is part of the large period-2 bud, while the open half-oval at right center is a period-17 bud on the north- east shore line of the period-2 bud. But whatever this oval area is, checking the orbits of the points in this image is very interesting, and not surprisingly, the orbits frequently take the shape of peanut holes. The effect of looking down from a mountain top onto a blue sea- shore with many long thin coves is rather striking. I tried to intensify the effect with the coloring. I also see the ghostly outlines of several volcanoes near the shore line of the large period-2 bud at the top. But who knows what these things mean? The rating of a 7 indicates that I kind of like the image. The calculation time of only 3-1/2 minutes indicates that quick satisfaction will be found by running the included parameter file. Those who desire instant satisfaction will find fulfill- ment on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted, already calculated. Now I must track down and eliminate whatever it is that keeps popping up on one of the computers, warning that a fatal trojan horse virus is about to destroy it. (That is unless I buy a cure-all program at a certain web site.) Near perfect summer conditions prevailed here at Fractal Central on Saturday, with partly sunny skies and a temperature of 82F 28C. The fractal cats perked up when a passing tomcat left his scent mark somewhere in the area, but soon settled down to do what cats do best -- sleep. My day was average: Sunday will likely be the same. The next FOTD will hopefully be posted on time in 8 hours or so. There are still two more trips to Seahorse Valley in the works. Until then, take care, and circulate among the big-time thinkers. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-28 { ; time=0:03:31.54-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=1 inside=0 center-mag=0.460478/0.175657/3.554948/0.2653/\ 179.409174596140105/-9.88243261062668 params=2.8/-7.3/90.3/-4.4/-0.76/0/-0.5/0/2/0 float=y maxiter=5200 periodicity=10 colors=000UBFTCFSDEREDQFDPGCOHBNIBMJALK9KL6JM9INCH\ OFGPIGQLJROMSQPUSSWUVZWYaY`d_cgafjdijglkjolmrlpums\ wlwwmzsnzoovmprjpmgqhercbsZ_sUXtPUuKRvFPvAQs6Rq6Ro\ 5Sm5Tk5Ti4Uf4Vd4Vb3W`3XZ3XX2YV2ZS2ZQ1_O1`M1`K0aI0a\ G0`I3_J5_K7ZLAYNCYOEXPHWQJWSLVTNUUQUVSTXUSYXSZZR_a\ QacQbePcgPdiTfkWgm_iobjqfksimumnwpoxmkykhzhdzfazd`\ zc`zb`za`z``z_`zZ`zY_zX_zW_zV_zT_zS_zR_zQZzPZzOZzN\ ZzMZzLZzKZzJZzI`zHazGbzFczFdzEezDgzChzCizBjzAkz9lz\ 8oz9mzAlzBkzCizDhzEgzFezGdzHczIazJ`zK_zLYzMXzNWzOU\ zPTzQSzRQzSPzTOzSOzSOzSOzSOzSOzSOzSOzSOzSOzSOzMKzS\ OzYSzcWze_zhZzkYznXzpWzh`zaezUjzNozFtz8yz8yz7sz7mz\ 6gz6bz7dz7ez7fz7gz8hz8iz8kz8lz9mz9nz9oz9pzCkzEgzGc\ zJZzLVzNRzPNzu5zi6zY7zN8zB9z0AzDOzQ`zbmznzzovzorzo\ nzojzpfzpbzpZzpWzl_zhczdfz`jzXnzTqzPuzMxzKwzJvzHvz\ GuzFuzDtzCtzAsz9sz8rz6rz5qz3qz2pz1pzJqz_qzpqzoqzoq\ zoqzoqzoqzRQzPOzcBz`BzYBz } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 27-06-09 (Seahorse Valley-27 [6])
by Jim Muth 27 Jun '09

27 Jun '09

FOTD -- June 27, 2009 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows an unfamiliar aspect of Seahorse Valley. In the image, the valley complex is viewed in a direction very close to the Oblate. In fact, it is sliced in a direction rotated only 0.5 degree toward the Parabolic direction. This slight rotation means that the lower half of the image skims the chaotic east (main bay) side of the valley, while the upper half shows the more organized detail on the west side. As is the case all over the valley complex and in all orienta- tions, those little peanut-hole things are everywhere, though with such a high maxiter they are filled in. The curious loops turn into attractive spirals when viewed in the Julia direction. The rating of a 6 seems about right for an image with more mathematical interest than artistic worth. The calculation time of 12-1/2 minutes is slow, but the finished image may be seen on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heat, haze and humidity prevailed here at new Fractal Central on Friday, with a temperature of 88F 31C and a slight thunder- shower late in the afternoon. The fractal cats enjoyed things as much as they could. The next FOTD will be posted within 24 hours. Until whenever, take care, and get green for all it's worth. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-27 { ; time=0:12:32.24-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=t center-mag=-1.46642/0/20.08762/1.9132 params=0/0/\ 90/0.5/-0.75/0/0/0/2/0 float=y maxiter=50000 inside=0 logmap=3 symmetry=none periodicity=10 colors=000bJAcJAdJAeJAfJAgJAhJAiKAjLAkMAlNBmOCnPDo\ QEpRFqSGqTIqUJpWKpYLp_NoaOocPoeQnfSnhTniUmkVmjWmiX\ mhYlgZkf_je`idahcbgbcfade`ed_fcZgbYhaXi`Wj_VkZUlYU\ mXUnWUoVUpUUqUUrUUsUUtSUuQUvLUwGUwBUw6Uv2Uu6Ut9UsC\ UrGUqJUpMUoPVnTWmWYlZ_kbajecihehkfgigfggeegddhcbhb\ `haZi`Yi_WiZUjYSjXRjWPjVNjUNjTMjSMjRMjQMhPMfOMdNMb\ MM`LMZKMXKMVKMTKMRKMPKMNLMLMMJNMHOMFQMDRMBSM8TM6UN\ 4UM5UL5UK5UK5UJ5UI5UI5UH7UG9UFBUFCUEEUDGUDIUCKUBMU\ BOUAQU9SU9UUAWUFYUK_UPaUUcUZeVcgWhiXmkYrkXviXzgXve\ WrcWmaWh_WcYVZWVUUVPSVKQUJOULMUMLUNJTOITPGTRFTSEST\ CSUBST8TVASWBSXCSYDSZER_FR`HRaIRbJRcKQdLQeMQhOQmPP\ qQPtRPvRPuQQqPRmOSkNTiMVgLXeL_cKcaKf_JiYJkWInUHrSI\ sQItOIuMJvKJwIJxGJyEKzDKzDKzDKzFLzHMzJOzKQzMSzOUzP\ WzRYzT_zUazWczYczZcz`cvbcscctahr`mp_roYvmXzlWzjUzi\ Tzgczfmzftz`zzVzzOzzIzzDzzCzzczzhzzmzzrzzvzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 26-06-09 (Seahorse Valley-26 [No Rating])
by Jim Muth 26 Jun '09

26 Jun '09

FOTD -- June 26, 2009 (No Rating) Fractal visionaries and enthusiasts: Things did not go according to plan at Old Fractal Central on Thursday, so I had to remain there overnight and finish the work Friday morning. When I got back to New Fractal Central at 5pm Friday, it was too late for a proper fractal search. I filled in the fractal blank with today's hasty but curious distortion of Seahorse Valley. The picture itself is not much to look at, but it calculates in a mere 15 seconds, so little time will be wasted in running the included parameter file. The question is: which part of the image is distorted -- the recognizable Seahorse Valley shape inside the narrow open slot, or the stretched-out stuff in the foreground which is covering parts of the valley? Actually, it's the Seahorse Valley shape that has been distor- ted. To return the image to its undistorted appearance, reset the magnification to 0.75, the X-Magnification Factor to 1, the Rotation Angle to zero and the Skew Angle to zero. Seahorse Valley is still in there, but it's a bit squeezed. Due to the hurried nature of the image, I gave it no rating. The brief calculation time may be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Very warm but otherwise harmless weather prevailed at both Old Fractal Central and New Fractal Central on Thursday, with a temperature around 90F 32C at both places. The fractal cats had little to say. The next FOTD, the one for June 27, will be not be posted on schedule, but neither will it be as late as today's FOTD. Until whenever, take care and be conservatively liberal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-26 { ; time=0:00:15.29-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 center-mag=0.00692656/\ -0.00129906/6.290885/0.05253/-7.5/-71.877681871366\ 1783 params=-43/-93/-85/88/-0.75/0/0/0/2/0 float=y maxiter=2500 inside=0 logmap=yes periodicity=10 colors=0007cvA`tCYsEWrHTpJQoLOnOLlQIkSGjVDhXAgZ8fa\ 5dc2ce0bc2`b4Z`5X_7WZ8UXASWCRVDPTFNSGMRIKPKIOLGNNF\ LODKQBJSAHT8GV6FW5GV8GVBGUEGUHHTKHTNHSQHSSIRVIRYIQ\ `IQcJPfJPiJOlJOnMRkOThQWeSYbU__WbXYdU_gRaiOckLenIg\ pFirDjlIkfMl`RmVVnP_oJcpDhq7lr9jrBhrDfsFesHcsJatL`\ tNZtPXuRVuTUuVSvXQvZPv`NwbLwdKwfIxhGxjExlDynByp9yr\ 8zt6zv4zx3v3ru4su5su5st6st6st7ss7ss8ss8sr9trAtrAtq\ BtqBtqCtpCtpDtpDtoEuoFuoFunGunGunHumHumIumIujIrgIp\ dInbIk_IiXIgVIdSIbPI`NIYKIWHIUFIRCIP9IN7ILBJNEKOHK\ PKLQOMRRMSUNTXOU_OVbMSeLQgKOjILlHJoGHqEEtDCvCAjDJZ\ DRND_BDg0DoACqKCrUCtcBumBwwBxvCvuCttCrtCpsCnrClrCj\ qChpCfoCdoCbnC`mCZmCXlCVkCTjCRjCPiCNhCLhCJgCHfCFfC\ DgEChGCiHCiJCjLCkMBkOBlQBmRBmTBnVBoWAoYApZAq`AqbAr\ c9se9sg9th9uj9ul9vm8wo8wq8xr8yt8yu8vsFsqMppTnmWljZ\ kg`idcgaef_hdXkbUmaRp_OrYLuXJwVQmTWdRaVPhMNnCMt3Ns\ 4Or5Or6Pq7Pq8Qp9QpARoBRnC } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 25-06-09 (Seahorse Valley-25 [Not Rated])
by Jim Muth 24 Jun '09

24 Jun '09

FOTD -- June 25, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image is a scene on the east side of the north branch of the twelfth valley out the negative stem of the Mandelbrot set, eleven valleys beyond Seahorse Valley. This valley has no name, and I intend to give it none. I arrived at the remote scene while I was searching for a limit. The more remote the valleys become, the more they start to look the same. Today's image shows what I assume to be the limit of the scenery in the higher-order valleys. Similar scenes first appear around the 4th valley out, and the scenes change little in the valleys beyond there. The ridiculous maxiter of 20-million is no mistake. All these iterations are actually necessary to fully resolve the scene. By comparison, a similar scene in the 4th valley would require a maxiter of only 100-thousand, and would calculate in a minute or two. The three brilliant yellow areas are filled-in peanut holes. It can be seen that the center filled-in hole in the peanut hole is actually the 'star' at the end of the filament extending from the bud. The two 'bulbs' on either side of the center are end- less spirals on either side of the star. I also see some kind of animals in the scene, though I'll not try to identify them. They're clearly not elephants, but they're not seahorses either. Maybe they're spider monkeys. I could hardly give a rating to an image with so little to offer and so much time required for the calculation. But I will say that 50 minutes may be saved by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a high temperature of 88F 31C and a hot sun, things were a bit too warm for absolute comfort here at Fractal Central on Wednesday. The fractal cats were skittish because of the noise of work being done on a neighboring house, but this did not keep them from checking often to see exactly what was happening. My day was busier than average but still well under control. I'll be taking a short trip back to Old Fractal Central on Thursday to do a little porch maintenance, so the FOTD for June 26 might be late. Until whenever, take care, and never doubt the word of science. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_valley-25 { ; time=0:50:55.84-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.4011550420563\ 79/+0.00000000901429934/4.398626e+009/1/-88/0 params=0/0 float=y maxiter=20000000 inside=255 logmap=-87270 periodicity=10 colors=000UYzU_zUazUczUezUgzUizUkzUmzUozUqzUnzTjzS\ dhQaZPRPOMKNIKNDKN7KM1KL0KK1KI7LGDMEJNCPOCUPDYQDaR\ EeSEiTFmTFpTJkUNfURaVVYVZTVbOWfJWjFWnAXr5Xv1X_MHDf\ 2Qj8UnDYqIapGepFipEmpDmpCmoBmoAmo9mo8mo7mn6mn5mn4c\ n3cn2cn1eo3ho4ko6no7qo8tpAwpBzpCzpEzpFzqHzqIzqJzqL\ zqMzqNzrRzsVztZztazudzvgzwjzwmzxpzyszyvzxtzwrzvpzu\ nztmzqoznpzkqzhrzeszbtz_uzXvzUwzRxz`tzjpztlzsmzsmz\ smzsmzsmzsmzsmzsmzsmzsmzsmzsmzqkzpjzohzngzmezldzkb\ zjazi_zhZzgXzfWzeUzdTzcSz_UzXVzUXzRYzNZzK`zHazEbzH\ ZzJWzLTzNQzPNzRKzTGzVDzXAzZ7z`4zb1z_2zY3zW3zT4zR5z\ P5zM6zK6zI7zF8zD8zB9z8Az6Az4Bz2Bz7GzCKzHOzMSzRWzW`\ z`dzehzjlzopzmnzklzijzghzfgzcdz`bzY_zVYzSVzQTzNQzK\ OzHLzEJzBGz9EzFIzLLzRPzWSzaVzgZzmazrdzlbzf`zaZzWXz\ QVzLUzQWzUXzZZzb_zf`zkbzoczsdzrdzqdzpdzodzmezlezke\ zjeziezhezffzeUzjVzpWzuXzjaz_ezQjzFnz5rzBizHazFWzE\ QzDLzCFzBAzATz9kz6Xz3XK0P } END PARAMETER FILE=========================================

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FOTD 24-06-09 (Seahorse Valley-24 [Not Rated])
by Jim Muth 23 Jun '09

23 Jun '09

FOTD -- June 24, 2009 (No Rating) Fractal visionaries and enthusiasts: At first glance, today's image is a disappointing and not very inspiring debris-filled Julia set, but it is an image that is intended to be tweaked, so don't hesitate to start changing the real(p1) and real(p2) parameters. I have seen rumors circulating around the list lately that the fourth spatial dimension doesn't exist. Of course it doesn't exist. The orbits of the planets, among many other things, definitely obey the mathematically rigid inverse square rule of three-dimensional space. But does this prove anything. After all, we invented math ourselves and designed it specially to work with what we observe with our senses. Does the fourth dimension exist then? There is a big difference between not existing and being impossible. There is nothing at all impossible about four-dimentional space with time as the fifth dimension. There is no impenetrable barrier beyond the third dimension other than the inability of our minds to visual- ize spaces higher than the familiar everyday 3-D space. One- two- and three-dimensional objects can be mathematically modeled and manipulated by computers. With some additional complexity, four-dimensional objects can be modeled and manipula- ted by computers just as well. The problem here is that a three- dimensional screen surface would be needed to properly display the resulting images of 4-D objects, and this 3-D surface would need to be viewed from the fourth dimension. Since our minds have evolved to interpret our sensory input as a true image of a surrounding space having three spatial dimensions, we will never be able to visualize a fourth dimension, but this in no way pre- vents us from knowing what we would observe if we were able to do so. Two of the more curious possibilities in 4-D space are absolute perpendicularity and double rotation. Two planes are absolutely perpendicular when they intersect in a point, with every line in one plane perpendicular to every line in the other. Double rotation exists when a 4-D object is subject to two independent rotations at the same time. The points in the object move in a circular hyperhelix, somewhat like a slinky toy stretched out and curved into a circle with its ends connected. When the two rotations are equal, as with today's scene, all the points except the stationary point at the center move in circular arcs. Don't try to picture this motion. I've been trying for years with no success yet. In today's FOTD we have double rotated around the point at +003i in the north branch of Seahorse Valley, and stopped only 1/500th of one degree from the Julia direction, which is absolutely per- pendicular to the Mandelbrot. To see the 4-D double rotation in action, decrease real(p1) and real(p2) toward 0 and 0, keeping the two parameters equal. At (0,0) the Mandelbrot set will fill the screen, with Seahorse Valley at the center. For a quick but dizzying trip through four-dimensional space, check the slices at (90,90) (89.998,89.998) (89.99,89.99) (89.96,89.96) (88,88) (82,82) (75,75) (62,62) (50,50) (30,30) (10,10). Notice that the closer we come to the Mandelbrot orientation, the slower things go. The final (10,10) slice is barely distinguishable from the actual M-set. The scene may also be rotated from the Julia to the Mandelbrot by two simple 3-D type rotations. Gradually reduce real(p1) to zero, which reveals the Oblate aspect of Seahorse Valley. Then gradually reduce real(p2) to zero, which rotates the Oblate aspect back to the Mandelbrot. Doing it this way passes through some quite interesting slices, while introducing quite a bit of stretching distortion. Keeping the real(p1) and real(p2) para- meters equal will prevent this distortion. The passes=t option is needed to avoid major drop-outs. Since the image is actually one in a series of images, I gave it no rating. The calculation time of 2 minutes may be eliminated by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted. Picture perfect weather prevailed here at Fractal Central on Tuesday, with digitally-enhanced blue skies, puffy clouds, and a temperature of 81F 27C. Taking things for granted, the fractal cats slept through most of the day. My day was once again average and uneventful. The next FOTD trip to Seahorse Valley will be posted in 24 hours. Until then, take care, and today's series of images could make an interesting animation, but it would require choosing some carefully measured increments. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-24 { ; time=0:01:54.26-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=t center-mag=0/0\ /0.7 params=89.998/0/89.998/0/-0.75/0.003/0/0/2/0 float=y maxiter=6400 inside=0 periodicity=10 colors=000QPGDC8MrzGdjBRV5DFTDsL9eE6S73E3gT2XL1ME0\ B7I_F9I7AG3581NPbRRlhJCM96TYzBWv8Og5GT28ExsjheZUSN\ FEBfHIWCDL89A44u0yRvByT8UU2FF13Nj1BNGwvpR4QD2HFteh\ 3SU2EF1wfLhWFULAFA5JsHC`B6I5W9_O6RG4I8294K02A09uV6\ aK3JAsYZ`MNIBBBvO7bG3J8a_UOyoJd9OHiC8NvmObXGJG8LfU\ np5PQ2XjKMVDBF6TACF5f72LW3_keid`CKU4AF2pMLQBAQy_Ji\ RDVI6F9UXwKMcABK49C268134rp5db3RQ2DD1J64C42621iu`f\ OiWIYLCNA6BjVkZN_NFOB7C5pIR2GI1A905RDxI8c94Kx81U40\ gEZDPT8GJ489zP9eG6L83p8`b6RQ4ID29hRrUI_F9IdYRtEqa9\ _J4IqUY_KMIABfaEWSALJ7A93e1WV0OL0GA08qSMREBxWnUGPZ\ k1HO0wEYc9MK4B7507pV1gR0MDEFDuMbTBJUGFKAAA55tlkikT\ NOEkYqOHRtZaeQSSHJE89VsnNeaFSP7ECWtoGSQqqY__MIIBHS\ S8EE1HK08As9pS4QVI7KC4A62sQK`HDI86wSGcIAK95gCOT8GE\ 48Xes`zzXfrTNjQ4c9XZZWLxV7qcOjldctukYnrChkP`e`UZlM\ TxFfFFWVVMjjeaTSPJFPMEC9V2uK1aA0J3Xk2MW1BGmfuPLTKe\ BFV8AL55A2DJw9Eh69U34FbaP } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 23-06-09 (Seahorse Valley-23 [7.5])
by Jim Muth 22 Jun '09

22 Jun '09

FOTD -- June 23, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Today's scene in Seahorse Valley actually has a seahorse in it. The little sea creature lies near the right edge of the frame, with its tail merging with an elephant's trunk. I have no idea what a ponderous elephant is doing in a valley reserved for sea- horses (and pipefish) but I only report what I see. There the elephant is, and I must show it. The scene lies in the Oblate direction at c=(-0.78), just to the west of the center of Seahorse Valley. The vertical direction has been stretched to about 3 times its normal height to make the seahorse recognizable. A nominal amount of skewing was needed to straighten things out. The rating of 7.5 rewards myself for a modicum of color work. The calculation time of under 11 minutes borders on slowness, but the calculation may be eliminated entirely by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather on Monday here at Fractal Central 60 miles north of Harrisburg was surely the reference standard to which all future claims of perfect weather must be compared. Start with a high temperature of 77F 25C, the middle of the human comfort range, continue with a humidity of 50 percent, again in the middle of the comfort range, go on with kodachrome (now digitally intensi- fied) blue skies and puffy cumulus clouds so clear and sharp it seemed you could reach out and touch them. Mix in a refreshing north breeze and just the right amount of ground moisture to let crops and gardens grow their best. Too bad it was just a bit too cool for a comfortable dip in the pool. The fractal cats slept through it all. My day was average. The next FOTD will appear in 24 hours. In it I will take a one-day break from the Seahorse Valley theme to demonstrate an incremental venture from our normal space into the fourth dimension. Until then, take care as always, and when the weather is perfect, don't cheer up. Remember that it can only get worse. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-23 { ; time=0:10:52.68-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=Oblate passes=1 center-mag=-0.37431977\ 2688398/+0.1190352122391917/4405.797/0.3045/0/\ 56.4525422252328042 params=0/0/-0.78/0 float=y maxiter=75000 inside=0 logmap=35 periodicity=10 colors=000R7rQ9qQBqPCqPEqOGpOHpNJpNLpMMoMNoLOoLPoK\ QnKRnJSnITnHUnGVmFWnEXoDYpCZqB_rA`rAaqAbpAcoAdnAem\ AflAgkAhhAieBjbBk_BlXCmVCnSCoPDpMDqJDrGDsEEqDEpDFo\ DFnDGlDGkDHjDHiDHgDIfDIeCJdCJbCKaCK`CK_CLYCLXCMWCM\ VCNTCNSBORBOQBORBPSBPTBRUBSVBUWBVXBWYBYZEZ_G_`I`aK\ __MZYOYWQYUSXSUWQWWOYVM_VKaVKcWLeWLgWLiXMkXMmXMoZL\ rXMqWNqVOqUPqTQpRRpQRpPSpOTpNUoLVoKWoJXoIXnHYnGZnE\ _nD`nCamBbmAbm8cm7dl6el5fl4gl3gl4hk5hk6hk7hk8hk9hk\ AikBikCikDikEikFikDkjFikGhkHgkJfkKekLclNblOalP`lQ_\ lSYmTXmUWmWVmXUmYSn_Rn`QnaPnaNobOnbPnbPnbQnbQnbRnb\ SnbSncTncTncUncVncVncWncWncXndYmdYmdZmdZmd_md`md`m\ dameamebmecmecmedmedmeemdfoeemfdkgdjhchhcgibejbdka\ bkaal`_m_Zn_XnZWoZUpYTqYRqXQrXOsWNtVLtVKuUIvUHwTFw\ TExSCySBzR9zR8yU7xX6x_6wb5wd4vg4vj3um2vp1uo2un2to2\ tp2tq2ur2vs2wt2xu2yv3zw3zx3zz3zz3zz3zz3zz3zz3zz3zz\ 4zz4zz4zz4zzJzzJzzJzzVzzf } frm:Oblate {; Jim Muth real(z),imag(c) z=real(pixel)+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================

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Re: [Fractint] The fourth spatial dimension -- in a zoom? (Hal Lane)
by JackOfTradeZ＠comcast.net 21 Jun '09

21 Jun '09

. For one thing, this "4th dimension" stuff is nonsense. There IS no 4th spatial dimension perceivable to human senses; I have never fully understood what people mean when they are talking about it relating to fractals. I have seen those "quat" animations before, Russ Walsmith has done a few, and there are some on youtube. They look intriguing but I never knew how to do it in fractint. (kinda looks like dough in a bread machine). If you (or someone else) can give me some code the fractint formula parser can deal with, and suggest parameter values / ranges, I would be glad to see what I can do with it. In fact, I would welcome this since I have totally run out of ideas for animations! My 4 main systems are chugging away on the E+112 zoom but I'm sure they would welcome a change from the monotony for a while. JoTz .

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FOTD 22-06-09 (Seahorse Valley-22 [No Rating])
by Jim Muth 21 Jun '09

21 Jun '09

FOTD -- June 22, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image is bogus! Its name is a lie! Today's image is not a scene in Seahorse Valley; it is a scene very deep in East Valley, which is otherwise known as Elephant Valley because the radicals there resemble elephants. While searching around for peanut holes in Seahorse Valley, I got a sudden urge to see whether there are also peanut holes in East Valley. Today's image is a sample of what I found. I found no signs of peanut holes this deep in East Valley. Nor did I find any elephants. What I did find is a whole slew of pinched-off rounded elements, not necessarily arranged symmetri- cally around the minibrot. Since I put very little effort into the coloring, and the image is not even in Seahorse Valley, I could not give the image a rating. But the calculation time of a few seconds over 5 min- utes means that little time will be wasted in the calculation. The task of calculation can be done away with entirely by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies and a temperature of 75F 24C made Sunday near perfect for all fathers on Father's Day here at Fractal Central. A few showers sprang up, but they passed so quickly that they were hardly noticed. The fractal cats alternated between sleeping and watching for unwanted cats. My day was fair enough. The next FOTD, a true scene in Seahorse Valley, will be posted in 24 hours, after I make a sincere act of contrition. Until then, take care, and look before you fractalize. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-22 { ; time=0:05:24.94-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=+0.2500\ 000899991309/-0.0000000000415371/3.657298e+012/1/\ 160/0 params=0/0 float=y maxiter=1250000 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000j55Y96DHKHEDiJBGH04zTAiLGTEQq0Oc3MQ5OYPN\ QJMJDjE4cD5YD6RC7IRUnx6__7y7ZGsDIhBJYAKN8BvmGZS8EZ\ pIGhGD`FBTD9qjjha``TRe96RJUCTpgNmaViXafSicNp`iwwXb\ iLIXT2O`I8OSSB`kjd0ehNfnSgsXhx`hkah_bhNchBdU9MN7JH\ 5GB3DE6BFkTG8AJA8YCmRCSoV__LL1wu8gdFSO_`_VSQQKGJ4N\ K8FaQDI8GKABw9LmAHcBEUCAUmXPVKfKoZH`SEMN8xMAfLBPsE\ OjDJaDFTCBk5w3QcT2cP7cIL`JI`KGULECoXj_MRz77o97eA7V\ B7j1Ta5LT9EHRALxEL_AtUAbL8GgbyCffqo`fcWXTQMIAT_lUb\ ePVZLNSGFYWjUR`RMROHHxeznYldRZVJL6RfANYEJPIFGeyVZh\ NSSFsmUjcOaVITLCnG2fF4_E5SD6jRccNVYJNRFFlNZeKSZHLS\ EEdKIYHEREAEE0mbJJlIKbFKUCLL93ikCTR`IZVGPQEGRcBPU9\ NL8fbHjFRNerFw9I_8R0zP3lO6ZM9LgBocUzcFzcEzcDzc8zcA\ zcBzcCzcCzcCzcCzc5zcpzcbzcPzcnzcazcPzcSzcwzckzc_zc\ OzcuzcizcZzcNzcbzcZzcTzcNzcHzcEzcbzcUzcLzcozcWzclz\ cbzcUzcLzcxzckzc_zcOzcwzcVzcOzcIzcEzcDzcazc0zc4zc8\ zcyzchzcSzc9zcAzcBzcCzc1z } END PARAMETER FILE=========================================

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Re: [Fractint] infinity
by JackOfTradeZ＠comcast.net 21 Jun '09

21 Jun '09

. "it can be thought in an abstract way as though the closer the scene gets to the singularity, that time is slowing down to the observer of the scene"" . that is exactly what happens when you fall into a black hole (if I understand correctly). the "fallee" will never get to the singularity - he will grow old and die of natural causes or something. but someone outside the event horizon will see him get sucked in real fast. more to the point, the mandelbrot is mathematically connected everywhere (that is theoretically proven now) - even the tiniest minibrot is connected by a very thin fillament ultimately to the main body. so the 2 main bulbs must ultimately be connected at real=-0.75, imag=0. but you need to get to infinity to see it. if you zoom in and see a "bridge" and then up the iterations it again disappears. ad infinitum. maybe the oft hyped (soon to arrive?) quantum computer will be able to do it........... .

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FOTD 21-06-09 (Seahorse Valley-21 [7.5])
by Jim Muth 20 Jun '09

20 Jun '09

FOTD -- June 21, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Would the real "Seahorse Valley" please stand up. Today's scene, with its unresolved minibrot and well-resolved peanut holes, lies in Seahorse Valley. But this valley is not the obvious one. It is the Seahorse Valley of the large minibrot at -1.75 on the main stem of the Mandelbrot set. It makes little difference however. The smaller version has all the features of the large 'true' valley, and even a few extra things such as filaments thrown in. In fact, today's image is located on one of these filaments leading from a bud on the west side of the parent valley. At a depth of +0.00003i, the scene is quite far down into the valley. Only the super-high-speed type=mandel algorithm enables the image to calculate in an astonishing 35 seconds. I would have switched to arbitrary precision math for a slightly better rendering, but a test showed that this would have increased the calculation time to a very slow 8-1/2 hours, hardly worth the slight improvement. There must be something of worth in the image, or else I would never have rated it at a 7-1/2. The greenish-blue background is of my creation; the program did the rest. If the calculation time of 37 seconds is too fast for comfort, why not zip out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. Saturday began with heavy rain here at Fractal Central. By noon the steady rain changed to heavy showers, which continued on and off into the evening. The temperature hovered around a reason- able 70F 21C all day. The fractal cats slept through most of the wetness, becoming active only at mealtime. My day was average -- enough said. Unless something totally un- expected happens, the next FOTD will be posted in 24 hours. Until then, take care, and with an added space 'nowhere' becomes 'now here'. (I saw it on a church bulletin board.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-21 { ; time=0:00:37.36-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.7685292334674\ 58/+0.00003283923918143/2.372069e+013/1/12.5/0 params=0/0 float=y maxiter=100000 bailout=6 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000zIizHczHZzKYzNXzQXzZbz_czadzcfzbezbdzbdz\ bczbczmbzaazmaza`za`zm_zm_zmZz`YzmYz`XzmXz`Wz`WzmY\ zYZzW_zV`zmazSczQdzmezNfzMgtLimJjcIkUGlKFmBDo8Cp6A\ q39r18s5Co8FlBIiELfHOcKR`OUXRXUU_RXbO_eLbhIcgJdfKe\ fLfeMgeNhdNidOjcPkbQlbRmaRnaSo`Tp`Uq_Vq_VqZTqYSqXR\ qWQrXOrYNrZMrZKr_Jr`IraHraFrbErcDrcBrdAre9rf8rf6rg\ 5rh4rh3lf7feBacFWbJQ`NL_RKYSJXSIWSHVSGUSFSSERSDQSC\ PSCOSBMTALT9KT8JT7IT6GT5FT4ET3DT3CT5EU6GV7HW9JXAKY\ BMZDO_EP_FR`HSaIUbJWcLXdMZeLadN_ePZeRYeSXfUVfWUfXT\ gZSg`QgaPhcOheNhfLihKijJinJoSQbOTcKVcGXcJ_eMagOciR\ ekTgmWjoZlq`nscpuervgqwhqwiqxjqxkpxlpymqzorzqszstz\ tuzuvzvwzwxzxyzyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzczzczzczzczzczzczzczzczzTfATd9Sb8S_8SY7RW6R\ U5RS5PT9NUCMVGKWJIXMHYQFZTD_XC`_Aab8bf7ci5dm3ep2fs\ 7cnCaiH_eMX`RVXWTS`QOeOJjMF`HNRDVH9b75jPMsj2Ti6Qi9\ Ojh`lgenfjpforetteyqdtnco } END PARAMETER FILE=========================================

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FOTD 20-06-09 (Seahorse Valley-20 [8])
by Jim Muth 19 Jun '09

19 Jun '09

FOTD -- June 20, 2009 (Rating 8) Fractal visionaries and enthusiasts: Blazing peanut holes, minibrots, and a trip to Seahorse Valley -- they're all present in today's image. The scene lies in the shell of a much larger peanut hole moderately deep in the true Seahorse Valley, which is the one in the classic Mandelbrot set. There is little to be said about the Mandelbrot set that has not often been said, so I will say little. But I do think that the image rates an honest 8, mostly because scenes in peanut holes are not that common. The calculation time of 3 minutes and 50 seconds is true on the P4-2000mhz machine. On the old P-200mhz the image takes 1 hour and 5 minutes to finish. And curiously enough, if the 'outside' is set to 'tdis', which makes an equally interesting image, the calculation takes over 9 hours even on the P4-2000. But why not forget all these timing hassles and hurry on out to the FOTD web site, where the finished image can be seen with no calculation required at all. <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday began here at Fractal Central with the threat of rain, but by noon the dark clouds had cleared away, leaving a blue sky speckled with clouds of the altocumulus variety and temperatures around 75F 24C. The fractal cats, unconcerned with clouds or temperature, kept their eyes on two beat-up stray cats prowling the area. When the intruders went away, the resident fractal cats congratulated themselves for a job well done. The next FOTD has a 67-percent chance of appearing in 24 hours. The other 33 percent is the chance that FL will be bitten by the antiquing bug again. Until next time, take care, and science has most all of the answers to some questions and some of the answers to most all the questions, but it never will have all the answers to all the questions. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-20 { ; time=0:03:50.86-SF5 on P4-2000 reset=2004 type=mandel periodicity=10 center-mag=-0.7499986559107982/+0.0023037519364358\ /1.847007e+010/1/177.5/0 params=0/0 float=y maxiter=1500000 inside=0 logmap=85987 symmetry=none colors=000zzmzwczwmzwcyyUxxKvuKtqKrnLpkFniElgBjeCh\ cCfaDd_IbYJ`WKZUKXSKVQKTOKRMKPKKNIKLGKJEFHKEHKEEKD\ CKKBKKBKKBNNVKcLK`2K4OM8KKAHJBEHCUKKPKKKKWFIMEDECF\ DKKAKKCKKVKKPKPJ`MMOJHI9qFCcDEQbeBPTCYxXqUuGMHDJFJ\ pq_OKakZT`RKQK8Fl9G`AGPxx`_aP1To0gw3`k6U_9NOFMQDKL\ CIH0mC3dD6XD9ODwYeZPRvd55dr7Wd9ORzat`RZz44m77`A9OD\ BqBLfDJWEHLFFEuMC`HVd7LSAL2fG9SeXAVRBLLC8BRAEKcccd\ fIyQLtRQpRUlRY9eJ4`l6nXMrfavpccysUrA`ZgQgXNYMJNwwz\ zzzghYXZRMPKzml`XVyF3vWSNgzK`mHUaENP0QI6LFwoqpHIWG\ FIijGaaEVUCNLDrdM4GcXpPOXj94ZC7NEAzuZG`O`H1zz27g69\ UAzzrPZDIPDmTc`OVOKMc5IU9GKDE1Te5OW8KMWIAQHBzzCGGD\ hoASYCMnGIbFzRE7_VzzBdTCzMDc34U870CcjUmZP`NKPyzn_F\ W_78NzB9kDfYkZTbRPUJKLyfFl_E_TENMDRMsAl`BaTBRLDiyC\ alCV`BNPCFeBGWBGMyi8_VBdaIXWGURKZZPccULhZHmcFrhEvm\ CzrDzvCzzBzz`zzUzzPzzUzzZzzczAhzCmzcrzQvzXzzczzmzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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FOTD 19-06-09 (Seahorse Valley-19 [7])
by Jim Muth 18 Jun '09

18 Jun '09

FOTD -- June 19, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today we have a scene very near the Julia set of Seahorse Valley of the (-Z)^(2.5)+C Mandeloid. Actually, the image has been rotated 6 degrees from the Julia orientation toward the Oblate orientation. Instead of being at -0.75 on the X-axis, the seahorse singular- ity in this Mandeloid lies near -0.760037363. To see the pure Julia set, which is far less interesting, change real(p1) to zero and reduce the maxiter to 150 to save time. The first thing I notice about the image is the open slit along the X-axis. This is the area near the singularity between the north and south arms of the valley. Next, I notice the many proto-peanut holes. Most have only two lobes, but the two at the left end of the fractal appear to have developed four lobes, and the brilliant open area on the X-axis just left of center is certainly a peanut hole in the making. Actually, I'm not sure that the image is mathematically correct. The X-axis symmetry might be an artifact of the math routine. To see the problem, set real(p1) to something like 0.0000000001. The image still has X-axis symmetry. Then set real(p1) to zero, and the right half of the resulting fractal totally changes. Such a small parameter change cannot possibly make such a large change in the resulting image. But real or an artifact, today's image rates a 7. The calculation time of 2-1/2 minutes is quite reasonable even for the most fanatical rationalists. And never forget that the finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday started with rain here at Fractal Central, but just after noon the sky brightened and the rain ended. One final sprinkle fell at 2pm, but after that the sun appeared and it was a fine day, with a temperature of 77F 25C. After chasing away a couple unwanted stray cats with their fierce glares and mighty growls, the resident fractal cats spent the day sleeping and ignoring the weather. My day was average. It's not boring; it's peaceful. The next FOTD will be posted in 24 hours. Until then, take care, and be fractalish. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-19 { ; time=0:02:27.18-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrotMin4 center-mag=-0.056338\ /0/1.03 params=84/0/90/0/-0.760036373/0/0/0/2.5/0 float=y maxiter=50000 inside=0 logmap=yes periodicity=10 colors=000hKdhLehMfhNghOihQjhRkhTmhVnhWphYqh_rh_th\ auhavhcwhcwhcwhdwhdwhewhewhfwhfwhfwhfwhfwT22V68X9D\ ZDI_GNaKScNXdQacP`bP_bO_aOZaOY`NY`NX_NWZMWZMVYMVYL\ UXLTXLTWKSWKRVJRUJQUJQTIPTIOSIOSHNRHMRHMQGLPGLPGKO\ FJOFJNEINEHMEHLDGLDGKDFKCEJCEJCDIBCIBCHBBGABGAAF99\ F99E98E87D87D86C76B75B74A64A63962952851640851951B6\ 2C62E72F73H83I83K84L94N94OA5QA5RB5TB6UB6WC6XC7ZD7_\ E8aF8bG8dH9eI9gJ9hKAjLAkMAmNBnOBpQBqSCsUCt`CvcDwcD\ xhDqmCmmBmmBmmAmlAmk9mj1mi5mh9mgDmfGmeKmaOv_SwYRwW\ RwUQwSQzQPzPPzOPzOOzOOzPNzPNzPMzPMvQMwQLuQLsRKqRKo\ RKmSJkSJiSIhSIhTHgTHfTHfUGeUGeUFdVFcVFcVEbVEbWDaWD\ aWC`XC_XC_XBZYBZYAYYAYYAX_9W`9Va9Uc8Td8Se8Rf8Qh7Pi\ 7Oj7Nk7Mm6Ln6Ko6Mp6Oq7Qr7Ss8Ut8Wu8Yv9_w9axAcyAezAg\ zBizBkzBmzCozCqzDszDuzDwzEyzEzzEzzFzzFzzGzzGzzHzzH\ zzLzzPzzUzzZzzczzhzzmzzrzzvzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrotMin4 {; 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=(-z)^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 17-06-09 (Seahorse Valley-17 [7])
by Vortex Swirling 18 Jun '09

18 Jun '09

Hi Jim, If the scene were calculated closer and closer to point -0.75, the camera could zoom in on it proportionally and keeping the apparent width of the valley the same. What ever the computer, it could do this until it ran out of time to complete the next scene. Interestingly, this shows that while the distance to the singularity is finite, there are an infinite number of increments before getting there. If the scenes get slower and slower to calculate, presumably because the number of digits past the decimal point also approaches infinity, it can be thought in an abstract way as though the closer the scene gets to the singularity, that time is slowing down to the observer of the scene. Actually these statements are probably true of the whole fractal I suppose. I also am wondering if all the buds are pinched off in this manor. Roger > I have also often wondered what lies at the point -0.75 of the > Mandelbrot set. What would we find there if we had a computer > of infinite speed, which would give infinite magnification? I > suspect that, at the -0.75 point, Seahorse Valley is kind of a > singularity with a width of zero, which means that even infinite > magnification would leave it with zero width. But a departure > of an infinitesimal value in the imaginary direction would > introduce an infinitesimal but real width, which an infinitely > fast machine would calculate and magnify to any degree in an > instant. Since infinitely fast machines will always exist only

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FOTD 18-06-09 (Seahorse Valley-18 [6])
by Jim Muth 17 Jun '09

17 Jun '09

FOTD -- June 18, 2009 (Rating 6) Fractal visionaries and enthusiasts: I have been wondering lately why I consider fractal spirals to be boring merely because there are so many of them, while never becoming bored with the almost constant flow of minibrot scenes I post in the FOTD. I guess beauty, as always, exists in the eye of the beholder. Today's venture into Seahorse Valley takes us into the valley of an oversized Mandelbrot set that is quadratic on the surface but cubic in its depths. The imaginary value of 0.0588... might not seem too deep, but the parent fractal is ten times the size of the classic Mandelbrot set, so the things we find here are more typical of the things at a depth of 0.00588... in the classic M-set. The expected peanut holes are there, though they are shaped more like circular disks than peanuts, and have three lobes rather than four. The minibrot at the center is pure cubic, but with a series of 2,6,18... elements surrounding it, rather than the expected 3,9,27... The rating of a 6 is all I could do for the image, since I could find nothing really exceptional about it. Also, the very slow calculation time of 1-1/3 hours, which is due to the overall unusually high iteration count, makes the calculation pretty much a computerized chore. Luckily, relief for fractal distress may be found on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where I have sent the finished image on ahead so that it could be posted as quickly as possible for instant excitement and total satisfaction. The clouds not only hung tough all day here at Fractal Central on Wednesday, but rain also fell all day, and the temperature never topped a very un-summery 61F 16C. The fractal cats liked this not at all, and showed their displeasure by squatting down and sulking in the middle of the hallway, where they had to be stepped over and could not possibly be un-noticed. Meanwhile, my day was fair enough. The next FOTD of a Seahorse Valley will be posted in 24 hours. Until then, take care, and what a frustration it would be to spend one's whole life searching for the answer, only to find the question was wrong. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-18 { ; time=1:19:31.82-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip center-mag=-7.450695707282017/+0.05885084210143485\ /1.29963e+011 params=3/10 float=y maxiter=100000 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000C9VDBWEDWEFXFHXGJYKLZPNZUP_ZR_cT`hV`mXam\ Zbm`bmbcmdcmfdmhdmjemlfmofmqgmtgmxhmzjmwfmscmnZmjU\ mdQm_LmVGhQBcL6ZG1UG2UH3UJ3PK4KL5FN5AO65Q64R74S84U\ 84V94X94YA5ZB5`B5aC5cC5dD5eE5gE6hF6jF6kG6lH6nH6oI4\ rG6pI8nJAmKCkLEjMGhNIgOKePMdQObRQ`SS_TUYUWXWYVX_UY\ aSZcR_eP`gNaiMbkKcmJdoHeqGfsEguDhtFgtGgsHgsIgsJgrK\ grLgrMgqNgqOgpPgpQgpRgoSgoTgoUfnVfnWfnXfmYfmZfl_fl\ `flafkbfkcfkdfjefjffjgfgedeccdedcfdbgeahe`if`jf_lf\ ZmgYngXohWphWqhXpiXoiXnjXmjXlkXkkXjkXilXhlXgmXfmXe\ nXdnXcoXbqXarX`tX_uXZwXYxXXyXWzXVzXUzXTzXSzXRzXRzY\ RwYRtYRqZRnZRkZRi_Rg_Re_Rc`Ra`R``RZaRXaRVaRTbRRbRQ\ bROcRMcRKcRIdRHdRFdRDeRBeR9gS7eR8dQ9bPAaPB_OBZNCXN\ DWMEULETLFSKGQJHPJINIIMHJKHKJGLHFLGFMEENDDO64ICDOI\ LTOTZUac_iigroeqncpmapl_okYojWnjUmiSmhQlgOlfNkfLje\ JjdHicFibDhaBga9g`7f_5fZ3eY0eZ2eY3eY4eY5eX7eX8eX9e\ XAeWCeWDeWEeVFeVHeVCCVB7U } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 17-06-09 (Seahorse Valley-17 [7])
by Jim Muth 16 Jun '09

16 Jun '09

FOTD -- June 17, 2008 (Rating 7) Fractal visionaries and enthusiasts: To begin today's discussion I must state that I do not have a calendar filled with fractal spirals hanging over the desk here at F.C. I have a calendar of photographs taken by the space telescope. This month's photograph shows the star-forming region LH 95 in the Large Magellanic Cloud. However, the photo- graph resembles many fractals I have seen during my 20 years in Fractal Land. The truth is that there has never been a fractal calendar hang- ing anywhere in F.C. The calendar themes of F.C. are astronomy, weather, flowers and new-age stuff. It should be no secret which themes I choose and which FL chooses. BTW, I find nothing wrong with fractal spirals, there are simply so many of them that they do not strike me as unusual. I have also often wondered what lies at the point -0.75 of the Mandelbrot set. What would we find there if we had a computer of infinite speed, which would give infinite magnification? I suspect that, at the -0.75 point, Seahorse Valley is kind of a singularity with a width of zero, which means that even infinite magnification would leave it with zero width. But a departure of an infinitesimal value in the imaginary direction would introduce an infinitesimal but real width, which an infinitely fast machine would calculate and magnify to any degree in an instant. Since infinitely fast machines will always exist only in fantasy land, we will never know what we would find at imag(zero), though I suspect the trip would be like trying to reach the number 2 through the series (1)+(1/2)+(1/4)+(1/8). . . We would keep getting closer but always slowing down, only to find it was impossible to reach the goal. Today's image, with its dark background and sparkles of light, somewhat resembles aa astronomical scene. Actually, it's a scene deep in the Seahorse Valley of the (-Z)^(2.5)+C Mandeloid. I rated it at a 7 because I kind of like it. And the calculation time of 5-1/4 minutes is more reasonable than the hours-long time of some recent images, and a few yet to come. The most efficient way to see the image is to travel electronically to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the already-calculated image is posted for immediate enjoyment. Heavy low clouds hung tough over Fractal Central on Tuesday, but it stayed dry and the fractal cats enjoyed things well enough. The temperature of 68F 20C was far below what might be expected in the middle of June. In my department things went along pretty much as expected. The next FOTD is likely to be posted in 24 hours as expected. Until then, take care, and if fractal spirals light your fire, grab a phone and dial 911. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-17 { ; time=0:05:15.39-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotMiN passes=1 center-mag=-0.01004178872932089/+0.011740780006324\ 42/1.997697e+010/1/-110/0 params=2.5/0/0/0/-0.75/0 float=y maxiter=15000 inside=0 periodicity=10 colors=000BetEilGldJoXLrPNuIRrKVoMZlObiPffRjcTn`Vr\ ZWdQORHG363D88drUYhPR_KKRFDIA695hrgMRM30N2FJ2CF19B\ 1670K3dOZUIQKzHAK84663z42z31z1`zRIzDHUFEQDCMBAI98F\ 76B54732316GuPshKi`G`UCSM8IF497lLheIb_FXUDSOAMI7GC\ zB6z5szRezKSzDEz65z43z32z21z1EzVBzP9zK7zF4zA2z5zsh\ e`ULIFiu0NT08ZZ5NN2BB42`31W31R21N21I10D109004`wzTk\ mM_`EOP7CCRDRK9KD6D636L`kHUcEOWAIO7CG368Baz5JVKnTH\ fOE_KBTG8LC5E8274KCQD8H648A`m5IPSqQOiMKaIGUECNB8F7\ 473PiDCN6LMrRvQIbH9J8Gm7Ef6C`5AV48P36I24C1260AHM8E\ J7CG6AD58B368245122opgYZTHHE4Wr2L_1AIQJsKFgFBXA7M5\ 3B7hy5`n4Ud3MV2FK17ASnhOgbLaXHVSEPMAJG7CB36551k30W\ 10GxTloOefKZYGSQCLH8E847hOv_JjREZI9N94B6qV5hP4_K3R\ F2IA195NWw4x72c41K2I1mF0eC0ZA0S70L50E207jMIb_PVSKN\ LFFEA775vRITD9sDe`8SI4EFoqCfhzz_zzR5HI289DzzAg48Z3\ 6Q24012z0ascSeUJSK9EA9i54N2MzLHzGDzC8z84z43zq2zh2z\ _1zR1zI0z9xzNozJfzGYzDQz9 } frm:MandelbrotMiN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=(-z)^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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Re: [Fractint] fast fractint
by JackOfTradeZ＠comcast.net 16 Jun '09

16 Jun '09

. OK, here are my benchmarks. For FOTD June 12, 2009, Seahorse Valley 12, rendered at 640x480. P3-933 system running naked DOS: 45 min 45 sec Athlon-64 dual core running in a WinXPME command shell: 25 min 15 sec Athlon-64 dual core booted with DOS-7 CD: 23 min 37 sec Gateway P4-3GHz dual core running in a WinXP command shell: 1 hr 25 min Athlon chips have long been known to gamers to be superior to Intel, that means better FPM units I think, and that should also mean better for fractals. Notice the extreme difference between my P4 and Athlon systems. The Athlon is 1 GHz, and the P4 is 3 GHz !!! Go figure. You can see my systems here: http://www.fractal-animation.net/machinez.html Don't Laf! They get the job dun! .

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FOTD 16-06-09 (Seahorse Valley-16 [7])
by Jim Muth 15 Jun '09

15 Jun '09

FOTD -- June 16, 2009 (Rating 7) Fractal visionaries and enthusiasts: Start with the number 5, extract the square root, add 1 to this root and divide the sum by 2. The result is the golden ratio, 1.618, where (a) is to (b) as (b) is to (a+b). Also, the reciprocal of 1.618 equals 1.618 minus 1, and all of this is curiously important in making fractals. Since this is Seahorse Valley month, I decided to see what goes on in the Seahorse Valley of the Z^1.618+C Mandeloid. The first thing I discovered is that this Mandeloid has no Seahorse Valley, but my disappointment did not last long, for the (-Z)^1.618+C Mandeloid, which is far more interesting, has a very well developed Seahorse Valley. In today's image we explore quite deep into this valley, where the going is very slow, but the rewards for the patient fractalist, very great. Due to a lack of time, today's image just scratches the surface of this part of the valley. In that scratch however I found a minibrot resembling a large ant swimming in elements resembling scalloped potato slices. Most of the detail in the potato slices was achieved by rendering the image with the outside set to 'tdis'. The rating of a 7 does not quite justify the calculation time of over an hour. I recommend saving an hour of so of precious time by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image posted there. Monday proved to be a repeat perfect day here at Fractal Central, with the thunder clouds again remaining far to the northeast. The crystal blue skies, puffy clouds overhead and temperature of 81F 27C made the fractal cats very happy. My day was average, which is the average situation. Tuesday will likely be average again, which is also average. The next FOTD will be posted in 24 hours, and this also is average. Until then, take care, and Theists say God created man, while Atheists say man created God. I say maybe they both are right. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-16 { ; time=1:04:08.30-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandelbrotMiN passes=1 center-mag=-0.7427380746032878/+0.0036673874259825\ /5266657/1/-80/0 params=1.618/0/0/0/0/0 float=y maxiter=32767 inside=0 outside=tdis periodicity=10 colors=000sSasRYtQVtPRtOOuNKuMHuLDvKAvJ6vI3uK4uM5u\ O6uQ7uS8uU9uW9uYAu_BuaCucDueEugFuiFqeHnaJjYLgUNcRP\ `NRXJTUFVQBXN8ZQ7XT7WW6VZ6U`5Tc5Sf5Ri4Ql4Pn3Oq3Nt2\ Mw2Ly2Kv7MsBNpFOmJPjNRhRSeVTbZU_bWXfXUjYSnZVhYYbY`\ XYbRYeLYhFYjAY_LYPWYEfY4pY8qZBr_Fr_Is`Mt`PtaSuaWvb\ Zvcbwcexdixdlyeoyepwfpvgpthqsiqrjqpkqolrnmrlnrkosj\ pshqsgrsfsqbpoZmmVklShjOehKcfG`eDZaEWZEUVFSSFQPFOL\ GLIGJEHHBHF8HDALCBOBCSADV9EZ9Ga8He7Ih6Jl5Ko5Ln7Mm9\ NmBNlDOkFPkGQjIQjKRiMShOThPTgRUfTVfVWeXWeYXeWTX`QP\ eMHjJ9nSCKVBPXAU_9Za8cc8he9ifAjgBkhCliDmjEnkFolGom\ HpnIqoJrpKsqLtrMusMunLljKdfJWbIOZIGaJDdJAgK7fJ8eI8\ dI9cH9bH9bGAaGA`FA_EBZEBZDCYDCXCCWCDVBDZA6VBDRCJOC\ PKDWGDaDEg9En5Ft2Fzu5Vt4Ss3Qr3Oq2Mq2JMFoPEmSDlWCjZ\ BiaAge9eh8dk7bn7aj9bfAbcBb_DbXEcTFcPHcMIcIJdFLdBMd\ 8Nd6J`5FY3BU27R13O2BK3IH4QE5XA6d77k4Bi5Eg6He6Lc7Oa\ 7R_8UY9YW9`UAcSAfQBrVhsTd } frm:MandelbrotMiN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=(-z)^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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Re: [Fractint] fast fractint
by Vortex Swirling 15 Jun '09

15 Jun '09

A couple of clarifications: I said: > Opsys is > Sun VirtualBox (freeware) running Ubuntu 64 (freeware). More completely, it is Vista 64 (Host) / Sun VirtualBox / Ubuntu 64 (Client) I said: > I was able to get one on > screen run also as 800x600 in 16 minutes. I just found that my bios was set for the wrong memory speed. I corrected this and now it takes 14 minutes. Roger

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Re: [Fractint] fast fractint
by JackOfTradeZ＠comcast.net 15 Jun '09

15 Jun '09

. Hey Roger - Send me the PAR or coordinates for the image you are testing, I will try it on my P3-933 and Athlon-64 Alienware systems. They are both screamers. I suspect you are having the same problem many do, you may have a blazing fast system (hardware) but there are many layers of hardware (and software!) translation to muddle thru when running old 8-16 bit programs on current systems, with WinXP or Vista, it kinda defeats the purpose of it all. .

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Re: [Fractint] Seahorse Valley-05
by Vortex Swirling 15 Jun '09

15 Jun '09

> Well, I think the 2 bulbs are mathemagically connected in theory, but > you can never see it cause as you continue to zoom in you just get the > same ever narrowing gulf. If you "see" a bridge between the bulbs its > cause the iterations aint high enuf. What I expect happens is that at REAL = -0.75 IMAG = 0 the iterations goes to infinity. (This is a guess. I'd like to hear professional commentary) If this (my theory) is true then there is a singularity. However, right next to the singularity there is all sorts of activity going on. It doesn't eventually go down to a triangle point or anything. This is very strange to think about. I suppose a sort of event horizon might be the place where the most powerful computer in the universe could still not resolve anything smaller. I have a trial version of UltraFractal (eeek!). When I upped the iteration limit on that my processor overheated, alarms and stuff. But when I upped the iteration limit in xfractint the processor was quite safe. At 1 billion I had a stack overflow. > BTW, I saw a swirling vortex last weekend - a full freakin' tornado! > NorthEast of Denver. It was comin' strait at me and it looked scary, > specially thru binoculars. Never saw one before - awesome! When I was first coming up with this email address I was trying to find something unique. I was looking up in some plain old fluffy cumulus clouds on a nice day and out of nowhere a vortex formed. Some clouds swirled around it for about a minute forming a sort of tunnel. I had never before or since seen such a thing happen. I was going to choose swirlingvortex but someone already had that on yahoo. I have seen true funnel clouds but no actual tornado. If I ever see one I want to be somewhere else when I do (not from my porch). I did see a waterspout which lasted at least 15 minutes out on the Atlantic coast. It was there so long a speed boater went to it and started going all the way around, circling the base of it. Wild. Roger

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Re: [Fractint] Seahorse Valley-05
by JackOfTradeZ＠comcast.net 15 Jun '09

15 Jun '09

. These are all interesting images, but the one "seahorse valley -05" looks like an image very deep down in the trench between the 2 main bulbs of the mandelbrot. I have been fascinated by this region forever, and it is VERY difficult to get down there. The "peanuts" look that way because they are not resolved - higher iterations are needed and deep enough, even fractint's max 2.1e9 iterations ain't enough. But if you zoom out from it it is not a mandelbrot. Interesting. Check out my post on the UFVP page "where no man has gone before". .

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FOTD 15-06-09 (Seahorse Valley-15 [6])
by Jim Muth 15 Jun '09

15 Jun '09

FOTD -- June 15, 2009 (Rating 6) Fractal visionaries and enthusiasts: Today we find ourselves still trapped in the Seahorse Valley complex, longing for some fresh scenery to enjoy, but with half a month yet to go before we escape from the four-dimensional trap. Today's image is a zoom into the stripe at the bottom edge of yesterday's image. We have raised the maxiter to 125,000 and given the stripe quite a bit of stretching in the vertical direction to make sense of it. Without the stretching, today's scene would be a single horizontal line across the screen. In my opinion, the sinuous hairline tendrils are the most interesting feature of the scene. At other angles such as the Mandelbrot and Julia, these tendrils form infinitely deep spirals, though nothing at all of a spiral nature is visible in today's image. (Actually, I consider fractal spirals to be over-rated and grossly over-represented.) I rated today's image at a 6, none of which is due to the bland coloring. And don't be shocked at the calculation time of an hour plus 20 minutes. Eliminate the calculation by hurrying to the FOTD web site instead, where the image is or soon will be posted. The web site may be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Absolutely perfect conditions prevailed here at Fractal Central on Sunday, though my weather-eye did spot one distant thunder cloud on the northeast horizon. The resident fractal cats spent the day enjoying the brilliant sun and temperature of 81F 27C. My day was spent recovering from the day before. The next FOTD will be posted in 24 hours. This is a virtual but not literal guarantee. Until then, take care, and know your chakras. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-15 { ; time=1:19:57.97-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=0/+0.00425094814353898/114330.5/\ 2.124e-005 params=90/30/2/0/0/0/-0.750035/0 float=y maxiter=125000 inside=0 symmetry=yaxis periodicity=10 mathtolerance=0.05/1 colors=000viPvhOugNufNteMtdLscLsbKraJr`Jq_IqZHpYHp\ XGoWFoVFnUEnTDmSDmRClQBlPBkOAkN9jM9jL8iK7iJ7hI6hH5\ gG5gF4fE3fD3eC2gC0eB2cA4bA6`98_8AY8CX7EV6GS1MT3KT4\ JU5IU6HV7GV8FV9EWADWBCXCBXDAYE9YF8YF2YG5YG7YG9YGBY\ GDYGFYGHYGJYGMYGOYGQYGSYGUYGWYGYYG_ZC_YE`YFaYGaYHb\ YIbYJcXLcXMdXNdXOeXPeXQfWSfWTgWUgWVhWWiWXiWYjV_jV`\ kVakVblVclVdmUfmUgnUhnUioUjoUkpVmpUlpTkpSkpRjpQjpP\ ipOipNhpNhpMgpLgpKfpJfpIepHepGdpGdpFcpEcpDbpCbpBap\ Aap9`p9`p9_o9_n9Zm9Zl9Yk9Yj9Xi9Xh9WgmWfkVeiVdgVceU\ bcTa_R`WQ_SOZQNYOMXMMWKLVILUGLUEKVCKWAJWAKXAJYAKYA\ JZAK_AJ_AK`AJ`AKaAJbAJbAJcAIdAIdAHeAHeAGfAGgBFgBFh\ BEiBEiBDjBDjBCkBClBClBBmBBnBAnBAoB9oB9pB8qB8qB7rB7\ sB6sB6tSkjOblLVnHMpEErB6tHWrIywKxuLwsMvqNupOunQtlR\ sjSriTrgUqeVpcXobYo`ZnZ_mX`lWalUckSdjReiPfhNghLigK\ jfIkeGleEmdDncBpb9qb7ra6s`4t_2u_1t`2t`2ta3ta3ta4tb\ 4tb5tb5tc6tc6tc7td7td8zb3 } frm:multirot-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 PARAMETER FILE=========================================

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Re: [Fractint] Seahorse Valley-05
by JackOfTradeZ＠comcast.net 14 Jun '09

14 Jun '09

Roger Swirling Vortex wrote: ""I checked out your movie and the one made by Michael Condron (Canyon Deep) of this area. Is this to say that the 2 main bulbs are really separated by a border that reaches from end to end? Are the two seahorse valleys connected? Or do the two come to a theoretical point at IMAG = 0? I watched your movie again and notice that once you find the trench you then zoom in to one side. What if instead you were to start moving south at this part in the animation. Would the trench become thinner to the point of not being able to be resolved? What I find most interesting about this is that the trench disappears and the reappears once you zoom in far enough. I can't figure out why this is. If you were to start moving north, wouldn't you eventually run into what we normally see as the tip of seahorse valley? Yet if I zoom in on one of those tips, it appears to come to an end and doesn't seem connected to the trench you have found!"" Well, I think the 2 bulbs are mathemagically connected in theory, but you can never see it cause as you continue to zoom in you just get the same ever narrowing gulf. If you "see" a bridge between the bulbs its cause the iterations aint high enuf. Moving South, it looks ever the same ad infinitum. Only thing is the "bulbs" get smaller relative to the width of the trench, but they all look the same - it even gets alittle boring. When you see the trench "disappear" then re-appear it is simply due to resolution and pixels. This is what I used to get down there - I kept diving south with maximum iterations till the trench walls did not resolve any more, then zoomed in to that point. Going way North will eventually take you to the familiar seahorsies again. Psalms 118:23 This is the LORD'S doing; it is marvellous in our eyes. Ain't it so! BTW, I saw a swirling vortex last weekend - a full freakin' tornado! NorthEast of Denver. It was comin' strait at me and it looked scary, specially thru binoculars. Never saw one before - awesome! Stay Amazed! JoTz .

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FOTD 14-06-09 (Seahorse Valley-14 [No rating])
by Jim Muth 14 Jun '09

14 Jun '09

FOTD -- June 14, 2009 (No Rating) Fractal visionaries and enthusiasts: Whenever the FOTD for Sunday is late, as it is today, it usually means a surprise antiquing trip erupted on Saturday, the day I find the Sunday image and write the discussion. This Saturday's trip took us to Carlisle, a town about 20 miles, 32km, west of Harrisburg. Luckily, FL found nothing absolutely necessary to our survival. The venitian blinds in today's image really are part of the 4-D Seahorse Valley complex. To save time, I'll not try to describe the direction in which the north branch of the valley complex was cut to give the effect. Since the area is four-dimensional, the words would have little meaning. But I will say that the open black strips are buds seen from the side, and I'll add that in 4-D space certain angles can have two independent values. I have posted similar images several times in the past, so I could not give today's image a rating. Another problem is that the image takes almost 1/2 hour to calculate on the 2000mhz machine, but this problem may be solved by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it will soon be, if it is not already, posted. A few showers were around the area on Saturday, but it stayed dry back here at Fractal Central, giving the 4-D fractal cats a hopefully pleasant day while their humans were away. I survived -- enough said. The next FOTD will be posted in 24 hours. Until then, take care, and measure your angles. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-14 { ; time=0:28:48.50-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=0/+0.004335/12072/0.000333 params=90/30/2/0/0/0/-0.750035/0 float=y inside=0 maxiter=25000 symmetry=yaxis periodicity=10 colors=000ulhukiukiukjukjukjtkktkktkltkltkmtjmtjnt\ jntjotjotjptjptjqtjqtjrtirtististittittiutiutivtiv\ tivdemQadBZWAa_9cc8eg7hk6jo5ls3mw4nw4nw4nw4nw4ow4o\ w4ow4ow4ow4pw4pw4pw4pw4qw4qw4qw4qw4qw4rw4rw4rw4rw4\ sw4sw4sw4sw4sw4tw4tw4tw4tw4uw4uw4uw4uw4uw4vw4vw4vw\ 4vw4vw7us9upCtmEtjHsgJsdMraOrZRqWTqTWpQYpN`oKcpGbo\ HanIamJ`mJ_lK_kLZkLYjMYiNXiNWhOWgPVgPUfQUeRTeRSdSS\ cTRcTRbUQaVP`WP`WO_XNZYNZYMYZLX_LX_KW`JVaJVaIUbHTc\ HTcGSdFReFReEQfEPgDOhCOhCNiBMjAMjALk9Kl8Kl8Jm7In6I\ n6Ho5Gp4Gp4Fq3Er2Er2Ds1Ct0Bu1Ct1Dt1Dt2Et2Et2Ft2Ft3\ Gt3Gs3Hs3Hs4Is4Is4Js4Js5Ks5Ks5Lr6Mr6Mr6Nr6Nr7Or7Or\ 7Pr7Pr8Qq8Qq8Rq8Rq9Sq9Sq9Tq9TqAUqAVpAVpBWpBWpBXpBX\ pCYpCYpCZpCZoD_oD_oD`oD`oEaoEaoEbo4_v9arEboJckOdhT\ edXfaahYfiVkjRpkOulKznGymHymHxmHxmIwmIwmIvmIvlJulJ\ ulJtlKtlKslKslKrlLrkLqkLqkMpkMpkMokMokNnkNnjNmjOmj\ OljOljOkjPkjPjjPjiQiiQiiQ } frm:multirot-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 PARAMETER FILE=========================================

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FOTD 13-06-09 (Seahorse Valley-13 [8])
by Jim Muth 12 Jun '09

12 Jun '09

FOTD -- June 13, 2009 (Rating 8) Fractal visionaries and enthusiasts: In today's image we slice the 4-D Seahorse Valley complex in the Elliptic direction. This orientation results when the imag(z) axis is perpendicular to the Mandelbrot plane and the resulting three-dimensional slice of the Julibrot is cut in a horizontal direction parallel to the top of the desk. Real(z) and/or imag(c) must be set a bit above or below zero, or else the slice misses Seahorse Valley, passing through the space between the two branches. In today's case, both values are set to 0.06, which eliminates X-axis symmetry in the parent fractal. In this parent, Seahorse Valley appears as a bridge between the north and south shores. Two micro-thin hairlines lie on the west edge of the bridge, with today's scene lying in the thinner hairline closer to the main body of the valley. These hairlines are actually parts of Seahorse Valley sub-buds seen from the side. A look at the crazy values in the parameter file will show that today's image was hugely stretched and skewed to bring it to a recognizable appearance. In fact, I did no actual skewing, but the rotating and stretching I did has the same effect as skewing. I rated the image at an 8. This includes a full point for the coloring, which turned into a study of getting smooth colors from a 256-color palette. The unusual in-to-infinity-and-out- again spiral accounts for the other 7 points. The calculation time of 6-3/4 minutes is barely within reason, so why not take a scenic trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and save the minor effort of setting up this letter so that it will run as a Fractint parameter file. The Friday weather was uneventful here at Fractal Central. The partly cloudy skies and temperature of 81F 27C were so close to normal that little else need be said. The fractal cats slept through most of the non-action. Meanwhile, my day was also close to average, and with any luck, tomorrow will be the same. The next FOTD is due to be posted in 24 hours. Until then, take care, and live in peace with fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-13 { ; time=0:06:44.61-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=Elliptic center-mag=-0.756516862636129\ 8/-0.3556880339637087/4.796564e+007/0.0006617/89.9\ 81502659185395/-89.0184738672499662 params=0.06/0/\ 0/0.06 float=y maxiter=15000 inside=255 logmap=2708 periodicity=10 mathtolerance=0.05/1 colors=000SEtTFtUGtVHsWIsXJsYJsZKr_Lr`MraNrbOqcOqd\ PqeQqfRpgSpgTqhTrgUrfVqeXpdYocZnb_ma`l`ak_bkZckYdk\ XekWfkVflUflTflSfkRfkQfkQfkQelRelTemVemXdnYdn_dnad\ occoecpfcphcqjbqlbqnbrpbrrastasvatwatwarw`qw_pv_nv\ ZmuZkuYitXgtXfsXdsXbsY`rY_rZYqZWq_Up`TpaRobPocNocM\ ocNncOmcPlcQkcRicSgcTedUceXafZ_g`YgcYfeZeg`ejadlbc\ nccpbboabnabm`bl`ak_ajZaiZahYagY`gX`fX`eW`dV`cV_bU\ _aU_`TZ_UY`TY_TXZTWYTVXTUWTSVTRUSPTSNSSMRSKQSJPSHO\ SGNREMRCLRBKR9JR8IR6HR5HQ6IQ7JP8KP9LOALOBMNCNNDOME\ PMFPLGQLGRLHSKITKJTJKUJLVIMWINXHOXHPYGQZGR_GR_HQ`I\ PaIObJNcKMdKLeLKfMJgMIhNHiNHimTGoTEzmDzTBzmAzUBzmB\ zUCzUCzmCzUDzmDzUEzmEzUEzmGzZIzmKzzLzdNzuPzhRzuSzl\ UzuWzpYzuZzt`zubzsdzuezuczrbzuapj_ngZlcYj_XhWVfSUd\ PTbLS`HQZDPX9OV3JW6NW8RWBVXDZXGbXHdXIeYMdZQdZUd_Xd\ _`d`ddahcakcbocbsccwcczcbyaay_`yZ_yXZyVYxUNCmLCnJB\ pHBrFAtB9vDAuEBuGCuHDuJEt } frm:Elliptic {; Jim Muth imag(z),real(c) z=flip(imag(pixel))+p1, c=real(pixel)+p2: z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 12-06-09 (Seahorse Valley-12 [No Rating])
by Jim Muth 11 Jun '09

11 Jun '09

FOTD -- June 12, 2009 (No Rating) Fractal visionaries and enthusiasts: It yesterday's image we set the real(z) axis perpendicular to the Mandelbrot plane at the -0.75 limit of Seahorse Valley. In today's image we do the same with the imag(z) axis, which gives us the Rectangular aspect of the valley. The question then immediately arises, which Z axis is actually perpendicular to the Mandelbrot plane. The answer is that they both are. And every other line in the Julia plane is perpendicular to the Mandelbrot plane as well. The two planes are absolutely perpen- dicular to each other, with every line in both planes perpendic- ular to every line in the other. Absolute perpendicularity is one of those strange unvisualizable things that cannot exist in spaces with dimensions less than 4. Seahorse Valley is filled with holes that resemble crossed peanuts, which I call peanut holes. Today's image shows one of these holes in its full glory, with many other holes scattered about. These holes are not true areas of trapped points, but bottomless pits of ever increasing iteration count. In today's image the maxiter is 110,000, but even this value leaves the peanut hole wide open. A much greater maxiter of 1,000,000,000 or so would totally close it however, greatly increasing the already very slow calculation time in the process. The unlikely values in the parameter file show that the image has been greatly stretched and skewed to bring the large peanut hole to a reasonably undistorted state. Such distortion that needs to be undone is very common in the Rectangular and other odd planes. I gave today's image no rating. After all, how could a mere peanut hole earn a rating? In addition, the calculation time of 1-1/3 hours will try the patience of even the most patient fractalist. I strongly recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds blanketed the Fractal Central area on Thursday, but no rain fell during the daylight hours and the temperature hovered around a very comfortable 73F 23C. The fractal cats had nothing to say about things. My day was occupied with work. But the efficiency eventually paid off and the work was finished by 4pm. The next FOTD will be posted in 24 hours. Until then, take care, and no comment at this time. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-12 { ; time=1:22:37.96-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=Rectangular center-mag=-0.790706186467\ 98470/+0.00044125005017076/5.971931e+007/0.0001521\ /0.0745896617071803714/-89.9801123768401396 params=0/0/-0.75/0 float=y maxiter=110000 inside=0 periodicity=10 colors=000BJDBIEBHFBFGBEHBDIBCJBAKB9LB8MB7N84LB6ND\ 7OF8PH9RJASLBTMCVNDWOEXRFZUH_XI`ZJb`KcbLddMffNghOh\ jPjlQkoQnnRlmRjlRhkRgjSeiSchSbgS`fTZeTXeTWdTUcUSbU\ RaUP`UN_VLZVKYVIXVGVSEXVFZXF`ZGa`GcbHedHgfIhhIjkIl\ mJnozoqKqszsuLuwzvyLtwzsvNqtzpsOnqzmpPlozjmRilzgjS\ fiSdgTcfUbeU`cV_bWY`WX_XKPiQUbWZXacRghLmmFxp4uqzsq\ zqqzoqzmqzkrHirJfrLdrNbrP`sSZsUXsWVsYSs_QtaOtcMteK\ tgItiEwrFunGtkGshHreHpbIo_InXJmUKkQKjNLiKLhHMfEMeB\ Nd8Mb2Nc5Od8OeBPeEPfHQgKRgNRhQSiSSjVTjYUk`UlcVlfVm\ iWnlifjbjlWnnPrpHzsIvqIsoJomJlkKijKehLbfLZdLWcMTaM\ P_NMYNIWOFVOCTP8RP5PQ1QP2OP3NP3MP4LP4KP5JP5IP6GP6F\ P7EP7DO8CO9BO9AOA8OA7OB6OB5OC4OC3OD2OD1QE4RF7SFATG\ CVHFWHIXILYJN_JQ`KTaLWbLYdM`eNcfNfgOhiPkjPnkQqlQrl\ QsiUmfXgc_a`bWYeQVhKOnDQlESkEUjEWhFXgFZfF`dFbcGdbG\ e`Gg_GiZHkXHkWIjWJjWIiVHiVGcVEYWDTWBNWAHWAFWBDWBCW\ ADUADSCDQFDPHDNJDLMEJOEIR } frm:Rectangular {; Jim Muth imag(z),imag(c) z=flip(real(pixel))+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 11-06-09 (Seahorse Valley-11 [8])
by Jim Muth 10 Jun '09

10 Jun '09

FOTD -- June 11, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a scene in the Oblate aspect of Seahorse Valley. The Oblate aspect is defined by the real(z) and imag(c) axes of the Julibrot. To find the Oblate view, take the point at -0.75 on the negative X-axis of the Mandelbrot set and imagine the real(z) axis cutting perpendicularly through this point, extending in front of and behind the screen. This line is actually the X-axis of the basic Julia set of Seahorse Valley, and when taken with the real and imaginary C axes defines a three-dimensional hyperslice of the four-dimensional Julibrot figure. Now rotate the 2-D image on the screen 90 degrees around the vertical axis, through this imaginary 3-D hyperslice until it sits in an upright position perpendicular to the screen, facing left and right. This is the oblate aspect of Seahorse Valley. It's easier to think about than describe in words. Now that we have our bearings in Seahorse Valley, what we find in there is a whole slew of those things I call peanut holes. In today's image the holes are filled in because of the maxiter of one-million, but they may be seen in their full glory by lowering the maxiter to 7,500. Curiously, these peanut holes appear in all aspects of Seahorse Valley, while the Mandeloid elements such as minibrots vanish soon after we leave the Mandelbrot orientation. I added superfluous detail to the scene by rendering it with the outside set to 'summ', and then I colored it to resemble a scene on some surreal alien planet. I rated it at an 8 because I kind of like scenes on alien planets. The calculation time of under 10 minutes will probably be cut to less than half on a current S.O.T.A. (state-of-the-art) machine, once the machine is taught how handle the Fractint program. Or perhaps it is best to forget teaching a new computer old tricks, and trek electronical- ly out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image in its full glory there. Thickening clouds here at Fractal Central on Wednesday did not dim the spirits of the fractal cats, who spent a good part of the day chasing each other up and down the hallway. The tempera- ture of 84F 29C was just about normal for the end of spring. My day was busy but under control. The next FOTD will be posted in 24 hours. Until then, take care, and does dark energy come from the world of fractals? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-11 { ; time=0:09:51.37-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=Oblate passes=1 center-mag=-1.18496393\ 032451400/+0.00512773353588221/33113.21/0.6062/\ -1.06803255737970959/-88.8155012674095872 params=0/0/-0.75/0 float=y maxiter=1000000 inside=0 outside=summ periodicity=10 colors=0001_z1Zz1Zz1Zz1Zz2Yz2Yz2Yz2Yz2Xz2Xz2Xz2Xa2\ W`2WZ2WY2WX3VW3VV3VT3VS3UR3TQ3SP3SO3RM3RL3QK3QJ4OI\ 4OG4MF4ME4LD4KC4KA4J94I84H74H64G56H57H58I59J5AI5BJ\ 5CG5DF5EE5GD5HC5IB5JA5KA5LA5NA5QC5TE5WG5YI5`M5cQ5c\ U5cW5cY5c_5cc5ca5c_5cY5cX5eX5gY5iY5kY5lY5kY5jZ5kZ5\ lZ5mZ5nZ5o_5p_5q_5r_5s_5rZ9rZDrZGrYKrYNrYRrYVrXYrX\ arXdrXhrWlrWorWsrWvqVuqVtpVtpVspVsoVroVroVqnVqnVpn\ VpmUomUnlUnlUmlUmkUlkUlkUkjUkjUjjUjiTiiThhThhTghTg\ gTfgTfgTefTezTdzTdzSczSbzSbzSazSazS`zS`mS_mS_mSZmS\ ZhTZgUZfVZcWZcXZcYZcZZc_Zc`ZcaZcbZccZcdZ`AtZCrYDpX\ FnVHlUJjTKiSMgQOePQcORaMT_LVYKXWJYVIUWHUXGVcGVcFVc\ EVcDWcDWcCWcBWcAWcAWc9Wc8Xb5Ya8ZbA_cC`dEadGbeJcfLd\ gNegPfhRgiThjWijYjk_klalmcmmennhoojpplqpnsqptrrurq\ spprnoqlopjnohmnflmdllbkk`jjZiiXihVhgTgfRfePfdNecL\ dbJ`hHdaHgVHjOHnHHqAHw2Et4Hq5Jo6Ml8Oi9QgATdCVbDY_E\ _XGaVHdSIfPKhNLkKMmIOpFPr } frm:Oblate {; Jim Muth real(z),imag(c) z=real(pixel)+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 10-06-09 (Seahorse Valley-10 [6])
by Jim Muth 09 Jun '09

09 Jun '09

FOTD -- June 10, 2009 (Rating 6) Fractal visionaries and enthusiasts: The theme of the month of June is Seahorse Valley of the Mandel- brot set. But there are many seahorse valleys other than the one in the M-set. In today's image we go quite deep into the valley that sets off the large bud on the negative X-axis of the Z^4+C Mandeloid. Not surprisingly, we find much of the same type of features that fill the depths of the classic M-set, though down here they come in powers of 4 rather than 2. There is not much more to be said about the image, except that I could rate it no higher than a 6. The calculation time of 15 minutes is a bit too slow to for such a mediocre image. Con- sidering all this, I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday dawned with a spectacular thunder-storm here at Fractal Central, but the rest of the day showed a big improvement, with partly cloudy skies and a temperature of 86F 30C. The fractal cats spent most of the day ignoring the weather while stretched on the floor. I am trying to talk FL into adding an occasional comment to the FOTD discussion to contrast with my rather cynical views, but so far she prefers to remain silently in the background. We'll keep working at it however. In the meantime, fractal cat Cassie says, "purrrrr", and cat Nicholas says, "meow". My day was busy enough to verge on being rushed, but at the end of the day, after ample complaints, everything had worked out to everyone's satisfaction. The next FOTD will be posted in about 24 hours. Until then, take care, and then do it again. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-10 { ; time=0:15:27.31-SF5 on P4-2000 reset=2004 type=mandel4 center-mag=-0.787450771623\ 8988/+0.00135232921300458/3.731695e+012/1/-35/0 params=0/0 float=y maxiter=350000 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000cL8eM8gN8fO8bP8_Q8XR8TS8QT8MY2NU8NQENNJN\ JPNGUNC_N9dN5jN2oP4qR6rS8sUAtWCvXEwZGx_HyXIsVImTIg\ RJaPJW3BKDFNNJQWNTzRmzcmzZawYXvXSuWNuWItVDsU8tW2sU\ 4rS5rQ6qP7pN9pLAoJBoICnGEmEFmCGlBHk9Jk7Kj5Li2Kj4Mj\ 6Oj8QjASjCTjEVkFXkHZkJ_kLakNckPekQfhNUeKHdG30rz0mm\ 2hf2dc2``2XY2TW2PT2LQ2IO5HN8GNBGMEFMHELKELNDKQCKTC\ JWBJZAIZ7G_9H`AIaBJbDKcELdFMZ4H`8JbCKdGMfKNgOOiSQk\ WRm_SocUpgVrkWzzzzzzzzvwwrurmsnhqkcogZmcVk`UhXTfTS\ dPRbMQ`IPZEOb8I`9KZAMXBNVCPTDQRESPFTNGVLHWJIYHIZGH\ _FH`EGaEGaDFbCFcCEcBEdADe9Df9Cf8Cg7Bh39o5Ak7Bh9CeB\ DbDE_FFXHGUJHRIHMLIONIPPIRRISUIUWIVYIW_JYaJZdJ`fJa\ hJcjJdp2_n8amDclJekOfjThiZjhckgimfnobwuespgoljkhlg\ doc`q_XtWTwPNvSPuURtWSsZUr`VqbXqdYpg_oiankbmndlpek\ rgZcSel`nwgkthhrhephbmh_khXihUghRdhObhL`hIYhFWhCUh\ 1Wk4Uj7TiAShCRgFQgIPfKOeNNdQMdSLcVKbYJaUIiXIe_IabI\ YeIUhIQSIMUILZIA_IA`JAaKA } END PARAMETER FILE=========================================

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FOTD 09-06-09 (Seahorse Valley-09 [6])
by Jim Muth 08 Jun '09

08 Jun '09

FOTD -- June 09, 2009 (Rating 6) Fractal visionaries and enthusiasts: While viewing today's image, which is the last time we'll see this particular Seahorse Valley minibrot, I started wondering exactly what a minibrot is. In the Mandelbrot set, minibrots appear as miniature Mandelbrot sets. But at the same time mini- brots extend beyond the Mandelbrot set in 2 perpendicular Julia directions, making it more appropriate when discussing minibrot rotation to consider minibrots as four-dimensional 'minibrot complexes'. The elements in these complexes are very large in the Z-plane directions and small in the C-plane directions. The complexes are open inside and extend throughout the Julibrot figure, appearing here and there until they are ultimately completely cut off by lower-iteration stuff. The great difference in the C and Z dimensions of the minibrot complexes also explains the extreme stretching that so often appears in the odd-plane directions. Today's image is another view of the past two days' minibrot complex, this time sliced in a direction rotated about halfway between the Oblate and Rectangular directions. Conveniently, it has X-axis symmetry, which not only gives a more pleasing appear- ance, but also cuts the calculation time in half. I had to stretch the image quite a bit in the horizontal direction to make it clear. Unfortunately, I could not rate the image at a 9, as Paul wondered, since this is the third consecutive trip to the same minibrot complex. But the rating of a 6 is still a bit above average and makes the 5 minutes required to run the parameter file just barely worth the effort. perhaps the best way to view the image is to surf out to the FOTD web site at <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> but try not to fall into the 4th dimension on the way. If you got turned around there, you would come back as anti-matter and destroy half the continent when you self-annihilate. The fractal cats enjoyed the typical early summer weather that prevailed here at Fractal Central on Monday. The temperature of 86F 30C and the humidity did not bother them at all, but I decided it was time to get the energy-saving fan out of the closet and stir up a breeze or two. The next FOTD will be posted in 24 hours. It will not be just another view of the same minibrot. Until then, take care, and would it be possible for a universe to exist with no conscious observers to observe it? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-09 { ; time=0:05:12.20-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=t periodicity=10 center-mag=0/0/108000/50000000/0 params=42.6/90/0/90/-0.7499841692570846/0.01444653\ 20644315/0/0/2/0 float=y maxiter=16000 inside=0 logmap=2000 symmetry=xaxis mathtolerance=0.05/1 colors=000zzzQYxTWwWUvZSuaQudOtgMsjKrmIqmGqkHmiHjg\ HgeIccI`cIYcJUcJRdJOeJLfLKgNJhPIiQHjSGkUFmVEnXDoZC\ p_BqaArc9sd9tc8ub7va6w`5x_4yZ3zY3vY8sYDoYIlYNhYSeY\ XaYaZYfVYkSYpOYuLYzOXxQXvSWuVWsXVrZVpaUocUmeUlT`bG\ gT4mJ8rLBvMEzNHzPKzQNvRQrTUmUXjV_iXbiYeiZhh`khanhb\ dg`VgZLgXBgVwpGumFsjEqhEoeDmbCk`CiYBgWBeTAcQ9aO9_L\ 8ZJ8ZO7ZT7ZX7Za7Zf7Zj7YiCXhGWgLWfPVeUUdYUdaYbbaabe\ `ch_ceYZcWU`UQZTLWRGUPCRN7PM3CEM07d66aC6ZH6XN5US5R\ Y5Pb4Mh4Jm4Hi5Ee6Ba69Y76U83Q81P95OA9NBDMCHLDKKEOKF\ SJGWIH_HIbGJfFKjELnEMqGQmHUiIXfJ`bKdZLgWMkSNoOmr0P\ vzQyzRuzRrzRozRkzShzSeLSaMSZNTWOTSPTPQTMRTJSRHQPGP\ NFNLDMJCKHBJF9HD8GB7E96DDBCGFBKJANO9QS8UW7X`6`d5ch\ 4fl3gg5hb6iY7jT8kP9lKAmFBnACo5Dz00z00z00z00z50zA0z\ F0zK0zP0zS0zV0zY0z`0zc0zf0zg0zi0zk0zm0zo0zq0zs0zu0\ zv0zw0zx0zy0zz0zz0zz0zz0zz0zzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 08-06-09 (Seahorse Valley-08 [8])
by Jim Muth 08 Jun '09

08 Jun '09

FOTD -- June 08, 2009 (Rating 8) Fractal visionaries and enthusiasts: Believe it or not! Today's image shows the same minibrot as yesterday's image. But it is no longer a minibrot. In fact I have no idea what to call it. Apparently, it's a slice through a four-dimensional object that twists and turns in four-dimensional space. But even the 2-4-8-16 series of elements has broken down. All I can say about the image is look at it and make what you will of it. The rating of an 8 is totally due to the mathematical interest. The colors are simply a slight tweaking of yesterday's color palette. Fractint's evolver feature was needed to find this strange angle, which explains the exceedingly critical parameters. The calculation time of 12-2/3 minutes can be eliminated by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather turned slightly muggy here at Fractal Central on Sunday, with a high temperature of 86F 30C. The fractal cats took the warmth stretched out to their full cat lengths. My day was slow, FL wasted a lot of energy trying to talk me into helping with the garden work. I eventually quieted her by lugging a 45-pound (20-kg) bag of mulch out of the shed. The next FOTD, another venture into Seahorse Valley, will be posted in 24 hours. Until then, take care, and see you in the seahorse valley of unimagined delights. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-08 { ; time=0:12:39.12-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=slicejulibrot4 passes=1 periodicity=10 center-mag=+0.00000000003557236/-0.000000000000080\ 27/2.137415e+012/0.0004748/0.155766213921201102/88\ .7811844407367943 params=-0.433319441053499/0.8160\ 148739585559/90.04358186208685/9.207151535843989/\ -0.7499841692570846/0.0144465320644315/-0.74998416\ 92570846/0.0144465320644315/2/0 maxiter=16000 inside=0 logmap=1850 float=y mathtolerance=0.05/1 colors=000zzzyrywmxuhwscvrcuqctpcsocrncqmcqkcmicjg\ cgecccc`ccYccUccRdcOecLfcKgcJhcIicHjcGkcFmcEncDocC\ pcBqcArc9sc9tc8ub7va6w`5x_4yZ3zY3vY8sYDoYIlYNhYSeY\ XaYaZYfVYkSYpOYuLYzOXxQXvSWuVWsXVrZVqaUpcUocUndUme\ VlfWkgXjhYihZhh_gh`fhaeibdiccjdbjeakf`kg_kh`khanh_\ piYrjWtkUukSvjQuhOsgMqfKoeImdGkcEicCgcBecAcc9ac9_c\ 8Zc8Zc7Zc7Zc7Zc7Zc7Zc7YcCXcGWcLWcPVcUUcYUdaYbbaabe\ `ch_ceYZcWU`UQZTLWRGUPCRN7PM3CEM07d66aC6ZH6XN5US5R\ Y5Pb4Mh4Jm4Hi5Ee6Ba69Y76U83Q81P95OA9NBDMCHLDKKEOKF\ SJGWIH_HIbGJfFK`ELtEMzGQmHUiIXfJ`bKdeLghMkmNorOrvP\ vzQyzRzzRvzRrzRmzShzSeLSaMSZNTWOTSPTPQTMRTJSRHQPGP\ NFNLDMJCKHBJF9HD8GB7E96DDBCGFBKJANO9QS8UW7X`6`d5ch\ 4fl3gg5hb6iY7jT8kP9lKAmFBnACo5Dz00z00z00z00z50zA0z\ F0zK0zP0zS0zV0zY0z`0zc0zf0zg0zi0zk0zm0zo0zq0zs0zu0\ zv0zw0zx0zy0zz0zz0zz0zz0zz0zzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 07-06-09 (Seahorse Valley-07 [7])
by Jim Muth 06 Jun '09

06 Jun '09

FOTD -- June 07, 2009 (Rating 7) Fractal visionaries and enthusiasts: The theme for June is Seahorse Valley of the Mandelbrot set. So today's image shows a tiny minibrot deep in the valley, near the limit of resolution. Since there is nothing unusual about Seahorse Valley minibrots, I added a bit of interest by giving the image an unusual color palette. As a result of this coloring effort, I was able to give the image a rating of a 7, which is enough to make the image worth the effort of producing it. The calculation time of 5-5/6 seconds is no mistake. The type=mandelbrot formula runs like a herd of tachyons on the 2000mhz unit. But it's still a lot of fun to roam out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the image posted there. In tomorrow's FOTD we'll check a different view of this same minibrot and see what havoc we can wreak on it. A notable improvement in the weather prevailed here at Fractal Central on Saturday, with lots of sun, gentle breezes and a near- perfect temperature of 79F 26C. The fractal cats, Nicholas and Cassandra, (Nico and Cassie for short), enjoyed the weather, but they would have been more at ease if fewer cats had wandered past their window. We seem to have a thriving cat colony in the area. My day was uneventful. If Sunday is a repeat, I'll have no complaints. The next FOTD will be posted in 24 hours. Until then, take care, and how do we get out of the matrix? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-07 { ; time=0:00:05.50-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.7499841692570\ 8460/+0.01444653206443146/1.046351e+012/1/-31/0 params=0/0 float=y maxiter=16000 inside=0 logmap=1650 periodicity=10 mathtolerance=0.05/1 colors=000zzzQYxTWwWUvZSuaQudOtgMsjKrmIqmGqkHmiHjg\ HgeIccI`cIYcJUcJRdJOeJLfLKgNJhPIiQHjSGkUFmVEnXDoZC\ p_BqaArc9sd9tc8ub7va6w`5x_4yZ3zY3vY8sYDoYIlYNhYSeY\ XaYaZYfVYkSYpOYuLYzOXxQXvSWuVWsXVrZVpaUocUmeUlT`bG\ gT4mJ8rLBvMEzNHzPKzQNvRQrTUmUXjV_iXbiYeiZhh`khanhb\ dg`VgZLgXBgVwpGumFsjEqhEoeDmbCk`CiYBgWBeTAcQ9aO9_L\ 8ZJ8ZO7ZT7ZX7Za7Zf7Zj7YiCXhGWgLWfPVeUUdYUdaYbbaabe\ `ch_ceYZcWU`UQZTLWRGUPCRN7PM3CEM07d66aC6ZH6XN5US5R\ Y5Pb4Mh4Jm4Hi5Ee6Ba69Y76U83Q81P95OA9NBDMCHLDKKEOKF\ SJGWIH_HIbGJfFKjELnEMqGQmHUiIXfJ`bKdZLgWMkSNoOmr0P\ vzQyzRuzRrzRozRkzShzSeLSaMSZNTWOTSPTPQTMRTJSRHQPGP\ NFNLDMJCKHBJF9HD8GB7E96DDBCGFBKJANO9QS8UW7X`6`d5ch\ 4fl3gg5hb6iY7jT8kP9lKAmFBnACo5Dz00z00z00z00z50zA0z\ F0zK0zP0zS0zV0zY0z`0zc0zf0zg0zi0zk0zm0zo0zq0zs0zu0\ zv0zw0zx0zy0zz0zz0zz0zz0zz0zzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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FOTD 06-06-09 (Seahorse Valley-06 [7])
by Jim Muth 05 Jun '09

05 Jun '09

FOTD -- June 06, 2009 (Rating 7) Fractal visionaries and enthusiasts: Fractals are filled with bottomless spirals. They are probably the most common features in the world of fractals. But how often have we seen a set of concentric fractal rings with a very definite bottom? After viewing today's Seahorse Valley scene, we have seen such a set at least once. But are these rings truly what they appear to be. And for that matter, are the everyday fractal spirals truly what they appear to be. The Mandelbrot set does not exist in isolation. It is a particular slice down the center of a four-dimensional monstros- ity known as the Z^2+C Julibrot. The elements in the Julibrot are 4-D objects that twist and turn in four-dimensions. Those very attractive spirals are actually 2-D slices of 4-D things that cannot be visualized but most likely approximate nested hyperspheres. Today's image is simply a slice in a different direction through one of these nested hyperspheres. The disk at the center of today's image is the next inner shell of the nested hyperspheres, which has not been cut entirely through. A bit of parameter tweaking will punch a hole in the center of the flat central disk, which will then become another ring. I have not yet tried tweaking the parameters, though it should not be very hard to find the right ones. I added a bit of extra life to the scene by rendering it with the outside set to 'summ'. The rating of a 7 is the lowest rating that brings satisfaction for a fractal well done. The calculation time of 8-2/3 minutes is slightly slow. A more efficient way of viewing the sliced nested hyperspheres is to surf out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it at leisure there. Solid clouds, steady light rain and a temperature of 61F 16C kept a strict damper on things here at Fractal Central on Fri- day. The fractal cats spent the day catching up on their sleep, though they did have a brief moment of excitement when a bedrag- gled stray cat passed by their window. My day was about average, as are most days. Hopefully, tomorrow will be the same. Unless we get involved in some kind of expedi- tion on Saturday, the next FOTD will be posted in 24 hours. Until next time, take care, and we know that an electron is a unit of energy, but is it a particle, a wave, a wave packet, or none of the above? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-06 { ; time=0:08:42.28-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=1 maxiter=2820 center-mag=+1.074127267031372/-0.1217313849462725/\ 6907.325/0.03441/-45.7342470354590063/-52.78617\ 25848204202 params=90.1/46.3/90.9/91.4/-0.75/0/0/\ 0/2/0 float=y inside=0 outside=summ periodicity=10 colors=000bhgchecibdj`ejZekXflUflSgmQhnOhnMioJipHj\ pFkqDkrAlr8ls6mt4nw0mt2lq3ko5kl6ji8ig9idBhbCg_DgXF\ fVGeSIePJdNLcKMbIMcINdIOeIPfIQfIQgIRhISiITiIUjIUkI\ VlIWlIXmIYnIYoIZoI_pI`qIarIarIbJ_GJZGJYGJYHIXHIWHI\ WHIVHHUHHUIHTIHSIGSIGRIGQIGQJFPJFOJFOJFNJFNJHMIJMI\ KMIMLHNLHPLHQKGSKGTKGVJFWJFYJFZIE`IEaIEcHDdHDfHDgG\ CiGCnF9jGCfHFbIHZJKVKNRLPNMSJNVFOXBP_8QaBSaEUaHVaJ\ XaMYaP_aS`aUbaXca_eabexafaagD`fF_fGZeHYeJXdKWdLVcM\ UcOTbPSbQRaSQaTP`UO`VN_XM_YLZZKZ_JYaIYbHXcGXeFWfEW\ gDVhCVjBUkAUlAUmCTlDTlETlFTlGTlHTlITlJTlKTlLTlMTkN\ TkOTkPTkQTkRTkTSkUSkVSkWSkXSkYSjZSj_Sj`SjaSjbSjcSj\ dSjeSjfSjgSjfUkeVkdWkcXkbYkaZk`_l_`lZalYblXdlWelVf\ lUgmThmSimRjmQkmPlmOmmNlnNlnMkoMkoMkoLjpLjpKipKiqK\ iqJhqJhrIgrIgrIgsHfsHfsGetGetGetFduFduDbtFduGfuHhu\ IiuKkuLmuMnvNpvPrvQsvRuvSwvTxvUuwVrwVoxWmxXjxXgyYd\ yYbyZcv_dt_dr`ep`fmafkbgi } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 05-06-09 (Seahorse Valley-05 [9])
by Jim Muth 04 Jun '09

04 Jun '09

FOTD -- June 05, 2009 (Rating 9) Fractal visionaries and enthusiasts: Anyone looking at yesterday's image can see at once that nothing interesting lies at the tips of those narrow brilliant diagonal lines inside the central bay of the Seahorse Valley Julia set. But not being 'anyone', I took a look anyway. The going was incredibly slow, but I finally found a scene that rates an honest 9. What I found is a screen filled with spider webs, peanut holes and glowing comets. This is exactly what I found in a recent trip to the deepest depths of the true Seahorse Valley. Today's image is not sliced in the Mandelbrot direction however. It is sliced in a virtual Julia direction, yet it is filled with the stuff normally found in the Mandelbrot direction. I did not check for Mandelbrot minibrots in the scene. The going is simply too slow. But the image has a minibrot feeling to it, and I would not be surprised to find some minibrots hiding in the depths, perhaps only slightly perturbed. And I wonder if this is a way of getting extra magnification for nothing. First we enlarge the valley as I did in yesterday's image, then we can dive into the already enlarged valley and get something for nothing. Of course, it is impossible to get some- thing for nothing, and I suspect that all we're doing here is shifting the decimal point, meaning that breakdown would happen at a much less magnitude. The name of the image is simply a catalog number. The rating of a 9 indicates that I am quite pleased with what I found in such an un-promising location. The calculation time of over 3 hours is no mistake. I very strongly recommend hurrying to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to enjoy the pleasure of seeing the image already calculated. FL asked no interesting questions Thursday, so I have no reason to wax philosophical. (BTW, where is Mister Phil O. Sophical?) The fractal cats had ample reason to complain however. The lack of sun and temperature of only 68F 20C was not to their liking, and they showed their dissatisfaction by tearing apart one of their catnip mice. My day was slightly busy, but otherwise uneventful. The next FOTD will be posted in 24 hours. Until next time, take care, and if we found why there is something instead of nothing, we would solve most other un-answerable questions. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-05 { ; time=3:01:36.89-SF5 on P4-2000 reset=2004 type=formula formulafile=jim.frm float=y formulaname=ObliqueManPlus inside=255 center-mag=+0.034148955808/+0.034200698652/205344/\ 1/-132.5/0 params=0/0/-0.75/0/0.0075/0.0075 maxiter=7500000 logmap=6129 periodicity=10 colors=000_Ef_Eh_Ej_Dk_Dm_Do_Cp_Cr_CsZDrYErXErXFrW\ FrVGrVGrUHrTHrTIrSIqRJqRJqQKqPLqPLqOMqNMqNNqMNqLOp\ KOpKPpJPpIQpIQpHRpGSpGSpFTpEToEUoDUoCVoCVoBWoAWoAX\ o9Xo8Yo8Yo9Zn9ZnAZnA_nB_nB_nB`nC`nC`mDamDamDamEbmE\ bmFbmFcmFcmGclGdlHdlHdlHdlIelIelJelJflKfkKfkKgkLgk\ LgkMhkMhkMhkNikNijOijOjjOjjPjjPkjQkjQkjQkjRkkSkkSk\ lTklUklUkmVkmWkmWknXknXknQmjJofDqb6sZ0tW1rX1pY2oZ2\ m_3l`3ja4ia4gb5fc5dd6be6af7_g7Zg8Xh8Wi9Uj9TkARlAPm\ BOmBMnCLoCJpDIqDGrDFrCEdBDRBCECDFCDGCDGCEHCEICEICF\ JCFKCFKCGLDGLDGMDHNDHNDHODIPDIPDIQDJQDJRDJSEKSEKTE\ KUELUELVELVEMWEMXEMXENYENZFNZFO_FO_FO`FPaFPaFPbFQc\ FQcFQdFQdGRcGSbHTaHTaIU`IV_JW_JWZKXYKYXLZXLZWM_VM`\ VNaUNaTNbTOcSOdRPdQPeQQfPRgOSgOThNUiMVjMWjLXkKYlJZ\ mJ_mI`nHaoHbpGcpFdqFerEfsDgsChtCiuBjvAkvAlw9mxCnxF\ owKpvPqwUrwUswUtxUuxUvxUwxUzyUzyUzyUzyUzzUzzXzz_zz\ bzzezzhzzkzznzzqzztzzwzzz } frm:ObliqueManPlus {;Jim Muth z=p1+pixel, c=p2+(p3*pixel): z=sqr(z)+c, |z| <=100 } END PARAMETER FILE=========================================

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FOTD 04-06-09 (Seahorse Valley-04 [No Rating])
by Jim Muth 03 Jun '09

03 Jun '09

FOTD -- June 04, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image, the fourth in the Seahorse Valley series, is a repeat of the thing I did in yesterday's image. But in today's image it is taken to the extreme. The Julia set of the valley is obvious. It fills the entire frame. But there is something quite unusual in the image. That brilliant diagonal line across the central bay is the Mandelbrot aspect of Seahorse Valley magnified a thousand or so times. In today's image it looks like a featureless line, but all the detail of the deepest parts of the valley is in there. Tomorrow's image, which is incredibly slow and already cooking, will show a surprising bit of this detail. The image is a fireball fast one, though it is still always fun to surf out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoy the finished product there. FL has a way of asking questions that activate my philosophical tendencies. On Wednesday she casually asked if science believes in ghosts. I replied that science is not an intelligent being. It is a rational way of gaining knowledge and determining truth. It doesn't believe or disbelieve. Its philosophical standpoint is materialistic and therefore it tries to explain things on a material basis. I explained that most scientists consider ghosts to be natural phenomena or psychological images in the physical brain. This assumption reduces ghosts to the material level. Science does not consider ghosts to be surviving spirits of the dead because it has no way of objectively studying spirits. But this does not imply that science denies the existence of human spirits. Perhaps spirits are fractals, things that also have no physical existence! Rain fell steadily most all day here at Fractal Central on Wednesday, while the temperature fizzled out at 59F 15C. The fractal cats took a quick glance at the outside conditions and settled down for another two-hour nap. My day was not too busy, but rather frustrating. The next FOTD will be posted in 24 hours. Until then, take care, and if you see a ghost, your brain did it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-04 { ; time=0:00:20.32-SF5 on P4-2000 reset=2004 type=formula formulafile=jim.frm formulaname=ObliqueManPlus passes=t center-mag=0/0/0.8503401 params=0/0/-0.75/0/0.0075\ /0.0075 float=y maxiter=50000 inside=0 logmap=yes symmetry=origin periodicity=10 colors=00040C_0Ac0Ff0Ki0Pl0Uo0Yp0Zq0_r0`s1at2bu3cv\ 4dv5eu6cu7at8_t9YtAWsBUsCSsDQqEVoF_hGKmO4mR6mT7mW9\ mYAm_BmbDmdEmfFmgHmgJmgLmiMmkNmmNmnSmoWmp_mpcmqgmr\ kCso6ssFqlNpfVn_bmUjlObjJVhENf9Fe5M_HSVSZQbdLmbXe`\ hYXGqbbVhy8Zn7Qd7GV77L78IE9GLAESACZBAeC8lC6rSGPWOM\ _VJbaHfiEjpBmw9ksHioPglXbh_YdaT`dOXfJTiEPk9Ln4HpGS\ lSaiclenvbprdqofslhtijuflwcnx`pyYqkN0nmQjnUfoYbpaZ\ peVqiRrmNrpXoreltnivlljko_jrOiuDftGdtIbsL_sNYrQWrS\ SiIO`9LT0RaJXi`bqreojgmcjlXljQzzJzzPzzVzz_zzYzzWzz\ _zzczzgzzkzzozzrzzVzzbzzjzzrzzyzzhzzSzzgzzgzzhzzhz\ zizzizzizzjzzjzzkzzkzzlzzlzzmzzmzznzznzzozzozzozzp\ zzpzzqzzqzzrzzrzzszzszztzztzzbzzczzczzczzdzzdzzdzz\ ezzezzezzezzfzzfzzfzzgzzgzzgzzhzzhzzhzzhzzizzizziz\ zjzzjzzjzzkzzkzzkzzkzzlzzlzzlzzmzzmzzmzznzznzznzzn\ zzozzozzozzpzzpzzpzzqzzqzzqzzqzzrzzrzzrzzszzszzszz\ tzztzztzzDzzEzzFzzFzzGzzG } frm:ObliqueManPlus {;Jim Muth z=p1+pixel, c=p2+(p3*pixel): z=sqr(z)+c, |z| <=100 } END PARAMETER FILE=========================================

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FOTD 03-06-09 (Seahorse Valley-03 [No Rating])
by Jim Muth 02 Jun '09

02 Jun '09

FOTD -- June 03, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image shows another surprising aspect of the four- dimensional Seahorse Valley complex. The outer drab blue area outlines a distorted version of the Seahorse Valley Julia set with a C-value of -0.75, while the brilliant reddish yellow elements inside the Julia outline are a grossly enlarged view of the Mandelbrot aspect of the valley. The enlargement of the Mandelbrot part of the image is due to its hypercylindrical four-dimensional shape and the angle at which it is sliced. In 4-D space, if the angle is right, a hypercylindrical 4-D object may be sliced by a plane so that all directions of the projection onto the plane are enlarged equally up to infinity. Some careful measuring and a bit of trigonome- try, (which I am not about to do), would reveal the angle of today's slice. I named the image "Seahorse Valley-03", which describes it quite well. Since the scene has little artistic value, I gave it no rating, though I consider it worth about a 6-1/2. The calculation time of 15 seconds will pass in a fractal flash. Another way to see the image is to flash out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there with zero effort exerted. Morning clouds and a few drops of rain gave way to plenty of sunshine and mild afternoon temperatures in the mid 70'sF, or around 24C. The fractal cats here at Fractal Central enjoyed the pleasant conditions, even catching a little afternoon sun. My day was rather busy. The next FOTD will be posted in 24 hours. Until then, take care, and regardless of whether it's scientific or unscientific, it still might or might not be true. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-03 { ; time=0:00:15.75-SF5 on P4-2000 reset=2004 type=formula formulafile=jim.frm formulaname=ObliqueMand passes=t center-mag=0/0/.86 params=0/0/-0.752/0/0/0.05 float=y maxiter=16000 inside=0 logmap=yes symmetry=yaxis periodicity=10 colors=000AGUAKUALUAMUANUAOUAPUAPUAQUARUARUASUATUA\ TUAUUAVUAVUAWUAXUAXUAYUAYUAZUAZUA_UA_UA_UA_UA`UA`U\ A`UcaUcaNcaQcaTcbWcbZcbXcbVcbTcbRccPccNccLccJccHcc\ FmcDmcBmc9mc7mc6mdKraNv_PzYRzWUzUWzSYzQ`zObzMdzKgz\ IizGkzLezQ_zUUzZOzcIzgCzl6zp0zn1zl2zj3zh4zf5zd6zb7\ z`7zZ8zX9zVAzTBzRCzPDzNEzLEzMLzMIzNFzNCzO9zO6zO4zQ\ 6zR7zS8zT9zUAzVBzWCzhSzXEzYFzZGz_Hz`IzaJzbKzcMzdNz\ eOzfPzgQzhRz44zD9zLEzUJzaOzP9zWGzbMzwQzsRzpRzlSzce\ zdczebze`zf_zfZzgXzhWzhUziTzsCzqFzpHznJzmMzkOzjQzH\ 6zREz`LzLSzPSzSSzVSzYSz`SzcSzfSzWozZjzaezd`zgWzjaz\ i`zi`zi_zi_ziZziZziZziYziYziXziXziXziWziWziVziVziU\ ziUziUziTziTziSziSz7jzAhzDgzGezJdzMbzPazS_zVZzYXz`\ WzcUzfTzryzopzmhzk_zubztazs`zs`zr_zq_zqZzpYzoYzoXz\ nXznWzmWzlVzlUzkUzjTzjTziSzanzdfzgZz_yzaszcmzdhzfb\ zhXzb0zc2zc3zc4zd6zd7zd8ze9zeBzeCzfDzfEzfGzgHzgIzg\ KzhLzhMzhNz6_z8WzATzCPzEL } frm:ObliqueMand {; Jim Muth z=sqr(p1)+pixel, c=p2+(pixel*p3): z=sqr(z)+c |z| <= 100 } END PARAMETER FILE=========================================

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FOTD 02-06-09 (Seahorse Valley-02 [4])
by Jim Muth 01 Jun '09

01 Jun '09

FOTD -- June 02, 2009 (Rating 4) Fractal visionaries and enthusiasts: Today's image is a quickie, fast and simple enough to get the FOTD back on its regular schedule. The image is a view of Seahorse Valley (believe it or not) sliced in an orientation 15 degrees from the Oblate direction toward the Rectangular direction. The narrow line across the center of the fractal is actually the space between the two branches of the valley as seen from the west side. We are in the large period-2 bud, looking east toward the valley wall that separates us from the main bay of the Mandelbrot set, which from this angle lies a short distance behind the screen. Bits and pieces of seahorse tails are scattered about the scene, though most of them must be stretched quite a bit before they become recognizable. But search as we may, we would never find a Mandelbrot minibrot. They do not exist at this angle. The name of the image is only a catalog number. The lowly rating of a 4 is all I could give an image that is basically a space filler. After yesterday's marathon calculation time, today's 7-second time is a blessed relief. And as always, the image is posted for instant satisfaction on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A mix of sun and clouds, and a slightly chilly temperature of 73F 23C made Monday acceptable for the fractal cats here at Fractal Central. They had a bit of excitement when one of the local stray cats found and made short work of a baby robin that had just fallen out of its nest. Luckily, FL missed the sad event. The next view of Seahorse Valley will be posted in 24 hours. Until then, take care, and if I were the Big Guy up there, I would never have designed a world where living creatures need to kill and eat other living creatures, and then said to man, "thou shalt not kill." Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-02 { ; time=0:00:07.43-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 center-mag=-0.121105/0/\ 1/1/90/0 params=15/90/0/90/-0.75/0/0/0/2/0 float=y maxiter=15000 inside=0 logmap=yes periodicity=10 colors=000NEOLEQKERJDSIDTHDVHCWHDXHEYHFZFKYKOYPQYU\ TYZWYcYXh`XmcXreXvhXzjXufTmcPc_MUXIJTLMQPKVUIZZHbc\ FfhUimcmrmqvuuzxxzzzzwxzpuziqzcnvYkrUhmUehXcc_aZb_\ YeYXgXWVWkIVzHWvGWrFWnFWjEXfDXbDX_CXWBYSBYOAYK9YG9\ YD7a76e17d68dA9dEAcIBcMBcQCbVDbZEbbFafGajGanEcjDdg\ CedAfa9gZ8iW6jT5kQ4lN3mKQaOkRSiTVgUXfVZdWacYcaZe`_\ hZ`jYal3mn9nmEolJpkPqjUriZshctgiufnveswdxxdwiMwV4x\ S8xQBxOExMHxKLxIOyFRyDUyBYy9`y7cy5fLx7Rs9WnAaiBfdD\ l_EqWFG_jL`iPaiTbhYbhachedgjdgnefrffvffuc_t`TsZNrW\ GqT9qR3iMDaINUDXM9fE5oG9pHDqJHrKLrLOsNStOWtP_uRcvS\ fwTjwVnxWryXuyQcmJNbC6SDFYEOcFXiGeoGntKhiOcZScOWcD\ Zc3Wc6Tc8QcBNcDKcGIcIFcLCcN9cQ6cS4cU0z00y00y00y00y\ 00y00x00x00x00x00x00w00w00w00w00zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0zz0zz0zz0zz0zz0zz } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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