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Stereo Synthesizer
by Jay Litwyn 07 Feb '11

07 Feb '11

Okay, about five or more years ago, I started composing with a synthesizer that turned out to be well-designed for what music theorists call just intonation (I called it "linear tuning" when I did not know any better), and recently, I asked myself, well...why don't I use one of FRACTINT's data ouputs, say the one designed for ACROSPIN and do the quantization for FRACTINT, too. Then I can get clean stereo wav files. The trouble is I do not really understand FRACTINT's quantization step. I could ignore it and come up with my own, perhaps. For instance, I've noticed that most serial tunes do not span more than two octaves, so I should probably consider the maximum of X and the minimum of X, then put negatives into the lower octave; same for Y on the right channel. I also hav a just intonation worked out that is twelve tones per octave, and curiously, the second octave is an inversion of the first octave (I will explain that in news:rec.music.theory.), except on one note. It seems just crazy enough to fool a lot of people, except for timing: Unless the preceeding note is the same as the current note, it will be all quarter notes. In simple terms, I will map all of the Xs to a number between 360 and 1440Hz in such a way that there are only twenty-four tones. For example, 675, 720, and 768 are in the middle of those two octaves, so any value from fractint, scaled and biased, that is equal to or greater than the mean of 720 and 675 will map to 720, while anything that is less than the mean of 720 and 768 will also map to 720. The remaining part of the trick is coming up with an appropriate image size for the length of tune and tempo I want. If I publish, here, then I will make the program print out a fractint parameter file. If it's any good, then maybe Mister Osuch will make up a neat interface for doing similar things with a plain old sine wave synthesizer that is built into fractint. Look ma...all dijital...no MIDI recording. If I do a good job, then my dynamics will be flat; amplitude inversely proportional to pitch.

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FOTD 06-02-11 (Extemporaneously-1 [7])
by Jim Muth 06 Feb '11

06 Feb '11

FOTD -- February 06, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a slightly deep scene in the East Valley of a minor minibrot lying in one of the side star-arms of a small period-16 bud on the northwest shore line of the main bay of the Mandelbrot set. Words fail to describe the fractal, which can be truly enjoyed only by the sense of vision. The colors were intensified in a sepatate color manipulation program. Then the intensified colors were recorded in the included parameter file. It works just fine. The result rated a 7. If I had been in a more pleasant mood, I might have rated the image an 8. The name "Extemporaneously-1" is a spur-of-the-moment thing, with no deep hidden meaning. Unfortunately, the image lies deep enough to make arbitrary- precision math necessary, which increases the calculation time to a rather dragging 17-plus minutes. A much speedier way to view the image is to enjoy it in finished form on the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original classic FOTD web site is at: <http://www.Nahee.com/FOTD/> Sleet and freezing rain with a temperature of 30F -1C made Satur- day a most unpleasant day here at Fractal Central. The fractal cats lost no time taking to their shelf by the heat and spending most of the day there, stretched out in total cat comfort. My day was occupied with trying to keep the fractal pavements free of ice -- a losing effort. I'll tackle the job again when the precipitation ends. FL kept the coffee hot. The next FOTD will likely be posted in 24 hours. Until then, take care, and those who are really running things, please stand up. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Extemporaneously-1 { ; time=0:17:41.65-SF5 on P4-2000 reset=2004 type=mandel float=y center-mag=-0.66179\ 18962338239283/0.3761897972111759289/8e+013/1/-102\ /0 params=0/0 maxiter=15000 inside=0 logmap=-1196 colors=000K0wK0wK0wK0wJ0wI0wH0vH0tH0qD0h90W62I24D0\ 648z00zM0Ub69sF0zO0zzv0zz2zz6zzzzzzzzzzvzzgzzXzzKz\ zOzz9nz0Mz00z00z00z00v00r40mD0hS0zl9zxOzzcdtOUUBF9\ 0000000000200H60YM0nb2Fk0Oi0Ug0be0ie0sb0z`0zK0zbBz\ ezzg`ziBzn0zk0zk0zk0zk0zi0zi0zi0zg0zi0zkOzkqxsYvxH\ sz4qz0zz0nz0Mz00z0D`H0QD0H908M0980900900900900H00Q\ 20YQ0en0Se0FY26SB0KM0DU08zvDzs6ss0gq0Yq0Oq0Dn04n00\ n60n04e0BX0HO0QH4X9De2O`0Qk0YvDgzUqznzzzzzzXnv2gz0\ Xq0M`0BM06F02920i80zD0z00z00n09e06i02k00q00sD0xS0z\ g0zg0zxMzzBnz9Bz2Kz0Sz0`q0ie0sUz0zz0zz0gz4MxF4xS0z\ x0xe0xO0x80z00x00v02s48q9FnFMkMUiS`gbOgnDgz4gz0bz0\ `v4Yn9XgDS`KQUOOOUMHYDSO8bF0n60z0XzS0z04z4HzFezbXz\ SOzKFz90z08z29zBBzKDzUDzb6z`0zY0zX0zU0zS0zQ0zH0zQ0\ zY0ze0zn0zx0zz0zz0z00zz0zz0zz6zvHzqXzkizgzznxzebzY\ MzS4zM0zFSz00z9`zbYzKUz9Yz4`z0bz0gz0iz0qz0kz0iz0gz\ 2ez9bzK`zUYze0zYXznzzXzzz } END PARAMETER FILE=========================================

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Online Gallery Show - - "Mathematically"
by AA 05 Feb '11

05 Feb '11

All these images were created with Fractint: http://fusegallerynyc.com/Line/11alexander/alexander.html Some images date as far back as the early 90's. All were recently redone in disk-video mode, 4,320 pixels high, promoted (in Corel PaintShopPro) to 24-bit color, then reduced to 480 pixels high and saved as .jpgs. No other photoshopping was done to these images.

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Re: [Fractint] under the weather
by JackOfTradeZ＠comcast.net 05 Feb '11

05 Feb '11

. """Get well soon! May the concentrated fractal nature of your body confuse the germs!""" We all wish well for JM and PNL; but remember, microorganisms (like all life and consciousness) are fractal in nature too! So what do you get when two fractals try to "out-fractal" each other?? This storm is gonna be extreme. In Denver we only are getting the tail end of it but it is already way sub-zero with wind, snow and ice. How can people deny Global Cooling? <G> .

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FOTD 05-02-11 (On What Y-Axis [5])
by Jim Muth 05 Feb '11

05 Feb '11

FOTD -- February 05, 2011 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a dip into one of the axes of the Mandelbrot set. We've had a lot of these axis-dips lately, but as far as I know, almost all of these dips have been into the X-axis. The reason is that the X-axis is a well-defined line of symmetry, while the Y-axis, the axis of today's dip, is a vague thing, with nothing to point it out amid its chaotic surroundings. The minibrots along the X-axis have an orderly arrangement that makes them quite interesting and artistically rewarding. Mini- brots along the Y-axis do not exist. The Y-axis does pass through some (an infinity) of minibrots, but it does so by acci- dent, and the minibrots can lie in any orientation. Today's minibrot lies not exactly on the Y-axis, merely very close to it, which explains the name "On What Y-Axis?" I could have found a minibrot that is actually intersected by the Y-axis, but I ran out of patience when, what I hope was one final fit of coughing erupted and put me in a cranky mood. If I had found a minibrot that actually intersected the Y-axis however, it would have looked almost like today's. The rating of a 5 is an admission that I could have done better. The calculation time of exactly 6 seconds will pass like an evening in June (in the Northern Hemisphere). The trip to the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> will take a somewhat longer time, but it will totally eliminate the small task of running the included parameter file. Meanwhile, keep in mind the original FOTD web site at: <http://www.Nahee.com/FOTD/> I'm not sure what will eventually become of the original site, but it still holds all the images and discussions prior to November 2010. The cloudy sky in the south gave stark contrast to the clear blue sky in the north here at Fractal Central on Friday, with the dividing line directly overhead. The temperature rose from a daybreak low of 9F -13C to an afternoon high of 30F -1C. Un- fortunately, the clouds in the south blocked most of the sun, driving the fractal cats to their shelf by the heat. They leaped down only to help finish the latest bowl of chicken soup. The forecast is for more snow and ice on Saturday. The rest of the day was spent getting the routine work caught up and pondering a philosophical question raised by FL -- what is wrong with people in the world? The next FOTD will be posted in 24 hours. Until then, take care, and look alive even if you're not. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= On_What_Y-Axis? { ; time=0:00:06.00-SF5 on P4-2000 reset=2004 type=mandel center-mag=+0.0000000009492\ 813/+0.6374553763585818/2.9e+010/1/157.5/0 float=y params=0/0 maxiter=32000 inside=0 logmap=-1400 colors=000zzzNNwC4IC6KC9MCBOCDQCGSDIUDLWDNYDPcDScD\ UmDXmEKzEMzEPzERwEUsKWqUUxebsponzrizzfzuezqdzmdzhc\ zdbK`bHWaFS`DO`BJ_9FZ4CW7BZ9B`BAbDAdG9fI9hK9kM8mP8\ oR7qT7sW3xV7uUAsTDqSGoRJmRNkQQiPTgOWeNZcMaaMe_LhYK\ kWJnUIqSItQLqRNnRPkRRiRTfSVcSXaSZZS`WScUTeRTgOTzzT\ zzTzzUzzUzzUzzUzzTzzUzzUzzVzzVzzWzzWzzWzzXzzXzzYzz\ YzzZzzZzzZzz_zz_zz`zz`zz`zz_zz_zz_zzZzzZzzZIzZIzYI\ zYIzYIzXIzXIzXIzXHzXGzXGzXFzXFzXEzXDzXDzXCzXCzXLzS\ TzN`zIhzEazAVz5Oz1Pz3Qz4Qz6Rz7Sz8SzATzBTzDUzEVzFVz\ HWzIWzJ`zOdzThzYmzbqzguzlvzetzWqzMozCmz2gz2bz2Yz2T\ z2Vz5Xz7Zz9`zCbzEdzGfzJhzLjzNlzPjzOhzOfzNdzNbzMazM\ bzQczUdzXez`fzcbze_zfXzgUzhRzjOzkLzlIzmFznCzp9zq6z\ r3zs0zt4zq8znBzlFziJzfMzdJzbHzaFz_CzZAzX8zW6zV7zU8\ zSAzRBzQCzODzNFzMGzKHzJJzIKzGLzFMzELzJKzNJzRJzVIzZ\ HzbHzfJzgLzgNzgOzgQzgSzgUzgVzgXzgZzg`zgazgczgezggz\ ghzgezibzk_zmYzoVzqSzsPzu } END PARAMETER FILE=========================================

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FOTD 04-02-11 (Wine From a Stone [8])
by Jim Muth 04 Feb '11

04 Feb '11

FOTD -- February 04, 2011 (Rating 8) Fractal visionaries and enthusiasts: Once again up and half about, I find it's time for the next FOTD. Today's image lies in the fantastically complex fractal that results when the formula Z^1.25+C is iterated 2.62 turns up the complex logarithmic hyperspiral. The name "Wine From a Stone" shows my surprise when I found such an attractive scene in such an unlikely parent fractal. The rating of an 8 might be a bit overblown, but after 2 fractal- less days, I was extra well pleased to find such an image so quickly. The calculation time of under 2 minutes is well within reason. An alternative way to view the image is to go to the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image is posted. and always remember the original FOTD web site: <http://www.Nahee.com/FOTD/> The 'storm of the century' dropped 3 inches (15cm) of snow, 2 inches (10cm) of sleet, and left trees coated with 1/2cm of ice as it passed just north of Fractal Central on Wednesday. The fractal cats displayed a notable lack of interest. Thursday brought brilliant cloudless skies but also a cold temperature around 23F -5C. My day Thursday was spent trying to get caught up in the work. I also noticed that the fractal driveway has frozen into 3 inches of solid ice. I spread salt on it and hoped for the best. The next FOTD is due in 24 hours. Until then, take care, and see you soon. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Wine_From_a_Stone { ; time=0:01:51.22-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=+0.7245512449658761/+0.2062643712917921/\ 1618732/1/-57.5/0 params=1.25/0/2.62/0 float=y maxiter=7500 inside=0 outside=tdis periodicity=6 colors=000sJkyHknNmcSoTYqJbsEUhALY6CN23D9AIFHMLNQP\ ULS`HWgCZn8au4`uC`uJ_uR_uYZueZulPgcGVV7IMBDUE9`I4h\ L0oN5fPAZQFRSKJUPBVU3TYAR`HQcOOgUNj`LmgKpmOngRmaVl\ XYkRajMdiGghBecDdZEbUGaPH`LIaOOaRTaUYaXba_gabladqX\ ZnSUlNPjIKgDFe8Ac45aEEbOMbYVcgbcqjcwtwviuvZsvOqvDo\ v3nnFpgRq`bsUntNzuMwvMuwMrxLpxLmyLkzLizIjqGkiDlaBl\ T8mL6nD4n5EeEOYNYPVgHcq9kjDjcHjXLiQPiJSiPUeUWb_YZd\ _WjaTocPueMzgJlgaia_gWZeQYbLX`FWZ9VX4UaF`eQgi`nmkt\ 8NeISVSXKPYGNYDLZAIZ6G_3E_07YA0XJAaNJeQSjU`nXis`rw\ clr`gmYbhVYcSTZPOVMXaFdh9ln3jdEiWPgSSfOUdKWcHYaD_`\ 9aZ5cY2eV9cSGbPNaMU`J`_GgZDnYAtXImVPfUX_ScTRKMPKGO\ KJQKMRKPSKSTKVUIPO2RP3PS3NV4JQ4FN5BJ57I63H60G95HC9\ HFFIIHJIJLILMINNTZ7O_8KW8GS8CO98K94H96I87I79J7AJ6C\ J5DK5FK4GM4IQ6KY8McAOiCQpESuGUzIQvGMpFImDEiCBfBJ_H\ RUMZOSfIXPVuMXpJYlGZgD_cA`Z7aV4bQ2cMAXRIQVQK_YDcd7\ g`RlXipLvTMrRUVk_SkfPklMk } 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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No FOTD for Feb 3
by Jim Muth 03 Feb '11

03 Feb '11

Fractal fans: I'm still alive, though not exactly well. I'll try to post a FOTD for Feb 4, but the work is falling so far behind that I can make no promises. Meanwhile, the fractal cats love to share the chicken soup. P.S. -- the big storm of the century was a bust here at FC. JIM

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use this link to access Google Julia Plotting
by Hal Lane 02 Feb '11

02 Feb '11

David's Google Julia Plotting link: http://juliamap.google.com failed to load a page for me: > Author: david > Date: 2011-02-01 18:54 -500 > To: Fractint and General Fractals Discussion > Subject: [Fractint] Google's JuliaMap app > > Browse around the Mandelbrot set using just Javascript and and > HTML5-capable browser (works in Chrome, FF 3.6 and probably other modern > browsers): > http://juliamap.google.com However, I found I could use these links to access Google's page: http://juliamap.googlelabs.com and: http://googleresearch.blogspot.com/2011/01/julia-meets-html-5.html or: http://tinyurl.com/Googles-Julia-Plotting The page did OK at calculating the images -- until I goofed and opened it in a couple of tabs... Then it brought my XP system to a standstill. There's a very limited choice of the fractals you can generate in your HTML5-capable browser (with Javascript enabled). But, if a dog plays chess -- but very poorly -- it's still a dog playing chess... My Chrome browser window was updated in blocks as it calculated. I wonder if the code assigns the blocks to different cores on multi-core systems? It kind of looks like the final pass of their Fractint-like triple pass calculation might have some anti-aliasing in it. >>---> Anyone care to comment on my conjectures? <---<< - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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Google's JuliaMap app
by david 01 Feb '11

01 Feb '11

Browse around the Mandelbrot set using just Javascript and and HTML5-capable browser (works in Chrome, FF 3.6 and probably other modern browsers): http://juliamap.google.com You can change the formula and select from a number of palettes. -- David gnome(a)hawaii.rr.com authenticity, honesty, community

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Since Jim is under the weather...
by Hal Lane 01 Feb '11

01 Feb '11

Since Jim is "under the weather," and there is no Fractal of the Day, I put some further zooms into Mike Frazier's 10^129 zoom into the Jan 25th FOTD that I did - each with increasing magnification -- onto the FOTD web site: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html which has been reformulated from a single oversized page to one page per month. The original FOTD web site remains at: http://www.Nahee.com/FOTD/ - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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No FOTD for Feb 01
by Jim Muth 01 Feb '11

01 Feb '11

Fractal fans: There will be no FOTD for Feb 1 because The fractal artist is under the weather. FL is doing her part with the steaming chicken soup. (She sure makes better chicken soup than I do.) The weather is also turning bad here at FC, with heavy snow and ice due on Tuesday and Wednesday. The fractal cats got their share of the chicken soup. The next FOTD will be posted as soon as I'm up and about. Jim Muth

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Re: [Fractint] FOTD 31-01-11 (For Those Cut Off [7])
by Jim Muth 31 Jan '11

31 Jan '11

At 07:37 PM 1/30/2011 -0500, you wrote: > >FOTD -- January 31, 2011 (Rating 7) > >Fractal visionaries and enthusiasts: > >In today's image the bailout radius of the parent Mandelbrot set >has been reduced to two. This cuts off even more of the set, >but does strange things to the elements close to the cut-off >line. In today's image I zoomed into the point where the west >branch of the filament that extends from the large north bud >disappears behind the cut-off line. > >To add to the interest, I rendered the image with the outside >set to 'tdis', which does add some interest, though not enough >to raise the rating above a 7. > >The name "For Those Cut Off" has something to do with the near- >ness of the image to the bailout radius. I forget exactly what >I had in mind. > >The calculation time of just under 9 minutes is surprisingly >fast for arbitrary precision math. > >And calculation may be bypassed entirely by viewing the finished >image on the active FOTD web site at: > ><http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> > >The original FOTD web site may be accessed at: > ><http://www.Nahee.com/FOTD/> > >but it is not up to date. > >Sunday turned into quite a pleasant day here at Fractal Central, >with partly cloudy skies and a temperature of 37F +3C. There >was not quite enough sun to lure the fractal cats to their >window shelf. They found total comfort on their shelf over the >heat. My day was reasonably pleasant, but I think I'm feeling >the first signs of whatever laid FL low. It might be her turn >to keep the chicken soup coming. The next FOTD will be posted >in 24 hours. Until then, take care, and if c plus c equals c, >then 1 plus 1 equals 1. (Just kidding. I know my relativity.) > > >Jim Muth >jamth(a)mindspring.com > > >START PARAMETER FILE======================================= > >For_Those_Cut_Off { ; time=0:08:53.64-SF5 on P4-2000 > reset=2004 type=mandel passes=1 center-mag=-0.1711\ > 33664958944136896783/1.04584546042623033322051/\ > 1.057108e+019/1/-117.5/0 params=0/0 float=y > maxiter=2500 bailout=2 inside=0 outside=tdis > colors=000kmagiYbeTQDGTKJVQLXWNqpWmmUjkTghSdfRacQp\ > 9XUUZVWXWXVXYUY_SZ`Q8xACtDGqFKnHOjJSgLWdN2XK8YLDZM\ > J_NO`OUaPx`wqankaedaXr8w__xZ`sZ`oZ`jZ`fZaaZaYZaTEG\ > MPROgu1er4dp7cmAbkDahG`fJ_cMrz5h3lADbK00RUTA0KKALK\ > GMAMNKKOA9LAFMlLNgRObXPCR`FTZIUYLWWOXVRYTU_SX`QkFE\ > iJGgMIePJcTLaWM_ZOzbCzOFnRHjUJfXLb_N000965DB8UUUcc\ > cmomljeWYNBC5FG8IKBzxzPRHTVKWZNqBFgPKzzdtt`ndwiXVc\ > gwlxwgkwbrwG__DHXIMV55KRUSVYQXGGYKIYOiYRLZVMZZOkTV\ > iVUgWveXScZRa_Q_`PG1rNEhTQZKWeNXbPY_SZXU_UX`Rp1zjE\ > mdQ`gfbiaZkWVmRRoLNYGJsBFiFQmCPp9Oz7NoDOlIOhNOWWUe\ > SPaXPPMBRPDSRFUTHVWJXYLY_NX1ZY6XYBWYFVYKUZPSZTRZYQ\ > EDuPQdTt0Vo7WjDYeJ4MBCQFKUISYMOAjQEgRHdTLaUO_VSXXV\ > UYZRGnOuC6iPG6zfBvcFr`JoZNkWRhUVdR0szIjgKzTNvSPrRR\ > oRzzAVhQXdP6PdCS`IVYOXVU_SmpUilSehRadQmz4jv7hrAfoD\ > dkGbhJ`dMDr_JmXOiUUeRA26JEDRQJ9I4FM9KQDPUHUYLo76lB\ > 9zFBhJEfNGdRIbVL`ZNuukpqf } > >END PARAMETER FILE========================================= > > > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > >

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<Mike Frazier> Any other fractal programs use multiple cores?
by Hal Lane 31 Jan '11

31 Jan '11

> > That's an awesome image at e+129; the PAR info says > > it only took 8 minutes?!?! > > The time is correct for one non anti-aliased frame > at e+129 on my fastest 8 core computer. Mike, Congratulations on solving the big bottleneck in calculating fractals -- not enough CPU power! Your getting 8 CPU cores attacking the fractal simultaneously is really great -- and on a Mac, too! Anyone know of any other fractal programs that use multiple CPU cores? - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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Re: [Fractint] Mike Frazier Question
by JackOfTradeZ＠comcast.net 31 Jan '11

31 Jan '11

. ""I looked at the Universe#3 one at: http://www.youtube.com/watch?v=_vnLG45dVPs That was awesome. A complete zoom on the negative x spike with over 5000 frames. There were several really nice fractals along the way. How long did it take you to do it? What was the final magnification? "" That was actually an earlier effort, not so good as you see "jerk" frames; that was before I learned to tweak the "bfdigits" parameter in fractint. That isnt my page BTW - someone "borrowed" it and posted - no problem as they give proper credit. Better versions are on the UFVP website or my page: youtube.com/fractalkemist That one goes to E+89, Universe-6Z goes to E+112. It took over 2 years on 4 systems. Interesting progression of concentric circles, getting ever more complex. The "kidney" and "Alien Eggs" are seen, and the Period Doubling effect is well illustrated. I think a zoom into Muth's fractal would look pretty much the same, so I decided not to do it. However, the E+129 Par you posted took me 2 hours and change, the E+140 about 6 hours. .

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Re: [Fractint] FOTD 25-01-11 (Hidden Minibrot [9])
by JackOfTradeZ＠comcast.net 31 Jan '11

31 Jan '11

. Hey Mike - if you want to see what a deep zoom into that type of fractal looks like checkout the UFVP web site or my YouTube page. Look for "Universe-3" and Universe-6" animations. .

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FOTD 31-01-11 (For Those Cut Off [7])
by Jim Muth 31 Jan '11

31 Jan '11

FOTD -- January 31, 2011 (Rating 7) Fractal visionaries and enthusiasts: In today's image the bailout radius of the parent Mandelbrot set has been reduced to two. This cuts off even more of the set, but does strange things to the elements close to the cut-off line. In today's image I zoomed into the point where the west branch of the filament that extends from the large north bud disappears behind the cut-off line. To add to the interest, I rendered the image with the outside set to 'tdis', which does add some interest, though not enough to raise the rating above a 7. The name "For Those Cut Off" has something to do with the near- ness of the image to the bailout radius. I forget exactly what I had in mind. The calculation time of just under 9 minutes is surprisingly fast for arbitrary precision math. And calculation may be bypassed entirely by viewing the finished image on the active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> but it is not up to date. Sunday turned into quite a pleasant day here at Fractal Central, with partly cloudy skies and a temperature of 37F +3C. There was not quite enough sun to lure the fractal cats to their window shelf. They found total comfort on their shelf over the heat. My day was reasonably pleasant, but I think I'm feeling the first signs of whatever laid FL low. It might be her turn to keep the chicken soup coming. The next FOTD will be posted in 24 hours. Until then, take care, and if c plus c equals c, then 1 plus 1 equals 1. (Just kidding. I know my relativity.) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= For_Those_Cut_Off { ; time=0:08:53.64-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.1711\ 33664958944136896783/1.04584546042623033322051/\ 1.057108e+019/1/-117.5/0 params=0/0 float=y maxiter=2500 bailout=2 inside=0 outside=tdis colors=000kmagiYbeTQDGTKJVQLXWNqpWmmUjkTghSdfRacQp\ 9XUUZVWXWXVXYUY_SZ`Q8xACtDGqFKnHOjJSgLWdN2XK8YLDZM\ J_NO`OUaPx`wqankaedaXr8w__xZ`sZ`oZ`jZ`fZaaZaYZaTEG\ MPROgu1er4dp7cmAbkDahG`fJ_cMrz5h3lADbK00RUTA0KKALK\ GMAMNKKOA9LAFMlLNgRObXPCR`FTZIUYLWWOXVRYTU_SX`QkFE\ iJGgMIePJcTLaWM_ZOzbCzOFnRHjUJfXLb_N000965DB8UUUcc\ cmomljeWYNBC5FG8IKBzxzPRHTVKWZNqBFgPKzzdtt`ndwiXVc\ gwlxwgkwbrwG__DHXIMV55KRUSVYQXGGYKIYOiYRLZVMZZOkTV\ iVUgWveXScZRa_Q_`PG1rNEhTQZKWeNXbPY_SZXU_UX`Rp1zjE\ mdQ`gfbiaZkWVmRRoLNYGJsBFiFQmCPp9Oz7NoDOlIOhNOWWUe\ SPaXPPMBRPDSRFUTHVWJXYLY_NX1ZY6XYBWYFVYKUZPSZTRZYQ\ EDuPQdTt0Vo7WjDYeJ4MBCQFKUISYMOAjQEgRHdTLaUO_VSXXV\ UYZRGnOuC6iPG6zfBvcFr`JoZNkWRhUVdR0szIjgKzTNvSPrRR\ oRzzAVhQXdP6PdCS`IVYOXVU_SmpUilSehRadQmz4jv7hrAfoD\ dkGbhJ`dMDr_JmXOiUUeRA26JEDRQJ9I4FM9KQDPUHUYLo76lB\ 9zFBhJEfNGdRIbVL`ZNuukpqf } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 25-01-11 (Hidden Minibrot [9])
by JackOfTradeZ＠comcast.net 31 Jan '11

31 Jan '11

. Thats an awesome image at e+129; the PAR info says it only took 8 minutes ?!?! Is FRACTON better than FractInt or is the current MAC platform better than WinDoZe/DOS ? I was thinking of doing a zoom animation also, it is an interesting fractal. But I would expect many months to do it based on previous experience. .

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FOTD 30-01-11 (Star of Ambiguity [6.5])
by Jim Muth 30 Jan '11

30 Jan '11

FOTD -- January 30, 2011 (Rating 6.5) Fractal visionaries and enthusiasts: Yesterday's scene was located in a side filament of the north- eastern period-10 bud on the main bay of the Mandelbrot set. Today's image is a close up of the 'star' on the main filament extending from that same bud. The color palette is a virtual repeat of yesterday's, with only a few minor changes. Once again, I rendered the scene with the outside set to 'tdis'. At this low magnitude the slow-down is still apparent, but with a calculation time of a mere 40 seconds, the delay is no problem. The rating of a 6-1/2 indicates that the image is worth at least a brief look, especially with a calculation time of 40 seconds. The name "Star of Ambiguity" implies that no one knows exactly what lies at the center of the 'star' in the image. Actually, the star has no limit, so all attempts to find what lies at its center are certain to be futile. The center always lies just beyond the limit of definition. With all the new-fangled programs inserting strange characters into text files, running parameter files from the internet can sometimes be tricky. The simplest way to avoid the problems caused by strange characters is to view the image already calcu- lated on the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site, currently inactive, may be accessed at: <http://www.Nahee.com/FOTD/> Steady snow fell all day Saturday here at Fractal Central, while the temperature hovered around a reasonable 28F -2C. By night- fall about 3-1/2 inches or 9cm of fresh snow had piled up. As I cleared the fractal driveway, the fractal cats watched the action from their window shelf. They took to their warmer shelf over the heat when the outside show ended. My day was busy, mostly with keeping the fractal pavements cleaned and keeping the chicken soup coming for FL, who is back on her feet, but still not up to par. The next FOTD will be posted in 24 hours. Until then, take care, and if the theory of relativity is correct, one plus one does not always equal two. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Star_of_Ambiguity { ; time=0:00:40.42-SF5 on P4-2000 reset=2004 type=mandel center-mag=+0.33481377/\ +0.04702896/1696 params=0/0 float=y maxiter=24000 bailout=9 inside=0 outside=tdis periodicity=6 colors=000jjGkkJklMlmPlnTmoWmpZnqanrdoshcccwwzmmmh\ hhUUU3A6UUU68C77E87H96JA5MB5PC4RD3UE3WJ9YOF_SKaXQc\ aVde`fjehokjspknmhjjefgbbd`ZbYV_VRXTNUQJSNFPLBMI7J\ F3HD7FHAEKDDNFCQHBSJBULAWN9ZP9`R8bT7dV7gX6iZ5k`5mb\ 9lcDkdGjeKifNigRhhVgjYfkaeldemhdnlcoobpsaqvaru`ru_\ stZstZttYtsXusWusWvrVvrUwqTwqTxqSxpRypQypQunTrlVnj\ XkhZgf`ddb`bdY`fZ_e__d`_daZcbZccZbdZa`OaaO`bO`cO_d\ NZeMZfLYgKYfNVeLSdKPfJMgIJgHHfGEfFB`E8_D5ZC2ZB0_C2\ `D4aE6bF8cGAdHBeIDfJFgKHmLJnMKoNMpYOqZQr_Sr_TncVjg\ XfkZbt`_xaXv_UuZRtYOsWLrVIlUFkTIiWKhYNg`PebSddUcgX\ biZ`ka_ncZpfXrhWukVwmUyjTvhSteSrcRpaRnZQlXQiUPgSPe\ QOcNOaLN_JNYKT`LZcMdfNihOokPunQzpSvqUsqVpqXmqYir_f\ r`crb`rdYreUsgRshOsjLskIshHmeHgcHa`HXYGRWGLTGFRGAN\ JJKLSGN_DPhARpDRkGRgJRcLR_ORWRRSUROWRKZRGaRCcR8QHO\ C7b9Da7Ia5Oa3Ta6V`8X_BYZD_ZFaYIbXKdWMeW8m8G_OOMbV8\ qU7pU7pT6oT6oiiGihCih9jiD } END PARAMETER FILE=========================================

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FOTD 25-01-11 (Hidden Minibrot [9])
by Jim Muth 29 Jan '11

29 Jan '11

FOTD -- January 25, 2011 (Rating 9) Fractal visionaries and enthusiasts: Things were quite busy again here at Fractal Central on Monday, which left little time for an intensive fractal search, but the war-horse Mandelbrot set again rushed to the rescue with an infinitesimal minibrot in the East Valley of a larger but still infinitesimal minibrot at the tip of the main spike. Images of minibrots near the tip of the main spike are common, but today's image is colored well enough to raise the image to a superlative 9. And most surprising, the colors were created with a tap of the <enter> key and only a few small tweaks by the human fractal tapper. Way out here on the spike, the bailout radius has a great effect on the appearance of the image. Raising the bailout of today's image to 10 totally destroys the artistic effect. (Lowering it to 3 is even worse -- the image vanishes.) The name "Hidden Minibrot" is not the name of an upcoming Chinese movie. It refers to the minibrot at the center, which does not become visible until a magnitude of 10^100 is reached. Actually, I have already been down there, and can report that the minibrot has potential. One thing that could be improved is the calculation time of today's image, which at 1/2 hour, is inconveniently long. But, considering the image's magnitude of over 7*(10^93), this is not unreasonable. The calculation may be forgotten by viewing the finished image on the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> but before going there, allow a short time for Hal to calculate and post the image. The traditional FOTD web site is available at: <http://www.Nahee.com/FOTD/> Those wondering when my own FOTD web site will be up and running will be disappointed by the news that, due to the heavy graphic design work, we made no further progress on Monday. The temperature rose from a very cold start of -4F -20C to a not very balmy afternoon max of 19F -7C here at Fractal Central on Monday. The day began sunny, but by midday the clouds moved in, with a forecast of light snow to come at night. The fractal cats were disappointed when the sun failed to reach their window shelf before the clouds arrived, but they found comfort on the shelf by the heat. As reported above, my day was very busy. FL's day was even busier. The next FOTD will be posted in 24 hours. Until then, take care, and try to keep your fractal politically correct. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Hidden_Minibrot { ; time=0:30:33.42-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.9999\ 99999999995570588474637616346760358903286522128797\ 5190794248519602192032643927978653766431435/0/7.09\ 7126e+093 params=0/0 float=y maxiter=12000 inside=0 colors=000SegQciPbjOakN`lM_nLZoKXpJWqIVsHUtGTuFSvE\ BIHDLKEONFROGSPHTQIU00URKWS0XTKYT0ZUO_VP`VQaYUYaYU\ wdppcgjbZdaQZ`HDT4LX7T`9`dBhhEplGxoIczERfK6`jFLPzz\ ce_CazfN63SBAWGH_DF_LN_SV__b`ij_fi_di_bhZ`hZZgZXgb\ Qm`TjZVgYYdW_aUbZTdWRgTXZGMhOLkLJnIIqFGtCFw9Ez6Mp7\ Tf7_X8fN8mD9t49r5Cq5Fp6Ho6Kn6Nm7Pl7Sk7Vj8Xi8_h8bg9\ df9ge9iUaOIz2Ty9czGnqNxmTnePdYLVQILIEBABR_GSaKSbOT\ cSTdVUeZUfbVgfVhi_ghdfhiehnehhajcZlZVnTSpOOrJLtEIu\ JOpOUlTWhYYdbk`gqXlzTmtWnrYnp_onapldpjfqhhqfjndkkb\ liamf_ndZoaXp_WqXUrUSsSRtPPuNOvKMwKMwFJUDIUFMUHPUJ\ TULWUN_SPbLQiDNeDLaEJUEGPFEMGCKGAIH7HI5GI3FJ1EJ30F\ 50B708A07C07EA6GF6JG6LI5NJ5PL4SM4UN4WP3YQ3_R3`NJaJ\ YaGlcHjdIheIffJdhJbiK`jK_kLYmMWpMUrNStNQvOOxONzY`m\ hmsghd_bX40O40G40840ZJEXHDSFDZDCeBBlKBsUAzcAuUEoKI\ jAMdCQ_ETVFbRHrMJzIKzKMzMOzOQzQSzSUzUVzWXzYZz_`Uab\ ObcMmWLzOLzGKz9KzdWze_zec } END PARAMETER FILE=========================================

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FOTD 29-01-11 (Party in Hyperspace [6])
by Jim Muth 29 Jan '11

29 Jan '11

FOTD -- January 29, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a scene in a side spiral of the period-10 bud on the northeast shore line of the Mandelbrot set. This area is very near the depth where the East Valley elephants start to appear, and hints of the ponderous pachyderms are indeed visible in the image. Most of the effect is a result of rendering the image with the outside set to 'tdis'. Setting the outside to 'iter' speeds up the image by 100 times, but also drops the acceptable rating of a 6 to an embarrassingly low 3. The name "Party in Hyperspace" does not imply 4-D festivities. It is merely some words that came to mind when I entered the 'naming' mode. The calculation time is a rather inconvenient 13 minutes. But a quick idea of the scene may be seen in 8 seconds by resetting the outside to 'iter' and the logmap to a negative 1916. All such calculation inconvenience may be avoided by surfing to the active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image is or soon will be posted. the original classic FOTD web site may be found at: <http://www.Nahee.com/FOTD/> Light snow fell all morning here at Fractal Central, though by the time it ended, only 1cm had piled up. The afternoon tempera- ture of 34F +1C quickly eliminated what had fallen in the morning. The fractal cats were ambivalent about the situation, and finally decided they would rather be well fed than cozy. With FL back in action, my day was improved, though there is still a backlog of stuff to clear up. The next FOTD will be posted in 24 hours. Until then, take care, and if you know what the stock market is going to do next, let me know. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Party_InHyperspace { ; time=0:13:01.22-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=+0.3265\ 79110841169/+0.05200630315369301/8.263762e+010/1/\ -80/0 params=0/0 float=y maxiter=24000 inside=0 outside=tdis periodicity=6 mathtolerance=0.05/1 colors=000ih9jiDjjGkkJklMlmPlnTmoWmpZnqanrdoshotkp\ unpvqpvtSYV3A659968C77E87H96JA5MB5PC4RD3UE3WJ9YOF_\ SKaXQcaVde`fjehokjspknmhjjefgbbd`ZbYV_VRXTNUQJSNFP\ LBMI7JF3HD7FHAEKDDNFCQHBSJBULAWN9ZP9`R8bT7dV7gX6iZ\ 5k`5mb9lcDkdGjeKifNigRhhVgjYfkaeldemhdnlcoobpsazvS\ zuRzuQztPztPztOzsNzsMzsMzrLzrKzqJzqJzqIzpHzpGzpHzn\ LzlPvjSrhVmfYhd`cbc``fZ_e__d`_d`Zc`Zc`Zb`ZaWOaXO`Y\ O`ZO__NZ`MZaLYbKYaNV`LS_KPaJMbIJbHHaGEaFB`E8_D5ZC2\ ZB0_C2`D4aE6bF8cGAdHBeIDfJFgKHmLJnMKoNMpYOqZQr_Sr_\ TncVjgXfkZbt`_xaXv_UuZRtYOsWLrVIlUFkTIiWKhYNg`PebS\ ddUcgXbiZ`ka_ncZpfXrhWukVwmUyjTvhSteSrcRpaRnZQlXQi\ UPgSPeQOcNOaLN_JNYKT`LZcMdfNihOokPunQzpSvqUsqVpqXm\ qYir_fr`crb`rdYreUsgRshOsjLskIshHmeHgcHa`HXYGRWGLT\ GFRGANJJKLSGN_DPhARpDRkGRgJRcLR_ORWRRSUROWRKZRGaRC\ cR8QHOC7b9Da7Ia5Oa3Ta6V`8X_BYZD_ZFaYIbXKdWMeW8m8G_\ OOMbV8qU7pU7pT6oT6oiiGihC } END PARAMETER FILE=========================================

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FOTD 28-01-11 (FMOD on the X-axis [7])
by Jim Muth 27 Jan '11

27 Jan '11

FOTD -- January 28, 2011 (Rating 7) Fractal visionaries and enthusiasts: Things were very hectic here at FC again on Thursday. (And I thought we were in a recession.) But at least FL is on the mend, and will likely be back in action by Friday, which will relieve the pressure on me and allow more time for a proper fractal search. But most likely, we will remain in the M-set. Today's image is another very deep scene at the end of the nega- tive X-axis of the Mandelbrot set. But today, the image has a difference. The bailout radius of the M-set has been set to 3, which causes the X-axis to be cut off at a point around sqrt(3). The tiny minibrot at the center of the image is located very near the end of this shortened main spike. The basic equal-iteration rendering of the scene was very dull, so I livened things up by rendering the scene with the outside set to 'fmod'. The result earns a rating of an honest 7. The name "FMOD on the X-axis" simply tells it like it is. Though the magnitude of the image is well within the range of arbitrary precision math, the actual magnitude of around 10^21 is much less than the magnitude of the images of the past few days, cutting the calculation time to a much more reasonable 9-1/4 minutes. But a calculation time of over 9 minutes is still a lot of time to devote to an FOTD image. The remedy is to surf down to the active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image is or soon will be posted. The original FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> A mix of clouds and sun, occasional flurries of snow, and a temp- erature just around freezing made Thursday a typical midwinter day here at Fractal Central. Two inches of fresh snow piled up overnight Wednesday, but on top of the foot (30cm) or so of old snow, made little difference. The fractal cat duo tried their window shelf, but soon decided the sun was too irregular, and took to the shelf over the heat. With FL feeling better but still out of action, my day was another hectic one, doing double duty. Luckily, the Mandelbrot set once again came to the fractal rescue with a quick image. The next FOTD will be posted in 24 hours. Most likely it will be another scene in the infinitely complex and extremely fast Mandelbrot set. Until then, take care, and what is wrong with the current world? (Maybe it's that I'm nearing codgerhood.) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= FMOD_on_the_X-Axis { ; time=0:09:15.35-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.7320\ 4993548250847092178/0/9.545e+020 params=0/0 float=y maxiter=5000 bailout=3 inside=0 proximity=0.0003 outside=fmod symmetry=xaxis periodicity=6 colors=000zZKyYIwWGuSErPCoMBlGAfC9`88U37KA0G70C508\ 92830410EzzMzzWzwVyuVxsUwqUvqUvqTupTupTtoStoSsoRsn\ RrnRqnQqmQpmQplPolPolPnkOnkOmjNmjNljNliMkiMjiMjhLi\ hLigKhgKhgKgfJgfJffJfeIeeIedIddHcdHccGbcGbbGabFabF\ `aF`aE_aE_`DZ`DZ_DY_CX_CXZCWZBWZBVYBVYAUXAUX9TX9TW\ 9SW8SV8RV8QV7QU7PU6PU6OT6OT5NS5NS5MS4MR4LR5JO4KP4L\ Q4LR4MS4NT4NT4OU4OV4PW4QX4QY4RY4RZ4S_4T`4Ta4Ua4Vb4\ Vc4Wd4We4Xf4Yf4Yg4Zh4Zi4_j4`j4`k4al4bm4bn4co4co4dp\ 4eq4er4fs0ev1fu2ft3ft4fs5fs5gr6gq7gq8gp9gpAgoAhnBh\ nChmDhmEhlFhlFikGijHijIiiJiiKihKjgLjgMjfNjfOjePjeP\ kdQkcRkcSkbTkbUkaUl`Vl`Wl_Xl_YlZWjWXkXYkYYlZZl_Zm`\ _ma_nb`nc`odaoeapfbpgbph`ng_lfYkeXidVhdUfcSdbRcaPa\ aO``MZ_LXZJWZIUYGTXFRWDOXEPWEQWEQWFRVFSVFSVGTUGTUG\ UUGVTHVTHWTHWSIXSIYSIYRIZRJZRJ_RJ`QK`QKaQKaPKbPLcP\ LcOLdOMdOMeNMfNMfNNgMNgMNhMOiLOiLNonNonNonNonNonMo\ nMonMonMonMonMonMonMon6ag } END PARAMETER FILE=========================================

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Re: [Fractint] Am I correct in thinking that the radialspokes...
by Jim Muth 27 Jan '11

27 Jan '11

At 01:44 PM 1/26/2011 -0500, Hal wrote: >Am I correct in thinking that the radial spokes in the >FOTD 25-01-11 (A Googol is Deep [No Rating]) >(it's actually January 26th's fractal) >are structures associated with period doubling? Yes, the radial spokes are associated with period doubling. The period continues doubling as a minibrot is approached, until I assume it reaches infinity at the edge of the minibrot. In minibrots of limited magnitude, the high-order elements lie so close to the minibrot that they cannot be resolved, but as the magnitude increases, the basins around the minibrots grow larger, and the farther from the minibrots the higher-order elements lie. The image of Jan 26 is of such a high magnitude that the period-1024 elements lie far enough from the minibrot to be rather easily resolved. The situation becomes complicated with minibrots that lie in the basin of a larger minibrot, as does the minibrot in the Jan 26 image. In this case the doubling sequence reaches infinity well away from the minibrot then resets itself to a lower value and starts doubling all over again. This is quite clear in the image for Jan 25, where we see 128 greenish then 256 amberish stripes around the edge, yet find only 16 amber-blue spokes at the center. >On a slightly different aspect of this image -- the fact >that it uses about 100 digits of arbitrary precision math -- >makes me wonder how many sheets of paper it would take >if all the numerical values of all the iterations calculated >for all the 1,080,000 pixels I calculated were printed out >on 8 1/2 x 11 inch paper... I imagine it would take a googol sheets of paper. ;-) Seriously, as a wild guess, the number would probably be well into the billions. Jim

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FOTD 27-01-11 (Backing Out [No Rating])
by Jim Muth 27 Jan '11

27 Jan '11

FOTD -- January 27, 2011 (No Rating) Fractal visionaries and enthusiasts: With FL out of action, it was another hectic day for me here at FC. The double work load left no time to search through a new parent fractal, so I returned to the immense minibrot basin of the two most recent images, where I found today's image. Today's image, with its magnitude of 2(10^87) is a back-out from yesterday's googol-deep minibrot. It actually lies about twice as far from the central minibrot as the image of two days ago, Jan 25, which lies in the same basin. I named the image "Back- ing Out", for obvious reasons. Since the image is the third consecutive one in the same mini- brot basin, I could not honestly rate it. Actually however, it's a rather pleasant image of slightly questionable character, and well worth a look. Since the scene is of a notably lesser magnitude, the calcula- tion time has been cut to a more reasonable 22 minutes, though this is still quite slow by FOTD standards. To speed up the satisfaction, I suggest viewing the finished image on the active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> But give Hal a bit of time to calculate and post it. The old original FOTD web site may be found at: <http://www.Nahee.com/FOTD/> The last time I checked, it was not up to date, but that was almost 2 weeks ago, and something might have happened since then. Heavy clouds hung over Fractal Central all day Wednesday, with snow flurries in the morning and steadier snow in the afternoon. The temperature of exactly freezing kept the fractal cats con- fined to their warm shelf. My day was quite busy. With FL down with the bug, it was up to me to do the work of the two of us and keep the hot chicken soup handy. Luckily, I knew the fractal was there before I ever saw it. The next FOTD will be posted in 24 hours. Until then, take care, and be thankful that fractals exist. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Backing_Out { ; time=0:22:25.89-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.9999\ 99999999995570588474637616346760358903286522128797\ 5190794248519602192032643927978653766/0.0/\ 2.388852e+087 params=0/0 float=y maxiter=12000 inside=0 symmetry=xaxis periodicity=6 colors=000SegQciPbjOakN`lM_nLZoKXpJWqIVsHUtGTuFSvE\ BIHDLKEONFROGSPHTQIU00URKWS0XTKYT0ZUO_VP`VQaYUYaYU\ wdppcgjbZdaQZ`HDT4LX7T`9`dBhhEplGxoIczERfK6`jFLPzz\ ce_CazfN63SBAWGH_DF_LN_SV__b`ij_fi_di_bhZ`hZZgZXgb\ Qm`TjZVgYYdW_aUbZTdWRgTXZGMhOLkLJnIIqFGtCFw9Ez6Mp7\ Tf7_X8fN8mD9t49r5Cq5Fp6Ho6Kn6Nm7Pl7Sk7Vj8Xi8_h8bg9\ df9ge9iUaOIz2Ty9czGnqNxmTnePdYLVQILIEBABR_GSaKSbOT\ cSTdVUeZUfbVgfVhi_ghdfhiehnehhajcZlZVnTSpOOrJLtEIu\ JOpOUlTWhYYdbk`gqXlzTmtWnrYnp_onapldpjfqhhqfjndkkb\ liamf_ndZoaXp_WqXUrUSsSRtPPuNOvKMwKMwFJUDIUFMUHPUJ\ TULWUN_SPbLQiDNeDLaEJUEGPFEMGCKGAIH7HI5GI3FJ1EJ30F\ 50B708A07C07EA6GF6JG6LI5NJ5PL4SM4UN4WP3YQ3_R3`NJaJ\ YaGlcHjdIheIffJdhJbiK`jK_kLYmMWpMUrNStNQvOOxONzY`m\ hmsghd_bX40O40G40840ZJEXHDSFDZDCeBBlKBsUAzcAuUEoKI\ jAMdCQ_ETVFbRHrMJzIKzKMzMOzOQzQSzSUzUVzWXzYZz_`Uab\ ObcMmWLzOLzGKz9KzdWze_zec } END PARAMETER FILE=========================================

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<Jim Muth> Am I correct in thinking that the radial spokes...
by Hal Lane 26 Jan '11

26 Jan '11

Am I correct in thinking that the radial spokes in the FOTD 25-01-11 (A Googol is Deep [No Rating]) (it's actually January 26th's fractal) are structures associated with period doubling? I'm used to seeing (for example) a pattern repeated eight times around a minibrot, surrounding a similar one repeated 16 times, surrounding a pattern repeating 32 times, etc. The largest number of these repeated structures that I've ever been able to see in the past was 256. In your FOTD there appear to be 128 of the largest spokes surrounding a smaller ring of (apparently) twice as many yellow and purple spokes, surrounding a smaller ring of (apparently) four times as many yellow and purple spokes -- still clearly visible. This would make 512 easily-visible period-doubled spokes, and is double my previous record. ;-) For a minute I had thought I had figured out that I was seeing 1024 spokes, but I had gotten it wrong. Perhaps one could see 1024 if the image were calculated at a substantially higher resolution. I'm not going to do that today, because the one I put on your FOTD web page at 1200 x 900 took about 6 1/2 hours on my 2.2 GHz machine. It's fortunate that "symmetry=xaxis" is in your parameter file and halves the calculation time... On a slightly different aspect of this image -- the fact that it uses about 100 digits of arbitrary precision math -- makes me wonder how many sheets of paper it would take if all the numerical values of all the iterations calculated for all the 1,080,000 pixels I calculated were printed out on 8 1/2 x 11 inch paper... Again, am I correct in thinking that the radial spokes in the "A Googol is Deep" image are associated with the usual period doubling seen in many fractals? - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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Re: [Fractint] Some Lyapunov Variations
by Tony (Anthony) Hanmer 26 Jan '11

26 Jan '11

Here are some pars (attached) from a variation of the Lyapunov fractal type, which has long been a favourite of mine - I asked for the variation so as to have more control over its parameters, and sometimes you get exactly what you wish for. These have quite a strong space/SF theme, and look great rendered as large as possible. Is there any *full-colour* freeware fractal programme which can handle such "homemade" as formula files as opposed to Fractint's "hard-wired" ones, and Fractint-type .par files as well? I'd really like to see these without the banding that the 256-colour map gives. Tony Hanmer Mestia, Republic of Georgia Ps NB This attached text and the next one want to be cut and pasted into Notebook or your equivalent text editor, then saved as TLYA2010.PAR ; then it can all be run in Fractint. Also, save the two formulae, Lyapunov02 and 07 (everything after frm:) deleting the "frm:" in each case, into a separate .frm file, called LyaVars.frm or whatever.

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FOTD 25-01-11 (A Googol is Deep [No Rating])
by Jim Muth 26 Jan '11

26 Jan '11

FOTD -- January 26, 2011 (No Rating) Fractal visionaries and enthusiasts: Yesterday's image showed the outer parts of the basin surround- ing a minibrot lying at a depth of one-googol on the main stem of the Mandelbrot set. In yesterday's image, the minibrot was invisible; today's image takes us down to the minibrot itself. At this extreme depth the minibrots have a tendency to all look the same, with little more than rings of concentric circles surrounding the minibrots and extending out to the point where the minibrot itself becomes invisible. Another problem is visible in today's image, where the finer details merge into a chaos of Moire interference patterns. Some- times these patterns can become quite interesting, though this is not the case in today's image, where they simply spoil the effect. Calculating the image at a higher resolution will reduce these interference patterns, but this will also increase the calculation time, which even at 640x480 is over one hour. I could give the image no rating. After all, it is a virtual repeat of yesterday's image. The name "A Googol is Deep" refers to the depth of today's scene. A googol is also a very large number, yet still merely an infinitesimal part of infinity. The calculation time runs just over one hour. To make the image worth the effort, I recommend viewing the finished image on the active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> remembering, of course, to give Hal a chance to render and post the finished image. And don't forget the original FOTD web site at: <http://www.Nahee.com/FOTD/> I see that some fractal fans on the list are still wondering what ever happened to the FOTD CD I was talking about a number of years ago. What happened was that I realized that the estimated profit from creating such a disk would fall far short of justifying the effort needed for its creation. Among other things, I would need to calculate high-resolution versions of all the past FOTD images. But the idea is still simmering on the back burner, and if I saw a reasonable demand from people who were willing to pay a fair price for the disk, I could produce it in about a month. As things stand now however, I feel such a demand is unlikely to happen. Meanwhile, the FOTD web site is on the way. Perhaps I was too optimistic in estimating the amount of time needed to create a satisfactory design and the amount of work required to achieve that design. To avoid further disappointment, I'll stop comment- ing on the web site's progress until it is up and running. Nondescript conditions prevailed here at Fractal Central on Tuesday. The cloudy skies and temperature of 34F +1C were a welcome relief from the bitter cold of the past several days. But the forecast is for more snow on Wednesday. The fractal cats spent their day keeping warm. I spent my day doing double duty, while FL spent her day trying to fight off a cold or the flu. She got rather annoyed when I jokingly said the flu shot she got in November must be finally starting to work. The next FOTD will be posted in 24 hours. Until then, take care, and if I am a Boltzmann brain, then Boltzmann brains are all in my mind. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= A_Googol_is_Deep { ; time=1:08:21.65-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.9999999999999\ 95570588474637616346760358903286522128797519079424\ 85196021920326439279786537664314359319502/0.0\ /1e+100 params=0/0 float=y maxiter=18000 inside=0 passes=1 symmetry=xaxis colors=000SegQciPbjOakN`lM_nLZoKXpJWqIVsHUtGTuFSvE\ BIHDLKEONFROGSPHTQIU00URKWS0XTKYT0ZUO_VP`VQaYUYaYU\ wdppcgjbZdaQZ`HDT4LX7T`9`dBhhEplGxoIczERfK6`jFLPzz\ ce_CazfN63SBAWGH_DF_LN_SV__b`ij_fi_di_bhZ`hZZgZXgb\ Qm`TjZVgYYdW_aUbZTdWRgTXZGMhOLkLJnIIqFGtCFw9Ez6Mp7\ Tf7_X8fN8mD9t49r5Cq5Fp6Ho6Kn6Nm7Pl7Sk7Vj8Xi8_h8bg9\ df9ge9iUaOIz2Ty9czGnqNxmTnePdYLVQILIEBABR_GSaKSbOT\ cSTdVUeZUfbVgfVhi_ghdfhiehnehhajcZlZVnTSpOOrJLtEIu\ JOpOUlTWhYYdbk`gqXlzTmtWnrYnp_onapldpjfqhhqfjndkkb\ liamf_ndZoaXp_WqXUrUSsSRtPPuNOvKMwKMwFJUDIUFMUHPUJ\ TULWUN_SPbLQiDNeDLaEJUEGPFEMGCKGAIH7HI5GI3FJ1EJ30F\ 50B708A07C07EA6GF6JG6LI5NJ5PL4SM4UN4WP3YQ3_R3`NJaJ\ YaGlcHjdIheIffJdhJbiK`jK_kLYmMWpMUrNStNQvOOxONzY`m\ hmsghd_bX40O40G40840ZJEXHDSFDZDCeBBlKBsUAzcAuUEoKI\ jAMdCQ_ETVFbRHrMJzIKzKMzMOzOQzQSzSUzUVzWXzYZz_`Uab\ ObcMmWLzOLzGKz9KzdWze_zec } END PARAMETER FILE=========================================

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RSS Feed
by Roger Kaufman 24 Jan '11

24 Jan '11

I tried the RSS feed on the Droid phone today using the RSS reader RssDemon. First I must say thanks for the great effort to organize the FOTD archive in this manor. One problem it has in the RSS feeder I am using is how the entries are ordered. There are several ways to sort the list and I am trying sort by ascending date. But when I try that, the top entry is "Filler Thriller" from April 21, 2009. This may be the last one generated? There is an option to sort by title. The date could be part of the title but that would cause the sort have the oldest at the top. There may be no way around this. For now I have marked them all unread and then any new ones will come in at the top of the list. But this sorts all the marked read ones by title and so again the oldest are at the top. The only thing I could suggest is that once the whole archive is generated that the RSS feed be regenerated from oldest to newest. But this world be a lot of work. Then there is the issue of how many entries one wants to download. It could be limited locally but I might be the only person thinking I'd want all of them on a hand held device! This may not be wise and instead maybe only the last months worth should be available? For now, if I click on the year/month in the title, it takes me to the xmission pages such that I could find the latest there. But this is a little less convenient. Roger

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FOTD 24-01-11 (Deep Underground [7])
by Jim Muth 24 Jan '11

24 Jan '11

FOTD -- January 24, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's scene lies in a side filament of the period-7 bud on the northwest shore line of the large minibrot on the main spike of the Mandelbrot set. It lies so deep that arbitrary precision math is required to calculate it, which means the calculation time is an inconveniently long 36 minutes. The rating of a 7 is more a matter of taking credit for some- thing I did no work on than a reward for my brilliant effort. I spent most of the day lost in thought. The fractint program did 90-percent of the work. The name "Deep Underground" refers mostly to the extreme depth of the scene, and partly to the depth of my ponderings on Sunday. The image may be seen by running the included parameter file and waiting a half hour or so, or by surfing down to the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image is posted. But it may take a short time for Hal to calculate and post it. The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> My own FOTD web site will soon be available on-line. Keep waiting for the announcement with bated but not abated breath. Ample sun but a chilly temperature of 23F -5C kept the fractal cats close to the heat here at Fractal Central on Sunday. My day was one of the slowest in quite a while. It was so slow in fact that laziness got the better of me, and FL had to ask if I felt all right. Luckily, when fractal time arrived, the M-set once again came to the rescue with one of its infinite mini- brots. But Monday will likely bring more work, so the peace will not last. The next FOTD will be posted in 24 hours. Until then, take care, and find the calmness that lies within. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Deep_Underground { ; time=00:36:14.79-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.76641\ 5736936545845601733295/0.00709681589493994603636566\ 88/1.526688e+023/1/21/0 params=0/0 float=y maxiter=12000 bailout=6 inside=0 colors=000qdZqeYpfXpfWqeTreQseNteKueHvdEwdBxd8yd5z\ d2zd0iZ9TTHDNPORMMTKLVJKXIIZHH`GGbFFcEDeDCgCBiB9kA\ 8m97o86p77q67q68q58r58r59r49s4As3As3At3Bt2Bt2Bt2Dn\ 5Fh8GcAIYDKTFLNINIKPCNQ7PO6NN6LL6JK6HI6FH6DF6BE69C\ 67B65963862D85IA7MCARDCWFF_HHdJKhKMePNcTNaYN_aNYfN\ _jNaoNcsNewNgzMizMkzMmzLozLqzLszKuzKwvKxrKymMshNmc\ Oh`PcYQZ`SUbTPeUPgVRiWkHvlHvlHwmHwmHxnHxnHxjFwfEvc\ Cv_BuW9tT8tSAsSCsSEsSGsSIsSJsSLsRNsRPsRRsRSsRUsRWs\ RYsQ_sQasQbsQdsQfsQhsQjsQksTrpW`rZJta2ub3qb3nb4kb4\ gb5db5ab6Yb6Vc6Sc7Oc7Lc8Ic8Ec9Bc98c95bD4aG4`J4`N4_\ Q4ZT4YW4Y_4Xb4We4Wh4ae8fbBk`FpYIuVMzTPYopShiMabGWW\ LSTQORVKP_HNdDLi9Jn5Hs2FpkJmzNjzQmwzmwzmwzmwzmwzmw\ wmwumwqmwmmwimyemxamwYmvUmuQmtMksIhqEeoAbmC_kDYiFV\ gGSdIQaJNZLKVNISOFPQCMMAIJ7FF4CC29DAGOHNUOUcV`iafs\ `dq_czZazY`zXZzWYzVWzUVzTTzSSzRQzQPzPNzOMzNLzWOzcR\ z`UzZWzWZzU`zRbzsazsbzrcz } END PARAMETER FILE=========================================

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FOTD 23-01-11 (The Edge of Forever [7])
by Jim Muth 23 Jan '11

23 Jan '11

FOTD -- January 23, 2011 (Rating 7) Fractal visionaries and enthusiasts: An unexpected antiquing trip arose Saturday morning here at FC, and by the time we returned, the sun had nearly set. To make things worse, extra work had come in by e-mail while we were away, forcing me to turn to the hyper-fast Mandelbrot set for a fractal in a hurry. Today's image is a scene in a small side spiral on the northwest shore line of the Mandelbrot set. It's something that has often been seen before, but I did put extra coloring effort into it, which allows a rating of a not-too-bad 7. The name "The Edge of Forever" refers to the limitless infini- ties that lie in the M-set, beyond today's scene. The calculation time of under 3 seconds shows how fast the type=mandel formula runs. The pre-calculated image is available on the FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The traditional FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> My own web site is coming along, but far too slowly. The temperature here at Fractal Central rose from a morning low of +7F -14C to an afternoon high of 19F -7C. But despite the cold, the sun was very strong, and the fractal cats took full advantage of the afternoon sun on their window shelf. When we returned from the antiquing expedition, they leaped from the shelf and ran to the door to greet us and complain about our absence. Unfortunately, when we checked the work, we found an unexpected job waiting. The rest of the day was busy. The next FOTD will be posted in 24 hours. Until then, take care, and bring it to completion. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= TheEdge_of_Forever { ; time=0:00:02.85-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.5252836856416\ /+0.5225261871496/5.846441e+008/1/175/0 params=0/0 float=y maxiter=5000 bailout=6 inside=0 logmap=-814 colors=000AFbAGaAH`AI_AJZBKYCLXEMYFN`GPcKRcOVgSZkW\ aoZdo_hqajsclwenzdpsdnuckzahz_dzZbzX`vVYrTWmRUhPSc\ NPZLNUJLSHIPFGNDELBCJADMADOAERAETAFWAFYAG`BGbDGdGH\ gJHiMJlPKnSMqVNsYPv`QxcRzcQyZPxUNwPMuKKsFJqAHo6Gm6\ Fj5Fh5E_5ES4EQ4DO3DM3CJ2CG2BD2BA1AA1AA09A09A09A6BN\ 6DL7FL7HK8IU8Kc9Mm9OmAQcARUAQKAPJBPHBOFBODBNB2L84N\ 95O96PA8RA9SBATBCVCDWCEXDGYDH_EI`EKaELcFMdFOeGPfGQ\ hHSiHTjIUlIWmJXmJYmJYmJZmEcm9cm7cm5cmFcmPcmYcmgccu\ cUpJMlNMhRLcVK_YKWaJSeINiIJmHFpHBmJDkKEiPFfSGdUHbW\ I_YJY_KWaLTcMReNPfOMgPKhQIiRFjSDkTBlUDmRFmPGmNImLK\ mJLmHNmFPmDRmAQmBQmBQmBPmBPmBPmBPmBOmBOmBOmBOmBNmB\ NmBNmBMmBMmBMmBMmBLmBLmBLmBAmBLmBWmLap`gsfmvfryfsz\ gtzhuziuzjvzlwzmxznyzoyzptzmozkjziezfazdXzbSz_NzYK\ zTJzWJzZIzaIzdHzfHziGzlGzoGzqSzUcz6fzCizIlzOozUrz_\ uzexzkzzpxznvzltzjrzhpzfnzelzcjzahz_fzYdzWbzV`zTZz\ RXzPVzNTzLRzKPzINzGnzLnzN } END PARAMETER FILE=========================================

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FOTD 22-01-11 (Five-Eighths There [7])
by Jim Muth 21 Jan '11

21 Jan '11

FOTD -- January 22, 2001 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us back once again to the parent almost- Mandelbrot set fractal of the Jan. 8 FOTD image. This time I checked the trunk of the period-46 elephant on the southern side of the valley. Only a slight distance into the trunk I found a quadratic minibrot caught morphing into a quintic minibrot. Today's scene lies in a chunk of left-over quadratic stuff inside the main bay of this minibrot. The much smaller minibrot at the center of today's image lies just beyond the limit of resolution, but it is a purely quintic one. The outer elements surrounding the minibrot are quadratic stuff however, which leads to a diamond-shaped area of confusion where one type of stuff changes to another. The rating of a 7 indicates that the image is a cut above aver- age. The name "Five-Eighths There" came about when I noticed the normal 2,4,8,16... quadratic series going through the area of confusion before changing into the unlikely quintic series of 5,25,125,625... The name doesn't make much sense, but a name is a name, and this will be the name of today's image. The calculation time of 5 minutes is a bit of a burden. The burden may be lifted however by surfing down to the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site at: <http://www.Nahee.com/FOTD/> is still worth a look. Due to the rush here at FC on Friday, my own FOTD web site made no progress. There is no time limit however, and before long the site will be up and running. About 3-1/2 inches (9cm) of snow fell overnight Thursday here at Fractal Central, which meant a Friday morning of sidewalk clearing. The fractal cats gave moral support by watching from the window, while FL kept the coffee hot and the work moving. Friday afternoon was partly cloudy, with snow flurries, brisk winds and steadily falling temperatures, which reached 19F -7C by sunset, with a forecast low of +7F -14C. The rest of the humans' day was again quite busy, which seems to be more the rule than the exception these days. Maybe it's a sign of the improving economy. The next FOTD will be posted in 24 hours. Until then, take the usual care, and when someone wonders about the meaning of life, tell them the question is meaningless and see if they consider the answer satisfactory. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Five-Eighths_There { ; time=0:04:31.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip float=y center-mag=+0.254554234183668/-0.00046753213376652\ /8e+012/1/-75/0 params=5/500000000.0/0/0 logmap=724 passes=1 maxiter=5000 inside=0 mathtolerance=0.05/1 colors=000BG_BG_CG_CG_DGZDGYEGXEGWFGVFGUGGTGGSEGRD\ GQCGPBGOBGNBGMBGLBGKBGJBGIAGHAGGAGGAGGAGGAGGAGGDGG\ FGGmGGmGGmGGmGGmGGzGGzGGzGGzGGzGGzGGzIGzKGzNGzRFzV\ DzZBzaAzd8zg6zi5zk5xm5zn5zn5zm5zk5zi7zf9zcAz`CzZEz\ XFzUHzQJzOKzMIzJHvGGrBFm7Eh4Dc6A_B8_H6_M5`R5`X5`a5\ `f5bc5c`5dY5eV7fSAgPDhMGiJIjGLkDOlBQiCRfCRcCS`CSZC\ TWCTTCUQCUNCVLCVICWFCWCCXACXCFWEHWGKVIMVJOVLRUNTUP\ WTRYTS_TQWVPTWNQXMNZKJ_JG`IDbGAcF6dD3fC0gB0h86j6Fl\ 4On2Xo7VlCTiHRfMPcRN`VLZ_JWdHTiFQnDNrBLpHNnNPlSRdN\ NYIKRDHWMU`VfaWdbXccXadY`eZZfZYg_Wh`Vi`TjXSoSReSQ`\ ePWnO`mieliilqilvilgileildilbil`il_ikYikWikVikTP45\ Q56S56S67U77V88W98Y99ZA9_BA`CAaDBbDBcECdFCeGDfHDmH\ DzIEzJ_zKFzL_zLGzM_zNHzO_zPIzP_z_JzRiz_KzTiz_LzUiz\ VMzWiz_Nz_vz_Nz_vz_Nz_vz_Nz_vz_Nz_vz_Nz_vz_Nz_vz_N\ z_vz_Nz_vz_Nz_vz_Nz_vz_Nz_vu_Nu_Nu_Nu_Nu_Nu_Nu_Nu_\ Nu_Nt_Nt_Nt_Nt_Nt_Nt_Nt_N } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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iDOS
by Mike Frazier 21 Jan '11

21 Jan '11

I thought I would mention that iDOS (free DOS emulator for the iPad) is now available on the app store. Because of the Apple app store rules only the developer can add programs to the emulator. I wrote the developer and asked them to add FractInt. If I get a response, I will post it here. -- Mike Frazier www.fracton.org

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FOTD 21-01-11 (Fohat-Prana-Kundalini [7.5])
by Jim Muth 21 Jan '11

21 Jan '11

FOTD -- January 21, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image returns us to the same pseudo-Mandelbrot set parent fractal that held the image of January 8, which is named "Elusive Butterfly". But instead of zooming into the main stem on the negative X-axis of the parent, I checked the west branch of the filament extending from the large period-3 north bud. I found a tiny minibrot on the filament that is just starting to morph from a quadratic into a quintic minibrot. Today's scene lies in a patch of the more-rapidly-morphing stuff. I was ready to name today's image "Butterfly Quintuplets" when FL, reading an article about yoga, said something about Kunda- lini, one of the three mystical energies. Kundalini is claimed to be an energy unknown to science, which normally lies inertly at the base of the spine, but sometimes rises during deep medita- tion to bring spiritual enlightenment to the properly prepared meditator. There is also another mystical energy unknown to science called Prana, which is basically the life energy. Prana, which is some- times called 'Chi' brings vitality to the living organism, and is the force that is activated during acupuncture. The final mystical energy, named Fohat, is nothing more than everyday elec- tricity. Fohat is the only mystical energy so far recognized and accepted by science. All this mysticism led me to name today's image "Fohat-Prana- Kundalini". But don't expect any kind of enlightenment in the image. It's just another fractal, though its rating of a 7-1/2 indicates that it is a cut above the average. Perhaps the most mystifying thing about the image is its calcula- tion time of 36 seconds, which is almost magically fast for an image of such magnitude. And even this brief wait may be avoided by surfing to the active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image is posted. The original FOTD web site at. <http://www.Nahee.com/FOTD/> still holds thousands of the older FOTD's from before November 2010. Due to the rush, my own web site made no progress today. But be patient. Anything worth having is worth waiting for. (But not forever.) Clouds and a temperature of freezing kept things suppressed here at Fractal Central on Thursday. The forecast of snow at night kept the snow shovels stored in a convenient place. The fractal cats never shovel snow, nor do they concern themselves with fore- casts. They make the most of things as they are at the present moment, and on Thursday the things of the moment kept them on their shelf by the heat. My day was busier than expected. FL had an even busier day on her side of the workroom. The next FOTD will be posted in 24 hours. Until then, take care, and I am skeptical about Prana and Kundalini because I have not actually observed these ener- gies, nor has science approved of belief in them. Of course, neither have I actually seen the equally mystical energy known as Fohat (or electricity), but I have often seen its effects, and belief in it is approved by science, so I guess it's all right to believe in it. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= FohatPranaKundlini { ; time=0:00:36.91-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip logmap=80 center-mag=-0.1346668034193643/+0.9983400168471678\ /3.452841e+012/1/37.5/0 params=5/500000000.0/0/0 float=y maxiter=1250 inside=0 mathtolerance=0.05/1 colors=000zzzzzzzzzzzzzyzzxmzwczuUzsKzqQ0110120231\ 3423534644755865976A86C86D86F86G86I86J86L86M86O86P\ 96R96T96U96W96X96Z97_ABaKGcSLdZNimSqsXwrrrzzzUPoUK\ hUF`UHYUKVUOSzRPzVMzYJzaGzdDzbLz`SzZZkYegXdcWd`WdX\ VdUVzQUzMTzJTzFSzCSzJWzQ_zabLnhPzkVznczqozkfzgbwb`\ nYajVgaRlXNrTLqPIpLGoHCmDAkGEcJHYLLSOOMzSGzVAzfCzz\ DvnCrkBmgBcdAU`9KY9HV8GR7GO7GK6FH5FD5FA4F74J85N95R\ A6VB6ZC7aC7eD7iE8mF8qG9uH9xH9pXJhkTazafsbjlcnfcr_d\ vUduWftXgsYhrZiq_jp`kpbmocnndomeplfqkgrkhshetecub`\ u_ZuYWuVUuSRuPPuNNuORsOUmOXgP`aPcWPfQYb`fZjoVtwSub\ LlIEVMFYPG_THbWHd_IgbJifJliKnmLqpLstMuzzzzNuyOuxPs\ wQpwRmsclpckmck_bI_aHZaHZ`GZ_GZ_FYZFYZEYYEYXDYXDXW\ CXVCXVBXUBWUAWTAYS9_S9aR8cQ8eQ7gP7iP6kO6mN5oN5qM4s\ 6_u8Xw9VxATyBQzCOzDMzEKzGHzHFzIDzJAzK8zL6zFezITzKG\ zUuzUTzUSzURzURzUQzUPzUPzUOzUNzUNzUMzULzULzUKzUKzU\ JzUIzUIzzzzzzzzzzzzzzzzzz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 20-01-11 (Ancient Symmetries [6])
by Jim Muth 20 Jan '11

20 Jan '11

FOTD -- January 20, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a scene near the large minibrot on the main stem of a distorted Mandelbrot set. Actually, the main stem of this parent Mandeloid is infinitely divided, with assorted parts of several large minibrots visible. Do not be deceived by the poetic name "Ancient Symmetries". I wrote it in a spate of poetic inspiration, but the image fails to live up to the promise. (The FOTD writer believes in truth in advertising.) The rating of a 6 is merely adequate. There is nothing outstand- ing in the image to make it worth the calculation time of over 6-1/2 minutes, so I recommend viewing the finished image on the currently active web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> you also might want to check the original FOTD web site at: <http://www.Nahee.com/FOTD/> It is currently not up to date, but one of these days Paul will be up and about, ready to bring things up to date. My own FOTD web site is still a work in progress, but progress *is* being made. The temperature of 41F +5C here at Fractal Central on Wednesday was reasonable, but the cloudy sky and melting slush made things unpleasant. Early in the day the fractal cats decided on the shelf by the heat. My day was about average; FL's also. The next FOTD will be posted in 24 hours. Until then, take care, and wait for the sunrise. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Ancient_Symmetries { ; time=0:06:37.28-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=-1.765864849188624/-0.00353536043588884\ /1.92565e+009/1/85/0 params=2.001/0/0.001/0 float=y maxiter=3600 inside=0 logmap=668 periodicity=6 colors=300E2LE7NB9OBBRAET9JUCR_F_fZnscszhzzgqz`kvS\ emNZcHQWBLO9HH5EH3AH34H36R32`90nAAhBGfBOoCHmEAlE4k\ JGcNTYaeTmsNtzHgzJ`tJapKaiKaeLc_LcWNdQNdLOdGOeCQe7\ Qe4Qg6Nh9KjBHkCFmFCoHBpJ9rL6tO4uQ1vT0xW0zX0z_0zb0z\ c0zh0zp5zx4zz2zz2zz1zz1zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz1zz7zzCzzJzzQzzWzzbzzizzpzznzzmzxmzpkzpktpitp\ htphtpftpftpetpctpczpbzpbzpYzpUzpQzpLzsHzqGtpGtnFt\ nFtmEtkEtkCtiCzhBzhBzfAzeAzeAzcBrbBj`BzLpS_xAnzEiz\ GexK`tNXqPTpmzzozppyYrxHrv2hq9amEVhKOcQH_XBWbAUcAT\ e9Rf9Qh9Oi8Nk8Lm8KnKJbWJR`FUdCXeA_h6`k4co1fr0hg6eZ\ CbQJ_HRXAYU3eR3mQ3BJF9WY6hr4vz1zz0xz0mz0cu0UzAQzTK\ zmFzzpzyFznKtcRkUXdKcYBiQ2qK2cE2R92F5244103963GK3O\ _3Yp3Up3Qp5Lp9HpEEzJAzO6zQ6zdEzZ4iaCveAxj0yo0zkBch\ OHeb0eX1dR5cL9cFCaAG`5KZ0OZ0NY0zY1zW1zW2zV4zU5zS5z\ P5zN5zL5zJ5zz40zR0zq0zf0zX0zNzzEzz5zz0zz0zzszzmzzh\ zzbzzYzzUzzOzzKzzGzzCzz9z } 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 19-01-11 (Seeing Triple [7])
by Jim Muth 19 Jan '11

19 Jan '11

FOTD -- January 19, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the same spread-out, wedge-shaped valley as yesterday's image, and it shows much the same kind of features. But while yesterday's image was located on the south side of the valley, today's image lies on the north side. A good part of today's image consists of 'inside' areas brought to life by the inside=zmag option. The inside stuff is so arranged that it's rather hard to tell where the outside ends and the inside begins. The rating of a 7 reflects my opinion of the basic worth of the image. I did put some effort into the coloring, but not enough earn a reward of a half-point coloring bonus. The name "Seeing Triple" refers to the cubic nature of the poorly-defined minibrot at the center. (The image should have a higher maxiter.) When I thought of the name, I was wondering how many eyes a four-dimensional being would need for 4-dimen- sional vision in his 4-D space. I decided on three eyes, but two might be sufficient. Regardless, the name refers to the minibrot, not a hypothetical hyperbeing. The calculation time of 2-1/3 minutes is about average for a fractal. Time may be saved by viewing the finished image on the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site at: <http://www.Nahee.com/FOTD/> is still waiting for Paul to recover. The snow and ice on Tuesday prevented any further work on the upcoming FOTD web site. Two inches, 5cm, of snow fell overnight Monday here at Fractal Central. The snow changed to freezing rain Tuesday morning, leaving a crunchy coating on the snow before ending by noon. The temperature finally rose one degree C above freezing in the afternoon, making the job of clearing the fractal sidewalk much easier. The fractal cats watched the outdoor action with much interest, but took frequent breaks on their shelf over the hall heater to keep warm. My day was occupied by moving snow and ice, while FL kept the commercial work moving and the coffee hot. The next FOTD will be posted in 24 hours. Until then, take care, and when the going gets tough, the tough look for help. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Seeing_Triple { ; time=0:02:22.25-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident float=y center-mag=-1.089025340083513/+0.00811676821096749\ /2.088175e+011/1/-100/0 params=3.001/0/0.001/0 maxiter=1500 inside=zmag logmap=406 periodicity=6 mathtolerance=0.05/1 colors=000A8FIgWDga9ag4Wm0Ps2Ni3L`5IR6GO7FO7EO8CR9\ AU9ASAATAAWEAXIAXMCYPEYZHQghIppAyw2ppBhiK_bTSX`TZc\ T_eU`hUbjVcmVdoQahMZbHWWDTQ8QJ4ND0K7ML7TOAZRCdUEjX\ GpZIjUNdQRZMWTH_NDdI9hNFeSLbXR`aXYfbVkhTpnQttOhqLY\ oINlFCjC1h97`LCUW9PY7L_5G`3Cb18c4Cd7Fd9JdCMeFQeHTe\ MQcQNbVLaZI_cGZgDYkBXgHYcMZ`SZXX_Ta`Qg`MlaJqaSgV_Z\ OaWMcTLeQKgNJiKIkHHUK_CMrLWsUesboskxsmttomuqbusSvu\ Ivw0wyOwpUshbo`kkTwgizcuz_zzWzz`LkdTfh_almAxXTpKIa\ JQcIXeHdgEU4F_IGeWecgTghu47gJKUYXECDFOOG_ZWFrSOoOW\ mKckN3HLFPKQWI`bVhBOjTotLan4WmFRlPMk_WPuSVrO`oKfl8\ zIBvPDrWFnb3m9dSeuPpUhxNjp7U9AZJCbSFg`lYRXd`c80YIC\ SSNMaZ7qxAotCnpFllMC1KLDJUOBMLGYE0CM5HW9LdEPnITwEW\ ILKPR9VQF_PLcOQgNWlM`pLftLyzNjyPjyRiyTizVhzXhzYhzW\ grVgjTgbSfVQfNPfGVj8_m1fWUmEvdY`XqFRrDMsBH09Cu77v6\ Iw6Sx6by6lz6vz6XzI7zTCzQHzNzzLzzIzzFzzDzzLzzSzzZzz\ ezzlzz`zzzzzzzzzzzzzzzzzz } 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 18-01-11 (Surreal Cubism [7.5])
by Jim Muth 18 Jan '11

18 Jan '11

FOTD -- January 18, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image differs from the usual image in that the minibrot at its center is cubic rather than the much more common quad- ratic. Its parent fractal is a small variation of the Z^3+C Man- deloid. The variation is that the exponent is 3.001 and the parent is calculated at a level 0.001 turns up the logarithmic hyperspiral. The parent fractal also is rotated 90 degrees, so that it lies on its side. As a result of all these differences, the negative X-axis cuts through the valley that normally would lie at the center of the large period-2 northern bud. This valley appears as a wedge, trying to split the bud down its center, and is of a type that does not exist in the classic Mandelbrot set In today's parent, the small departure from the true ground- level Z^3 Mandeloid causes the negative X-axis to be infinitely divided, which does strange things to the parts of the fractal that happen to fall there. Exactly what kind of strangeness takes place is apparent in today's image. I named the image "Surreal Cubism", which must mean something, though I doubt that it has any connection to early 20th-century art forms. The rating of a 7-1/2 includes a half-point for the coloring. The image might or might not be worth it. The calculation time is quite brief -- under 1-3/4 minutes. This will keep impatience suppressed. The task of calculation may be totally eliminated by viewing the finished image on the active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site may be found at: <http://www.Nahee.com/FOTD/> though it is not up to date. Bleak gray skies and a temperature around 23F -5C kept the fractal cats very near the heat all day Monday here at Fractal Central. The forecast of snow overnight and ice on Tuesday promises another bleak day to come. The fractal cats are unconcerned. They live in the present, and never worry about the future until it actually happens. The Monday of the humans, (a good name for a horror movie), was busier than expected, which left no time to get involved in the upcoming web site. The next FOTD will be posted in 24 hours. Until then, take care, and keep the controversy at a minimum. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Surreal_Cubism { ; time=0:01:43.53-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident inside=0 center-mag=-1.097220314469322/+0.00347417864711567\ /9.5e+011/1/-45/0 params=3.001/0/0.001/0 logmap=166 float=y maxiter=1200 passes=1 mathtolerance=0.05/1 colors=000fVgdWebXc`XdVYeN_f9bg5bZ5WQ2IH0C8LHtABSY\ QqRLfKHWDDL69A_RDSMALI7ED5792zzzu_pfHXYCNP9HL7DG68\ C70060F6RD6NA6I75D559254vF5Cgw9Yh6OU3EFsDIlCFeBDZA\ BS99r86zK4rF2lCDfHAYF8QC6HA487216O05K05H05D05A0560\ 53XLVOHNGDF897DA5A94783572261z7QV6Diao_VdROVIIK9BA\ 6cT5YO4SJ3ME2G91A43xcnZaeUVYPPPKJHFC8A616M05I05F05\ C059056053mxzmxzExzB_T7QJ3F9pgnZVYHIHLGMHEIECEAAB7\ 87363PYAIQ7CJ56C25AifMQZJLSGHLDDEA8774KzezzdzzdLzc\ zgcLzbzzbLzbMfaMzaMf`Mz`Ne_Nz_NeZNeZNzZOeYOeYOdXOd\ XPdWPdWPdVPdVWBWSQVPdVNrXMsWMsVMsUMsUMtTMtSMtRMtRM\ uQMuPMuOMuOMvNMvMMvLHxNMvLQrKVoIZkH`jEaiFbhGcgGdfH\ eeHfdIgcIhbJiaKj`Kk_LkZLlYMmXMnWNoVOpUOqTPrSPsRQtQ\ QuPRuPRsRTqSUoUVmVWlXYjYZh__f``dbacccaed_feYhfXigV\ jiTljRmkPolOpnMroKspIuqGvrFxtDxuBxv9xw7xz8xy8xx9xw\ 9xw9xvAxuAxuBxtBwsBvsCurCuqDtpDspDroEqnEpnFpmFolFn\ lGmkGljHkiHkiHjhIigIhgJgf } 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] AOTD 1_8_11
by JackOfTradeZ＠comcast.net 17 Jan '11

17 Jan '11

. Zoom-In to FOTD 1/8/11 "Elusive Butterfly" is posted: http://www.fractal-animation.net/vid/eb.zip .

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<JoTz> What's the significance of/reason for the color map shifting?
by Hal Lane 17 Jan '11

17 Jan '11

JoTz, Thanks for posting the link to your: Zoom-In to FOTD 1/8/11 "Elusive Butterfly" Very nice. Enjoyed the zoom. What's the significance of/reason for the color map shifting and then apparently returning to its previous values as the zoom progresses? Does the non-zero logmap value make the color map automatically adjust as the zoom progresses? Sometimes the map shifts slowly -- other times it changes quickly or rapidly pulses. If it *is* the non-zero logmap doing it, I'm puzzled by why the color map appears to return to its previous value after a change... - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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FOTD 17-01-11 (Testing the Second [?])
by Jim Muth 17 Jan '11

17 Jan '11

FOTD -- January 17, 2011 (Rating ?) Fractal visionaries and enthusiasts: Today's quick fractal lies on the southwest shore line of the main bud of the Z^(2.002)+C Mandeloid. But it's not what would be expected at this location. The entire parent fractal has been rotated so that the negative X-axis cuts through the bud at this point, and things almost always get somewhat chaotic near the X-axis of fractals with fractional exponents of Z. The rating of a ? means that I was undecided on how to rate the image. On one hand, it's something never before seen; on the other hand, it's just another picture of a minibrot with a fancy basin around it. The name "Testing the Second" is a re-arrangement of the first title that came to mind -- "The Second Test". There was a first version of the same scene that failed miserably. The whole image is still little more than a test, which is another reason why I could not decide on a rating. The calculation time of 1/100 second under 2 minutes is fast enough to keep boredom at bay, yet slow enough to allow time to pour a drink in preparation for the grand revelation of the never-before-seen image. Those who would rather not run a parameter file may view the full image in hi-def, rendered by Hal Lane and posted to the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Paul's original FOTD web site is still at: <http://www.Nahee.com/FOTD/> though it has not been updated in a while. I think we'll begin uploading stuff to my own FOTD web site on Monday, so be prepared for an upcoming announcement. Except for a heavy but brief snow shower in the morning, Sunday was a typical midwinter day here at Fractal Central, with ample sun and a temperature of 34F +1C. The fractal cats took full advantage of the sun while it was shining, and fled to the warmth of the shelf over the heat when the sun sank beneath the top branches of a tree across the road. The humans had an active but not hectic day. The next FOTD will be posted in 24 hours. Until then, take care, and sometimes the answer to a perplexing problem is found where least expected. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Testing_the_Second { ; time=0:01:59.99-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident logmap=214 center-mag=-1.189344865796988/+0.00123281218592462\ /2.17847e+010/1/2.57/-0 params=2.002/0/0.1/0 float=y maxiter=1200 periodicity=6 inside=255 mathtolerance=0.05/1 colors=000Q0PS0QU0RW0SY0T_0Ua0Vc0We1Xg2Yi3Zk4_m5an\ 6bm7ci7`f6Yb6V_6SW5PT5MP5JM4GI4DF4AB37834531762892\ AB2BE2DG2EJ2GM3HO3JR3KT3MW3NY3CyFHsDMnCQhAVc9_Z8cT\ 6hO5mJ4qD2v81z30t6Do9PjC`eFlaMnYSpUYrQctMivIoxEuya\ VucWaeXJfX0d`3bc6`g8ZjBZmEdqGjtJlwLjtJdqIZnGUkFPiD\ LfCHcAF`9EZ7DW6BT4AQ39O2DS5HV8LYBO`EScHWfK_iNblQfo\ TjrWmuYjp_gl`egbbcc_ZeYVfVRgSMiQIjNDlK9mI5ncFTxP7s\ SCoVGpZJqaMrdPshStkVunYri_odal_biVdfQf8GV8GV8GU7GU\ 7FU7FU7FU7FU7FU7FU7FU7EU7EU7EU7EU7EU6EU6DU6DU6DU6D\ U6DU6DU6DU6CT6CT6CT6CT5CT5CT5BT5BT5BT5BT5BT5BT5BT5\ AT5AT5AT4AT4AT4AT4AT49T49T49S49S49S49S48S48S48S38S\ 38S38S38S37S37S37S37S37S37S36S36S26S26S26S26R26R25\ R25R25R25R25R25R24R14R14R14R14R14R14R13R13R13R13R1\ 3R13R22Q13R13R13R14R14R14S15S15S15S16S16T16T17T17T\ 17T18T18U18U18U19U19U19V1AV1AV1AV1BV1BV1BW1CW1CW1C\ W1DW1DX1DX1DX1EX1EX1EXzzz } 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 16-01-11 (The Ins and Outs of It [No Rating])
by Jim Muth 15 Jan '11

15 Jan '11

FOTD -- January 16, 2011 (No Rating) Fractal visionaries and enthusiasts: Today's image is an experimental one, which is why I gave it no rating. It came about as I was trying different color palettes in search of a way to add the strongest 3-D effect to a fractal. I decided to experiment with the FOTD image for this past Janu- ary 9 because it is filled with assorted hills and valleys. The Jan 9 image is named "Chaos Incorporated". Today's image is a small outzoom of that earlier image. After trying several handmade color palettes with little suc- cess, I brought up the built-in ctrl(f1) palette. A little color tweaking gave me just about what I wanted. In today's image, the antiminibrot hills are bright at their centers, while the normal minibrot valleys dark centers surrounded by lighter circular ridges, making the difference quite easy to recognize. Today's image is named "Ins and Outs of It". The name refers to the tiny hills and basins that fill the image. The calculation time of 2 minutes is blessedly brief, though I have no idea who or what might be giving the blessing. The image may be seen without the inconvenience of calculating a parameter file by visiting the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where Ken is doing a fine job while Paul is under the weather. Paul's original web site is available at: <http://www.Nahee.com/FOTD/> My own web site is in the advanced planning stage. The delay is due to a lack of time, always a problem here at FC, but the big announcement is not too far off. Lots of clouds, a morning low temperature of 19F -7C and an afternoon high of 34F +2C made things rather unpleasant here at Fractal Central on Saturday. The fractal cats lost hope for sun early in the afternoon, and spent their time by the heat. The day of the humans was uneventful, though rather busy. The next FOTD will be posted in 24 hours. Until then, take care, and be lucky. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Ins_and_Outs_of_It { ; time=0:02:04.69-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+0.3438119752193325/-0.0560302035781431\ /1.625815e+013/1/-32.65/0 params=5/10000000000.0\ /0/0 float=y maxiter=1250 inside=0 logmap=164 periodicity=6 mathtolerance=0.05/1 colors=000zzuzzuzzuzzuzzuzzuzzuzzuzzuzzuzzuzzuzzuz\ zuzzuzzvzzvzzvzzvzzvzzvzyuzxtzxtzwszwszvrzsrzsqysq\ yspxsqxspxspwrowrovqnvqnupmupntomtomrnlrnlqmkqmkpl\ jolknkjnkjmjimjilihlihjhgjhgigfigfhfehfegedgededce\ dddccdcccbbcbbbaabaaa``a```__`__ZZZZZZYYYYYYXXXXXX\ WWWWWWVVVVVVVVVUUUUUUTTTTTTSSSSSSRRRRRRQQQQQQPPPPP\ POOOOOONNNNNNMMMMMMLLLLLLKKKKKKJJJJJJIIIIIIIIIIIIH\ HHHHHHHHHHHGGGGGGGGGGGGFFFFFFFFFFFFEEEEEEEEFEEFDDE\ DDECCDCCDBBCBBCAABAAC99B99B88A88A77977966966955855\ 855855855866966A77B77B88C88C99D99DAAE99EAAFAAFBBGA\ AFBBGBBGCCHBBGCCHCCHDDICCHDDIDDIEEJDDIEEJEEJFFKFFK\ GGLGGLHHMHHMIINIINJJOJJOKKPKKPLLQLLQMMRMMRNNSNNSOO\ TOOTPPUPPUQQVQQVRRWRRWSSXSSXTTYTTYUUZUUZVV_VV_VV_W\ W`WW`XXaXXaYYbYYbZZcZZc__d__d``e``eaafaafbbgbbgcch\ cchddiddieejeejffkffkgglgglhhmhhmiiniinjjojjokkpkk\ pllqllqmmrmmrnnsnnsootoot } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 15-01-11 (Yugen of a Fractal [7])
by Jim Muth 15 Jan '11

15 Jan '11

FOTD -- January 15, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes almost two hours to finish, even when calculated with the fastest option, the passes=b. The reason, of course, is that the image lies at a depth where arbitrary precision math is required. The scene lies in the valley of the large bud on the northeast shore-line of the main bay of the large minibrot on the stem of the Mandelbrot set. No trickery was used in the image, which was rendered with the usual equal-iteration band method. The name "Yugen of a Fractal" came to me while I was contempla- ting the image and all the smaller minibrots deeper within it, which will never be seen. (Yugen is a Japanese word, almost impossible to translate, but roughly describing the feeling of adventurous longing one experiences when gazing at something mysterious and unattainable, yet strangely beautiful, barely visible in the distance.) The image rates a 7, which is not too bad, considering that it is just another scene not all that deep in the Mandelbrot set. The burdensome calculation time of over 1-3/4 hours may be bypassed by surfing over to the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image is or soon will be posted. The original FOTD web site at: <http://www.Nahee.com/FOTD/> is still up and running, at least when I last checked. A typical midwinter day came and went without a notable event here at Fractal Central on Friday. The sky was partly cloudy with a temperature around 28F -2C. The fractal cats were their typical midwinter selves, spending most of the day on the warm shelf, and taking a break only to chase a string and eat their food. My day was fairly normal, as most days are. The next FOTD will be posted in 24 hours, which is absolutely normal. Until then, take care, and one person's deep meaning is another person's nonsense. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Yugen_of_a_Fractal { ; time=1:48:54.11-SF5 on P4-2000 reset=2004 type=mandel passes=b center-mag=-1.750568515302929251321618/0.009853308\ 3431521213283303/1.545503e+020/1/35/0 params=0/0 float=y maxiter=52000 bailout=9 inside=120 periodicity=6 mathtolerance=0.05/0 colors=0009LKAOLBSNDYOEbQFeUGiZIlcJphKsmPvrUsvZpzc\ nzmkvsirwfmwdhwacw_ZwXUwVPvSKrQFmNEhLDeKCbKC_KBYKB\ VKASHAQF9NA9K88I88F87F87KA6PC6UF5ZJ5cN7hR9mVBrZDvb\ FzfHthNpjImcDjY9kcMkiZzuhknkYgmK`p4Ut6Vr7Wq8Xp9XoA\ YmBZlCZkD_jF`hG`gHafIbeJbcKcbLdaIe_Md`Pd`SdaVdaYdb\ `dbcdb__aXW`US`RN_OJZLFZJKYIOYGSXFWZD_cCdhAhm9lr7q\ v6tz5xzEzzKzzPzzUzzUzzZzzczzhzzmzzrzzvzzzzzzzzzzzz\ zzM_NLXRKUUIRXHP`zz0FJgEGjDEmCKfBQ_AWU9aN8gH7mA7r4\ 9p7AoAmnDmmGmlJmkMmjPmiSmhVmgYmdSmebmfdmfemgfmghzh\ izhjzfgzeezdczc`zaZz`Xi_ViZShYQhWOhVLgUJgTHgSFjWHl\ ZJnbKpeMriOtlPofOjaNeWN`RMWLLRGLMAKH5JC0JB1MA1PA1R\ 92U82W82Z73`73c63f54h54k44m35p35r25u25w78rBBmGEiKH\ dgdzedzcdzadz_dzXdzVdzTdzRdzPdzNdXPbYQaZS`ZT__UZ`W\ Y`XXaZWb_Vb`UcbTdcSdeRefQfgPfiOgjNhlMhmLinKid92cD5\ bG8aJB`ME_QHZTKZWNYZQXbTWeWVhZUkaUndQi`0880990AA0B\ B1CC2DD3EE4FF5GG6HH7II8JJ } END PARAMETER FILE=========================================

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FOTD 14-01-11 (The Far North [6])
by Jim Muth 14 Jan '11

14 Jan '11

FOTD -- January 14, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's image takes us deep into the parent side of the west branch of the prominent valley of the large period-3 bud on the northern side of the main bay of the Mandelbrot set, where after a minor bit of exploration, we find today's scene, featuring the usual central minibrot. The image was rendered with the outside set to 'summ', though the only improvement over the normal 'iter' rendering is a few brilliant highlights. Perhaps the best rendering is achieved by resetting the logmap to 'yes' and setting the outside to 'tdis'. Unfortunately, this increases the calculation time to an hour, and I'm not sure the result is worth the effort. Since the Mandelbrot set has been examined and examined again so many times, I could give the image a rating no higher than an average 6, but it's really a rather pleasant scene, with its strikingly intense colors. The name "The Far North" indicates the location of the scene in respect to the main bay of the M-set. Those who wish to be reminded of Greenland by the name, may do so at their pleasure. The 41-second calculation time of the fast parameter file will pass in a flash. Those who decide to run the slow version will have their decision rewarded by a slightly different, question- ably better version of the same scene. The fast 'summ' version of the image may be seen in finished form on the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and if Ken decides to post the slightly different slow version, it may be found there also. In the meantime, the original FOTD web site is still online at: <http://www.Nahee.com/FOTD/> though the last time I checked, it was not up to date. The sun was quite strong all day Thursday here at Fractal Central, and the fractal cats made the most of it by spending the entire afternoon on the shelf in the sunniest window. The outside temperature of 28F -2C bothered them not at all. My day was routine. The next FOTD will be posted in 24 hours. Until then, take care, and to find the meaning of life, look beneath the surface of the world. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= The_Far_North-fast { ; time=0:00:41.12-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.1281832946783\ 11/+0.649523014799861/1.291657e+011/1/120/0 float=y params=0/0 maxiter=250000 inside=0 outside=summ passes=1 logmap=5600 mathtolerance=0.05/1 colors=00000Kz0uz0zz0xz0gz0Pz5AiI8SW8Cg8zK0z00z10m\ C5SMG5YS0ga0ig5imEisOixMcsKYoISkGMgEGce0Wk0Oq3GxC7\ zK0zU0za0zW0zS0zO0zI3zE7zACz5Gz1Mz0Pz0Uz0_z0cz0iz0\ mz0qz0gz0_z0Sz0Kz0Cs05m00e00_00U00O00P00P00P07P0KS\ 7YSIkSSzSczSmzYazcPziEzo3zu0zz0zz0zz0zCIxm0zP0zqx0\ ck0S_GEOeGizCazAWz7Pz5Kzz8zqAziAzaCzWCzOCzGEz8EzOI\ 1CGYq80eA0WC7MCPCEi0Kz0Iz0Iz0Gz0Gz0Gz0Ez1EzzW0za5u\ UPUMiz5Az8OkAaOCoczoYzqSqsMiuIaxCUz7Mzzzzicz0zz0xz\ 0qz0iz0cz0Yz1Pz3Kzi0q_3uS7xI8zACz000M0Ee0E0Pe_3zUM\ zOKzIIzCGz7EzzzzeazoSgsm0zukxuequYmeSiuMexE_x8zx1z\ x0za0Um0Yc0aU1eK5cA7U1Ac0Em0Iw0Mz0Oz0Kx0Gs0Cq78mI5\ iU1gc0co0_z0Yz0Kz77zP0xi7oeGgcPa__UYiOUsGSzAPz5Mz1\ Kx0Ix0Gc0Ec0Cc0Ac08o07o05m03z01k00g01c03a05Y07W08z\ 0AO7CMCEIKGGPICYK8cM7kO3qP1xPzqOzsOzuOzxOzzOzzMzzM\ zzMzzMzzMzzKzzKzzKzzKzzKzzIzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } The_Far_North-slow { ; time=1:01:56.06-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.1281832946783\ 11/+0.649523014799861/1.29166e+011/1/120/0 float=y params=0/0 maxiter=250000 inside=0 outside=tdis logmap=yes mathtolerance=0.05/1 colors=00000Kz0uz0zz0xz0gz0Pz5AiI8SW8Cg8zK0z00z10m\ C5SMG5YS0ga0ig5imEisOixMcsKYoISkGMgEGce0Wk0Oq3GxC7\ zK0zU0za0zW0zS0zO0zI3zE7zACz5Gz1Mz0Pz0Uz0_z0cz0iz0\ mz0qz0gz0_z0Sz0Kz0Cs05m00e00_00U00O00P00P00P07P0KS\ 7YSIkSSzSczSmzYazcPziEzo3zu0zz0zz0zz0zCIxm0zP0zqx0\ ck0S_GEOeGizCazAWz7Pz5Kzz8zqAziAzaCzWCzOCzGEz8EzOI\ 1CGYq80eA0WC7MCPCEi0Kz0Iz0Iz0Gz0Gz0Gz0Ez1EzzW0za5u\ UPUMiz5Az8OkAaOCoczoYzqSqsMiuIaxCUz7Mzzzzicz0zz0xz\ 0qz0iz0cz0Yz1Pz3Kzi0q_3uS7xI8zACz000M0E_BL0Pe_3zU7\ cOKzI7zCGz70KjhzeazoSg0Z0zukxuequYmeSiuMexE_x8zx1z\ x0za0Um0Yc0aU1eK5cA7U1Ac0Em0Iw0Mz0Oz0Kx0Gs0Cq78mI5\ iU1gc0co0_z0Yz0Kz77zP0xi7oeGgcPa__UYiOUsGSzAPz5Mz1\ Kx0Ix0Gc0Ec0Cc0Ac08o07o05m03z01k00g01c03a05Y07W08z\ 0AO7CMCEIKGGPICYK8cM7kO3qP1xPzqOzsOzuOzxOzzOzzMzzM\ zzMzzMzzMzzKzzKzzKzzKzzKzzIzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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FOTD 13-01-11 (A Hole in Time [5.5])
by Jim Muth 13 Jan '11

13 Jan '11

FOTD -- January 13, 2011 (Rating 5.5) Fractal visionaries and enthusiasts: As I forecast in yesterday's FOTD, today's image is a descent into the inside of the debris-filled minibrot of yesterday's image. The scene is located near the center of the main bay, just south of the centers of the concentric rings. The name "A Hole in Time" is a fantasy. I assumed that time is the fourth dimension and today's image is a hole in its ceaseless flow. The rating of a 5-1/2 equals the amount of snow (in inches) that fell overnight here at FC. It also implies that the image is not quite up to FOTD standards. At first glance, the open areas in today's image appear as though they would fill in with a higher maxiter. This is not so. The points of the open areas are trapped forever. I raised the maxiter to 50,000 and found no change in the resulting image. (Actually there was a change. The calculation time more than tripled.) The calculation time of 2-1/3 minutes is a bit slow for such a modestly rated image. The way to avoid immodesty is to view the finished image in its full glory on the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And don't forget the original site at: <http://www.Nahee.com/FOTD/> Snow fell through the night Tuesday here at Fractal Central, and by daybreak Wednesday 5-1/2 inches 13cm were on the ground. The temperature rose from 23F -5C to 28F -2C by afternoon, as the clouds hung on and a few snow flurries continued. The fractal cats watched alertly from their window shelf as I cleared the pavement, then decided the shelf was too chilly and took to the shelf by the heat. The rest of the day was incident free. The next FOTD will be posted in 24 hours. Until then, take care, and search for the runaway fractal. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= A_Hole_in_Time { ; time=0:02:21.95-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 center-mag=+0.25963570772/-0.001512409298/5413836/\ 1/12.5/0 params=0/0/0/0/-4.4/0/1e-100/0 float=y maxiter=5000 inside=0 periodicity=0 colors=000zzBzzCEzCzzCFzCzzCHzCzzDzzDJzDzzDzzDzzDz\ zFPkHRkJSkLUkNWkPXkQZkS`kUUb5Ud5Ug5Ui5Uk5Xf6Zb6`Y7\ bU7ZQAWNCTKEQGGMDJJALG6ND3PA0RG7SLESQLSVRSYWO`_Lcc\ IfgFikBlo8os5rw2pr4om5nh7mc8lZAjUBiPDhKEgFGfAHe6IR\ XJDvKCuICuHCuGCuFCtECtDCtCCtBCs9Cs8Cs7Cs6Cr5Cr4Cr3\ Cr2Eq5Gp7HpAJoCKnEMnHNmJPlLRlOSkQUjSVjVXiXYiZcfaid\ dnbfi_gdXg_VhVShQQiLNiGKjBIj6Fk1Dk5Cl9BmCAnGAoJ9oN\ 8pR7qU7rY6s`5sd4th4uk3vo2wr2wj6jcAYWELPI8NMALPCKSE\ IVGGYIF`KDcMBfOAiQ8lS6oU5rW3uY2xZ4vX6tW8rUAqTCoSEm\ QGkPIjOKhMMfLOdKQcISaHU_GWYEYXD_VCaTAcR9eQ8eO9eM9e\ L9eJAeIAeGAeFAeDBeCBeABe9BfACfADfBEfBEfCFfCGfDHfDH\ fEIfEJfFKfFKfGLfGMfHMfHNfIOfIPfJPfJQfKRfKSfLSfLTfM\ UfMUgNVhOVhPWiQWiRWjSXjSXkTXkUYlVYU9KP9AS9DV9GYAJa\ AMdAPgDUjGXmLZnR`pWbr_btcbvgcxhcwcctYdqSenMfjGggAh\ d4ia0jZ0hW0fT0dQ0bN0`K0ZH0XE0VB0T80R50P30N40L50J60\ H60F70C8099LB9MBAOBBPBBPB } 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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FOTD 12-01-11 (A Brot in a Spot [6])
by Jim Muth 12 Jan '11

12 Jan '11

FOTD -- January 12, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's excursion into the HyperMandelbrot set takes us to the East Valley area, where we check the condition of the large minibrot on the shoulder of the period-32 elephant on the southern side of East Valley. What we find is "A MiniBrot in a Spot". Minibrots are supposed to be empty on the inside -- this emptiness is what defines a minibrot. But the minibrot in today's image is filled with superfluous, concentric rings of curious stuff that makes me wonder whether it is still proper to call it a minibrot at all. I suspect that this extra stuff is not truly real. It easily might be an artifact of the math routine, when such tiny values as 10^(-100) are entered into it. But wherever the stuff comes from, it is one of the most curious things I have stumbled upon in all my 20-some years of fractal exploration. In tomorrow's image I will see what unexpected surprise goodies I can find on the inside of today's minibrot. The rating of a 6 is not as high as I would have preferred, but the fast calculation time of just over 2 minutes means that little effort will be required to run the attached parameter file. And for those with calculation problems, the finished image is available on the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site, maintained by Paul Lee for almost 14 years, may be accessed at: <http://www.Nahee.com/FOTD/> but it is probably not up to date. Heavy clouds hung over Fractal Central all day Tuesday, and to make matters worse, snow began at 3pm. The temperature rose from 16F -9C at daybreak to an afternoon high of 28F -2C. The fractal cats checked the outside a couple times to keep track of the snow, then settled on their shelf by the heat. My day was about normal, which means everything stayed well under control. The next FOTD will be posted in 24 hours. Until then, take care, and it seems as though the more I learn, the less I know. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= A_Brot_in_a_Spot { ; time=0:02:06.93-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 passes=1 float=y center-mag=+0.2596401989/-0.0015216554/33755.27/1\ /-162.5/0 params=0/0/0/0/-4.4/0/1e-100/0 maxiter=3000 inside=0 logmap=84 periodicity=0 colors=000MUWMTWNSVNSUNRUOQTOPTOPSPORPNRPMQPMQNPRM\ RRLTSJVSIXTHZTGaUEcUDeVCgVAiW9kW8nX7pX5rY4tY3vZ2xZ\ 4vX6tW8rUAqTCoSEmQGkPIjOKhMMfLOdKQcISaHU_GWYEYXD_V\ CaTAcR9eQ8eO9eM9eL9eJAeIAeGAeFAeDBeCBeABe9BfACfADf\ BEfBEfCFfCGfDHfDHfEIfEJfFKfFKfGLfGMfHMfHNfIOfIPfJP\ fJQfKRfKSfLSfLTfMUfMUgNVhOVhPWiQWiRWjSXjSXkTXkUYlV\ YlWZmXZmYZnY_nZ_o__o``pa`pbaqcaqcardbrebsfbsgcthct\ hcpgdmfeifffegceh_diXdjUckQclNbmKbnHZhFVcDRZBOU9KO\ 7GJ5CE3994BA5DA6EA6GA7HA8JA9LB9MBAOBBPBCRBCSBDUCEW\ CFXCFZCG_CHaCIcDIdDJfDKgDLiDLjDNkFPkHRkJSkLUkNWkPX\ kQZkS`kUbkWckYek_gkahkbil`il_ilZimYjmXjmWjnVjnUknT\ koSkoRkoQlpOlpNlpMlqLmqKmqJmrImsHntGpwFrzEtzDvzCxz\ DzyEzxKzwPzvUzuZztczshzrmzqrzpvzozznzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzumzymzzmzzmzzmzKOfPWyVUj`PUmOHzVz\ czzzz0tlJUzCz`khPzcDzcDzg2zQZzXcz0hzTmzXmz`mzHmzNm\ zTmzZmzFmzPmzZmzgmzlmzpmz } 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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FOTD 11-01-11 (In the New World [?])
by Jim Muth 11 Jan '11

11 Jan '11

FOTD -- January 11, 2011 (Rating ?) Fractal visionaries and enthusiasts: Since I have no idea what's happening in today's image, I'll not try to analyze it to find out what's going on. All I know about it is that the parent fractal is a Mandelbrot set with a lot of extra stuff along the shorelines of the bays and buds. Today's image lies in the extra stuff that clogs the Seahorse Valley area of the parent. The bud in the image is like none I have seen anywhere. One thing certain is that the image lies in the Hypercomplex Mandelbrot set, though I have no idea why the ridiculously tiny real(p4) parameter makes such a difference. The image might be an artifact of imprecision, but even if this is so, it has all the attributes of a 'real' fractal, (whatever a real fractal might be). The rating of a ? expresses my confusion about such images. Also, the artistic worth is lacking, and I did not want to give an embarrassingly low rating. The name "In the New World" does not refer to the era of explora- tion. It indicates that the image exists in an entirely new world of fractals, a world that, BTW, is in need of quite a bit of exploration. The calculation time of 7-1/2 minutes is a bit expensive for the result. The slowness is necessary because periodicity must be turned off when the HyperMandelbrot2 formula is used. A better time bargain may be found on the active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image is or soon will be posted. The original FOTD web site at: <http://www.Nahee.com/FOTD/> is not up to date. Monday here at Fractal Central began with a temperature of 14F -10C, and reached an afternoon high of 34F +1C. The fractal cats enjoyed the sun that filtered through the high clouds. My day was kept busy trying to explain the Boltzmann brain problem to FL. (In fact, I'm still trying to explain it to myself.) If all goes well, the next FOTD will be posted in 24 hours. Until then, take care, and when I grow up, I'm going to be a Boltzmann brain. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= In_the_New_World { ; time=0:07:31.05-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 passes=t float=y center-mag=-0.7500761333772764/-0.0002675458948816\ /8.292033e+009/1/-31.5/0 params=0/0/0/0/-4.3/0/\ 1e-150/0 maxiter=5000 logmap=2556 periodicity=0 colors=0000006ET5EV5EW4EY4E_3E`3Eb2Ed2Fe6Gf9IfCKgF\ MgIOhLQhOSiRUiUWiYYb`_WcaPfcIieBjgDjiEkkFkmGloIloJ\ mpKmpLnoNnnOomPolQokRmjVkiZihaggeeficeladp_csYboWa\ kV`gUbcTe`SiXSlURpRQsNPwKPzHQpORgURZ`SQfSHlTJkULjV\ NiWPhXRgYTfZVeZWe_Yd`_caabbcace`dg_dh_ZkUUnOPqJSlK\ VhKYcL`_LcVLfRMiMMlIMoDNr9Nu5NsCMqILoPKmVJlaJjgIhn\ HftGezGAwWBuWBsWCqWDoWCmYDmWEmVFmTGmSHmRImPJmOKmNL\ mLMmKNmJOmHPmGQmERmDSmCTmAUm9Vm8Wm6Xm5Zm1Ym4Xm7XmA\ WmCVmFVmIUmKUmNTmQSmSSmVRmYRm_SmZTmYUmYVmUVmUWmUXm\ UYmUZmUYmUYmUYmU_mUYmUXmUVmUUmUSmURmUUmmUmmUmmUmmU\ mmUmmUmmUmmUmmUmmUmmUmmUmmUmmUmmUmmcmzcmzcmzcmzcmz\ cmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzmmzmmzmmzmmzmmzmm\ zmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzzmzzmzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmz\ zmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzm\ zzmzzmzzmzzmzzmzzmzEmzFmz } 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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Recording "legacy" MIDI synth
by Jay Litwyn 10 Jan '11

10 Jan '11

I hav my sound card's line out feeding into my amplifier/radio's video-in, and a tape deck is on it, so I can record, then feed the line out from my amp to my computer's line-in. To eliminate possibility of feedback, I never do both at once. So, I can record synth output onto tape, then transfer that back to my computer. It is not neat. It is not low noise. It just works. I am just wondering if anyone plans to implement "windows sound system" calls, so that all I hav to do is call up "sound recorder", select 44.1kHz/mono and press the rec button before I make winfract play something. _______ http://ecn.ab.ca/~brewhaha/Sound/Puppy.mp3

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FOTD 10-01-11 (In de-Sitter Chaos [6.5])
by Jim Muth 10 Jan '11

10 Jan '11

FOTD -- January 10, 2011 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image is a scene in the Seahorse Valley area of the Hypermandelbrot set. And yes, that is a minibrot at the center of the screen. But as is immediately obvious, the minibrot has a problem. It is filled in. I have no idea why such an infini- tesimal value as 10^(-150) should make such a great change in the appearance of the minibrot. But the change is real, and it is possible to zoom into the interior of the minibrot. The name "In de-Sitter Chaos" refers to the overall chaotic appearance of the image, which is typical of scenes in Hyper- Mandelbrot fractals. de-Sitter space is, by current cosmolog- ical thinking, the ultimate state of the universe if it keeps expanding and cooling indefinitely -- an infinite and eternal space of maximum entropy, a featureless soup of vacuum energy and seething virtual particles at a temperature of something like 0.00000000000000000000000000001 degree Kelvin. And it's hard to get any colder or any more chaotic than that. The rating of a 6-1/2 includes no personal reward for the color- ing. I simply could not decide between a rating of a 6 or a 7. The calculation time of 8 minutes is a bit slow. Luckily, the finished image is available on the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> the original FOTD web site may be accessed at: but it is probably not up to date. <http://www.Nahee.com/FOTD/> Sunday here at Fractal central was partly cloudy with a morning low temperature of 19F -7C and an afternoon high of freezing. The fractal cats found the on-and-off sunshine annoying, and took up residence for the afternoon on the shelf by the heat, where the warmth is more dependable. My day was average. The next FOTD will be posted in 24 hours. Until then, take care, and why are we like that? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= In_de-Sitter_Chaos { ; time=0:08:05.18-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 passes=1 float=y center-mag=-0.7377505903290246/+0.1741944660245706\ /1e+010/1/58.7/0 params=0/0/0/0/-4.3/0/1e-150/0 maxiter=5000 inside=0 logmap=-1176 periodicity=0 colors=00089R9ASABTBCUCDVDEWEFXFGYGHZDIS9DL69E347c\ oEXfBQY9KQ7DH4682T1KN0GH0CB08504Z29Q16H14802DKNVRH\ FD8gJ2XE1M91B40xgCcT8KE4lFU_BMO7FC37HcxDWkAO_6GO38\ C9H0480GEYA9M54BFJF797ZWWSPPLJJECC766QaGKUCFM9AF65\ 73dsqZkiTcaNWUHONBGFz87c0c0ccc0c0ccc0c0ccc0c0ccz7Y\ zzMz2BgwiTcUDgtCuIM`RWG_kqRgVHd87fFAgMDhSGiZIzeLzm\ OztRzzTzzm5F1U_HKOBAC5_VeyrVVRFHeYQ3kM2dI2YE1RB1K7\ 0D306zfzzEcnYMfTI_mFTJCLE9E96743uPyiKlYF`NAOB5CQxr\ LmhHc_DUR8KI4A9jWYNGHHwu8UTOezIVVFDUzAAs0zzmKzsczv\ mzzozzqzztzzwzzzzz0QnOMfKI_HETDBLA7E6373j6Ud5QZ4MT\ 3IN3FH2BB17503hLfaI_WFUPCOJ9IV6CF36BMM8HH6DD488244\ axBUk8M_6FO47C2piVzsWoiQe`LVSGLIAA95oSqhOjbLcWHXQE\ RJAKD7D636oKwdGkVC_K8OA4C`f4X7RG3DX40Q30J20D10600c\ 1kY0dS0YM0RH0KB0D506VoZNbQFQH7D8PfrgNNaKKXHHREEMBB\ G88B55522g0HT0BE05TnyLaiEPV7CFtV_hOSYILMCEB67LimIb\ eFWZCQS9JL6DE3673s7BvP9lK } 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] FOTDs
by JackOfTradeZ＠comcast.net 09 Jan '11

09 Jan '11

. FOTD -- January 07, 2011 Mandel in a Petri Dish loox like freakin' strawberry slices. Strawberries rule! May try to animate it. FOTD -- January 08, 2011 Elusive Butterfly nice one Jim! Zooming back out yields some interesting stuff, finally ending in what loox like a normal Mandelbrot. Doing the zoom animation now, but loox like gonna take a while .... Stay Amazed JoTz .

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FOTD 09-01-11 (Chaos Incorporated [7.5])
by Jim Muth 09 Jan '11

09 Jan '11

FOTD -- January 09, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: As long as one does not look too deeply into the parent fractal of today's image, it appears to be an everyday Mandelbrot set, but in its depths a certain strangeness starts to creep in. The surface minibrots are perfect miniature M-sets, but as we go deeper, the minibrots become confused, as though they are undecided whether to be quadratic or quintic miniatures. Then, when we reach the deepest depths, the minibrots are purely quintic, with the four lobes and everything else expected in such minibrots. Normally, quintic minibrots are rather boring things, with a tendency to all look the same, but the minibrot in today's image is far from boring. Minibrots usually lie at the center of a basin, with the iteration count steadily increasing as the minibrot is approached. Some minibrots in fractals created with certain formulas, such as the minibrot in today's image, are like volcanoes however -- rising mountains with deep craters at their peaks. As we near these minibrots, the iteration count first decreases gradually, then rises rapidly as we approach the minibrot itself. The reddish parts of today's image are the lowest iteration stuff. The sky-blue stuff behind the dark blue blobs surrounding the flat circular red ridge, as well as the stuff near the minibrot, is the actual high-iteration stuff. The image is located in the trunk of the period-10 elephant on the southeast shore line of the parent M-set. It is quite close to the limit of resolution, which makes the 'mathtolerance' entry necessary in the included parameter file. The name "Chaos Incorporated" expresses my impression of the background areas surrounding the red mountain. The rating of a 7-1/2 includes a half point for the coloring, which is a not-insignificant part of the image. (My modesty prevents me from rewarding myself with more than a half-point bonus.) The calculation time of 2-1/3 minutes is a fair price for such a curious image. The image may be seen for free on the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site, not up to date, may be seen at: <http://www.Nahee.com/FOTD/> Lots of clouds filled the skies over Fractal Central on Satur- day, while the temperature hung around 27F -3C. Light snow also fell most all day, but by evening had amounted to no more than 1cm. The fractal cats complained about the lack of sun and then found comfort on the shelf over the hall radiator. My day was enjoyably slow. We needed the rest after the hectic days of the past few weeks. The next FOTD will be posted in 24 hours. Until then, take care, and be in there with the big time thinkers. (I leave it to the individual to decide who the big time thinkers are.) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Chaos_Incorporated { ; time=0:02:23.30-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+0.3438119752193327/-0.0560302035781458\ /2.973926e+013/1/-12.6/0 params=5/10000000000.0/0/0 float=y maxiter=1250 inside=0 logmap=164 periodicity=6 mathtolerance=0.05/1 colors=000zhdzkfwkftmhrokmrmktohtodwrbxtZzwXzxVzzR\ zzPzzNzzJzzHzzFzzVZXh11x00w00t00r00o00m00m00k00h00\ f00d00d10f00h00h00k00m00m00o00o00r01t0Kt0Uw0cw0mx0\ mz0iw0ft0cq0`n0Tj0Le0D_07V01Z04`05a07d0Ag1Ci2Dk4Fm\ 7Jo8LrANrDRtFTtHVwJXxN`xPbzRdzTfwRhrRhmRhhRkdRk`Rk\ XRkTRmPRmLPmHPmDPoAPo7Po4Po1Pr0Pr0Pr0Pr0Tt0Vw0Xw0Z\ x0`x0bz0dz0fz0hz0kz0mz0oz0rz0tz0wz0xz0zz0zz0zz0zz0\ zz0xw4tkAo`HkRNfJVbAbZ2kV0tR0zP0wR0tT0rV0oV0mX0kZ0\ h`0f`0db0bd0`f0Zf0Vh0Tk0Rm0Pm0No0Lr0Jt0Ht0Fw0Dx0Cz\ 0Az0Dt0Fm0Hf0J`0LV0NP1PL4TF5VA8X5AZ1D`0Fb0Jd0L`0NX\ 0NT0NR0NN0NJ2PH4PD5PA8P8AP5CP2FR1HR0LR0NR0PR0TT0VT\ 0XT0`T0XT0TT0PV0LV0HV0DX0AX07X04X01c01h01c01r01e01\ j01e01x01g01n01g01x01i01n01i01z`kz`kz`kz`kz`kz`kz`\ kz`kz`kz`kz`kz`kz`kz`kz`kz`kzwwzwwzwwzwwzwwzwwzwwz\ wwzwwzwwzwwzwwzwwzwwzwwzwwzwwzwwzwwzwwzwwzwwzwwzww\ zwwzwwzwwzwwzwwzwwzwwzwwz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 08-01-11 (Elusive Butterfly [7])
by Jim Muth 08 Jan '11

08 Jan '11

FOTD -- January 08, 2010 (Rating 7) Fractal visionaries and enthusiasts: After several days of philosophizing, I seem to have exhausted my philosophical energies, so today's discussion will be philos- ophy free. But have no worry, with the world going as it is, my energies will soon be restored. Today's FOTD features a quintic minibrot at the center of a fractal butterfly. Since the image was a bit hard to find, I named it "Elusive Butterfly". The image is located in a valley on the northwest shore line of a tiny half-morphed minibrot on the main spike of the parent pseudo-Mandelbrot set. The rating of a 7 is what I consider satisfactory for a FOTD image. The calculation time of a brief 51 seconds will pass in what seems half that time once the outline of the butterfly comes into view. Those who would rather not calculate may see the butterfly fluttering on the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and don't forget the original web site at: <http://www.Nahee.com/FOTD/> I haven't checked the original site in several days, so who knows when it might once again be up to date. I will have my own web site up and running as soon as the currently heavy graphics work slows down enough to give time to set up the web site. About 2 inches, (5cm) of snow fell overnight here at Fractal Central, but by midday the clouds broke, leading to a partly sunny afternoon with a temperature near freezing. The fractal cats were quite satisfied with the sun, and spent the better part of the afternoon on the shelf by the window. After sweep- ing the snow from the pavement in the morning, my day was totally routine. The next FOTD will be posted in 24 hours. Until then, take care, and see a great light. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Elusive_Butterfly { ; time=0:00:51.30-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip float=y center-mag=-1.571577951264321/+0.00000063922382444\ /1.002156e+010/1/-58.5/0 params=5/500000000.0/0/0 maxiter=1250 inside=0 logmap=122 periodicity=6 colors=00001101202313423534644755865976A86C86D86F8\ 6G86I86J86L86M86O86P96R96T96U96W96X96Z97_ABaKGcSLd\ ZNedSfjXjpcpzmznPofKhZF`aHYcKVeOSgRPiVMkYJmaGodDnb\ Lm`SlZZkYegXdcWd`WdXVdUVdQUcMTcJTcFScCScJWZQ_UabLn\ hPzkVznczqozkfzgbwb`nYajVgaRlXNrTLqPIpLGoHCmDAkGEc\ JHYLLSOOMzSGzVAzfCzzDvnCrkBmgBcdAU`9KY9HV8GR7GO7GK\ 6FH5FD5FA4F74J85N95RA6VB6ZC7aC7eD7iE8mF8qG9uH9xH9p\ XJhkTazafsbjlcnfcr_dvUduWftXgsYhrZiq_jp`kpbmocnndo\ meplfqkgrkhshetecub`u_ZuYWuVUuSRuPPuNNuORsOUmOXgP`\ aPcWPfQYb`fZjoVtwSubLlIEVMFYPG_THbWHd_IgbJifJliKnm\ LqpLstMuwNuzNuyOuxPswQpwRmsclpckmck_bI_aHZaHZ`GZ_G\ Z_FYZFYZEYYEYXDYXDXWCXVCXVBXUBWUAWTAYS9_S9aR8cQ8eQ\ 7gP7iP6kO6mN5oN5qM4s6_u8Xw9VxATyBQzCOzDMzEKzGHzHFz\ IDzJAzK8zL6zFezITzKGzUuzUTzUSzURzURzUQzUPzUPzUOzUN\ zUNzUMzULzULzUKzUKzUJzUIzUIzgHzfGzdGzcFzbEzaEz`Dz_\ CzhSzeQzbOz`MzYJzVHzTFzqQ } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 07-01-11 (Mandel in a Petri Dish [6.5])
by Jim Muth 06 Jan '11

06 Jan '11

FOTD -- January 07, 2011 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image rates a 6.5. I was torn between a rating of a 6 and a 7, and the best way to settle the dilemma was to give the image a rating of 6-1/2. But unlike most fractional ratings, today's includes no bonus for the coloring, which was achieved almost entirely by the Fractint program. When I saw the image, it brought back memories of bacterial cultures in the old biology classes. The name "Mandel in a Petri Dish" seems quite appropriate. The image combines features of the Z^2 and Z^4 Mandeloids, though at the depth of the image the Z^4 features predominate. The central minibrot is filled with concentric rings of alterna- ting chaos and order; the chaotic areas are filled with smaller minibrots as well as 'antiminibrots' with peaks instead of valleys at their centers. Perhaps the best feature of the image is its relatively speedy calculation time of just over 2 minutes, which is about the time it will take to surf down to the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image is posted. The original web site at: <http://www.Nahee.com/FOTD/> is still available, and always worth a quick check. While watching the TV news during the Thursday lunch break, I saw a report of several localized showers of falling birds. No one knows the actual cause, but it appears the flocks of birds became disoriented and flew into things. The question of what caused the birds to lose their bearings remains unanswered, but in my opinion, the cause could have been the electromagnetic haze created by the current proliferation of wireless devices and the necessary cell towers to support them. It is known that some birds navigate by sensing earth's magnetic field. Perhaps the electromagnetic signals emitted by the ever- increasing number of cell towers is interfering with the birds' ability to orient themselves. If this is true however, it is unlikely the news media, which is controlled by the giant commun- ication corporations, would cover such a story. I also wonder whether the 'greenie' activists who claim to care so much about the environment would be willing to give up their wireless devices to save the birds. A final thought -- maybe the birds are like canaries in a coal mine. Maybe we should consider their deaths a warning. Yeah, yeah, I know the old mantra -- there is no solid evidence that wireless radiation is harmful. But the hints of danger are everywhere. What I want to see is solid evidence that it is safe. A mix of sun and clouds and a high temperature of freezing made Thursday another typical winter day here at Fractal Central. The fractal cats grew bored with the on-and-off sun and settled for the afternoon in the warmest places they could find. With the work up to date, my day was fair enough. And the plans for the FOTD web site here at FC are coming along. Expect an announcement in a couple weeks. The next FOTD will be posted in 24 hours, more or less. Until then, take care, and watch for scattered showers of falling birds. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= MandelInAPetriDish { ; time=0:02:07.70-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+0.3602110240053605/+0.6436979362830387\ /9.9012e+007/1/10/0 params=4/4444/0/0 float=y maxiter=1500 inside=0 logmap=100 periodicity=6 colors=000MTALUBKVBJWCIXCHYDGZDFZEE_FD`FCaGBbGAcH9\ dH8eI7eIBdJEdJHcKKcKNbKRbLUaLXaL_`Mb`Mf_Ni_NlZNoZO\ rYOvYOvWNwVMwTLxSKwQJwPJvOIvMHuLGuJFtIFsHErFDrECqC\ BpBAoAAo89n78m57l46l36g47b47Z47V57R57M58I68E68A686\ 688899AAACBCDBDFCEHDGJEHKEIMFKOGLQHMRHOTIPVJQWJSXK\ UXLWXMYXN_XOaXPcXQeXRgXSiXTkXUmXVoXWqXXsXYuXZwX_yX\ `zXazW_zWZzWYzWXzWWzWVzWUzWSzWRzWQzWPzWOzWNzWMzWKz\ WJzWIzWHzWGzWFzWEwUGuTIsSKqQMoPOmOQkNSiLUgKzdKzbKz\ `KzZKzXKzVKzTKzRKzPKzNKzOKzPKzQKzRKzSKzTUzUUzVUzWU\ zXUzYUzZUz_Uz`UzaUzbUzcUzdUzeUzfUzgUzhczicziczjczk\ czlczmczkczjcziczgczfczeczcczbczacz`czZczYczXczVcz\ UczTczRczQczPczOczYczgczqczpczocznhzmhzlhzkhzjhzih\ zhhzghzfhzfhzehzdhzchzbhzahz`hz_mzZmzYmzXmzWmzWmzV\ mzVmzUmzUmzTmzTmzSmzSmzSmzTmzmmzmmzmmzmmzmmzmmzmmz\ mmzmmzmmzmmzmmzmmzmmzmmzmmzmrzmrzmrzmrzmrzmrzmrzmr\ zmrzmrzmrzmrzmrzmrzmrzmrz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Lyapunov...
by Tony (Anthony) Hanmer 06 Jan '11

06 Jan '11

I'm looking for the order number translation for the string bbbbbbaaaaaa to use in Fractint, which produces this Lyapunov fractal: http://commons.wikimedia.org/wiki/File:Lyapunov-fractal.png (It's a famous one, called Zircon City.) Any help? Thanks, Tony Hanmer

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FOTD 06-01-11 (Golden Epiphany [7])
by Jim Muth 06 Jan '11

06 Jan '11

FOTD -- January 06, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image is finally one worth a rating of a 7, the level at which I consider a day's effort a success. The image is a scene in the Seahorse Valley area of a hypercomplex Julia set. Until now I have put very little, in fact, almost no effort into the type=hypercomplexj fractals. Perhaps I have been put off by the eight dimensions involved, but as today's image shows, with a bit of extra effort in the coloring, the hypercomplex stuff can be quite interesting. I named the image "Golden Epiphany". In the religious calendar, today is the day celebrating the arrival of the wise men from the east -- astrologers who brought their gifts to the baby in Bethlehem, recognizing him as a world savior. There is also a good bit of gold in the image, fully justifying the name. Thanks to expert programming and a 2000mhz machine, the image is a very fast one, finishing in a mere 35 seconds. The most convenient way to view the image is on the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> the original FOTD web site, not up to date, may be found at: <http://www.Nahee.com/FOTD/> The typical mix of sun and clouds prevailed here at Fractal Central on Wednesday, with a typical temperature of 34F +1C. The fractal cats would have preferred more sun, but satisfied themselves with what sun they could find. My day was near normal. The standard work was out of the way by early afternoon and nothing unexpected arrived. This left the time to dredge up today's image. During the midday break, the topic of my own FOTD web site came up. FL wondered whether she might add some positive philosophy to the daily FOTD discussions to balance what she considers the negative stuff I write. The web site will probably be up and running in a couple weeks, so I told her to go ahead and write whatever she wishes. The next FOTD will be posted in near 24 hours. Until then, take care, and what could be more negative than an eternally con- scious brain in the middle of an otherwise empty infinite space? (If it were me, I would wait for a supercomputer pre-loaded with version 2,000,000 of Super-Fractint to pop out of the vacuum beside me.) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Golden_Epiphany { ; time=0:00:35.54-SF5 on P4-2000 reset=2004 type=hypercomplexj function=sqr center-mag=0/0/1.10375 params=-0.23117/-0.02833/0/\ 0.52/0/0 float=y maxiter=4500 inside=255 logmap=yes colors=00083673952C42F76I99LBCOEFRGIUILXLO_NRbPVeS\ YhU`kWcnZfq`itblwdozgjzifzkbzmZzoVzlYzj_zhazfczdez\ bgz`izZkzXmzVozTqz3rx5ow7mv8kvAiuCguDetFctHasI_sKY\ rMWrNUqPSqRQpSOpTPqTQqURqUSqVTrVTrWUrWVrWWsXXsXXsY\ YsYZtZ_tZ`tZ`tY`tYatYatXbtXbtXbtWctWctWduVduVeuVeu\ UeuUfuUfuUguTguTguThuShuSivSivRjvRjvRjvQkvQkvQlvPl\ vPmvPmvOmvOnwOnwNowNowNpwMpwMpwMqwLqwLrwLrwLrwKqvK\ puJotJnsJmrIlqIkpIjoHinHimHhmHhlGgkGfjGeiFdhFcgFbf\ EaeE`dE_cD_bDZaDY`CX_CWZCVYBUXBTWBSVARUART9QS9PR9O\ Q8NP8MO8LN7KM7JL7IK6IJ6HI6GH5FG5EF5DE4CD4BC4AB39A3\ 99388277266255144133122011000zuHzrGzpGznGtfGsfFreF\ reFqdFpcEocEsiEzjElaDlaDk`Dj_Di_CqbCgZCgYCfYCeXBdW\ BiWBbVBaVAaUAhUA_TAZS9YS9XR9XR9WP8VP8UO8TN8SM8RL7R\ L7QK7PJ7OI6NH6MH6MF6LF5KE5JE5IC5HB4GB4GA4FA4E94D93\ C83B73B73A6296285275264153153142031020010000000000\ 0000000000000000000000000 } END PARAMETER FILE=========================================

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FOTD 05-01-11 (Reason Prevails [6])
by Jim Muth 05 Jan '11

05 Jan '11

FOTD -- January 05, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a continuation of the current series of below- standard FOTD images. The rating of a 6 is certainly nothing to get worked up about. The most unusual aspect is that the image was rendered with the outside set to 'fmod' and the inside set to the color 253. This trickery raises the everyday scene to a level marginally worthy of being declared a FOTD. The name "Reason Prevails" has nothing to do with the image. It came about when I caught myself trying to make sense of the currently faddish (at least among some thinkers) cosmological theories. The parent fractal, which was created by the expression 2.5*(Z^0.5)+0.5*(Z^2.5)+C, resembles a distorted Mandelbrot set facing northwest, with a southern period-3 bud larger than its main period-2 bud. Today's scene is located on a filament extending from the large period-3 bud, near the point where the filament terminates in an irregular open area. The shape of this open area is mirrored in the small brilliant patches scattered about today's image, which actually are open areas themselves. The calculation time of 1-1/5 minutes is quite brief, leaving no danger that half a day will have been wasted if the result is not up to expectations. The most convenient way to view the image is to hop down to the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and view the finished product there. Paul's original FOTD web site at: <http://www.Nahee.com/FOTD/> is currently not up to date. But I am still waiting to hear from Paul, telling me that he is once again feeling well enough to start getting the site caught up. As soon as I struck the 'send' button to send off yesterday's FOTD, I wondered if I had gone too far in lambasting the disci- pline of science. Even though it certainly falls short of perfection, science is the best method we currently have of explaining the 'how' of things of the natural world, at least at the macroscopic physical level. But it seems as though the older I grow, the more I see science being mis-used. In fact, as I see people, especially the young, walking about in near trance states, totally fascinated by their latest wireless internet gadgets, I see technology gone amok. Then I wonder whether the progress of mankind is nearing a peak, beyond which we will slip into a downward curve of regression until we settle into a state of helpless zombiehood, ruled by our overlords, the elite of the giant computer and communication corporations. The good news is that we had a mix of sun and clouds here at Fractal Central on Tuesday, with a temperature of a pleasant 43F +6C. The fractal cats enjoyed the sun while it was shining, and the heat when the sun went behind a cloud. My day was success- ful enough, since I avoided a philosophical debate with FL when she casually asked what I have against science. The next FOTD will be posted in 24 hours. Until then, take care, and be on the winning side. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Reason_Prevails { ; time=0:01:12.61-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.9953029291869159/+0.2475891945519297\ /2.455e+009/1/40/0 params=2.5/0.5/0.5/2.5/0/0/0/0 float=y maxiter=1000 inside=253 proximity=0.05 outside=fmod logmap=yes periodicity=6 colors=000TbvUauV`tW_sXZrYYqZXp_Wo`VnaUmbTlcSkdRje\ QifPhgPihQjiQkiRljSmkSnlTomTpnUqoUrpVsqWtrWusXvtXw\ uYxw`zv_yvZxuYxuXwtWvtVvsUusUurTtrSsqRsqQrpPrpOqoN\ poNpnMonLomKnmJmlKmlJllIlkIkjIjjIjiIiiIihIhgIhgIgf\ IgfIfeIeeIedIdcIdcIcbIcbIbaIbaIa`J`_J`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`7Pa6Pa6Pb6Pc6Pc5Pd5Pe5\ Pe5Pf4Pg4Pg4Ph4Przzi3Pj3P } 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 04-01-11 (Cirgle of Power [5])
by Jim Muth 04 Jan '11

04 Jan '11

FOTD -- January 04, 2011 (Rating 5) Fractal visionaries and enthusiasts: Today's scene lies in the parent fractal that comes about when 1.4 negative parts of Z^(-1.2) are combined with 0.7 negative part of Z^(-3.3) and (1/C) is added on each iteration. The magnitude of the image lies very near the limit of math precision, so it was necessary to include the 'mathtolerance' entry in the parameter file. The name "Circle of Power" came to mind when I imagined a circle of Samurai warriors surrounding and defending the central mini- brot. The minibrot is well beyond resolution, by the way. The rating of a 5 is not all that exciting, but the calculation time of under 2 minutes will keep the time that has been wasted to a minimum if the result proves disappointing. All risk of disappointment may be eliminated by viewing the finished image on the active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be found at: <http://www.Nahee.com/FOTD/> but it is not up to date. I read in a book that FL gave me for Christmas that we could possibly be something known as 'Boltzmann brains', disembodied objects, not necessarily resembling human brains, but with the faculty of self-awareness, floating in an infinite, empty space known as de Sitter space. We could exist in infinite numbers because of random fluctuations in the quantum vacuum, exactly as an infinity of monkeys typing random letters on typewriters would by random accident type out an infinite number of copies of 'Hamlet' every nanosecond. (And indeed, an infinity of them could very possibly be out there actually doing it right now.) Surrounded by eternal emptiness, and with no sense organs, we floating consciousnesses could be suffering sensory deprivation and hallucinating an objective universe around ourselves, filled with stars, planets and other supposedly conscious beings. It's the stuff pure fantasy is made of, ('The Matrix' film comes to mind.) yet no one knows of a sure way to totally eliminate this absurd possibility. The author of the book avoids the trap by saying that such a condition would be cognitively unstable, leaving no sensible way to think and behave. In other words, the possibility of Boltzmann brains is fully scientific, and it just possibly might be true. A surprising consequence of having an infinity of conscious units is that the unique brain state that creates my particular individual consciousness must exist an infinity of times through- out de Sitter space. Talk about megalomania! I didn't know I was that great. But I wonder who these other versions of myself are. (Maybe it's time to get back to things that make more sense, like ghosts and goblins.) Compared to this 'scientific' craziness, the existence of para- normal things such as Astrology, telepathy, fortune telling, psychokinesis, Astral planes and even ghosts of dead people, as well as the various claims of the religious mystics, are almost rational. In my opinion, our science is out of control. It has become a discipline fit to be the subject of jokes and ridicule. Apparently, no one knows anything for sure. Maybe we truly are disembodied brains, inventing the external world in our minds to prevent eternal boredom as we drift through empty space and end- less time. (But isn't this view known as solipsism?) Now on to the fractal weather. Total sunshine here at Fractal Central on Monday kept the temp- erature of 34F +1C from feeling quite as cold as it otherwise would have. The fractal cats took full advantage of the sun by spending their afternoon on the shelf in the sunniest southwest window. My day was close to average as far as the work goes, but I was in one of my more philosophical mental states, which prevented total relaxation when the work was finished. FL, being more practical than philosophical, had a more relaxing day. The next FOTD will be posted in 24 hours. Until then, take care, and wait 'till the nun signs Shelly. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Circle_of_Power { ; time=0:01:58.96-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.600616015104951/-3.586496457834565/\ 2.462703e+012/1/72.5/0 params=-1.4/-1.2/-0.7/-3.3/\ 0/0/0/0 float=y maxiter=1000 inside=0 logmap=225 periodicity=6 mathtolerance=0.05/1 colors=000D0FE0GF1IF2KG3LG4NI5PK6QL7SN8UP9VPAXQBZP\ C_ODYMEWKCTI9QG8NE0KD0KC0KB0KB9K7FKIGITWGmmUzwUzzz\ zwmztczrUzqKzoMzlOziQffSddUabW_`YYZ_VXaTVcRYzPWzOX\ zTQzSPzROzQOzQMzPLzOKzOZzOZzPZzPZzPZzPZzPZzPZzPZzQ\ ZzQZzQZzQZzQZzQZzQZzRZzRUzRUzRUzRUzRUzRUzSUzSUzSIz\ SIzSJzSJzSJzTJzTKzTKzTKzTKzTLzTLzULzULzUMzUMzUMlUM\ lUMlTNkTOkTPkSQjSRjSSjRTjRUiRWiQXiQYhQZhR_hS`iTajU\ bkVclWdmXenYfoZgp_hq`irajsbktckudkvelwfmxgkxgkxgkx\ gjxgjxgjxgjxgjwgiwgiwgiwgiwghwghwghwghvfhvfgvfgvfg\ vfgvfgvffvffuffuffufeufeufeufeufeufdtfdtfdtedtedte\ ctectectecsebsebsebsebsebseaseaseareare`re`rd`rd`r\ d`rd_rd_qd_qd_qd_qdZqdZqdZqdZqdYpdzpdzpdzpdzpdzpcz\ pczpczoczoczoczoczoczoczoczocznzznzznzznzznzznzznz\ znzztzzszzrzzrzzqzzpzzpzzozznzznzzmzzlzzlzzkzzjzzj\ zzizzhzzizzhzzhzzhzzgzzgzzgdzgczfczfbzfazfaze`ze`z\ e_ze_zdZzdZzdYzdXzcXzcWzc } 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 03-01-11 (Lazy-Day Fractal [4])
by Jim Muth 03 Jan '11

03 Jan '11

FOTD -- January 03, 2011 (Rating 4) Fractal visionaries and enthusiasts: Sunday was totally relaxed here at FC, and my fractal ambition was limited to finding an interesting fractal, which I did. I present it here for entertainment purposes only. No one is expected to take it seriously. The name "Lazy-Day Fractal" confirms the lack of effort. The rating of a 4 is well below average for FOTD images. Actually, there could be some pretty good sub-images in today's parent fractal. Unfortunately, I could not work up the energy to go searching for them. Luckily, the calculation time is only 1-3/4 minutes, making running the parameter file a minor task, and even this small effort may be eliminated by surfing to the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image is posted. The original FOTD web site can be accessed at: <http://www.Nahee.com/FOTD/> But it is not yet up to date. A little rain fell Saturday night but cleared away by 11am Sunday. Lots of sun and a temperature of 45F +7C for the rest of the day kept the fractal cats stretched on their window shelf. The humans did little more than the cats did, except for a bit of speculating about what might happen for the rest of the year. The next FOTD will be posted in 24 hours. Until then, take care, and a Boltzmann brain is a self-aware unit that appears spontaneously from nowhere. No one takes their exist- ence seriously, but some of the latest cosmological theories make their existence inevitable, at least in an infinite and eternal universe at maximum entropy, a condition that our uni- verse currently seems to be destined for. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Lazy-Day_Fractal { ; time=0:01:43.92-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.438185/-0.626305/0.9363296/1/140/0 params=-1/-3.3/-3/-1.1/0/-75/0/0 float=y maxiter=1500 inside=253 outside=tdis periodicity=6 colors=000`RVdUYhW_lZbpadtdgwfiqYalPUgGMb7FcBLdERe\ HWfLagOggRllSaqSSvSHzS7wR9tQBqPDnOEkNGhMIeLJbKL_JN\ XIPUHQRGSOFULEVJFSIGQHHOFIMEJKDKIBKGALE9MC7NA6O85P\ 64P4FgQPyjNylMymLyoKypJyqIysHytGyuFywEyxDyyGqnIicK\ aTMVJLSGKQDJOAE`UFaUGbTHcTIdTJeTKeTOgSShSWjS_kSS`F\ KQ3YK7kEAHzETaNdEWOhHR`GUUFXNFTUNQ_UMe`JlhFroCxvDu\ tErsForFmqGjoHgnIdmIblJ_jKXiLUhLSgMPeNMdOJcOHbMK`K\ N_JQZHTYGWXEZWCaVBdU9gT8jS6mR5pQC`aJMmQ7xWCraGmgKh\ mOcjVYg`TdfO6`PBXRFTSJPU2n83mA4mC5lE6lG7kI8kJ9jLAi\ NBiPChRDhTEgVEgW`QRv9NoESiJWbO_XTcQYgKbkDgo7ls1pw2\ mr3km3ih4gd5e_5cV6aQ7_M7YH8WC9U79S3FVBLXJQZRW`Z`bf\ fdnkfuheveevbev_dvXdvUdvRdvOcwLcwIcwFbwCbw9bw7bwBc\ tFdrIepMfmQgkThiXif`jdckbgl_kmYnmWkhZicafZddVghZbk\ bZoeVriRulNskMrjLqjLpiKniJmhJlgIkgHifHhfGgeFfeFihI\ kjLnlOpnRsqUusXxu_zwarpYkiVdbRYWOQPKJIHCBD54A97DDA\ GHDILGLPINTLQXOS0AFSOrQMk } 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 02-01-11 (The Least of the Beast [6])
by Jim Muth 02 Jan '11

02 Jan '11

FOTD -- January 02, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's image is the parent fractal that results when 3 parts of Z^(-2.1) are mixed with 0.9 part of Z^(-4.2) and (1/C) is added. Actually, it is not accurate to call it a 'parent' because it has not yet produced any children. But this is no cause for alarm; the fractal is obviously filled with interesting nooks and crannies that hold infinite goodies. Perhaps the most interesting thing about the fractal is that it appears to be in 2 parts -- the chaotic low-iteration, greenish outer part and the far more organized high-iteration, brilliant- pinkish inner part. The overall impression is that the initial value of Z is not critical, though the abundance of minibrots indicates that it is indeed critical. Perhaps the generating formula has more than one critical value, but if this is so, I have yet to find the value that would clear away the overlying stuff and bring the ghostly submerged stuff to the surface. The name of the image -- "The Least of the Beast" -- originally had some meaning. Whatever it was, I have forgotten it. The rating of a 6 is above average but nothing to get excited about. The calculation time of 40 seconds makes running the included parameter file a very small chore. Those with machine problems such as incompatible operating systems, retarded vesa-impared video cards, or merely spoiled machines that panic at the sight of DOS will find their satisfaction in the form of the pre- calculated image at the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site at: <http://www.Nahee.com/FOTD/> is currently inactive, though when Paul recovers, it will be brought up to date. The first day of the new year started sunny enough here at Frac- tal Central, but clouds moved in before noon, and rain showers arrived later in the afternoon. The fractal cats approved of the temperature of 48F +9C but wished there had been more sun- light. (Actually their greatest wish is for someone to let them go into that immense forbidden area on the outside of the three doors they never get to go through.) The humans has a peaceful enough day. The new year arrived on schedule at FC and nothing much changed. The next FOTD image will be posted in 24 hours. Until then, take care, and: I never saw a Boltzmann brain, I hope I never see one, But I can tell you anyhow, I'd rather see than be one. (I'll have a lot to say about these strange creatures in a few days.) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= TheLeastOfTheBeast { ; time=0:00:40.75-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=0.107083/0/0.6/1/90/0 params=3/-2.1/0.9\ /-4.2/0/0/0/0 float=y maxiter=22500 inside=0 logmap=yes symmetry=none periodicity=6 colors=000FEKFFKFGKFGKFHJFIIFJIFKHFKHFKHFKHFKHFLHF\ LHFMHLNGLMEMMKMMPNMUNLZPMcULhZLmcKrcKvcJzcKzcKzcLz\ cNz_dzaczbbzcazd_zeZzgYzhXziWzjUzlTzmSznRzoQzpOzrN\ zsMztLzuKzyIzwJzvJztJzsJzrJzpJzoJzmJzmJzmJzmJzmJzm\ KzmKzmKzmKzmKzmKzmKzmKzmKzmKzmKzmKzmKzmLzmLzmLzmLz\ mLzmLzmLzmLzmLzmLzmLzmLzmLzmMzmNzmOzmPzmQzmRzmSzmT\ zmUzmVzmWzmXzmYzmZzm_zm`zmazmbzmczmdzmezmezifzjfzk\ gzlgzmgznhzoizpizqizrjzsjzsjzskztkztkzulzulzulzvmz\ vmzxlzwmzvmzvmzunztnztnzsozsozrozqpzqpzpozopzoqznr\ znszmtzluzlvzkwzjxzjyzizzizzhzzgzzgzzfzzezzezzdzzd\ zzczzbzzbzzazz`zz`zz_zz_zzZzzYzzYzzXzzWzzWzzVzzVzz\ UzzTzzTzzSzzSzzTzzTzzTzzTzzUzzUzzUzzUzzVzzVzzVzzVz\ zWzzWzzWzzWzzXzzXzzXzzXzzXzzYzzYzzYzzYzzZzzZzzZzzZ\ zz_zz_zz_zz_zz`zz`zz`zz`zz_zz`zz`zz`zzazzazzazzbzz\ bzzbzzbzzczzczzczzdzzdzzdzzezzezzezzezzfzzfzzfzzgz\ zgzzgzzhzzhzzhzzhzzizzizz } 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 01-01-11 (Etched in Numbers [7])
by Jim Muth 01 Jan '11

01 Jan '11

FOTD -- January 01, 2011 (Rating 7) Fractal visionaries and enthusiasts: To kick off a new year of FOTD images, we return to the parent fractal of the fuzzy image of two days ago, which was created by the expression Z^(1.75)+C. This parent has a disconnected mini- brot lying some distance southwest of the main body. The image of two days ago is located near this minibrot. The parent also has a smaller minibrot located much closer to the northeast side of its main body. Today's image is located in a kind of valley in this smaller, closer minibrot. The name "Etched in Numbers" is true of all fractals, and has no particular significance to today's fractal. I have been searching the Mandeloids with exponents between 1 and 2 for quite a few years, in the hope that some unexpected treasure might lie hidden in one of them. So far the treasure has eluded me, but I continue searching. Who knows, one day I might find it. Today's image is hardly a treasure, but it's worth a rating of a 7, which makes the calculation time of 3 minutes almost worth the effort. The calculation may be totally done away with however by viewing the finished image on the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And don't forget to keep checking the original FOTD web site at: <http://www.Nahee.com/FOTD/> Friday brought thick clouds but warmer temperatures to Fractal Central. The temperature of 46F +8C was not quite warm enough for the fractal cats however, and they spent half the afternoon on the shelf over the heat. My day was pretty settled, as was FL's day also. In the afternoon I spent an hour or so on the internet, checking 'Boltzmann brains', which is just about the most ridiculous idea our over-educated scientists have come up with -- so far, that is. I'll have much to say about these hypothetical creatures lurking in outer space in future FOTD discussions. The next FOTD will be posted in 24 hours. Until then, take care, and is that a disembodied brain coming up behind you? (We cannot prove that they are not there.) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Etched_in_Numbers { ; time=0:02:59.98-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.6043991509829967/+0.5801826859547423\ /1.876538e+007/1/-17.5/0 params=1.75/0/11/0 float=y maxiter=1800 inside=0 logmap=247 colors=000ACIADIAELAGNAIPAKRAMTAOVAQXAS_AUaAWcASeA\ ZgAYiAM_AUfASbAQZAOUAKQAHMADHAADA69A35B69C9CCCGDEJ\ DHMEKQENTFPXFS_GVbGYfH_iHbmIepIgsJitKjtLktMmtNntOo\ tUqtcrumsvttwzuxzvyzwzzxzzyzzzzVJqUHqUGqTErTDrSBrS\ AsR8sR7sS9qTApUCoVDmWElXGkYHiZIh_Kg`LeaNdbOccPadR`\ eS_eTZbUX_UVYUUVVSTVQQVPeNGdMJcLNaKQ`JU_HXYG`XFcWE\ gVDjRCgOBeLAbH9`E9YB8W77T46R66PI7SL8UP8WT9Y_A_hAaq\ BcpBejAbdA_YAYS9VR9SQ9QO9NN8KL8IL8FJ8CI7AH77G74G72\ IB7LEBNHGQKKTNPVQTXTYYWa_YZa_XbaVdbSfdQgfOihMkiJlk\ HnmFonDlkFihHfeIccKa`LZYNWWOTTQQQSONTLLVIIWFFYDDZG\ MUJVQMbMOcNQdNReNTfNUgOWhOXiOZiO`jPakPclPdmzznQgoz\ zpQjpzznPilzzjNiizmgMieLidKibKh`JhcIhYHhcHhVGhcFhR\ EhcEgNDfKDeHCdECcBBc8BzS9zQAzcAzcAzcBzcBzhBzKDzmEz\ SFzWGzZHzbJzfKzjLznMzqNzpOzoPzzPzzQzzQzzmzzmzzmzzz\ 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 31-12-10 (Totally New Aspect [6])
by Jim Muth 31 Dec '10

31 Dec '10

FOTD -- December 31, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image is named "Totally New Aspect", which means it is a totally new aspect of the Mandelbrot set, or more correctly, of the Z^2+C Julibrot. The scene lies near the Seahorse Valley area of the M-set, near a point where a number of heavy arms converge. The image has been stretched and skewed to bring it as close as possible to a recognizable aspect of the M-set. The M-set is a 'connected' object, in one piece. Every minibrot is connected to the main body of the set by an infinitely thin filament, giving the set only one infinitely long and convoluted shore line. Yet in today's image we see ring-like elements that are obviously not connected. Most likely these elements are connected to the main body of the Julibrot somewhere in the fourth dimension, though I am not sure if it has ever been demonstrated whether the Z^2+C Julibrot is or is not connected. The rating of a 6 is adequate for a FOTD, but implies nothing outstanding. The calculation time of 2-2/3 minutes is within reason. The finished image is or soon will be available on the currently active web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> the original web site is located at: <http://www.Nahee.com/FOTD/> though it is not up to date. Thursday brought a mix of sun and clouds to Fractal Central, with a temperature of 39F +4C, which was a virtual repeat of Wednesday. These conditions gave the fractal cats the choice of lying on the shelf in the window, where the warmth of the sun was intermittent, but the view was better, or on the shelf in the hallway, where the warmth was guaranteed, but the view was boring. Nicholas chose the window; Cassie chose the hallway. The humans had a typical day, wrapping up the straggling odds and ends. Actually, today, the 31st, is the end of the first decade of the 21st Century, but in the popular mind, the decade ended a year ago. The next FOTD will be posted in 24 hours. Until then, take care, and the last time I checked, none of the people I know were Boltzmann brains. (I'll have more to say about these hypothetical disembodied brains floating around in outer space sometime in the future.) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Totally_New_Aspect { ; time=0:02:40.28-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 float=y center-mag=-0.06323373791458239/+0.152854337845338\ 30/63.53143/86.095/-90/-10.3180927723985381 params=100/0/90/0/-0.7525/0/0.5/0 maxiter=1500 inside=0 periodicity=0 mathtolerance=0.05/1 colors=0002jZ3lY4lX5lX6lW7lV9lVAlUBlTClTDlSElRFlRN\ oQUqP`sOgvNnxMuzMpyLkyKfyJayJXxISxHNxGIxGMuHQsHUqH\ YoHamHejIihImfIqdIubIpaJlaKhaLd`M_`NW`OS_PO_QJ_RFZ\ SBZT7ZT8VV9SWAPXBMYCJZDG_ED`FAaJKVNUPRbIVlCZu6WoAU\ jDSdHQ_KOUOMPRKJVIEYG9`IDaKGaLJaNMaOPaQSaSVbTYbV`b\ WcbYfbZibXj`WkZVlXTmVSnTRoRPpPOqNNrLLsJKtHJuGIsHIr\ HHqIHpIGnJGmJFlKFkKFjKDfPBcT9_Y7Xa5Tf4Qj7ShAUgDWeG\ XdJZbM`aPb`ScZVeYYdWYbVY`UYZGZXF_VF`TEaREcSDeUDfVD\ hWCsjCqiBohBmgAkfAheAedJbcRZaZV_fRZeNZeJZdF_dD_fC_\ gBZhAYiFZfK_cP_`T`ZY`WbaTfaRe`Te_Ve_XeZZdY`dYbdXdd\ WfdWhcVjcUlcUncTpcTqeUpgUpiUpjUplUpnUppUoqUosUouUo\ wUoxUo`wf_wd_wc_vaZv`Zv_ZuYYuXYtVYtUXtTXsRXsQWrOWr\ NWrMVpKUoITnJSmLRlNQkPPjRQiTRhVRhXUi_Xia_icbieeigh\ iikikmjnmjpmjrljtljvljxljzjaqhTifK`dBTbCUaDU`EV_EV\ YFVXGWWGWVHWTIXSIXRJYQKYOKYNLZMMZLMZNNYOOXQPWRRVST\ UUVUVXTWZSY`RYbQZdQMfTAhW } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 30-12-10 (Fractal Uncertainty [?])
by Jim Muth 30 Dec '10

30 Dec '10

FOTD -- December 30, 2010 (Rating ?) Fractal visionaries and enthusiasts: Today's image has a strange look about it. In fact, the strange look is all the image has going for it. The grainy effect is due to the magnitude of the image being beyond the limit of math- ematical precision. The name "Fractal Uncertainty" expresses this imprecision. The parent fractal was created when I calculated the formula Z^(1.75)+C eleven turns up the complex logarithmic hyperspiral with no function applied. The image could be a troublesome one, since there is no guarantee that the accuracy will fail in exactly the same way on all machines. Since I'm not sure what will result when the parameter file is run on different machines, I could give the image only a rating of a question mark. To be sure of seeing the correct image, I suggest viewing it on the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The traditional FOTD web site may still be accessed at: <http://www.Nahee.com/FOTD/> but it is not yet up to date. The temperature reached 40F 4.5C here at Fractal Central on Wednesday, which was the warmest in almost a month. The fractal cats leaped to their window shelf as soon as the sun reached it, and stayed until the sun moved on several hours later. The humans' day was about average -- dull but peaceful. The next FOTD will be posted in 24 hours. Until then, take care, and maybe we're all merely Boltzmann brains. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= FractalUncertainty { ; time=0:05:24.72-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-1.7800606505427/-0.1605412639414543/\ 1.082816e+013/1/-17.4/0 params=1.75/0/11/0 float=y maxiter=1500 inside=0 mathtolerance=0.05/1 colors=000OESKBNG9JC7E84942zfUbLFJ2_j1Ub1OV1IN0CF0\ 67ELVAFN7AF3570IK0EG0AC078034zQz9cXU005DU00I000qtD\ zz6kZqaSfSLWJEL97ASl8IW59G2Ei1Cc0AY08S07N05H03B015\ 0OUMzKE8A7c`nQOYHGREFVCE_9Dc6Ch4Bl8JjBQiFXhIcgJ271\ jV9lPGnKNoFVqAas5ht0jm6lfCn`IoUNqNTsHZuAdv4ikNWadI\ Sv5KJ9JMFJOKIRQITVHW`HYeH_jIbcJeXJhRKkKKnELq7Ls1Ef\ J7V_0JpFErT9sf4ut0v10g93fG6fN9eVCeaFdhIdoKdqFjsAou\ 5tv0yw4ox8fyCXzFO3A7qCKhAH_8DR6AI46923MbuBJTrsljke\ bcZVWSNOLFGE787uRZfKQTDHz68lbNzQFzD7zE6zC58z4z835z\ 2z41120cG1K80vMUjHOZDIz8Cz46frTYgNPXHHMB8B5LzxFByB\ 8i75V32FVntPejKYaFPSAHJ5z9qfHhZE_SBRL8IE5972rJdR9K\ BHQ9EL7BH58D3581243vY2lS2bM1TH1Jz095TarEJRW`3RV2MQ\ 2IL1DF19Az450ezkLVOTv5Nj4HZ3BN25B17w7zc42K2zDHmAD`\ 7AP56z23zQQ0HH088Cp`FZ5BQ37H2381TOtPLlLIeIFZzCSA9L\ 76Ez375CD4AB399378266144133011rUnOpPIbICQC6D6m1TWO\ fRK_MHUIDODAI96C436WJaSGX } 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] FOTD 29-12-10 (The Life on Vega-E [8])
by Jim Muth 29 Dec '10

29 Dec '10

FOTD -- December 29, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's image was created by the formula Z^2.01+C. The parent fractal of the image is shaped like a Mandelbrot set with two main stems and a large minibrot on each stem. The scene lies in the East Valley of the large minibrot on the northern stem of the parent, where the stem is infinitely divided. I named the image "The Life on Vega-E", when I imagined what kind of life might exist on a hypothetical fifth planet circling the star Vega. The star Vega is brighter than earth's sun, so I assumed the fifth planet would lie in the habitable zone of the star. Of course, if the type of life involves chemical pro- cesses unknown on earth, the habitable zone might lie somewhere else. The life I conjured up resembles a kind of lumpy sickly-green caterpillar of the earth variety, such as what we see around the edges of today's image. Much smaller caterpillars lie closer to the central minibrot, though these are more difficult to pick out. The rating of an 8 gives me credit for the coloring. The calcu- lation time of one minute will pass in two flashes for those with machines that do not panic at the sight of a command line. Those afflicted with such over-qualified units may view the finished image on the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The other esoteric fractal fanatics will find past images back to April, 1997 on the original FOTD web site at: <http://www.Nahee.com/FOTD/> The site is not up to date however. We had lots of sun here at Fractal Central on Tuesday, but the blustery wind and temperature that hung around freezing made it unpleasant out in the open. The fractal cats, who probably will never be out in the open, were unconcerned with the outside chill. They were quite happy on their shelf in the window when the sun was shining, and on their shelf over the hall radiator when it was not. The human side of things went along according to plan. In fact one job needed no work at all to be done on it. The next FOTD will be posted in 24 hours. Until then, take care, and they say each individual is an ephemeral emergent phenomenon. I guess that answers all the big questions about the meaning of life. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= The_Life_on_Vega-E { ; time=0:01:04.32-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=-1.740172267\ 040917/+0.0449669196782342/7.03338e+008/1/-102.5/0 params=0/0/0/0/0/0/0/0/2.01/0 float=y maxiter=2500 inside=0 logmap=240 periodicity=6 colors=0007DY7FZ7HZAJaDMcGQeKVjPZpUdpYjsdpshvtoytr\ zpvzlzwhztdwp`rnXmjYhfYccYZ_YUXYWTYXPYYMYZIY_FYbOd\ eXjhepjnvhltgjrfipegncelbdjabh``f__eYXgWVhUSjTQkRN\ mPLnOJoPMnPPmQSmQUlRXlR_kSbkSdjTgjTjiTliVmgWmfYmdZ\ nc`naan`coZdoYeoWgpVhpTjpSkqQmpPnoNmnMklLhjKdgKacJ\ X_ISWIOSHKPGGMGCJF9HFAIGAIGAHHBGHBGIBHICIJCJJCJJFK\ HIKFLKDOKBRK9UK7XK5_K3aK1`P2_U3ZZ4Yc5Xh6Wm7Wq8XrAY\ sCZsDZtF_uG`uIavJawLbwMcxOcxPHXSGVTFUUETUESVDQVCPW\ BOWBNXALY9KY8JZ8IZ7G_6F_5E`5D`HFXSHTcJQnLMyNJwUIv`\ IufHtmHssHrpKrmNrkQrhTrfWrcZraamZdUWTPUjPRmPPpPMsU\ KuXPk`Ta_XSU`IOd8WbAc`CkZErYFq_KpaOpcToeXogasiewki\ efcYacQYcjUHiWGiYFi_EiaDicCieBhgBhiAhk9hm8ho7hq6zr\ ziqBzpFknJllOljSmhWnf`oddobhp`gpZfqZeqZdrccrccpcen\ cfmhgkhhimjhmkfrlermcvoazp`zqZzrYzsWzoVzlUziTzeRzb\ Qz_PzXOzTNzQLzNKzJJzGIzDHzAGzEFzHEzKDzNCzQBzUAzX9z\ _8zb8ze7zd7zc7zb7zb7za7z` } frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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FOTD 28-12-10 (Multiple-Moon Light [8])
by Jim Muth 28 Dec '10

28 Dec '10

FOTD -- December 28, 2010 (Rating 8) Fractal visionaries and enthusiasts: I named today's image "Multiple-Moon Light", implying light from multiple moons. The rating of an 8 might be a little liberal, but what the heck, it's a rather pleasing and peaceful image to meditate upon, so why not give it a rating of 8? The formula behind the peacefulness combines 8 negative parts of Z^(-1.5) with one negative part of Z^(-5.5), then adds (1/C). The resulting parent fractal is a north-south string of large irregular bays, with a cut-off ring just south of the main mass of bays. Today's scene is located in the interior of this cut- off ring. Actually, the image is 'evaporated'. The escape radius of one- googol makes sure that all outside parts have evaporated. The scene consists entirely of 'bof61' inside fill. The calculation time of 33 seconds will pass in a flash for those who run this letter as a parameter file. Others will need to surf electronically down to the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image will soon be posted. The original web site at: <http://www.Nahee.com/FOTD/> is presently inactive, but will be brought up to date when Paul gets back on his feet. The generous sunshine here at Fractal Central on Monday was nullified by a temperature of 25F +1C and a strong blustery wind from the north. The Sunday evening snow amounted to a whopping trace. The fractal cats, who are indoor cats and never concern themselves with outside conditions, were quite happy all after- noon on their sunny shelf in the window. The humans' day featured getting back into the everyday routine, which took very little effort. The next FOTD will be posted in 24 hours. Until then, take care, and activate your chi energy. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Multiple-MoonLight { ; time=0:00:33.34-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+0.0784946918398598/-2.088888523004933\ /5.5e+009/1/-7.5/0 params=-1/-5.5/-8/-1.5/0/1e+100\ /0/0 maxiter=1500 inside=bof61 sound=off colors=000boIaoJaoJ`oK`oK_pLZpLZpM000YpNXpNXpOWpOW\ pPVpPUpQUpQTpRTpRSpSSpSRpT000SlSShRSeQSaPSYOSVNTRN\ TOMTKLTGKTDJT9IV5JT6IR7IP8IN9ILAIKBHEHQGDHEGQC9HBF\ QACJAGKAELKJc9MOQUc9OQ9QR9RS8SU8UV8VW8WX8XY7Z_7_`7\ `a7bb6cd6de6ef6gg6hh5ij5kkQkl5mm_on6qodroiwpktprwn\ rtmrqlmnjmkimhhmefmbeC_dCYcDZdEZeEZeFZfGZgGZgH_hH_\ iI_iJ_jJ_kK_kL`lL`mM`mM`nN`oO`oOapPaqQaqQarRasRasS\ _tSYtTWuTUuTSvUQvUPwVNwVLxVJxWHyWFyVCzWEyWFyWHxWIx\ WKwWLwWNwWOvWQvWRuXTuXUtXWtXXtXZsX_sXarXbrXdqXeqXf\ q_dmbcidbfgab`duYawWZyXYvXXtXWrYVpYUnYTlZTjZShZRf_\ Qd_Pa_O_`NY`NW`MUaLSaKQaJObIMbHKaJGbHIcGKdFMeDNfCP\ gBRh9Si8Uj7Wm4Zk6Xj7Wi8Vh9UgASfCReDQdEPcFNbGMaHL`J\ K_KIZLHYMGXNFWOEVQGVSIUTKUVMTWOT0QS0SS0UR0WR0YQ0_Q\ 0aP0cP0eO0gO0iN0kN0lM0hM0dM0`M0XM0TL0PL0LL0HL0DL09\ O03L05J06H07E08C09A0A70B50C30D60H80KA0NC0QE0TG0WI0\ Zf0Ef0Fe0Fe0Gd0Gc0Hc0Hb0I } 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 27-12-10 (Repeat Performance [6])
by Jim Muth 26 Dec '10

26 Dec '10

FOTD -- December 27, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's super-fast image rates only a 6. This is because it is the third consecutive image of a minibrot lying in the field of chaos near the shore line of a Mandelbrot bay or bud. Today's scene is located on the western shore line of the period-5 bud on the northwest shore line of the main bay of the Mandelbrot set. The name "Repeat Performance" indicates that today's image is similar to the two most recent FOTD images. It might actually be the best of the three, but 'might be's' carry little weight when rating images. The calculation time of 8 seconds will pass in a flash. Those with non-cooperative machines may see the finished image on the presently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> Sunday brought lots of clouds, brisk north winds and a tempera- ture of 27F -3C to Fractal Central. Snow showers moved in just after nightfall, but at post time had amounted to only a dusting. The fractal cats passed the unusually chilly day on their shelf by the heat, exhausted after yesterday's battle with the gift wrappings. The humans' day was spent recovering from yesterday. The next FOTD will be posted in 24 hours. Until then, take care, live to learn and learn to live. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Repeat_Performance { ; time=0:00:08.51-SF5 on P4-2000 reset=2004 type=mandel passes=2 center-mag=-0.5407\ 452833814538/+0.577023247902471/3.5297e+011/1/87.5\ /0 params=0/0 float=y maxiter=15000 inside=0 logmap=-1242 periodicity=6 colors=000PTjQTkRUkSUlSVmTWnUXoVYoWZpX_qY`rZar_bs`\ ctadubdvcfwdhxejyflzfnzeozepzeqzdrzdszdtzcuzcvzcwz\ cxzbyzcPceOagM_rrzrrzrrzwwzuuzrrzrrzrrzrrz0AI08GZ7\ FZ6DY4B039027Y16037057W780980B8WC9VE9VGAVIAVKAULBU\ NBUPCTRCTTCmUDTWDSYDS_ESaERbFRdFRfFRhGQjGzzHQmHPzH\ PqIPsIPtIOqJOoJOmzOkzOiLOgLOeLOcMOaMO_NOYNOWNNUONS\ ONQPNOPNMQNKQNIQNGRNERNCSNASN8SOCPOFNPILPLJQOHQRFR\ UDRXBS_9Sb7Te5Th3Tk1Ui4Ug6Vf8VdAVcCWaEW`GHhaHgaIga\ JgaKgaKfaLfaMf`Me`Ne`Oe`Od`Pd`Qd`Qc`Rc`Sc`Tc`Tb`Ub\ `Vb`Va_Wa_Xa_X`_Y`_Z`__`____`__a__aZ_bZ_cZ_cY_dYZe\ YZeXZfXZgXZhXZhWZiWZjWZjVZkVZlVZlUZmUZnUYnTYoTYpTY\ qTYqSYrSYsSYsRYtRYuRYuQYvQYwQYxRZwQYwQYxQXxQXxQWxQ\ WyQVyQVyQVyQUzQUzPTzPTzPSzPSzPRzPRzPRzPQzPQzPPzPPz\ OOzOOzOOzONzONzOMzOMzOLzOLzOKzOKzNKzNJzNJzNIzNIzNH\ zNHzNGzNGzNGzNFzMFzMEzMEzMDzMDzMDzMCzMCzMBzMBzMAzL\ AzL9zL9zL9zL8zL8zL7zL7zL6 } END PARAMETER FILE=========================================

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FOTD 26-12-10 (Surprise Mandelbrot [7])
by Jim Muth 26 Dec '10

26 Dec '10

FOTD -- December 26, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image is not only late, it is very simple -- another scene on the northwest shore line of the main bay, but this time the main bay of the large minibrot on the main stem of the Mandelbrot set. The scene lies on a filament, just beyond the point where it separates from the main body of chaos. I named the image "Surprise Mandelbrot" because of the elements surrounding the central minibrot, which surprisingly point in toward the center rather than outward. The rating of a 7 is perhaps a bit above what might be expected for a fractal found on a day with so many other things to do. The calculation time of 10 minutes is due to the necessity of using arbitrary precision math, and is slower than I would have preferred. But calculation may be avoided by checking the web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image will soon be posted. and don't forget the original web site at: <http://www.Nahee.com/FOTD/> Clouds all day and a temperature of freezing kept things subdued here at Fractal Central on Christmas day. The fractal cats were too busy romping in the wrapping paper to notice the outside conditions. The next FOTD will be posted in 10 hours or more. Until then, take care, and relax. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= SurpriseMandelbrot { ; time=0:10:17.80-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.7652273461461\ 26424/0.00851359743301010303/9.468406e+014/1/147.5\ /0 params=0/0 float=y maxiter=5600 bailout=36 inside=0 logmap=-565 periodicity=6 colors=000QAGRAGSAGTAGUAGVAGWAFXAEYADZAC`ABaAAcA9d\ A8fA7g86hE9iJCjOFkTIlYLmcOnhRomUprXpwZrwXtwWvwVwxU\ xxSyzRzzQzzPrrmichc_a_XZXVXTSUQPRMMOJKLFHITEFNBCI9\ AH2CC3E00G00IaVJYZMVaOSeRPhTLkWIzYFz`CzbmzemzgmzjM\ zlmzzczqTzsmzvXzxZzzmzsVzzmzzSzzmzzPMPNIJMEDKA7J61\ L96MCBOFGPHLRKQSNVUQ_VSdXViYYn_`s`bxZarY`lW_gVZaTY\ XSXRQWMPVGOVBQYAS_9Ub8Wd7Yg6_i5al4cn3eq2gs1Kw`JwZI\ wXHwVGwUFuSFsQFqPEoNEmLEkKDiIDgGDeFCcDCaBCzABzDAzG\ 9zI9zL8zN7zQ6zT6zV5zY4z_3zb3ze2zg1zj1zl4zk7zkAzkDz\ kGzkJzkMzkPzkSzkVzkYzk`zkczkfzkizklzkpzOmzPkzQizRg\ zSezTczTazU_zVYzWWzXUzYSzYTzZTzZUzZUzZVz_Vz_Vz_Wz_\ Wz`Xz`Xz`Xz`ZzZ`zYbzWdzVfzThzSjzQlzPnzNpzMrzKtzJvz\ HwzGvzFvzEuzDuzCuzBtzAtzAsz9sz8sz7rz6rz5rz5nz6kz7g\ z8dz9`zAYzBSz9Mz7Gz5Jz9MzCOzFRzJUzMWzPSzWPzaMzgJzm\ GzsJzqLzpOznQzmSzlTziTzfTzcTzaTzZUzWUzTUzRUzOUzLVz\ IVzGVzDVzAVz7Vz5NzCGzI8zO } END PARAMETER FILE=========================================

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FOTD 25-12-10 (Merry Season [7])
by Jim Muth 25 Dec '10

25 Dec '10

FOTD -- December 25, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image is an unpretentious scene deep on the northwest shore line of the main bay of the Mandelbrot set. I have named it "Merry Season" because it covers a multitude of festivals connected with bringing light to the darkest time of the year, the winter solstice. The most celebrated solstice festival in our culture is Christmas, which unfortunately has become more of a marketing opportunity than a celebration of divine salvation. The colors traditionally associated with Christmas are red and green, probably associated with red holly berries. I have given the image a red and green theme in keeping with the seasonal colors. Red and green also remind me of the holly grove back at Old Fractal Central, where the now deceased original fractal cats romped and lurked for almost twenty years. New Fractal Central has but one scrawny holly tree, but that tree is presently covered with a full crop of red berries, which add their share to the feeling of the season. The new fractal cats get their share of action indoors however. The image rates a 7, fair enough for a mere Mandelbrot scene. The calculation time of under 2 seconds is as fast as Santa coming down the chimney. The finished image is or soon will be posted on the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And don't forget the original FOTD web site at: <http://www.Nahee.com/FOTD/> which Paul has kept going for over 13 years. While tending to last-minute Christmas details on Friday, I heard a version of 'Oh Come Emanuel' on the radio, with drums and traps beating out a syncopated rhythm in the background. I wondered why the beat had been added to such a simple song. The traditional melody is an old plainchant, which has no rhythm. The only reason for the intrusive beat that I could think of was that over the years the purpose of music has changed from lifting the spirit through melody, to getting the body moving with a catchy beat. (But then again, times keep changing, and I just might be old-fashioned. FL heard nothing intrusive in the arrangement.) The mix of sun and clouds with a temperature just above freezing that we had here at Fractal Central on Friday made the day just about average. The fractal cats enjoyed the sun, and when the sun failed, they went to the heat. The day of the humans was filled with last minute preparations for whatever may come. The next FOTD is due in 24 hours, but if it does not appear until Sunday, do not be surprised. Until whenever, take care, and I don't want to leave the impression that I'm cynical at this time of year. I want to state it outright. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Merry_Season { ; time=0:00:01.92-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.4228394615443\ 275/+0.5720091755518583/4.164996e+011/1/11.5/0 params=0/0 float=y maxiter=15000 inside=0 logmap=266 periodicity=6 mathtolerance=0.05/1 colors=000A1QB3UC6XD8_EAcGCfHEiIGmJIpKKsLOsMPrORrP\ UrQXqR_qSapTfpVhpWkoXooYpoZrn_snatmbvmcxmdzlezlfzl\ bzi_zfWxcTuaQrZMlWJcUFcRCcO9bMA_LBXLCULDULEULFULGU\ LHULIULJULKULLULMULNULOULPULQULRULSULTULUVLVWLWXLX\ YLYZLZ_L_`L`aLabLbbLccLddLeeLgfLifLkhLmjLomLqmLsmL\ umLumLsmLmcJjbIg`HcYG`VFYUEUUCRUBNU9KU8HU7DU5AU46U\ 23U1KUDGUACU78U54U2_U5YU4WU4VU4TU4SU3QU3PU3NU3LU3K\ U2IU2HU2FU2EU1CU1AU19U17U16U04U03U01U0yYzvWzsVzpTz\ nSzkQzhPzfNzcMmcKccJUcHKcGEcEDcDBcBAcA9c87c76c55c4\ 3c22c11cJlcIjcHhcGfcGdcFbbE`aDZ`DX_CWZBUZAShAQh9Oc\ 8Mh8Kh7Iu6Gu5Fu5Du4Bu39u27u25u13u01uFkuAWu5GZyzzzz\ Lzzzzz7zzzzz0zzzzz0zzzzz0zzzzz0zzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzz_zzZzzYzzWzzVzzUzzTzzRzzQzzPzzOzzMzztzztzzuzz\ uzzvzzvzzwzzwzzxzzxzzyzzyzzzzzzzzzzzrzzjzzczzWzzOz\ zHzz9zz2zz4zz5zz6zz7zz8zz } END PARAMETER FILE=========================================

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FOTD 24-12-10 (Light in Darkness [7.5])
by Jim Muth 24 Dec '10

24 Dec '10

FOTD -- December 24, 2010 (Rating 7.5) Fractal visionaries and enthusiasts: Things are rather busy here at Fractal Central as I write this on the evening of the 23rd. The discussion will be short. On the surface, today's image, with its preponderance of dark blues, is a bleak one indeed. But in its depths it holds a minibrot with a warm and shining heart. After a minute of deep thought, I named the image "Light in Darkness". The parent fractal came about when I mixed three negative parts of Z^(-1.3) with one negative part of Z^(-3.3). This parent is obviously a Mandeloid of some sort, though I was unable to make any sense of it. If it actually has a Seahorse Valley and an East Valley, they are quite hard to locate. The rating of a 7-1/2 includes 1/2 point reward to myself for the coloring, which is the major part of the effect of the image. The calculation time of 4-2/3 minutes is within reason. The easiest way to view the image is to truck down to the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image is or soon will be posted. All the past FOTD images are available on the original FOTD web site at: <http://www.Nahee.com/FOTD/> though the site is not up to date. Morning clouds and afternoon sun kept the fractal cats happy on their window shelf here at Fractal Central on Thursday. The temperature of 37F +3C was warmer than we have seen recently, but still chilly. The humans were kept busy with holiday tasks. The next FOTD will be posted in 24 hours. Until then, take care, and be at peace with the powers that be as you try to figure out what this time of year is really all about. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Light_in_Darkness { ; time=0:04:41.17-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=+2.340247772835/-0.41997288768/6.5e+007\ /1/-37.5/0 params=-3/-1.3/-1/-3.3/0/0/0/0 float=y maxiter=5400 inside=0 logmap=-760 periodicity=6 colors=000A0KA0KA0KA0KA0KA0KA0KA0KA0KA0KA0KA0KA0KA\ 0KA0KA0KA0KA0KA0KA0KA0KA0KA0KA0KA0KA0KA2JB4HC6FC8D\ CABCEECFGCHLCIPCJUCKZCLbCMbCO_CPaCQdCRgCSjCTlDUjEU\ iEVhFVgGWeGWdHXcIXbIY`JY_KZZKZYLZWM_VM_UN`TO`ROaQP\ aPYbOcbMYcLSaKScJQaLP`MNZOMYPLPRJVSIUUHTVFKXEQYDQ_\ BF`AGU9EUHBU91MJ3LM4LS6KW7dY8h`AcaBZcCUfEPgFKiHHkI\ GmJGoLGrMFsUFvcExmEzcEzcGycIxUKvPLuPNtPPrORqOSqOUp\ NWpNXpNZoO`oQboScnUenWgnYim_jmalmcnmcokcnjcmicmhel\ gglfikekkdmjcmibmi`mh_ohZqgYsgXufWweVweUwdTwdSwcRu\ cTsbUqbVobXmaYkaZia`gaae`bc`da`e_`fY_zX_zW_zV_zUZz\ TZzSZzRZzQYzPYzOYzOYzQ_zR`zSazUbzVczWdzYezZfz_gzah\ zbizcjzekzflzgmzinzjozkpzlqzmmznjzofzpczq`zrXzsUzt\ RzuNzvKzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzz\ wzzwzzwzzwzzwzzwzzwzzwzzxzzyzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzIzzKzzMzzOzzQzzSzzUzzWz\ zYzz_zzazzczzezzfzzgzzhzz } 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 23-12-10 (Spring Comes Early [7])
by Jim Muth 23 Dec '10

23 Dec '10

FOTD -- December 23, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today (Dec 22) is the first full day of winter in this part of the northern hemisphere, so what could be more appropriate than a screen filled with pink apple blossoms, bringing a hint of the warmth that is yet three months away. I named the preview image "Spring Comes Early". It was created with the iterated expression Z^(-11)+11(1/Z)+C. The parent fractal created by this expression must be seen to be believed. In my opinion, the image is worth an above-average 7, a rating made all the more worthwhile by the fireball calculation time of 27 seconds. Those who run parameter files with difficulty can soon find the finished image on the new FOTD web site maintained by Hal Lane at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site at: <http://www.Nahee.com/FOTD/> maintained by Paul Lee is still there, but Paul has not been able to update it for a while. Sun, clouds and a temperature of 34F +1C made Wednesday a rather pleasant day here at Fractal Central. The fractal cats soaked up the sun when it was shining on their window shelf and kept warm on their shelf over the heat when it was not. My day was typically busy for a day three days before Christmas. The next FOTD will be posted in 24 hours. Until then, take care, and if spring and summer are coming soon up here, autumn and winter are coming soon down there. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Spring_Comes_Early { ; time=0:00:27.57-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.5378244047/+1.1918257186/199729/1/15\ /0 params=1/-11/11/-1/0/0/0/0 float=y maxiter=767 inside=fmod proximity=0.95 outside=real colors=000zcslapfbj_ceUc_NdUHePAfJ4fEMeHceKteMZONE\ 6OF6MG6LM6JU6Ic8GmDUPNzzX_zzSzmZWcdfJjpGooKinOcmSZ\ lVTkZPfZUaYZYXcUWg`OkgAlm3ldDhWMdNV`EcX5lUAgQFbNKZ\ JPUGTQDQQKOQRMQXKQcIQjGQpEXeCcVAjL8qA6x07v77tE7sL7\ qR7oY7nd7lk7kqN7_KBaHEcFIdCLf9Ph7Si6Oh5Kg4Hg3Df29e\ 16e8AfFEfMIgTMg_QhfUhmYitaiuTlvKowBrw2toDlhNe`YYUg\ RNqKKpMIoOGnPDmRBlS9kU7jVDkUIlUOmTTnTZoScpShqSjiYl\ abmUgoMmqErr6wn_lhWecS_YOUTKNNGHICBD95MpbbhlDQMDPL\ COKCNICMHCLGBKFBJEBIDBHC`Ku_KsZKrZKqYKpXKoXKnWKmWK\ lVKkUKjUKhTKfTKeSKdRKdRKbQKbQKaPK`OK_OKZNKYNKWMKWL\ KULKUKKSKKRJKQIKPIKOHKNHKLGKKFKJFKIEKHEKGDJFCIECHD\ BGC6FB7EA7D97C87B77A679578477376275174073082081080\ 280480680880A80C80E80F80F80F90F90F90E90E90E90E90E9\ 0E9KE9JE9JD9JDAJDAJDAJDAJDAIDAIDAIDAICAICAICAICAHC\ BHCBHCBHCBHCBHBBHBBGBBGBBGBBGBBFBBEBADAACAABAAAAA9\ AA8AA7AA6AA5AA4AA3AA2AA1A } 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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Paul is still "under the weather"; Speedy recovery, Paul!
by Hal Lane 22 Dec '10

22 Dec '10

I just spoke with a friend of Paul Lee's who says that Paul is still "under the weather." We all wish you a speedy recovery, Paul! - Hal Lane ######################### # hallane(a)earthlink.net # #########################

2 1

FOTD 22-12-10 (Everyday Event [5])
by Jim Muth 22 Dec '10

22 Dec '10

FOTD -- December 22, 2010 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a very lucky one. My finger was one inch from the delete button that would have sent it to neverland when I decided to make it FOTD for the day. Nothing is really wrong with the image, but nothing is really right either. It's an *everyday event*, the kind of image I turn up all the time in my never ending search for a better fractal. This is what I named it. The formula behind the image is Z^(1.95)+C, iterated at ground level. The parent fractal is quite a bit more distorted than what might be expected from a formula so close to Z^2+C, but all the parts are there, even though they are not so easily recognized. There is nothing wrong with the rating of a 5. It's equal to a grade of 'C', which means average performance. If its calcula- tion time had been a bit faster than 6 minutes, the image might have rated a point higher. Those who do not calculate may view the finished image on the new FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site is still there, though it is not up to date. The original site may be accessed at: <http://www.Nahee.com/FOTD/> Wall-to-wall sunshine and a temperature of 36F +2C made the shortest day of the year somewhat pleasant here at Fractal Central on Tuesday. The fractal cats must have agreed, for they spent most of the day on the shelf by the sunny southwest window. Most everything else went according to plan. The next FOTD will be posted in 24 hours. Until then, take care, and they say it's all a dream. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Everyday_Event { ; time=0:06:16.89-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.2318797787712759/+0.1330343967606758\ /1.479257e+013/1/107.5/0 params=1.95/0/0/0 float=y maxiter=1800 inside=0 logmap=543 periodicity=6 mathtolerance=0.05/1 colors=000AABAABAACAADAADAAEBAFCAFDAGEAHFAHGAIHAJI\ AJJAKKALKALKAMKANKANKAOKAPKAPKAQKARKARKASKASK9RK8R\ K8RK7QK6QK5QK5PK4PK3PK2RK3RK3RK3RK3RK4RK4RK4RK4RK4\ RKAQKAPKAOKANKAMKALKAKJAJHAIGAHFAGDAFC9EB8D97C86B7\ 5B55B45B35B45B45C45D45E45F45G45G45G45G45G45G45G46G\ 46G56F57F57F57F57F57F57F58F58F58F58F58F59F59FXKDZK\ I`KMbKRcKVeK_gKciKhjKlkMmkOmlQnlRnmTomVonWpnYpn_qo\ `qobrpdrpesqgsqitqjtRhl1fe8ebFd_McYSbVZaTe`Qk`OhZN\ fYMdXLaWK_UJYTIVSHTRGRPFOOEMNDKMCILCHPBGSAFV9EY8E`\ 7Dd6Cg5Bj4Am3Ap38_J6JZ42mD7jLCgTHeQNbOS_MXYKaVIfSG\ kQEpNCuKAzIEwFItDMqAPo8RpDSqIUrMVsRXtWYt_1UjUlAZnC\ bpDgrFktGpvItxJsuIrrHqpGpmFokEnhDmfClcCkaBjZAiX9hU\ 8gS7fP6fN6`VEVbMPjUKr`WXffBkgDjgFjgHjgJjgLigNigPig\ RigThgVhgXhgYhe_gc`faae_cdYdcWecUfbShaQi`Oj_Nk_P_i\ OZiOZhOYhNYhNYhNXgMXgMWgMWfLWfWZ_lVxiSpfQicNa`LVPU\ `Daf2ik7kiBmhFngJpfNqeSsc } 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=========================================

1 0

FOTD 21-12-10 (Test Pattern [6])
by Jim Muth 21 Dec '10

21 Dec '10

FOTD -- December 21, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows a minibrot of order 1.1. For some reason I continue to search for interesting minibrots down in this range, even though I rarely find anything worthwhile. (Today's image shows a rare exception.) The parent fractal of today's image came about when I calculated the formula Z^(1.1)+C at a level 11 turns up the logarithmic hyper-spiral with no function applied. This parent is shaped like a cut-off parabola with a few areas of chaos along its edges. Not surprisingly, today's image is found in one of these chaotic areas. I named the image "Test Pattern" because of the flat, highly colored, sharp-edged shapes filling it, which might be only a test of what might lie deeper in the parent. The rating of a humble 6 indicates that I do not consider it one of the better FOTD images. With a calculation time of a mere one-minute however, the image is worth the effort despite its modest achievements. Calculation may be totally avoided by viewing the finished image on the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD web site at: <http://www.Nahee.com/FOTD/> might not be up to date, but it is worth a quick check. A mix of sun and clouds, with a high temperature of 34F +2C, made Monday pretty close to normal here at Fractal Central. The fractal cats spent their time alternating between the shelf over the heat and the shelf by the window, which is also pretty close to normal. The rest of the activity at FC was totally routine. The next FOTD will be posted in 24 hours. Until then, take care, and maybe we're all serfs, laboring on the lands of our overlords, the big corporations. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Test_Pattern { ; time=0:01:04.05-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-2.447903993/+2.790388926/4195/1/75/0 params=1.1/0/11/0 float=y maxiter=10000 inside=0 logmap=87 periodicity=6 colors=000C4FB4E93C83A628527415213101_OEOKCBHA9D86\ A6464232zuTmpQclOUhMKzzAln9Xc8TU6OK5KA4G83C6284142\ HZ`FVXDSUCPQzz09JK0m06CD49A366133zcyG_zaWlCSfAO`9K\ V7GO5CI38C146q5gm4ci4`e3Ya3VY3SU2PR2MN2IJ1FF1CB197\ 06303wA5r94m84i73d63_63W52R42N31I31D219104001UZ0PT\ 0KN0FH0AB055pHfjFadDXZBST9NN7JUGQUIPVKOVMMVOLWQKWS\ JWUIVVLVVOVVRUWTUWWUWZUW`TXcTXfTXiSYkSYnSYqSYsVVgX\ TW_RKaP8jGNr8`z0zu4zq7zmBziEzdHz`LzXOzTSzOczKczGcz\ Ccz8czAczCczEczFczHczJczKczMczOczPczQczQmzQmzQmzRm\ zRmzRmzRmzRmzOmz6mzMmzJmzHmzEmzCmz9mz7mz4mz2mzFmzA\ mz5mzWmzGmzkmzemz`mzWmzQmzLmzGmzAmz5zzzzzuzzqzzmzz\ izzezz`zzXzzTzzPzzLzzGzzCzz8zz4zzIzzDzz9zz4zz8zz6z\ z4zz3zz1zzrzz_zzIzz1zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zzqzzRzzWzzOzzGzz8zz\ MzzIzzEzzBzz7zz3zzTzzPzzMzzJzzGzzCzz9zz6zz3zzJzzCz\ z6zzMzzKzzJzzHzzGzzFzzDzz } 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] Sampling Frequency and oversampling
by Richard 20 Dec '10

20 Dec '10

In article <4D0FB01F.3050909(a)fractalus.com>, Damien Jones <dmj(a)fractalus.com> writes: > > The Nyquist-Shannon sampling theorem says that a sampling frequency > > f cannot possibly represent signals with frequencies greater than 2f. > > I think you meant 1/2 f and not 2f. Yes, you're correct, I had my factor of two in the wrong direction. -- "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download <http://legalizeadulthood.wordpress.com/the-direct3d-graphics-pipeline/> Legalize Adulthood! <http://legalizeadulthood.wordpress.com>

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RSS feed now caught up
by Richard 20 Dec '10

20 Dec '10

The FOTD RSS feed at <http://www.xmission.com/~legalize/fractals/fotd/fotd-rss.xml> is now caught up with the latest images, so you can get nice 1600x1200 3x antialiased renderings of Jim Muth's FOTD series via that feed, or by browsing <http://www.xmission.com/~legalize/fractals/fotd/>. Jim's message text is included in each .PAR file as a big comment. Now that the feed has caught up to the current images, I'll continue backfilling older images from the archives (only 3198 images to go!). -- "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download <http://legalizeadulthood.wordpress.com/the-direct3d-graphics-pipeline/> Legalize Adulthood! <http://legalizeadulthood.wordpress.com>

2 6

FOTD 20-12-10 (Holiday Seasons [5])
by Jim Muth 20 Dec '10

20 Dec '10

FOTD -- December 20, 2010 (Rating 5) Fractal visionaries and enthusiasts: Today's image is another quickie, worth only a 5. Something is wrong with the colors, (muddiness), and this keeps the rating at such a modest level. But with a rather fast calculation time of 4 minutes, the image is still worth at least a brief look. The name "Holiday Seasons" refers to the mood here at FC on Sunday as I was trying to find a fractal and make holiday preparations at the same time. The image lies in one of the typical double-negative fractals that results when various portions of Z^(-1.6) and Z^(-6.1) are mixed together and (1/C) is added. There are two ways to view the image: first, by running the included parameter file and seeing it almost at once; second, by checking the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where, if the image is not already posted, it soon will be. And keep checking the original FOTD web site at: <http://www.Nahee.com/FOTD/> It's far too early to give up on it. Sunday here at Fractal Central began with a temperature of 14F -10C, and with total sunshine, reached a high of exactly freezing. And speaking of freezing, the Susquehanna River, which flows only 1/4 mile from FC, is almost frozen solid, the first time I have seen it so. The fractal cats, who will never see the river, spent the day on their comfortable shelf over the heat. The shelf has become a surprisingly big hit with them. FL spent much of the day watching a couple of those latin soap-novellas. The next FOTD will be posted in 24 hours. Until then, take care, and do well. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Holiday_Seasons { ; time=0:04:12.77-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.6109095943025089/-1.41001144689752/\ 3.204e+011/1/170/0 params=-6/-1.6/-0.6/-6.1/0/0/0/0 float=y maxiter=3000 inside=0 logmap=408 periodicity=6 mathtolerance=0.05/1 colors=000FAKFAKEAKEAKDAKDAKCAKCAKBAKBAKAAK9AK8AK7\ AK6AK5AK4AK3AK2AK1AK3AK4AK6AK7AK9AKAAKCAKDAKEAKFAK\ FAKGAKHAKHAKIAKIAKJAKKAKKAKLAKLAKMAKNAKNAKOAKPAKPA\ KOAKOAKLAKKAKIAKGAKEAKEAKEAKEAKGAKJAKKAKPAKMAKVAKP\ AK_AKVAKWAKSAKNAKIAKEAK9AK6AK5AK5AK5AK5AK5AK5AK5ca\ 5ca5ca5c`5c`5c`5c_5c_5c_5cZ5cZ5cZ5cZ9dWCeUFfRIgPLh\ NPhKSiIVjGYkD`lBbp8ci9diAeeAfcBg`BgYChVDiSDjPEkMEl\ LFnKClIFjIIhJKfLNdNQbOS`QVaPZ_RXZQWXPVWOUVNSTMRSLQ\ RKPPJNOIMMHLLGKKEIIDHHCGGBFEADD9CB8BA7A96875764644\ 353553753953B53D53F53H63J63L63N63P63R63T63V72W72Y7\ 2_72a72d72g75j8Am8Fp8Ks8Nv8Qy8Tz8Uu8Qv9Mu9Kt9Is9Hr\ 9GqACpADoAFnAGmAIzBKzBLzBPzBUzBUzCcfCceCcdCccChbDm\ aDm`Dm_DmZDmYEmXEmWErVEvUEzTCzSmmTmlTmkUmjUmiUmhVm\ gVmfVmeWmdWmcWmbXmaXmaXm`Ym_YmZZmYZmXZmW_mV_mU_mT`\ mS`mR`oQaqPatObwPazPazP`zQ`zQ_zQ_zRZzRZzRYzSYzSXzS\ XzTWzTWzTVzYJzWKzULzSMzRN } 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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Fractint under Windows Vista
by Bob Lester 19 Dec '10

19 Dec '10

Good Day to everyone, I've been following the discussions lately about running Fractint under various platforms, DOSBOX (never heard of this before), etc. I absolutely LOVED the DOS version of Fractint but have not been able to use it for a long time now with the advent of the newer Windows OSs. I don't have the experience in computer operations that a lot of you here obviously have. I would really like to be able to use DOS Fractint again. How would I go about setting it up to run under Windows Vista? I would need a very detailed listing of what to do. My computer is an Acer Aspire M5100, 32 bit OS, AMD Athlon 64 X2 Dual core processor 4400+, 2.30 GHz, 3GB of RAM. Thanks for your attention! Bob Lester

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Re: [Fractint] DOSBOX?
by JackOfTradeZ＠comcast.net 19 Dec '10

19 Dec '10

. My Alienware has Athlon 64 dualcore, GeForce 8600, it is about 4 years old, WinXP Media. And it runs fractint screamin' demon fast - all i do is click on the file. My other system is a pig. I think it is hardware, NOT WinXP itself - this proves it. For running animations (thousands of images, 24/7 for long periods), I boot up with a DOS boot CD and use a FAT partition on the HD - works fine. This may be a good option for all you with modern systems also. .

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FOTD 19-12-10 (Theme and Variations [7])
by Jim Muth 19 Dec '10

19 Dec '10

FOTD -- December 19, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a variation on the theme of the western suburbs of the large minibrot on the main spike of the Mandelbrot set. Even though the image is so distorted that nothing at all of the Mandelbrot shape remains, the name "Theme and Variations" still seems appropriate. Perhaps a name like "Fiery Cataclysm" would have been more appropriate. There certainly is a suggestion of an erupting volcano in the image. The extreme distortion was achieved by applying the exponential function to initial C, which in effect places the viewer in the middle of the fractal. The color palette is merely a slightly tweaked version of the Fractint default palette, which is for test purposes and pretty terrible as color palettes go. But in today's image the exaggerated colors give just the right touch to the scene. The more adventurous might check deeper into the solid parts of the chaotic areas. They hold a nearly limitless variety of Moire patterns. The rating of a 7 is on the liberal side, and the calculation time of 8 minutes is admittedly slow. The way out of this dilemma is to stop by the new web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the completed image soon will be posted for immediate gratification. The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> though I have not checked to see if it is up to date. The temperature actually rose well above freezing here at Fractal Central on Saturday, to a high of 36F +2C, with lots of sun for good measure. But the milder weather was too little for the fractal cats, who spent most of the day on their new favorite spot -- the shelf over the large radiator in the hallway. Except for a brief sprint for some last-minute seasonal stuff, my day was quiet enough. The next FOTD will be posted in 24 hours. Until then, take care, and I sometimes wonder whether the faculty of reason is up to the task. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= ThemeAndVariations { ; time=0:08:04.89-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotFunct function=ident/exp passes=1 center-mag=-20.0652/3.14704/0.2774471/\ 3.1323/-90/0 params=0/1/0/0 float=y maxiter=3000 symmetry=none periodicity=0 colors=000A7GBGFBGGBFGBDGBCG0000000000000000000000\ 0000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000\ 555888BBBEEEHHHKKKOOOSSSWWW___ccchhhmmmssszzz00zG0\ zV0zj00k00n00q00t80zD0zG0zV0zj0zz0jz0Vz0Gz00z00zG0\ zV0zj0zz0jz0Vz0GzVVzbVzjVzrVzzVzzVrzVjzVbzVVzbVzjV\ zrVzzzzzwzzmzzczuczuczpcupcVpzQhzQ`zLTzZUzYUzYUzaU\ zfZzfZufZqfZlfFhfJhfOhfShfahaahqahlzhhzhhzlhzqhzuh\ zzhuzhqzhlz00S70SE0SL0SS0SS0LS0ES07S00S70SE0SL0SS0\ LS0ES07S00S00S70SE0SL0SS0LS0ES07SEESHESLESOESSESSE\ OSELSEHSEESHESLESOESSEOSELSEHSEESEESHESLESOESSEOSE\ LSEHSKKSMKSOKSQKSSKSSKQSKOSKMSKKSMKSOKSQKSSKQSKOSK\ MSKKSKKSMKSOKSQKSSKQSKOSKMS00G40G80GC0GG0GG0CG08G0\ 4G00G40G80GC0GG0CG08G04G00G00G40G80GC0GG0CG08G04G8\ 8GA8GC8GE8GG8GG8EG8CG8AG88GA8GC8GE8GG8EG8CG8AG88G8\ 8GA8GC8GE8GG8EG8CG8AGBBGCBGDBGFBGGBGGBFGBDGBCGBBGC\ BGDBGFBGGBFGBDGBCGBBGBBGC } frm:MandelbrotFunct {; Jim Muth real(c),imag(c) z=fn1(p1), c=fn2(pixel)+p2: z=sqr(z)+c, |z| < 16 } END PARAMETER FILE=========================================

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Re: [Fractint] DOSBOX?
by JackOfTradeZ＠comcast.net 18 Dec '10

18 Dec '10

. DOSBOX rocks? Uhh ... maybe, but why not just use real genuine DOS ? You gotta be losing some performance with all the hardware/software translation in any emulation setup. What am I missing here? Does a given fractal actually render faster in DOSBOX on a current system then it would in DOS/Win9X on a P3-933 for example? .

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Re: [Fractint] DOSBOX?
by Hal Lane 18 Dec '10

18 Dec '10

JoTz, > You gotta be losing some performance with all the hardware/software translation > in any emulation setup. You're absolutely right. It may be that some people are pleased with the convenience of having Fractint available on their current Windows (and possibly only) computer, and this fact compensates for the program's decrease in speed. And the decrease in speed is somewhat compensated for by the (typically) faster CPU on recent Windows machines... - Hal Lane On 2010-12-17 23:36, JackOfTradeZ wrote: > > DOSBOX rocks? Uhh ... maybe, but why not just use real genuine DOS ? > You gotta be losing some performance with all the hardware/software translation in any emulation setup. > > What am I missing here? > > Does a given fractal actually render faster in DOSBOX on a current system then it would in DOS/Win9X on a P3-933 for example? >

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FOTD 18-12-10 (Great Ghost-Bud [6])
by Jim Muth 17 Dec '10

17 Dec '10

FOTD -- December 18, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's quickie image shows one of the perturbed Mandelbrot things that I call a 'ghost bud', which explains the name "Great Ghost-Bud". A ghost bud is the left over remnant of the intact bud that appears at the same spot in the un-perturbed M-set. (To see the bud of today's image in its true form, simply change the parameters to 0,0.) The rating of a 6 is all I could give the image. I was doing similar perturbed scenes almost 20 years ago, and there is very little shock value left in such images. (If indeed, there ever was any.) The scene of the action lies on the southern shore line of the main bay of the Mandelbrot set, just west of the large period-3 bud. The location may be a bit confusing because the image has been calculated upside-down. (In my opinion, the proper posi- tion for a bud is on top of or to the left of its valley.) The initial value of Z has been set to 0.3096,1.6056, which perturbs the appearance of the M-set. In fact, it nearly wipes it out. (For some reason the type=mandel actually initializes Z to the square root of the entered value. This is inaccurate, but if it were changed, the type=mandel images made with earlier versions of the program would no longer work.) Another curiosity of the parameter file is that the reset is set to zero. Resetting this value to the usual 2004 makes a small but noticeable change in the spacing of the color bands. Despite the extreme maxiter of 250,000, the type=mandel formula is so efficient that the image calculates in 28 seconds. The image may also be seen in finished form at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> All the past FOTD images may be viewed at: <http://www.Nahee.com/FOTD/> though the site is probably not up to date. Some sun, some clouds and a temperature around 30F -1C here at Fractal Central on Friday brought some improvement to the area. The fractal cats spent most of the day sleeping by the heat, but the fractal cat Nicholas, who is usually quite friendly with strangers, lost a few points when he swore at a customer who dropped by in the afternoon and got a bit too familiar with him. The next FOTD is due in 24 hours. For all I know it will actually be ready on time. Until then, take care, and beware of synchronicity. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Great_Ghost-Bud { ; time=0:00:28.16-SF5 on P4-2000 reset=0 type=mandel passes=1 center-mag=-0.2438\ 2329/-0.639263/476/1/-168.5/0 params=0.3096/1.6056 float=y maxiter=250000 bailout=100 logmap=yes colors=000BA0aoK`oK`oK_nK_nKZnKYnKYnKXmKXmKWmKVmKV\ mKUlLUlLTlLSlLSlLRkLRkLQkLPkLPjLOjLOjLNjLMjLMiMLiM\ LiMKiMJiMJhMIhMIhMHhMGhMGgMFgMFgMEgMEgMDfNDfNDeNDe\ NDdNDdNDcNDcNDbNDbNDaODaOD`OD`OD_OD_ODZODZOCYOCYOC\ XOCXPCWPCWPCVPCVPCUPCUPCTPCTPCSPCSQCRQCRQCQQCQQCQQ\ BPQBPQBOQBOQBNQBNRBMRBMRBLRBLRBKRBKRBJRBJRBIRBISBH\ SBHSAGSAGSAFSAFSAESAESADSADSACTACTABTABTAATAATA9TA\ 9TA8TA8TA8TC9UE9UF9UHAUIAUKAULAUNBUOBUQBUPCUPCUOCU\ OCUNDUQDUSDUVEUXEU_EUaEUdFUfFUiFUkFUkFUm2ck2cj2ch2\ cg2cf2cd2cc2cb2c`2c_2cZ2cX3cW4cV5cU5cT6cR7cQ8cQ8cQ\ 9cQAcPAcPBcOCcNDcMDcLEcJFcIFcHGcGHcFIcDIdCJeBKfAKg\ 9Li7Mk6Nm5No4Oq3Ps2Pu2Qw2Rx2Ry2Sz2Tz2Uz2Vz2Vz2Xz2X\ z2Yz2Zz2_z2`z2`z2az2cz2cz2dz2dz2fz2fz3gz4gz5gz6hz7\ hz8hz9hzAizBizCizDizEjzFjzGjzHjzIlzJnzKpzLrzMtzNvw\ OxzPyzQzzRzzSzzUzzWzzYzz_zzazzczzezzgzzizzkzznzzqz\ ztzzwzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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Re: [Fractint] <Tim, Rich> DOS Fractint's img&txt vis inWinXP's DOSmode; Rich's FractintForWinBeta5
by jimmckenzie＠earthlink.net 17 Dec '10

17 Dec '10

Pretty much "DOS MODE" is not available at all during boot-up. There is no option like that even if you press F8 or F5 and bring up the advanced boot options menus. M$ idea is that DOS was the cause of most instabilities in older Windows releases so they "fixed" that by doing away with it. As for how well that worked out, that's a matter of how you use your computer, for a lot of folks it didn't help, for some it did. Older DOS based programs like FRACTINT are just going to be out and out frozen out because everything that they needed to work was so very DOS-centric. As for the Windows versions of Fractint I've had no luck what-so-ever with them. They just won't run right for me. Maybe in future releases that'll change but so far no dice. -----Original Message----- >From: Hal Lane <hallane(a)earthlink.net> >Sent: Dec 12, 2010 8:43 PM >To: Richard_Fractint4win <legalize(a)xmission.com>, Fractint_msg <fractint(a)mailman.xmission.com>, "Wegner, Tim" <twegner(a)swbell.net> >Subject: [Fractint] <Tim, Rich> DOS Fractint's img&txt vis inWinXP's DOSmode; Rich's FractintForWinBeta5 > >Tim, >> ...under Windows 7 in XP compatibility mode, if I set >> "tools->disable integration features", running the DOS >> fractint shows nothing, but after pressing F3, a fractal >> is indeed generated. > >I can get both images & text to appear in Win XP's DOS mode, >but apparently my video card only does one VESA graphics mode, >640 x 480 -- as well as the needed text mode. I then set "High" >Idle Sensitivity on the shortcut and use <alt>Enter to switch >back and forth between full screen and windowed Fractint. > >I can only make this switch without disrupting Fractint if the >program is in text mode, so I can't leave an image calculating >in a window while I (say) read email. To get around this, I >first "locate" my fractal in my one working video mode & then >calculate it in Disk Video mode -- which keeps Fractint in >text mode. > >Fractint's intense CPU usage leaves a very sluggish computer, >though. > > >> Hard to use, though, without any text screens showing. >I hope the problem is not your graphics card not implementing >the needed DOS text mode... > >Can you run another text only DOS program to see if your >problem of no DOS Fractint text is reproducible in another >DOS program? > >Can Chkdsk still be run at boot time in DOS mode in Win7 or is >"DOS mode" gone -- and not available to test your graphics >card's being able to enter a DOS text mode? > >BIOS Setup routines have, in the past at least, likely used >DOS text mode. What are they using these days? > >Are there docs available describing the video modes available on >your graphics card? > > >It's my understanding that it's primarily the video card/chip >companies no longer implementing many DOS modes in graphics cards >being the problem with getting DOS Fractint to run on recent >computers... > > >> Hmmm, might be possible to run a PAR file from the command >> line. >That sounds like a possibly workable scenario. > >> Of course Rich's windows version does work nunder Windows 7 >> (albeit without mouse support). >I've found that I can move the cursor around (when in Palette >Editing mode: "e") using <ctrl> and arrow keys, but this really >isn't as convenient as using a mouse. > > >Rich, Tim, >When using Rich's Fractint for Windows beta 5 to render Jim's FOTD, >I have found a couple of items that give me a problem, only one of >which I can overcome. > >The X dimension of every fractal calculated from Jim's parameter >files is stretched too wide. By trial & error I found that >reducing the X Magnification Factor by a factor of 0.75 (z, F6), >can reproduce the aspect ratio of the same image calculated by >DOS Fractint. > > >Another problem (that I've *not* been able to overcome) is that >the program always creates a single color image for any fractal >that uses the MandelbrotBC3 formula. Amazingly, the almost >identical MandelbrotBC1 and MandelbrotBC2 formulas produce correct >images. This fact may be of some help in locating the source >of the problem. > >The examples of Jim's FOTD that I used to discover this behavior >are listed below my signature. > > >Also, images created using the rotation of the zoom box behave >in a different way than the DOS zoom box. This may, in part >at least, be related to the different X Magnification Factor >factor of 0.75 . > > >Jim's FOTD for Dec. 4th, 2010 (a "native" Fractint Julia fractal) >rendered in Fractint for Windows beta 5 also doesn't quite match >the one created by DOS Fractint. I pasted a copy of Jim's PAR >file for this fractal at the end of this email. > > >Rich's excellent post to his blog about the philosophy of his >creation of Fractint for Windows is here: >http://legalizeadulthood.wordpress.com/2007/04/13/fractint-for-windows-beta- >5/ >or: >http://tinyurl.com/richs-fractint-for-win-blog > >There is also a //download link// and the comments section >includes a link to where you can register and //post issues// >you have with the program. > > > - Hal Lane > >######################### ># hallane(a)earthlink.net # >######################### > > >############################################################ >############################################################ >http://www.nahee.com/FOTD/FotD_02-02-02.html >http://home.att.net/~Fractals_2/FotD_02-02-02.html > >The formula behind the image is a very simple one -- >Z^2.003+C, made more interesting by displaying the part of >the infinite fractal that lies 1029 turns up the logarithmic >hyperspiral. At this lofty height, the parent fractal >resembles the Mandelbrot set rotated 180 degrees, so that >the split along the negative X-axis cuts the East Valley >area, which at the same time begins to broaden. > > >---------------------------------------------------- >MandelbrotBC1 *Works* in Fractint for Windows beta 5!!!!! >---------------------------------------------------- > > >START 20.0 PAR-FORMULA FILE================================ > >The_Primary_Colors { ; time=0:15:14.28--SF5 on a P200 > reset=2002 type=formula formulafile=allinone.frm > formulaname=MandelbrotBC1 function=floor passes=1 > center-mag=-0.26445764184686160/-0.003322320467831\ > 68/1.109666e+011/1/-42.5037/0.00146395122998561888 > params=2.003/0/1029/0 float=y maxiter=6000 inside=0 > logmap=298 colors=000XOjZRjaSibRidUgfUgiXfjbfmidom\ > drtbtzbvzbtrZtfUrOPqIMr6Ir0Ds0At3Cv9DxFDzFFzKFyJLu\ > MPpOWmS_ZZdSdjOloIrvCyz8zzCtzFjzIayLSwOIoR9hU0bX0W\ > U0NR8TOGZLOcIWKFdLClF9vA6z6cz11w80nD0XJ0LP09W08_09\ > X09U1AR3AO4CL6CI4FD4IA4J64M34O0CGFI9UO1iU0y_0zZ0zX\ > 0zX0zW0zU0wU1tS4qS6mR9jPCgPDdOGbOI_MLXLOULPRJSOJUL\ > IXIG_FGaCFd9Ff8CZS9Rm8JzLJzXCyR0tC0o00S00U00U00U00\ > W00W00W00W00X00X00X00Z00Z00Z00Z13X1AX3IW3PW4RU4RU6\ > RS6RS8RR8RR9RUARXARZCRaCRbDRfDRiFRjFRmGRoIRrIRvJRw\ > JRzLRzLRzMRzMRzORwOOtMLqKInIFkGChE9fC6fA4f82i60l40\ > o40r40v40y30z30z30z30z30z30z30z40z40z40z43z46z48z6\ > Az6Cz6Fz6Iz6Jz6Mz8Oz8Rz8Uz8Wz8Zz8_z9Zz9Xz9Xz9Wz9Uz\ > AUzASzARzARzARzCRzCRzCRzCRzCRzDRzDRzDRzDRzDRzDRzGR\ > zIRzJRzLRzORzPRzRRzSRzURzWRzWRzWRzWRzWRzWRzWRzWRzW\ > RzWRzWRzURzURzURzSRzSRzSRzSRzRRzRRzRRzPRzPRzPRzPRz\ > ORzORzORzMRzIRzJRzLRzORzPRzRRzSRzWRz } > >frm:MandelbrotBC1 { ; by several Fractint users > e=p1, a=imag(p2)+100 > p=real(p2)+PI > q=2*PI*fn1(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 20.0 PAR-FORMULA FILE================================== > >############################################################ >############################################################ >http://www.nahee.com/FOTD/FotD_06-08-29.html >http://home.att.net/~Fractals_3/FotD_06-08-29.html > >Today's harmless little scene appears in the >Z^sqrt(sqrt(2))+C Mandeloid as it appears 59 levels up the >complex logarithmic ladder. (The logarithmic ladder is >explained below.) > . . . >The 'complex logarithmic ladder' is a phrase I invented. >I sometimes refer to the same thing by the name 'logarithmic >hyperspiral'. Neither phrase will be found on the >internet. I invented the phrases because the complex >logarithmic function is multi-valued, and can have an >infinity of solutions. Each solution gives a unique >four-dimensional Julibrot fractal, complete with both >Mandelbrot and Julia slices. In my mind, I simply >stacked these four-dimensional fractals onto one >another until they formed a single many-layered >hyper-object of 5 or so dimensions. It is the stack of >all the Julibrot fractals possible to create with a >single exponent of Z that I call the logarithmic >ladder. Today's parent fractal for example exists on the >59th level of this ladder. The ladder could perhaps be >more conveniently thought of as the 59th floor of an >infinitely tall skyscraper. > >In the MandelbrotBC2 formula, the p1 parameter determines >the exponent of Z, while the p2 parameter determines the >level of the ladder we wish to explore. > >---------------------------------------------------- >MandelbrotBC2 *Works* in Fractint for Windows beta 5!!!!! >---------------------------------------------------- > >START PARAMETER FILE======================================= > >TheyAllLookTheSame-2 { ; time=0:18:51.96--SF5 on a P200 > reset=2004 type=formula formulafile=allinone.frm > formulaname=MandelbrotBC2 passes=1 > center-mag=-0.13962249185463330/-0.000766113336763\ > 77/5.149203e+007 params=1.1892/0/59/0 float=y > maxiter=25000 inside=0 outside=tdis periodicity=10 > colors=0000Gz0Gz0Gz0Gz0Hz0Hz0Hz0Hz0Jz0Jz0Jz0Jz0Jz0\ > Lz0Lz0Lz0Lz0Nz0Nz0Nz0Nz0Pz0Pz0Pz0Pz0Nz0Pz4RzARzETz\ > JVzNVzTXzXXxbVxeVxkVxoTxuTxxTxzRxuRsmRmeRg`PbTNXLN\ > TEJN8HH0HC0J60L00L00N00U00V00W00X00Y00Z02_06`08a0C\ > b0Ec0Hd2Ji2Nm2Pq2Tu2Vv2JuAAqH0oN0bV0Td0R`0RZ0PX0PV\ > 0NR0NP0LN0LL0JH0JG0HE0HC0H80G60G40E20E00C02C04A04A\ > 0680880A608806A04C04C02E00G00G00H00J00J20L40N60N80\ > PA0RE0zG0TH0VJ0XL0XN0ZP0`T0`V0bX0dZ0d`0eb0gd0ge8uJ\ > ez0gz2iz6kxAmvEmuGosJqoNsmRskVuiXvg`xedxbgz`kzZmzX\ > qzVuzTxzPzfNzzLzzkzzHzzGzzkzzgzzEzzEzzEzzEzzEzxEzv\ > EzuCzqCzoCzkCxiCueCsdCq`CoZAmzAkTAgRAezAdLAbHA`GAZ\ > EAXzC`LEbPGeRGgTEeTEdzEdTEbTEbTE`TE`TEZTEXTEXTEVTE\ > VTETTETTERTEPTEPTENTENTELTELTEJL0LTEJVdC`gHdkNgoRm\ > sXqvbuzexzkzzqzzuzzzzzzzzvzzqzzizxdzsXzoRziJzeEudX\ > kbo``zR`zTbzTdzVezVezXzzXizXizZkzZmz`ox`ovbqubsqbs\ > odumdziexgexe0Ez0Ez0Ez0Ez } > >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========================================= > > >############################################################ >############################################################ >http://www.nahee.com/FOTD/FotD_09-09-23.html >http://home.att.net/~Fractals_3/FotD_09-09-23.html > >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. > >---------------------------------------------------- >---------------------------------------------------- >---------------------------------------------------- >MandelbrotBC3 ***Fails*** in Fractint for Windows beta 5!! >---------------------------------------------------- >---------------------------------------------------- >---------------------------------------------------- > >START PARAMETER FILE======================================= > >AgitatedIterations { ; time=0:01:33.85-SF5 on P4-2000 > reset=2004 type=formula formulafile=basicer.frm > formulaname=MandelbrotBC3 function=ident logmap=168 > center-mag=-1.748190276984/+0.019122558784/5e+007/1/\ > -105.5/0 float=y inside=0 maxiter=1750 periodicity=10 > params=2.001/0/0/0 > 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========================================= > >############################################################ >############################################################ >############################################################ > >---- Tim wrote: --------------------- >Author: Tim Wegner >Date: 2010-12-11 17:10 -500 >To: Fractint and General Fractals Discussion >Old-Topics: [Fractint] FOTD 11-12-10 (The Midas Untouch [7]) >Subject: [Fractint] Windows 7 64 bit > >For what it's worth (not much other than as a curious fact), under >Windows 7 in XP compatability mode, if I set "tools->disable >integration features", running the DOS fractint shows nothing, but >after pressing F3, a fractal is indeed generated. Hard to use, >though, without any text screens showing. Hmmm, might be possible to >run a PAR file from the command line. > >Of course Rich's windows version does work nunder Windows 7 (albeit >without mouse support). > >I have done very little with virtual machines. Just for my education >I might try installing DOS or Windows XP itself under Virtual PC, or >maybe VirtualBox. > >(later) > >Guess what, I tried Winfract (Jonathan's 16 bit version), and it does >work, apparently just fine, on Windows 7 64 bit in XP compatability >mode! This time the "enable integration features" setting didn't >matter. Even the mouse works ... > >Tim >---------------------------------- > >##################################################################### >##################################################################### >##################################################################### >Jim's FOTD for Dec. 4th, 2010: > >1/4_of_the_Pie { ; time=0:02:31.55-SF5 on P4-2000 > reset=2004 type=julia passes=1 center-mag=0/0/1137\ > 532/1/143/0 params=0.2983562075159729/-0.018519436\ > 2269525 float=y maxiter=60010 inside=0 outside=imag > logmap=-54679 periodicity=0 > colors=000dBCdABe9Be9BhABjBBlCBnDBpEBrEBsJEsOGsTIt\ > YKtaMtXPuaRufTulVzhXzdUtdSs`QsWNrSKrOJqJGqFEpBCp7A\ > lADiDGfEJcGL`HOYJRVLKTHGSDDQ99P56O13R27U3AW4DZ5G`6\ > Kc7Ne8Qh9TkAWmB_pCbrDeuEhwFkrHgmJdhL`cNYZPVURRPTOK\ > VKFXHAZED`FGbFJdFMeFPgFRiFUkGXlG_nGbpGerGgsGetJdtM\ > ctPbuS`uV_uYZv`YvcXvfWrgVnhUkhTgiScjR`jQXkPTlOQlLQ\ > kJQjGQjEQiBQh9Qh6Qg4Qf2Qf4Ng6Lh7Jh9HiAFiCDjEBkF9kH\ > 7lI5lK3mL1mqGYlH_hI`cJa_JcVKdRLeNLfUOa`QYfSUmVPtXL\ > zZHrhhocilZjiVkfQlcLm`HnYCoV8p`RffiXhh_jgalfdmefod\ > hqcksbmtaov`rx_ty_vtcoofhkjafmVbpOdnPflQgjRihSjgTl\ > eUmcVoaWp_XrZYsXZuV_vT`xRayQbsMfnIjhEmcAqY6uT2xW5s\ > Z8naBidEdgH_jKVmNQoQLnUPnXSn_VnbYmeamhdmkgmnjjjigg\ > iedibai`ZiYViWSiTPiQMiOJiLFiJCiG9iE9iBFU99WAEYAJ_A\ > OaAXcfaClbHrbMsaKt`It`Hu_FvZDvZCpOOjDZcHXXLWROVKSU\ > DWT7ZSmQ1kR2jR3hR4gR5fR6dR7cR8bR9dYLedX0lP8nUFpYMr\ > aTtf_vjfxnmzrhsdclSZeEU_1 } > >----- > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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FOTD 17-12-10 (Totally Eclipsed [6])
by Jim Muth 17 Dec '10

17 Dec '10

FOTD -- December 17, 2010 (Rating 6) Fractal visionaries and enthusiasts: With things pretty busy here at FC, today's image is another fast one. The image lies in the parent fractal that results when Z^(1.618) (golden ratio) is iterated Z(-3.142) (minus-PI) levels up the complex logarithmic hyper-spiral with the 'floor' function applied, and C is added. The parent fractal closely resembles a non-critical Mandelbrot set with its main bud pointing northeast and a nest of cut-off zigzagging filaments just beyond the bud. Today's scene lies deep in the most prominent cut-off filament. I rated the image at a 6. The colors are fair enough, but I have used a similar palette much too recently to allow a rating any higher than the 6. The name "Totally Eclipsed" came about when I imagined I saw a solar eclipse in the image. The calculation time of 1 minute is conveniently fast, at least for those with DOS-capable machines. And the finished image will soon be posted on the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site at: <http://www.Nahee.com/FOTD/> is still available, and holds over 13 years of FOTD's. But it might not be up to date. Thick clouds and a temperature around 25F -4C kept things suppressed here at Fractal Central on Thursday. The fractal cats kept happy on their warm shelf, taking breaks only often enough to be sure things were under control outside. My day was hurried enough. The next FOTD will be posted in 24 hours. Until then, take care, and could something sinister be going on behind the scenes? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Totally_Eclipsed { ; time=0:01:04.21-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=floor float=y center-mag=+1.502630890717709/+1.587875052969523/\ 1.5721e+012/1/60/0 params=1.618/0/-3.142/0 inside=0 maxiter=400 logmap=176 mathtolerance=0.05/1 colors=00010220430640850A60C70E80G90IA0KA0MA0OA1QA\ 2SA3UA4WA5YA6_A7aA8cA9eAAgABiACkCDmEEmGFmIGmJImKKm\ LMmKOmLQmMSmNUmPWmQYmR_mSamUcmVemWgmWioWlsXouXrydu\ zmzzLFUJKWQPYVP_ZR`fZbkadogetogxsinjjgklXln`loTjnQ\ inNgnKfnHenEcnBbn9anMgkZmiksgjocjl_jiXjfTjcPj`MjYI\ jVEjSBjP7jM4lL5mK6nJ7oJ8qI9rHAsGBtGCvFDwEExDFyDFoF\ DeGCWHAMJ9CK73L64N84OA4QB4RD4SF4UG4VI5XK5YL5ZN5`P5\ aQ5cS5dU5eV6fY7f`8gc9gfAgiBhlChoDhqIjnNklSmiXngaoe\ fqbkr`ptYuuWzvUswXmxZgyaazcWzfQzhKzkEzm8zp2zrLzmcz\ hvzcuzbtzaszarz`qz_pz_pzZozZnzYmzXlzXkzWkzWhzYfzZc\ z_azaZzbXzcUzeSzfPzgNzhMzgLzgKzgJzfJzeIzdIzcIzcHzb\ HzaGz`Gz_Gz_DzgBzo9zwGzLEzGCzCxzwZzYLzKKzJJzIIzHHz\ GGzFFzEFzDEzCDzBCzABz9Az8UzlSzgQzc8zD5zA3z77zABzDF\ zFJzINzKRzNVzQZzSbzVfzXjz_mzaPzuQzuQzuRzuRzuSzuSzu\ TzuTzuTzuUzuUzuVzuVzuWzuWzuWzu_zwbzyezzdzyczybzyaz\ yazyczmdzafzQgzEezDczDazC } 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 16-12-10 (Pyrotechnic Fractal [8])
by Jim Muth 16 Dec '10

16 Dec '10

FOTD -- December 16, 2010 (Rating 8) Fractal visionaries and enthusiasts: Due to a big rush at work, today's usually big FOTD discussion is reduced to a small trial size. The image lies in the oversized parent fractal that results when 0.11 part of Z^100 is combined with 1.1 parts of straight Z and (1/C) is added. The name "Pyrotechnic Fractal" refers to the fiery red hues and sparkling highlights infesting nearly every part of the image. The colors were created almost entirely by the under-rated Fractint coloring system. The colors alone earn the image a rating of an 8. Without the colors, the image would be rated closer to a humdrum rating of 6. The calculation time of under 2 minutes will seem insignificant once a glimpse of the sparkling colors appears at the top of the screen. Calculation may be avoided entirely by viewing the finished image on the web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site is at: <http://www.Nahee.com/FOTD/> though I have not checked in a while to see if Paul has been able to work on it. Plenty clouds, numerous snow flurries and a temperature around 25F -4C prevailed here at Fractal Central on Wednesday. The fractal cats preferred to spend the day on the new shelf over the radiator. We have put their scratching post beside the shelf to make it easier for them to leap up onto when a chill strikes. My day was quite busy; the above-average FOTD was a matter of luck. The next FOTD will be posted in 24 hours. Until then, take care, and if the end of one thing is the beginning of some- thing else, what will follow the end of everything? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= PyrotechnicFractal { ; time=0:01:52.10-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-21.352824077544/+0.6778222366/4216772/\ 1/1.7/0 params=0.11/100/1.1/1/0/0/0/0 float=y maxiter=1250 inside=0 logmap=-195 periodicity=6 colors=000A00D10E10D30E40G50I51K51M52O52Q52S53U53Y\ 43a44e44i44m45tA5zH5vA4r74o84j94gB4dC6aDAYEEVFISHM\ OIQLJUIKYFP_IWcL_gOckPgiQihRifSieTidUjbVjaWj`XjZYj\ YZkW_kV`kUakSblRcmQbnTdnZfndhrijvolztailSUdIFX56Q9\ 8NEAKJBHPDEUFB_K8cP5hU2lZ0pc0kh0cm0Si7NgDpJfpHgZRa\ I`WETQALK6DE359J4PY4ckFVxQM2zz8kzEecJ`_PVVVPQiQmgg\ stkFsdDrYBqR9pL7oE5n73m12h55c98ZDAUHDPLGKPIFTLBWNM\ NZXEig6tvrFkdS`RdQDpSHkUKfWOaXRYZVT`YOa`KdUX_Z_Vcb\ RhdMmgIriKnaLjVNgOOcHQ_ARX3YZAc_Hj`OpaVlWUiRTfMTcH\ S`CSZEPXGMVIJUJGSOLRTPPXTOaYMeaLjeKniIhgGbeEXcCSaA\ M_8GY6AW45VDCYLI_UOaaVdj`frfhseasdWscQsbJsaDsa7keE\ dhKXlRQoXIscBvi4yoEspNmqWgrdar`dsYfsVhtRjtOluLnuOb\ IEOUKSTQVSVYR`aQedPkgOpjOngQmdSlaUj_WiXYhU_gS`cUb`\ VdYWfVXhSYjPZlU`iYbgadefebjg`niZrjXs``tScuJfuAinJm\ gSp``sgTemLTbUSTbSOeSKgSFjSBlS6oS2qS8oTDmUIkVOiWTg\ XYeY_d``cbbbecage`if_lhZn } 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 15-12-10 (Lucy Lucent [6])
by Jim Muth 14 Dec '10

14 Dec '10

FOTD -- December 15, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that was created when I combined two negative parts of straight Z with one part of Z^(-2) before adding (1/C). I should say the image lies *near* the parent fractal, since the parent is a small, slightly distorted Mandelbrot set surrounded by much smaller and totally disconnected M-sets. Today's scene actually lies some distance northwest of the small but main body of the parent. I named the image "Lucy Lucent" for reasons unknown even to myself. I rated it at a 6 because, even though it has little fractal-math content, the striking colors raise it to FOTD status. Most of the effect came about when I applied the 'tdis' option to the original rather boring 'iter' image. The calculation time of 52 seconds sets no speed record, but it is brief enough to keep impatience at bay. And the finished image will soon be available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Eventually, it will be available on the original FOTD web site at: <http://www.Nahee.com/FOTD/> Lots of clouds, frequent flurries of snow and a temperature around 23F -5C kept the fractal cats close to their warm shelf most all day Tuesday here at Fractal Central, while the seasonal rush kept me close to the FC work desk. The next FOTD will be posted in 24 hours. Until then, take care, and you never know when the FOTD will be a real prize-winner. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Lucy_Lucent { ; time=0:00:52.29-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+0.1161003092660847/-0.1610893155094485\ /5.049423e+010/1/-127.5/0 params=-2/1/1/-2/0/0/0/0 maxiter=1500 inside=0 outside=tdis periodicity=6 colors=000`KG_KGZJGZJFYJFYIFXIEWIEWHEVHEVHDUGDTGDT\ GDSFCSFCRFCRECQEBPEBPDBODBODANDAMCAMC9LC9LB9KB9JB8\ JA8IA8IA8H97H97G97F87F86E86E76DU6C75c65B65B6cA5495\ 495484384A74K73U63c53U52K42A421311211211100100000j\ pwiovmourrtzzzrsrmnqejpd_pCTRDRSEPTFNUGKVHIWIGXIEX\ HKaHPeHUiHZmHcqIblJbhJadKa`L`XL`TM`PN_LN_HOZDPZ9PZ\ 5Sb4Vf3Xi2_m2ap1dt0fw0`o1Vh1Pa2JU2DN38G3AE4CD5DC6F\ B7HA8I99K8AM7BN6CP5DR4ES3EjxHgtGepGclF`hFZeFXaEVYE\ SUDQQDONDMJCJFCHBBF7BD4BG8AJBAME9OH9RK8UN8XR7ZU7aX\ 6d_6gb5ie5l`EnWNqRWsMduHmtPnsWnrbnqinppnownpxbpySp\ zHtoOxeUuaTsYTqUToQTmMTkJTjKUiLUhLVgMVfMWfNWeOXdOX\ cPYbPYaQZaQZC82zXvxTnvQgtN`rKTpHMnEFlB8kFDjIHiLMhO\ QgRUfUZeXbd_fcbkbeoahs`ep_bn__lZXjYUhYSfXPdWMbWJ`V\ GZVEXTDVSCURCSPBROBQNAOL9NK9LJ8KH7IG7HE6FD6EC5DA4B\ 94A838637525414000212101jQLiPKhPKhPKgOJgOJfOJeNJeN\ IdNIdMIcMIbMHbLHaLHaLH`KG } 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] AOTD 12_10_2010
by JackOfTradeZ＠comcast.net 14 Dec '10

14 Dec '10

. Zoom animation of FOTD 12/10/2010 is posted: http://www.fractal-animation.net/vid/spacebubbles.zip stay cool .

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FOTD 14-12-10 (Fade-Out [5])
by Jim Muth 14 Dec '10

14 Dec '10

FOTD -- December 14, 2010 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a scene in a Mandelbrot set that in its depths is starting to morph into a quintic set. The scene is located inside a minibrot on a stem of the star of the period-7 bud on the northwest shore line of the main bay of its Mandelbrot parent. The image is filled with both minibrots and antiminibrots, which are a bit tricky to tell apart at a casual glance. I named the image "Fade-Out" because of the way the upper part of the image appears to fade into the mist. The rating of a 5 is conservative. The actual rating might be closer to a 6. I leave it to the individual fractalist to decide whether the finished product is worth the calculation time of 7 minutes. For the convenience of those who do not calculate, the finished image should soon be available on the web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> My own web site is still in the planning stage. The entire catalog of past FOTD images is available on the original FOTD web site at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds, a biting northwest wind and a tempera- ture of 25F -4C made Monday a rough day to be outdoors here at Fractal Central. The fractal cats spent a good part of the day lounging on their new shelf by the heat, though they did get up several times to go to their window shelf to check that things were under control outside. My day was busy; FL's day was the same. The next FOTD will be posted in 24 hours. Until then, take care, and do it with style. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Fade-Out { ; time=0:07:11.21-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-0.657357075207177/+0.4680315673679433/\ 6.384688e+011/1/47.5/0 params=5/2000000.0/0/0 float=y maxiter=10000 inside=255 logmap=114 colors=000zzyzzxzzwzzvzzuzztzyszyrzyqzypzyozxnzxmz\ xlyxkxxjwwivwhuwgtwfsvervdqvcpvbovanv`mv_lvZkuYjuX\ iuWiuTitQhtMisNisNirOjrOjqOjqPkpPkpPkoQlnQlnQlmRlm\ RmlRmkSmkSnjSnjTniTohTohUogUogUpdSpbRq`PqZOqXNrULr\ SKsQJsOHsMGtJFtHDuFCuDBuB9v88v67w45w24w03u25s36q48\ o59m6Bk7Ci8Dg9FeAGcBIaCJ_DLYEMWFNUGPSHQQISOJTD2PKZ\ 8KY8KY8KX8KW8JW8JV8JU8JU9JT9IS9IS9IR9IQ9IQ9IP9HO9H\ O9HNAHMAHMAGLAGKAGKAGJAGIAFIAFHAFGBFGBFFBFEBEEBEDB\ ECBECBEBBDABDACD9CD8CD8CC7CC6CC6CC5CC4CC4CB6EB7GB8\ HA9JABKACM9DN9EP9GQ8HS8IT8JV7LX7MY7N_6O`6Qb6Rc5Se5\ Tf5Vh4Wi4Xk4Yl5Xm6Xm6Xm7Xm8Xm8Xn9WnAWnAWnBWnBWnCWo\ DVoDVoEVoFVoFVoGVpGVpHUpIUpIUpJUpKUqKUqLTqMTqMTqNT\ qNTrOTrPSrPSrQSrRSrRSsSSsSSsTRsURsURtVRtWRtWRtXQtY\ QtYQuZQuZQu_Qu`Pu`PuaPvbPvbPvcPvcPvdOveOweOwfOwgOw\ gOwhNwiNxiNxjNxjNxkNxlMxmMymKznKzoKzpKzqKzrKzsKztK\ zuKzvKzwKzxKzyKzzKzzKzzKz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 13-12-10 (Moth-Eaten Fractal [7])
by Jim Muth 13 Dec '10

13 Dec '10

FOTD -- December 13, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that results when 1.6 negative parts of Z^3 are combined with 2.4 negative parts of Z^2 and C is added on each iteration. The resulting parent fractal is a Mandelbrot set with some extra stuff added mostly along the X-axis. Today's scene lies in some of this extra stuff that is just starting to sprout along the positive X-axis. The rating of a 7 might be a bit liberal. The image really is a bit too chaotic and the colors too disorganized for maximum effect. But I kind of like it anyway, with its preponderance of grays, so the rating of 7 will remain. The name "Moth-Eaten Fractal" came about when I realized that the thing was full of holes, like an old woolen sweater than has hung in the closet too many months with no moth repellant. The calculation time of over 22 minutes is admittedly slow, but may be cut to 14 minutes by rendering the image with the passes set to 'g'. Doing so however will cause some loss of accuracy. To avoid all calculation, check the web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image should soon be posted. The original web site, complete with almost 14 years of FOTD's is still located at: <http://www.Nahee.com/FOTD/> but the last time I checked, it was not up to date. The temperature reached a mild enough 50F 10C here at Fractal Central on Sunday, but a steady rain fell all day, spoiling the brief respite from the chill. The fractal cats seemed uncon- cerned. We are installing a shelf over the large radiator in the hallway, where they can leap any time they wish and be as warm as a cat by an open fire. If all goes as planned, the next FOTD will be posted in 24 hours. Until then, take care, and be lively. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Moth-Eaten_Fractal { ; time=0:22:37.71-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.69362781933042/+0.01361539169399/3.0\ 909e+010/1/147.5/0 params=-1.6/3/-2.4/2/0/-97.5/0/0 float=y maxiter=8000 inside=0 outside=imag logmap=1235 colors=000UUUGa08J0zsBz_8m06NM4BB2sXtgQhXJYMDMB6BA\ cp8We6OV4GL28Al6Cc5AW48O36z24812jwrNUR5VLcaVWUOOMI\ GFC876PY5KS4mM3CH28B1450GnyzaizPVzCFzc5z74zz3z326z\ 1zHzzz9zG4zzizVYzzNzABzz2zK1zzSzlNzzIzTEzz9z94zztz\ YjzzazKSzzJzz9zvnzzYzJHzzTzWNzzHzGBzz5zAnzzcz6UzzK\ z2AzzdzzZCBT99N76H44B225_ZCRQ9IH6983PjwLdoIZhFT`CN\ U9HM6BF357_OkOGWC8GJnPCYG6H8zR1mL0`G0PA0C50`qBWj9R\ c8NX6IR5DK49D246115e03S01EjCmN6PkkXaaQSSJJJD9964Uu\ 3Mf2FT17ELHKA8A6Bt48e35S12EnSpYIZH9HlDm_9`O6PC3CTp\ uNeiHVYBLN5AB8i86a65U54N42F21712Uu1Oi1IY0CN06BjzEH\ ttDhhAYY6MM3BBgQ8ZK6QF4HA3851GDO86Cccc5J8PGnC8Pgma\ afXX`SRVNMPJGIEBC9564vuSgfLTTEEE76zX4mQ3`JzK01C6Ad\ BuiFTN7CxhWZyOQiGHV88FRDSNBOJ9KF7GB5C738314sq_zczz\ RzzDzzLzzFzzAzz5zzgzz`zzVzzPzzczzVzzczzMzzczzGzzcz\ zWzzZzz`zzbzzdzzWzzNzzFzzFzzczzczzczzczzczzczzczzc\ zzczzczzczzczzczzczzczzcz } 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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<Tim, Rich> DOS Fractint's img&txt vis inWinXP's DOSmode; Rich's FractintForWinBeta5
by Hal Lane 13 Dec '10

13 Dec '10

Tim, > ...under Windows 7 in XP compatibility mode, if I set > "tools->disable integration features", running the DOS > fractint shows nothing, but after pressing F3, a fractal > is indeed generated. I can get both images & text to appear in Win XP's DOS mode, but apparently my video card only does one VESA graphics mode, 640 x 480 -- as well as the needed text mode. I then set "High" Idle Sensitivity on the shortcut and use <alt>Enter to switch back and forth between full screen and windowed Fractint. I can only make this switch without disrupting Fractint if the program is in text mode, so I can't leave an image calculating in a window while I (say) read email. To get around this, I first "locate" my fractal in my one working video mode & then calculate it in Disk Video mode -- which keeps Fractint in text mode. Fractint's intense CPU usage leaves a very sluggish computer, though. > Hard to use, though, without any text screens showing. I hope the problem is not your graphics card not implementing the needed DOS text mode... Can you run another text only DOS program to see if your problem of no DOS Fractint text is reproducible in another DOS program? Can Chkdsk still be run at boot time in DOS mode in Win7 or is "DOS mode" gone -- and not available to test your graphics card's being able to enter a DOS text mode? BIOS Setup routines have, in the past at least, likely used DOS text mode. What are they using these days? Are there docs available describing the video modes available on your graphics card? It's my understanding that it's primarily the video card/chip companies no longer implementing many DOS modes in graphics cards being the problem with getting DOS Fractint to run on recent computers... > Hmmm, might be possible to run a PAR file from the command > line. That sounds like a possibly workable scenario. > Of course Rich's windows version does work nunder Windows 7 > (albeit without mouse support). I've found that I can move the cursor around (when in Palette Editing mode: "e") using <ctrl> and arrow keys, but this really isn't as convenient as using a mouse. Rich, Tim, When using Rich's Fractint for Windows beta 5 to render Jim's FOTD, I have found a couple of items that give me a problem, only one of which I can overcome. The X dimension of every fractal calculated from Jim's parameter files is stretched too wide. By trial & error I found that reducing the X Magnification Factor by a factor of 0.75 (z, F6), can reproduce the aspect ratio of the same image calculated by DOS Fractint. Another problem (that I've *not* been able to overcome) is that the program always creates a single color image for any fractal that uses the MandelbrotBC3 formula. Amazingly, the almost identical MandelbrotBC1 and MandelbrotBC2 formulas produce correct images. This fact may be of some help in locating the source of the problem. The examples of Jim's FOTD that I used to discover this behavior are listed below my signature. Also, images created using the rotation of the zoom box behave in a different way than the DOS zoom box. This may, in part at least, be related to the different X Magnification Factor factor of 0.75 . Jim's FOTD for Dec. 4th, 2010 (a "native" Fractint Julia fractal) rendered in Fractint for Windows beta 5 also doesn't quite match the one created by DOS Fractint. I pasted a copy of Jim's PAR file for this fractal at the end of this email. Rich's excellent post to his blog about the philosophy of his creation of Fractint for Windows is here: http://legalizeadulthood.wordpress.com/2007/04/13/fractint-for-windows-beta- 5/ or: http://tinyurl.com/richs-fractint-for-win-blog There is also a //download link// and the comments section includes a link to where you can register and //post issues// you have with the program. - Hal Lane ######################### # hallane(a)earthlink.net # ######################### ############################################################ ############################################################ http://www.nahee.com/FOTD/FotD_02-02-02.html http://home.att.net/~Fractals_2/FotD_02-02-02.html The formula behind the image is a very simple one -- Z^2.003+C, made more interesting by displaying the part of the infinite fractal that lies 1029 turns up the logarithmic hyperspiral. At this lofty height, the parent fractal resembles the Mandelbrot set rotated 180 degrees, so that the split along the negative X-axis cuts the East Valley area, which at the same time begins to broaden. ---------------------------------------------------- MandelbrotBC1 *Works* in Fractint for Windows beta 5!!!!! ---------------------------------------------------- START 20.0 PAR-FORMULA FILE================================ The_Primary_Colors { ; time=0:15:14.28--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.26445764184686160/-0.003322320467831\ 68/1.109666e+011/1/-42.5037/0.00146395122998561888 params=2.003/0/1029/0 float=y maxiter=6000 inside=0 logmap=298 colors=000XOjZRjaSibRidUgfUgiXfjbfmidom\ drtbtzbvzbtrZtfUrOPqIMr6Ir0Ds0At3Cv9DxFDzFFzKFyJLu\ MPpOWmS_ZZdSdjOloIrvCyz8zzCtzFjzIayLSwOIoR9hU0bX0W\ U0NR8TOGZLOcIWKFdLClF9vA6z6cz11w80nD0XJ0LP09W08_09\ X09U1AR3AO4CL6CI4FD4IA4J64M34O0CGFI9UO1iU0y_0zZ0zX\ 0zX0zW0zU0wU1tS4qS6mR9jPCgPDdOGbOI_MLXLOULPRJSOJUL\ IXIG_FGaCFd9Ff8CZS9Rm8JzLJzXCyR0tC0o00S00U00U00U00\ W00W00W00W00X00X00X00Z00Z00Z00Z13X1AX3IW3PW4RU4RU6\ RS6RS8RR8RR9RUARXARZCRaCRbDRfDRiFRjFRmGRoIRrIRvJRw\ JRzLRzLRzMRzMRzORwOOtMLqKInIFkGChE9fC6fA4f82i60l40\ o40r40v40y30z30z30z30z30z30z30z40z40z40z43z46z48z6\ Az6Cz6Fz6Iz6Jz6Mz8Oz8Rz8Uz8Wz8Zz8_z9Zz9Xz9Xz9Wz9Uz\ AUzASzARzARzARzCRzCRzCRzCRzCRzDRzDRzDRzDRzDRzDRzGR\ zIRzJRzLRzORzPRzRRzSRzURzWRzWRzWRzWRzWRzWRzWRzWRzW\ RzWRzWRzURzURzURzSRzSRzSRzSRzRRzRRzRRzPRzPRzPRzPRz\ ORzORzORzMRzIRzJRzLRzORzPRzRRzSRzWRz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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 20.0 PAR-FORMULA FILE================================== ############################################################ ############################################################ http://www.nahee.com/FOTD/FotD_06-08-29.html http://home.att.net/~Fractals_3/FotD_06-08-29.html Today's harmless little scene appears in the Z^sqrt(sqrt(2))+C Mandeloid as it appears 59 levels up the complex logarithmic ladder. (The logarithmic ladder is explained below.) . . . The 'complex logarithmic ladder' is a phrase I invented. I sometimes refer to the same thing by the name 'logarithmic hyperspiral'. Neither phrase will be found on the internet. I invented the phrases because the complex logarithmic function is multi-valued, and can have an infinity of solutions. Each solution gives a unique four-dimensional Julibrot fractal, complete with both Mandelbrot and Julia slices. In my mind, I simply stacked these four-dimensional fractals onto one another until they formed a single many-layered hyper-object of 5 or so dimensions. It is the stack of all the Julibrot fractals possible to create with a single exponent of Z that I call the logarithmic ladder. Today's parent fractal for example exists on the 59th level of this ladder. The ladder could perhaps be more conveniently thought of as the 59th floor of an infinitely tall skyscraper. In the MandelbrotBC2 formula, the p1 parameter determines the exponent of Z, while the p2 parameter determines the level of the ladder we wish to explore. ---------------------------------------------------- MandelbrotBC2 *Works* in Fractint for Windows beta 5!!!!! ---------------------------------------------------- START PARAMETER FILE======================================= TheyAllLookTheSame-2 { ; time=0:18:51.96--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.13962249185463330/-0.000766113336763\ 77/5.149203e+007 params=1.1892/0/59/0 float=y maxiter=25000 inside=0 outside=tdis periodicity=10 colors=0000Gz0Gz0Gz0Gz0Hz0Hz0Hz0Hz0Jz0Jz0Jz0Jz0Jz0\ Lz0Lz0Lz0Lz0Nz0Nz0Nz0Nz0Pz0Pz0Pz0Pz0Nz0Pz4RzARzETz\ JVzNVzTXzXXxbVxeVxkVxoTxuTxxTxzRxuRsmRmeRg`PbTNXLN\ TEJN8HH0HC0J60L00L00N00U00V00W00X00Y00Z02_06`08a0C\ b0Ec0Hd2Ji2Nm2Pq2Tu2Vv2JuAAqH0oN0bV0Td0R`0RZ0PX0PV\ 0NR0NP0LN0LL0JH0JG0HE0HC0H80G60G40E20E00C02C04A04A\ 0680880A608806A04C04C02E00G00G00H00J00J20L40N60N80\ PA0RE0zG0TH0VJ0XL0XN0ZP0`T0`V0bX0dZ0d`0eb0gd0ge8uJ\ ez0gz2iz6kxAmvEmuGosJqoNsmRskVuiXvg`xedxbgz`kzZmzX\ qzVuzTxzPzfNzzLzzkzzHzzGzzkzzgzzEzzEzzEzzEzzEzxEzv\ EzuCzqCzoCzkCxiCueCsdCq`CoZAmzAkTAgRAezAdLAbHA`GAZ\ EAXzC`LEbPGeRGgTEeTEdzEdTEbTEbTE`TE`TEZTEXTEXTEVTE\ VTETTETTERTEPTEPTENTENTELTELTEJL0LTEJVdC`gHdkNgoRm\ sXqvbuzexzkzzqzzuzzzzzzzzvzzqzzizxdzsXzoRziJzeEudX\ kbo``zR`zTbzTdzVezVezXzzXizXizZkzZmz`ox`ovbqubsqbs\ odumdziexgexe0Ez0Ez0Ez0Ez } 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========================================= ############################################################ ############################################################ http://www.nahee.com/FOTD/FotD_09-09-23.html http://home.att.net/~Fractals_3/FotD_09-09-23.html 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. ---------------------------------------------------- ---------------------------------------------------- ---------------------------------------------------- MandelbrotBC3 ***Fails*** in Fractint for Windows beta 5!! ---------------------------------------------------- ---------------------------------------------------- ---------------------------------------------------- START PARAMETER FILE======================================= AgitatedIterations { ; time=0:01:33.85-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident logmap=168 center-mag=-1.748190276984/+0.019122558784/5e+007/1/\ -105.5/0 float=y inside=0 maxiter=1750 periodicity=10 params=2.001/0/0/0 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========================================= ############################################################ ############################################################ ############################################################ ---- Tim wrote: --------------------- Author: Tim Wegner Date: 2010-12-11 17:10 -500 To: Fractint and General Fractals Discussion Old-Topics: [Fractint] FOTD 11-12-10 (The Midas Untouch [7]) Subject: [Fractint] Windows 7 64 bit For what it's worth (not much other than as a curious fact), under Windows 7 in XP compatability mode, if I set "tools->disable integration features", running the DOS fractint shows nothing, but after pressing F3, a fractal is indeed generated. Hard to use, though, without any text screens showing. Hmmm, might be possible to run a PAR file from the command line. Of course Rich's windows version does work nunder Windows 7 (albeit without mouse support). I have done very little with virtual machines. Just for my education I might try installing DOS or Windows XP itself under Virtual PC, or maybe VirtualBox. (later) Guess what, I tried Winfract (Jonathan's 16 bit version), and it does work, apparently just fine, on Windows 7 64 bit in XP compatability mode! This time the "enable integration features" setting didn't matter. Even the mouse works ... Tim ---------------------------------- ##################################################################### ##################################################################### ##################################################################### Jim's FOTD for Dec. 4th, 2010: 1/4_of_the_Pie { ; time=0:02:31.55-SF5 on P4-2000 reset=2004 type=julia passes=1 center-mag=0/0/1137\ 532/1/143/0 params=0.2983562075159729/-0.018519436\ 2269525 float=y maxiter=60010 inside=0 outside=imag logmap=-54679 periodicity=0 colors=000dBCdABe9Be9BhABjBBlCBnDBpEBrEBsJEsOGsTIt\ YKtaMtXPuaRufTulVzhXzdUtdSs`QsWNrSKrOJqJGqFEpBCp7A\ lADiDGfEJcGL`HOYJRVLKTHGSDDQ99P56O13R27U3AW4DZ5G`6\ Kc7Ne8Qh9TkAWmB_pCbrDeuEhwFkrHgmJdhL`cNYZPVURRPTOK\ VKFXHAZED`FGbFJdFMeFPgFRiFUkGXlG_nGbpGerGgsGetJdtM\ ctPbuS`uV_uYZv`YvcXvfWrgVnhUkhTgiScjR`jQXkPTlOQlLQ\ kJQjGQjEQiBQh9Qh6Qg4Qf2Qf4Ng6Lh7Jh9HiAFiCDjEBkF9kH\ 7lI5lK3mL1mqGYlH_hI`cJa_JcVKdRLeNLfUOa`QYfSUmVPtXL\ zZHrhhocilZjiVkfQlcLm`HnYCoV8p`RffiXhh_jgalfdmefod\ hqcksbmtaov`rx_ty_vtcoofhkjafmVbpOdnPflQgjRihSjgTl\ eUmcVoaWp_XrZYsXZuV_vT`xRayQbsMfnIjhEmcAqY6uT2xW5s\ Z8naBidEdgH_jKVmNQoQLnUPnXSn_VnbYmeamhdmkgmnjjjigg\ iedibai`ZiYViWSiTPiQMiOJiLFiJCiG9iE9iBFU99WAEYAJ_A\ OaAXcfaClbHrbMsaKt`It`Hu_FvZDvZCpOOjDZcHXXLWROVKSU\ DWT7ZSmQ1kR2jR3hR4gR5fR6dR7cR8bR9dYLedX0lP8nUFpYMr\ aTtf_vjfxnmzrhsdclSZeEU_1 } -----

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FOTD 12-12-10 (Grated Remnants [7])
by Jim Muth 12 Dec '10

12 Dec '10

FOTD -- December 12, 2010 (Rating 7) Fractal visionaries and enthusiasts: As expected, an unplanned shopping trip arose by surprise on Saturday, which kept FL, (and myself also to some degree), occupied most of the day, exploring the Susquehanna Mall, a place that I always avoid assiduously. But thanks to provi- dence, (whatever that is), the task was eventually completed, and we found ourselves back at FC before daylight failed. This left enough time to find a respectable but not quite outstanding fractal, but not enough time to finish the discussion. The generating formula is total whimsy. I took eleven negative parts of Z^(-1.1) and combined them with 1.1 negative parts of Z^(-11) before adding straight C. The parent fractal is a most unpromising thing -- an oversized open oval with a small blob and a small wedge floating in its center. But the wedge is full of detail, and a quick search led me to today's scene, which lies in a more chaotic area of the wedge. I named the image "Grated Remnants". The texture of the eight obvious features surrounding the central minibrot reminds me of a kitchen grater. I rated the image at a 7, which is kind of a FOTD standard. The calculation time of 8-1/3 minutes could cause a bit of fidgeting among those with too many other things to get done. To prevent fidgeting, the finished image will soon be available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> (But the last I heard, the site at: <http://www.fractal-animation.net/fotd2.zip> was no longer being kept up to date.) I do not know what the situation is at the original FOTD web site at: <http://www.Nahee.com/FOTD/> I have not heard from Paul in several weeks, though I continue to send the finished images to him. A mix of clouds and sun and a not-too-chilly temperature of 39F +4C made Saturday a near-average mid-December day here at Fractal Central. The fractal cats must have agreed, for when we returned from the shopping, we found them waiting in the window. After surviving the shopping, I had a day that was acceptably uneventful. The next FOTD will be posted in 13 hours or so, but with no promises made as to the quality of the fractal. Until then, take care, and if seven is lucky and thirteen is unlucky, what happens if you combine them and come up with twenty? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Grated_Remnants { ; time=0:08:22.68-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.16182984183858/+0.29257778317738/\ 4.2912e+009/1/165/0 params=-11/-1.1/-1.1/-11/0/525\ /0/0 float=y maxiter=3600 inside=0 logmap=522 colors=000B0SC1TD6UE3VF9WG7XHCYIBZIF_JG`KI`KKaLKbM\ KcMKdNKdOKeOKfPKgQKhQKhPKeOKdOK_NK`MKVMKYLKPKKMKLJ\ JJHIHEIFBHD8HB6GD9GFCGHFGJIGKKGMNGOQGQTGRVCKa9Dh66\ o30v57r7Dn9JjBQfDWbFaZHhVJnRLtNNzKUyRizYfxctwjsvqy\ vwvtrvuorqirrfmn`kmWikRgjNdhIbgE`e9Zd5X`7VY8TV9RRA\ POBNLCLHDJEEHBFF8GDBECEDAHC9JB7MA6P94S83U79SVFQrIP\ sMPsPPsVPsSOtUOtVOtaOtcNu_NuaNuZNu_Nu_OrVPoLQlGRjB\ Sg6Td1Ub5XX9ZRDaLHcFKeAJg9Ih9Hi9Gk8Fl8Em8Do8Dp7Cq7\ Bs7At79u68w67x67y6EjRLXkJSmHNoFIqDDsC8uKvXBwf3xo6v\ h9ubBtXEsQHrKJqEQbDXOCc9CU9IK9NA9S09X2DX4HX5LX7PX8\ TXAXXB`Xkd6dY4ZR3TIENAPI2ZRKYZ`XfqW7glceeccZmaSm`L\ zZEzc7zm0zcUzXwmUdmRNcP5HJFLEPO9YLD`JGbGJdEMfBQi9T\ k6Wm4ZoCihKsaJlVIeOHZHGSAGL4MMYRMzSKySIxSGxTEwTCvT\ AvQEvOIvMLvKPvISvGWvEZvIVmLReOmYRmPUmHXm9WmGWmNWmT\ cmdjmpEwFFwDGwCHwBKzDNzFPzHSzJUzKXzLzzMzzMzzNzzNzz\ Ozzzzzzzzzzzzzzzzzzzzzzzz } 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 11-12-10 (The Midas Untouch [7])
by Jim Muth 11 Dec '10

11 Dec '10

FOTD -- December 11, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us back to the MandAutoCritInZ formula, still the most productive formula in my oversized and underused collection. I named the scene "The Midas Untouch" because sometimes every fractal I find seems to turn to lead. Most of the effect of today's image is due to its coloring. The sinuous bands that hold the golden colors were created by rendering the scene with the outside set to 'tdis'. The rather unlikely generating formula combines 8.4 parts of Z^(-2.2) with 17.5 parts of Z^(-5.2) then adds (1/C). The par- ent fractal is a shapeless thing with a large but disconnected minibrot just southwest of the main body of the fractal, which is one of the most twisted minibrots I have yet come upon. Today's scene lies in the East Valley area of this minibrot. The rating of a 7 makes the 47-second calculation time a bargain. Other bargains may be found at the following web sites: <http://www.fractal-animation.net/fotd2.zip> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> where the finished image soon will be posted. Clouds moved in just after sunrise and hung tough here at Fractal Central the rest of the day on Friday, tough enough for about 1/2 inch, 1cm of snow to fall in the afternoon. The temperature rose from 16F -9C at sunrise to 30F -1C in the afternoon, assuring that the small snowfall made things slippery. The fractal cats grew bored watching snowflakes after a half hour, and spent the rest of the afternoon in a warmer location. My day was quite busy trying to clear away a lot of little nuisance jobs. The next FOTD is due in 24 hours, but with the holiday rush near its peak I will give no guarantee that it will be ready on time. Until whenever, take care, and . . . . Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= The_Midas_Untouch { ; time=0:00:47.90-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=-0.704523766169/-0.703511014168/6e+007/\ 1/100/0 params=8.4/-2.2/17.5/-5.2/0/0/0/0 float=y maxiter=2700 inside=0 outside=tdis periodicity=6 colors=00000N00H55BAACFFCKKCPPCUUCZZCccChhCmmCrrCv\ vCzzCGiCIlCJoCFgOC`Z8Tj5Mu1Is0Fr0Cp09o06m03l00k0Gh\ 0We0kb0lZ1lW9mSHmPPnLWnIToLQoNOoPLoRJoTGoVEoXBzZ8p\ a6pc3pe1pg0piVpkppm0po0mp0kp0ip0gp0ep0cp0ap0_p0Yp0\ Wp3bhFi`QpULiZGcbBYg6Sk1Mp0Gt0Ax0Du0Fs0Ip0Kn0Mk0Pi\ 0Rf0Ud0Wa0Y_0`X0bV0dT0eOAfKRfGPcENaDL_CJXBIVAGT9EQ\ 7CO6BM59J47H35F24D13F62HA1JE0LJ0NN0PR0RW0T_0Vc0Xh0\ Zl0`p0at0bl0ce0dZ0eS0eQ0eO0eM0eL0eJ0eH0eG1bJ4_M6XO\ 9URCSUEPWHMZmU`MHcPEfRBhU8kW6m6Ro0jq0lp0mp0np0po0q\ o0ro0tn0unmvn0tk0sh0qfmpc0n`1mZ5kW9jTDhRHgOLeLPdJT\ bGXaEWeNViWVldUpmUsuVmnVhhVbbWYWWSQWNKXHDXC7X71VA3\ TD5RG7PJ9NMBMODKRFIUHGXJE_LDaM4WJ0QH0LF0YK0jP3wU2w\ T2wT1wT1wT0wT0wT0wT0wT0wS0wS0wS0wS0wS0wS0wS0wSBl30\ TN0UR0UU0VX0V`0Vc0Wf0Wj0Xm0XpGEK3Uo6Rk8OhBLdDIaFFY\ HCUI9RK6NK3KJ5LH7LH9MHBMHDNHFNHGOHHOHIMGILGHLGGKGF\ JGEGGDFGCDGACG9A61d41Z21T } 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 10-12-10 (Trapped in a Bubble [7-1/2])
by Jim Muth 10 Dec '10

10 Dec '10

FOTD -- December 10, 2010 (Rating 7-1/2) Fractal visionaries and enthusiasts: Today's image takes us back to the center of the largest bubble in the December 07 image. After a bit of exploration in the bubble's depths, I found a not-totally-unexpected minibrot sur- rounded by smaller bubbles. Since the image lies inside a much larger bubble, from which it can never be removed without being changed into something else, I named it "Trapped in a Bubble. Today's image shows a minibrot with zigzag filaments shooting off in all directions and terminating in smaller bubbles. The smaller bubbles of course are filled with still smaller bubbles, etc. etc., down to the infinitesimal. As the meditating hermit on the mountaintop told the weary pilgrim seeking truth, it's turtles (in this case, bubbles) all the way down. The rating of a 7-1/2 is far enough above average to make the calculation time of 7 seconds a real bargain. I could have rated the image higher, but the main point of the image is the coloring, and today's coloring trick worked its magic three days ago. Something three days old is never as good as when it was fresh. There is an alternative to running the parameter file and wait- ing several minutes, and that is to check one of the following web sites for the finished image. <http://www.fractal-animation.net/fotd2.zip> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> Even though winter is still 12 days off, Thursday was a typical midwinter day here at Fractal Central, with partly cloudy skies, brisk biting winds, and a temperature that rose from a low of 21F -6C to a high of 32F 0C. The fractal cats appear to have settled in for the long haul of chilly conditions. My day was quite busy, which is both good news and bad. But the next FOTD will be posted in 24 hours, and that is certainly good news. Until next time, take care, and I doubt that anything truly supernatural or paranormal exists, but I believe that a vast number of unknown things such as ghosts and telepathy do in fact exist, and when, if ever, they are recognized by science, the natural world will be expanded to include the 'paranormal' things, which will then be seen to operate by perfectly natural laws. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Trappd_in_a_Bubble { ; time=0:00:07.08-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=-4.869604058196/+10.91879372671/3029232\ /1/62.3/0 params=-20/-5.2/-22/-1.2/0/125/0/0 maxiter=500 inside=0 logmap=29 periodicity=0 colors=00000NGAO00PFAR00RFBU00TFDX00VEF_00XGIb00ZH\ Le00`HQi10bNTm32d_cz84fXmzD6gcrzI8imvzNAjzzzSFkzzz\ XKmb_naPngaofUplcpkZqqeuocrshsqfsuitriqvkouklvljvm\ gvnevnbvoavoYvqWvpTvrQvqOvsMvsJvsHvtEvtMwuHwvMxwRx\ xWyy`yzeyzixyjwykwykvyluymuymtynszoszorzprzpqzqpzr\ pzrozsnztnztmwumzujzqhznfzkdzhbze`zbZz_XzXVzUmzzzz\ zmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzm\ zzmzzmzzmzzmzzmzzmzzmzzizznzzrzzvzzzzzvzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmz\ zmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzzzNzzNzzOzzOzzPz\ zPzzQzzQzzQzzSszTqzUozWmzXkzYiz_gz`rzarzcrzdrzerzg\ rzhrzirzkrzlrzmrzlrzkrzjrzirzhmkgzkfzmezmezmdzmczo\ bzqazs`zt_zuZzvZzwYzxXzyWzzVzzUzzTzzSzzSzzTzzUzzVz\ zWzzXzzYzzZzz_zz`zzazzbzzczzdzzezzfzzgzzhzzizzjzzh\ zzgzzezzdzzczzazz`zzZzzYmzXzzVzzUzzSzzRzzQzzOzzNzz\ LzzKzzJzzIzzHzzHzzGzzGzAM } 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 09-12-10 (The Galactic Halo [7])
by Jim Muth 09 Dec '10

09 Dec '10

FOTD -- December 09, 2010 (Rating 7) Fractal visionaries and enthusiasts: In today's image we take a trip to the northwest ring of the parent fractal of 2 days ago, where we check deep into the convergence on the southwest side of the ring. The scene we find there is rather harmless. I named it "The Galactic Halo" even though the actual galactic halo is made up of globular clusters instead of fractal rings. (But then, could globular clusters be merely a different aspect of fractal rings.) The rating of a 7 is close to average. The rating might have been a half-point higher if the colors did not remind me of stuffed olives, the most disgusting food I ever tried to eat. The calculation time of under three minutes should bring fidgety impatience to no one. Those who dislike running parameter files can try one of the following web sites, where the finished image will soon be found. <http://www.fractal-animation.net/fotd2.zip> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> Before long, my own web site should be added to the above list. Brisk winds, scudding clouds, snow flurries, a little sunshine and a high temperature of only freezing made Wednesday here at Fractal Central less than ideal. The fractal cats kept busy by sleeping. My day was quite busy with holiday stuff, though I still found time to dredge up a fractal. The next fractal will be posted in 24 hours. Until then, take care, and if the outer world isn't real, then what is real? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= The_Galactic_Halo { ; time=0:02:50.38-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+1.633449982985433/+18.85948164243031/\ 7.437228e+009/1/-30/0 params=-20/-5.2/-22/-1.2/0/\ 125/0/0 float=y maxiter=2400 inside=0 outside=real periodicity=0 colors=000mMzoMzuRzrOzpMznKzlIzjGzhE\ zfCzdAzb8z`6zZ4zY5zY6zX6zX7zW7zW8zV8mV9mU9mUAmTAmT\ BmSBcSCcRCcRDcQDcQEDPF6QE9QECRDFRDISCLSCORAPSCQTEQ\ UFQUHRVJRWKRWMSXNSYPSYRTZST_UT_VU`XUaZUa_VbaVccVcd\ WdfWegWeiXfkXglXgnYhoYiqYisZjtZkvZkwZbfbUReMBhNDiN\ EiNGiNHiNIiNKiNLjNMjNOjNPjORjOSjOTkOVkOWkOXkOZkO_k\ OakOblOclPelPflPglPilPjmPlmPmmPnmPpmPqmNtqPrmRpjTo\ gUmcWk`YjYZhV`fRbeOdcLeaHg`EiZBlZ5kY7jY8iY9hYAgYBf\ XCeXDdXFcXGbXHaWI`WJ_WKZWLYWNXVOWVPVVQUVRTVSRZWSXU\ SVTSTSRRRRPQQNOPLNPJMOHLOFKNDJMBHN9GN7FO5EO3DO2CN4\ BM5BL6BK7AJ8AJAAJB9JC9JD9JE9JF8KH8KI8KJ7KK7KL7LM4K\ M7JL9IKCHJEGIHFHJEHMDHOCIPCJQCKRDMSEOTFQUISVKUWMWY\ OYWO_XQa_Sc`UeaVgbXjcYmd_oe`rfbtgcvhexifzjjzjpzjvz\ j`WjZOjYHzW9zU0zV2zW3zW4zX5zY6zY7zZ8z_9z_Az`BzaCza\ DzbEzcFzcGzdHzeIzeJzfKzgLzgMzhNziOzkOziPzhQzgRzfSz\ eTzdTzSLzULzWLzYLz_LzaLzcLzeMzgMziMzkMz } 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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The FoTD *images* on my server are now complete from Nov 14th.
by Hal Lane 08 Dec '10

08 Dec '10

Jim, Paul, Fractal Friends, The set of Fractal of the Day *images* on my server is now currently complete from November 14th thru December 8th, 2010 -- all 1200x900 or 1024x768: (I like lots of detail.) http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html But I don't have most of the text from all your posts available on my page. That's currently available on the Fractint email list serve in your posts. I'm considering the possibility of adding your text and data on my page above until Paul can resume his Fractal of the Day page creation again. If I did this, my pages of your posts would collect four posts something like this: http://www.emarketingiseasy.com/TESTS/FOTD/FOTD-Nov14-17-2010.html Quick and dirty, but the posts would be accessible from my list of images page... - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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I'm posting the images from Jim Muth's Fractal of the Day.
by Hal Lane 08 Dec '10

08 Dec '10

While Paul Lee (who maintains Jim Muth's Fractal of the Day site: http://www.Nahee.com/FOTD/) is recovering, I will render and post (just the image of) Jim's Fractal of the Day. I like detail, so I always create them at a resolution of 1,200 x 900 pixels. The images seem to work OK when viewed in a browser. Make sure you maximize the size of your browser window and click on the image -- so the browser isn't resizing the image for you -- and losing a lot of the detail. My versions of Jim's images are here: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html In Firefox, the F11 key removes and restores the browser menus, address bar, etc. to let you have the largest possible window. When F11 has been pushed to remove the menus, etc, there's no "Back" button. Just use the "Backspace" key to take you back one page. Occasionally, I increase the maximum iterations to try to maintain a "sharply pointed" feature in the fractal that would be less attractive (to me) if lost at the higher resolution. I'm using an unreleased version of Richard's "Fractint for Windows" (beta 5), so occasionally there may be a fractal that's not rendered the same as the official DOS Fractint. Get well soon, Paul. - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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FOTD 08-12-10 (Cosmic Coincidence [7])
by Jim Muth 08 Dec '10

08 Dec '10

FOTD -- December 08, 2010 (Rating 7) Fractal visionaries and enthusiasts: Yesterday's image is the parent fractal of today's FOTD. Today's image is the scene I found yesterday in that parent fractal. It is located on the eastern shore line of the largest bay of the parent fractal. The exact location is just across the break from the left edge of the 'fan', where an East Valley would be expected, but is missing. The name "Cosmic Coincidence" means whatever the fractalist wants. To me it refers to the unlikely coincidence that a parent fractal could rate two points higher than a scene within it, plus a bit of wonder about cosmic mysteries. The rating of a 7 is all I could do for today's image. When compared to yesterday's, it leaves me 'cold'. Its main problem is that it is too brilliant, but even then, a rating of a 7 is still above average. The calculation time of 2 minutes is pretty hot however. Those with computers and operating systems able to run one of the various versions of Fractint will be pleased. Others will need to view the image at: <http://www.fractal-animation.net/fotd2.zip> where it will soon be posted, or to wait for the original web site at: <http://www.Nahee.com/FOTD/> to be brought up to date. I have convinced FL that our own FOTD web site is a necessity. But due to the holiday rush, it will probably not be up until after the holidays. Also, you might check for a finished image posted on Hal Lane's site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> After 6 inches 15cm of snow here at Fractal Central Monday and Monday night, Tuesday dawned cloudy but cold. The clouds broke in the afternoon, letting some sun through, but the temperature never rose above 34F +1C. The fractal cats took advantage of the sun when it was shining and the house heat when it was not. Except for 45 minutes of sidewalk clearing in the morning, my day was uneventful. FL had the hot coffee waiting when the job was finished. The next FOTD will be posted in 24 hours. Until then, take care, and where will we be located one-thousand years from now? Why in the past, of course. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Cosmic_Coincidence { ; time=0:02:02.12-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=-0.57837687552/+1.59323544876/1.26e+007\ /1/62/0 params=-20/-5.2/-22/-1.2/0/125/0/0 float=y maxiter=1800 inside=0 logmap=156 periodicity=0 colors=0000AM0AN0AO0AP0AQ0AR0AS0BT0CU0DV0EW0FX0GY0\ HZ0I_0J`0Ka1Lb2Mc3Nd6Oe8PfBQgDRgGShITiLUiNVjQWkSXk\ VYlZZm__nc`ndaogbpicpkdqnerofrrgsrhttittjqukovklvl\ jvmgvmevnbvn`voYvpWvpTvqRvqOvrMvsJvsHvtEvtCwuHwvMx\ wRxxWyy`yzeyzixykwymwyovxquxsuxutxwswxswzrwzrwzqzz\ pzzpzzozznzznzzmzzmzvjwrhsnfokdmhbke`gbZe_XdXVdUTd\ URdUPdTNdTLeTJeSHeSFeSMeSLeRKeRJfRHfQGfQFfQEgPDgPG\ dOJbNM_MPYLUVKZTKcRJhOImMHrKGvPFzSFvPErKEmEEhEEcEE\ _EEXEEVEESDDQDDODDMDDJDDHDDFDDDDDFEEHEEJFFLFFMGGOG\ GQGHSHHTHIVIIXIJZIJ`JKaJKcKLeKLgKMhLMjLNlMNnMOzcOz\ cPzcPzcQzcQxcQzcSzcTzcUoSWmTXkUYiV_gW`eWabXc`YdZZe\ X_gVchThiRmkPmlNmmOmlOmkPmjPriPvhQzgQzfRzemzemzdmz\ cmzbmzamz`mz_mzZmzZmzYmzXmzWmzVzzUzzTzzSzzSzzTzzUz\ zVzzWzzXzzYzzZzz_zz`zzazzbzzczzdzzezzfzzgzzhzzizzj\ zzhzzgzzezzdzzczzazz`zzZzzYzzXzzVzzUzzSzzRzzQzzOzz\ NzzLzzKzzJzzIzzHzzHzzGzzG } 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 07-12-10 (Something to Enjoy [9])
by Jim Muth 07 Dec '10

07 Dec '10

FOTD -- December 07, 2010 (Rating 9) Fractal visionaries and enthusiasts: Today's image is only the parent fractal of tomorrow's FOTD. But what a parent it is! How could I let such a visionary parent fractal, with its hints of celestial wonders, go unrecognized? Does the image really rate a celestial 9? In my opinion it does, even though most of the effect is a result of Fractint and my color tweaking. The name "Something to Enjoy" fairly describes the impression the image will have on the viewer. And the calculation time of an incredibly short 8 seconds will be over before the fractalist knows it has begun. But there is always the problem of fractalists with new fangled over-qualified machines and operating systems that are afflicted with DOS-phobia. These viewers may bypass the fun of running the included parameter file by viewing the finished image on the JackOfTradeZ web site at: <http://www.fractal-animation.net/fotd2.zip> The images will be posted there until the original web site at: <http://www.Nahee.com/FOTD/> is again up to date. I have not yet checked to see how quickly the images will be posted to the new web site. There might be a day or so delay. At any rate, as soon as I get a break from the holiday rush, I will set up my own web site -- date and URL yet to be determined. Winter arrived in force here at Fractal Central on Monday as a band of snow off Lake Erie moved in just after midday, bringing snow all afternoon and well into the night. At post time about 4 inches 10cm of snow are on the ground and the intensity is increasing. The high temp of 30F -1C was just far enough below freezing to assure that things got slippery. The fractal cats watched the big fluffy flakes with interest for an hour or so, then curled up by the heat to sleep away the afternoon. My day was average, though there is that snow on the sidewalk that I will need to clear away. The next FOTD will be posted in 24 hours. Until then, take care, and the best fractals are yet to come. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Something_to_Enjoy { ; time=0:00:08.19-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=-3.60121/9.20892/0.1168224/1/90/0 params=-20/-5.2/-22/-1.2/0/125/0/0 maxiter=2400 inside=0 logmap=3 periodicity=0 colors=0000AM0ANBAO0APCAR0AREBU0ATGDX0AVIF_0AXKIb0\ AZMMe0A`OQi1AbQTm3AdSUo8EfUVqDHgUWrIKiUXsNNjUYuSQk\ UZvXTmb_naWngaof_plcpkbqqeuocrshsqfsuitriqvkouklvl\ jvmgvnevnbvoavoYvqWvpTvrQvqOvsMvsJvsHvtEvtMwuHwvMx\ wRxxWyy`yzeyzixyjwykwykvyluymuymtynszoszorzprzpqzq\ pzrpzrozsnztnztmwumzujzqhznfzkdzhbze`zbZz_XzXVzUTz\ UzzUPzUNzULzUJzUHzUFzUMzTLzSKzSJzRHzRGzQFzQEzPDzPG\ zOJzNMzMPzLSzKVzKYzJ`zIczHizGnzFrzFvzEzzEvzErzEmzE\ hzEczEZzEUzDQzDOzDMzDJzDHzDFzDDzDFzEHzEJzFLzFMzGOz\ GQzHSzHTzIVzIXzJZzJ`zKazKczLezLgzMhzMzzNzzNzzOzzOz\ zPzzPzzQzzQzzQzzSszTqzUozWmzXkzYiz_gz`ezabzc`zdZze\ XzgVzhTziRzkPzlNzmOzlOzkPzjPziPzhQkgQkfRmeRmeRmdSm\ cSobTqaTs`Tt_UuZUvZVwYVxXVyWWzVzzUzzTzzSzzSzzTzzUz\ zVzzWzzXzzYzzZzz_zz`zzazzbzzczzdzzezzfzzgzzhzzizzj\ zzhzzgzzezzdzzczzazz`zzZzzYmzXmzVmzUmzSmzRmzQmzOmz\ NmzLmzKmzJmzImzHmzHmzGmzG } 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_RENDER
by JackOfTradeZ＠comcast.net 06 Dec '10

06 Dec '10

. And this file contains all the remaining FOTD pars images rendered up to 12/5/10: http://www.fractal-animation.net/fotd2.zip it is 2.5 MEG .

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FOTD 06-12-10 (The Great Pyramid [4+4=8])
by Jim Muth 06 Dec '10

06 Dec '10

FOTD -- December 06, 2010 (Rating 4+4=8) Fractal visionaries and enthusiasts: Today's image has a strange rating. In my opinion, the image, which shows a surrealistic view of a pyramid, is worth a rating of an 8. But I found the image on the 'Fractal Creations' CD, in the 'dodson' directory, under the name 'Martian'. I could not take full credit for the image, so I split the difference, giving half the credit to Dodson and the other half to myself. I have no idea who Dodson is, but some real person certainly created the original image, which is a modified rendering of the Sierpinski Gasket. All I did was take that image and make a few coloring changes, which made the triangle more closely resemble an actual pyramid. The name "The Great Pyramid" refers not to the one in Egypt, but to the one we once hoped existed on Mars, next to the hill that resembled an alien head. The Martian head and pyramid have since been found to be merely light-and-shadow effects, but it's still fun to imagine they were sculpted long ago by a vanished race of Martians. The image finishes in a miraculously brief one second. This short time leaves no excuse for failing to render the image from the parameter file, unless, that is, the fractalist is burdened by a DOS-illiterate computer or an e-mail program that insists on inserting nonsense characters into the e-mail. If the image is yet not available on the original FOTD web site, there is a chance I will soon be able to put up a new FOTD web site and keep it current until Paul gets back on his feet. The original site can be found at: <http://www.Nahee.com/FOTD/> The cold, blustery conditions continued here at Fractal Central on Sunday, which was a virtual repeat of Saturday. The fractal cats had a virtual repeat of their Saturday, though with more human company to observe their displeasure. My day was spent getting caught up in various non-work things. The next FOTD, almost certainly an original, will be posted in all of 24 hours. Until then, take care, and then take even more care, but do not take too much care, or nothing will be left. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= The_Great_Pyramid { ; time=0:00:01.01-SF5 on P4-2000 reset=0 type=sierpinski center-mag=0.245756/0.2509\ 58/1.155207/1/-135/0 float=y maxiter=1000 bailout=9999 inside=253 outside=summ logmap=yes finattract=y periodicity=0 colors=0AKO9WO8WO8WO8WO8WO8WO8WOAWO9WOBWOAWODWOCWP\ CWQEWREWSFWTFWTGWUGWVHWVHWWIXXJXYJXYKXZLX_LX_MX`NX\ aNXaOXbOXcPXdQXdQXeRYfSYfSYgTYhUYiUYiVYjVYkWYkXYlX\ YmYYnZYnZYo_Yp`Zp`ZqaZrbZrbZscZtcZudZueZveZwfZwgZx\ gZyhZzi_zi_zj_zj_zk_zl_zl_zm_zn_zn_zo_zp_zn_zq_zn`\ zq_zq_zo_zpZznZzoZzoYznYznYzmXzmXzlXzlWzlWzkWzkVzj\ VzjVzjUyiUyiUxhUxhTwgTwgTvgSvfSufSueRteRsaRsdQsdQq\ bQrcPqbPqbPpbOpaOoaOo`On`Nn`Nm_Nm_MlZMlZMkYLkYLjYL\ iXKiXKhWKhWJgVJgVJfVIfUIeUIeTIdTHdTHcSHcSGbRGbRGaQ\ FaQF`QF`PE_PE_OEZODZODYNDYNCXMCXMCWLCWLBVLBVKBUKAU\ JATJATJ9SI9SI9RH8RH8QG8QG7PG7PF7OF6OE6NE6I92KB4MC5\ NE6PF7RG8SI9UJAWKBXMCZND`OEaQFcRGeSIfUJhVKjWLkYMm_\ Nn`OpaPrbQtcRueSwfTyfTxgUxgUxgUxgUxgUxgUxgUxgUxgUx\ gUxgUxgUxgUxgUxgUxgUxgUxgUxgUxgUxgVxgVxgVxgVxgVwgV\ wgVwgVwgVwgVwgVwgVwgVwgVwgVwgVwgVwgVwgVwgVwgVwgWwg\ WwgWwgWwgWwgWwgWwgWwgWwgW } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD_RENDER
by JackOfTradeZ＠comcast.net 05 Dec '10

05 Dec '10

. I don't know what the problem is, but I will start rendering the FOTD pars and posting on my server; you then can just download the images (zip collection), which are named for the date. I have 5 so far; I will do the others over the next day or so, and continue with the new/current posts. the first one is http://www.fractal-animation.net/fotd1.zip .

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FOTD 05-12-10 (Omelets [No Rating])
by Jim Muth 05 Dec '10

05 Dec '10

FOTD -- December 05, 2010 (No Rating) Fractal visionaries and enthusiasts: As feared but expected, I had no chance to find an original fractal on Saturday, so I turned to the CD that came with the second "Fractal Creations" book. In the first directory on the disk, named dodson, I found a fractal named 'eggs'. I scrambled the parameters and named the result "Omelets". The image was created by the type=barnsleyj2 formula. The image is an 'inverted' one, which basically means it is turned inside-out. I have never tried this option, so I can say little about the effect it might have on various fractals, but at least in today's image, it makes an interesting picture. Since the image is not my own, it would be unfair to rate it. The calculation time of 2 seconds will do away with impatience. Those with over-qualified machines may have to wait until the FOTD web site is again up to date. Actually, I am thinking of posting the FOTD images to our own web site until things get back to normal at the original site. And the idea of a FOTD CD will not go away. We'll have to see how things go. The origi- nal FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Typical midwinter conditions prevailed here at Fractal Central on Saturday. In central Pennsylvania this means partly cloudy skies, brisk northwest winds, occasional flurries of snow and a high temperature just above freezing. The fractal cats do not like such conditions, so they spent the day curled up by the heat. My day was busier than usual, making holiday preparations. The next FOTD is due in about 6 hours. It might be an original, or it might be another second-hand one. Check to see. Until whenever, take care, and I hear they just discovered a new conti- nent north of the Arctic Ocean. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Omelets { ; time=0:00:02.58-SF5 on P4-2000 reset=0 type=barnsleyj2 center-mag=0.188788/-0.047\ 3137/0.636055/1/-32.5/0 params=0.0106725095/0.9751\ 392915 float=y maxiter=20 inside=bof60 outside=mult invert=0.5/0.0533336997032166/0 colors=000zzUzvHzrFzmCzhAxc7uZ5rU2oS2lQ2iO3fM3cK3`\ I3ZG3XE3UC4SA4Q94O84M74K65I55G45E35C25A15806606306\ 42863975B87DA8HBAKCCLEDOFERGFTIGWJIYKK_MLbNMdONfQP\ i_QkcdzmqrzvzzzzPUpQToRSoSSnSRmTQmUPlVOkWOjXNjYMiq\ BugHoYMiOScHGaHI`HL`GN_GP_GSZGUZGXYGZYF`XFcXFeWXFx\ TMqOUjK`bFgWHgWKfXMfXPeXReYUdYWdZYdZ`cZbc_eb_gb_ja\ `la`vWgtYeq_coaalcZjeXggVeiTfhBeiFeiJdjNckRclVblZa\ mb`nf`nj_onenwbnt`oqYonVokSohQpeNpb5lgAmeGobLp`RrY\ WsWp0ZmAYjJXhTWeaVbkU`tU_rVZpWYnXXlXWjYVhZXdUWeWVg\ ZUh`SibRjdQlgPmiOnkKrpMqnNpmPokQmjSlhTkgVjeWidYhbZ\ ga`f_adZccXdbWfaUtceqbbnb_jaWg`Td`Qa_NYZJVYGSYDPXA\ LW6IW3FV0GU1IT1JS2LR2MR3OQ3PP4RO4SN5UM6VL6WK7YJ7ZI\ 8`I8aH9cG9dFAfEAgDBv8UqANlCHi61i84hB7hDAhFEgIHgKKg\ MNgOQfRTfTXfV_eYbe_ejWiiXiiYihYigZif_if`ieaidbidbh\ cchbdhbehafh`gh_gh_hhZiheyyKuMMtOPtPRsRTsSWrUYrV_q\ XbqYdp_fp`hmYijVkgTldQmaN } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD Posts
by JackOfTradeZ＠comcast.net 04 Dec '10

04 Dec '10

. Hey folks - there hasn't been a FOTD posted since Nov 13; I assume it isn't my issue, some other "problem". I can volunteer to render the images as Muth posts the PARS, then put them on my server with a download link. If so, I would need to go back to Nov 13 and start there; where to go for that? .

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FOTD 04-12-10 (1/4 of the Pie [6])
by Jim Muth 04 Dec '10

04 Dec '10

FOTD -- December 04, 2010 (Rating 6) Fractal visionaries and enthusiasts: Enough work to keep me busy most all day Friday left little time for a proper fractal search. Luckily, fractals are so numerous that I found one after an improper search. Today's image is closely related to yesterday's FOTD. It is the Julia set of a point in the north valley of a minibrot in East Valley of the Mandelbrot set. The image is very sensitive to maxiter changes. Even a small change will totally change the color, while a substantial maxiter increase will fill in the open areas. I named the image "1/4 of the Pie" because of the four well- defined quarters into which the scene is divided. The rating of a 6 is nothing to get excited about, but to assure continued tranquility, the calculation time of 2-1/2 minutes will leave no chance for excitement to build. The finished FOTD images are posted on the FOTD web site at: <http://www.Nahee.com/FOTD/> but Paul, who has maintained the web site for over 17 years, is still recovering, and might not be able to keep the site up to date. Until he fully recovers, I will post only fast images that finish in a minute or two. Lots of clouds, brisk winds, flurries of snow and a temperature of 36F +2C made Friday a day to keep a traveler invigorated. The fractal cats would rather have had sun. My day was busy but not excessively so. The next FOTD is due to be posted in 24 hours, but as is always the case with Sunday images, it might be late. Until whenever, take care, and reality may not be natural. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= 1/4_of_the_Pie { ; time=0:02:31.55-SF5 on P4-2000 reset=2004 type=julia passes=1 center-mag=0/0/1137\ 532/1/143/0 params=0.2983562075159729/-0.018519436\ 2269525 float=y maxiter=60010 inside=0 outside=imag logmap=-54679 periodicity=0 colors=000dBCdABe9Be9BhABjBBlCBnDBpEBrEBsJEsOGsTIt\ YKtaMtXPuaRufTulVzhXzdUtdSs`QsWNrSKrOJqJGqFEpBCp7A\ lADiDGfEJcGL`HOYJRVLKTHGSDDQ99P56O13R27U3AW4DZ5G`6\ Kc7Ne8Qh9TkAWmB_pCbrDeuEhwFkrHgmJdhL`cNYZPVURRPTOK\ VKFXHAZED`FGbFJdFMeFPgFRiFUkGXlG_nGbpGerGgsGetJdtM\ ctPbuS`uV_uYZv`YvcXvfWrgVnhUkhTgiScjR`jQXkPTlOQlLQ\ kJQjGQjEQiBQh9Qh6Qg4Qf2Qf4Ng6Lh7Jh9HiAFiCDjEBkF9kH\ 7lI5lK3mL1mqGYlH_hI`cJa_JcVKdRLeNLfUOa`QYfSUmVPtXL\ zZHrhhocilZjiVkfQlcLm`HnYCoV8p`RffiXhh_jgalfdmefod\ hqcksbmtaov`rx_ty_vtcoofhkjafmVbpOdnPflQgjRihSjgTl\ eUmcVoaWp_XrZYsXZuV_vT`xRayQbsMfnIjhEmcAqY6uT2xW5s\ Z8naBidEdgH_jKVmNQoQLnUPnXSn_VnbYmeamhdmkgmnjjjigg\ iedibai`ZiYViWSiTPiQMiOJiLFiJCiG9iE9iBFU99WAEYAJ_A\ OaAXcfaClbHrbMsaKt`It`Hu_FvZDvZCpOOjDZcHXXLWROVKSU\ DWT7ZSmQ1kR2jR3hR4gR5fR6dR7cR8bR9dYLedX0lP8nUFpYMr\ aTtf_vjfxnmzrhsdclSZeEU_1 } END PARAMETER FILE=========================================

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FOTD 03-12-10 (Mandelbrot Eruption [6])
by Jim Muth 03 Dec '10

03 Dec '10

FOTD -- December 03, 2010 (Rating 6) Fractal visionaries and enthusiasts: Due to a minor rush here at FC on Thursday, the day I work on Friday's FOTD's, the discussion will be on the brief side. Today's image is an unperturbed view of the area of yesterday's image. I named it "Mandelbrot Eruption" because of the detail that suddenly erupted inside the central Julia-type feature as I raised the maxiter beyond 33,000. Actually, I'm not sure the Julia thing is actually a Julia thing at all. It certainly is no minibrot, nor does it resemble any Seahorse or East Valley type Julia set that I have come across. Of course, I have checked only an infinitesimal part of the total number of possible Z^2+C East-and-Seahorse type Julia sets. The rating of a 6 indicates a modest amount of artistic worth in addition to the mathematical interest. The calculation time of 54 seconds will demand no patience at all. Simply copy this entire letter into the Fractint directory (folder), in text mode, with a *.par extension, and run it as you would any other parameter file. And if Paul's recovery is on schedule, the finished image already is or soon will be available on the FOTD web site at: <http://www.Nahee.com/FOTD/> Scudding clouds, brisk winds and a temperature of 36F +2C brought the feeling of winter to the Fractal Central area on Thursday. The fractal cats would have preferred more sun, but were reasonably happy by the heat. With the work backup cleared away, my day was satisfactorily busy. The next FOTD will be posted in 24 hours. Until then, take care, and I lean toward conservative views, and I think we're fighting for freedom, but I always wonder what it is that we're fighting to be free from. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= MandelbrotEruption { ; time=0:00:54.54-SF5 on P4-2000 reset=2004 type=mandel center-mag=+0.2985719667698\ 861/-0.01848742851637421/2.480859e+012/1/155/0 params=0/0 float=y maxiter=33225 inside=0 outside=summ periodicity=0 mathtolerance=0.05/1 colors=000mGNkGLiGJgHHeHFcHDbHCg3qd4rb5r`5rZ6rX6rV\ 7rT8rR8rP9rN9rLArJBrHBrFCrDCrBGsAKs9Os8St7Vt6Zt5bu\ 4fu3iu7frAcoD`mHYjKWhNTeQQbUN`XKY_IWbFTfCQi9Ol6Lo4\ JTHC6T5L`BZgGloLzvQzuHuzVzzhhzgzzfOzezzd3zczzc4Ic5\ Jc6Jb6Jbzzb7zbzza9zazzaAzazzazz`Cz`Cz`DM`DM_EN_FN_\ FN_GNZGOZHOZIOZIPZJPYJPYKPYLQYLQXMQXMQXNRXORWORWPS\ WPSWQSWRSVRTVSTVSTVTTUUUUUUUVUUVUUWTTWSTWRTWQSWPSW\ PSWOSWNRWMRWLRWKQWKQWJQWIQWHPWGPWFPWFPWEOWDOWCOWBN\ WANWANW9NW8MW7MW6MW5LW5LW4LW3LW2KW1KW0KW0KY0LZ0M_0\ N`0Oa0Ob0Pc0Qd0Re0Rf0Sg0Th0Ui0Uj0Vl0Wm0Xn0Xo0Yp0Zq\ 0_r0_s0`t0au0bv0bw0cx0dy0ez0ew2au3Ys5Uq6Qo7Mm9IkAE\ iCAgD6eE2cG7aIB`KFZMJXONWQRUSVSUZRWbPYfN_jManKcrJd\ vIcuIbtHat00L00M00N00O10P20Q30R40S50T60U70V70W60X6\ 0Y60Z50_50`40a40b30c30d41e52f63f64e65e56d57c48c49b\ 4Ab3Ba3C`2D`2D_1C_1BZ1BZ2F`3Ia4Mc5Pd5Se6Wg7Zh8bj9e\ k9hlAlnBooCsqDvrDysFwqoGP } END PARAMETER FILE=========================================

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FOTD 02-12-10 (Weird Julibrot Set [No Rating])
by Jim Muth 02 Dec '10

02 Dec '10

FOTD -- December 02, 2010 (No Rating) Fractal visionaries and enthusiasts: Due to a power failure at FC on Wednesday, today's image is a slow one that only the stout-hearted will care to calculate. With the electric power out all morning and the work backed up all afternoon, I had no time to do a fractal search. But I did have a spare fractal in readiness. After I posted yesterday's FOTD, I checked the object at the center of that image. Since the resulting fractal took over an hour to finish, I did not intend it to be an FOTD, but the fates determined that the fractal should indeed be today's FOTD. The object at the center of today's image exists in a perturbed Mandelbrot plane. I leave it to the viewer to decide what kind of a thing it is. Since the image was never intended to be a FOTD, I could not rate it. The name "Weird Julibrot Set" fairly describes the image. The calculation time of over one hour on my 2000mhz machine will separate the fractal professionals from the fractal amateurs. The pros will run the included parameter file and wait it out. The amateurs will shrug and say, "I'm not really that interested in the image." If Paul is feeling well enough, both pros and tyros may find time relief on the FOTD web site at: <http://www.Nahee.com/FOTD/> where the finished image could be posted. Wednesday began with steady rain and a temperature of 63F 17C here at Fractal Central. Around 10am a fierce squall arrived with torrential rain and winds of 55mph 88kph. When the excite- ment ended, the lights were out, the fractal basement had taken on water and the temperature was down to 39F +4C. Most of the rest of the day was spent waiting for the lights to come back on and getting the work caught up, while the fractal cats wondered what all the excitement was about. The next FOTD will be posted in 24 hours. Until then, take care, and how can the belief in karma be true if we live on earth only once? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Weird_Julibrot_Set { ; time=1:01:07.20-SF5 on P4-2000 reset=2004 type=mandel center-mag=+0.2985719666083\ 7880/-0.01848742792247442/1.529455e+011/1/142.5/0 params=0.3101057985168/0.8009060914945 float=y maxiter=24000 inside=0 outside=tdis periodicity=6 colors=000JaLJ`MJ_NI_OIZPHYQHXRGXSGWTGVUFUVFUWETXE\ SYESZGT_IT`KUaLUbNUcPVcQVdSWeUWfWWgXXgZXh`XiaYjcYk\ eZkgZlhZmj_nl_om_oYXdJVUMUVOTVQTVSSVVSVXRWZRW`QWcP\ WePWgOXiOXlNXnNXpMXrMXiNP`OHSP9JQ2KR3KR3KR4KR4KR5K\ S5KS6KS6KS7KS7KS7JS7JS8JS8IS8IS8HS80S9Yv_Yu_gzehzd\ izckzblzamz`nz`kzaizbgzcezdczeaxf_vfYtgWrhUpiSnjQl\ kOjlMhlKfmIdnGboE`pCZqAXr8WrEXpJYoOYmTZlYZkc_ih`hm\ `fraewadv`eu`ft`gs_hr_ir_jqZkpZloZm50650750850950A\ 50C50D50D60F70F60H50I60I50I40H31J22J11I02K02H53QA4\ NF6RJ7WO9_SBcVDhZElbHpeJtfMrfNqfPpgPngRlgRjhThhUfh\ VdhWbiX`iYZiZWj_Uj`SjaQjaOkbMkbKkcIlcGldEldCleAkfB\ jgBihBhjBglCgnCfpCerGdtKcvPcxUhzZmzcmzemzgmzivzkzz\ mzzozzqzzszzuzzsrzrhzqZzpPyoMvnmsmcplmnkcljmjichjU\ fkcdlcbmZ`mZemcmpUgtUbsUerSXrQXqOWpMWpKVnIVmGUlEUk\ CUjATiATgATfBSeCSdCRcDRbER`EP_FOZFNYGMXHLWHKUIJTJJ\ SJIRKIQKIPMmzmdzLmzKbJKbK } END PARAMETER FILE=========================================

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FOTD 01-12-10 (Seahorse Elephants [7])
by Jim Muth 01 Dec '10

01 Dec '10

FOTD -- December 01, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image is obviously a Seahorse-Valley type Julia set. So what then is it doing in one of the perturbed Mandelbrot sets, where it is surrounded by pieces of East Valley elephants? Actually, it's no mystery at all. The Julia shapes are univer- sal in all orientations of the 4-D Julibrot. The Mandelbrot shapes are special however, existing in their pure form only in the Mandelbrot planes, which are defined by real and imag 'C'. Today's seahorse Julia shape is surrounded by elephants because the perturbed scene is located at the 'C' coordinates of Seahorse Valley of a minibrot that lies in East Valley of the Mandelbrot set. The name "Seahorse Elephants" describes this relation. I found the image by first zooming deep into the Seahorse Valley of the largest Minibrot in the radical complex of the period-14 elephant on the southern side of East Valley of the M-set. Then, by using the evolver feature of Fractint, I found a per- turbed value of Z where a chaotic area overlies the minibrot's Seahorse Valley. The holes in this overlying layer appear as variations of the shape of the Julia set of whatever part of the Mandelbrot valley lies directly beneath them. And the image holds some Julia-type figures that are even more interesting. For more craziness, increase the maxiter and check the small but twisted set at the center of today's image. The rating of a 7 is what I think the image is worth. But I do not think the image is worth the 11-1/2 minutes it will take to finish the calculation. To get a quick glimpse of the general shape, I suggest changing the outside from 'tdis' to 'iter' and setting the logmap to negative 215, which will shift the calcula- tion to machine language and cut the calculation time to a few seconds. I rendered the image with the outside set to 'tdis' because this spreads the colors in the best manner. When the outside is set to 'iter' or any of the 'real' family, (real, iter, mult, summ), the color bands are either too narrow, giving a totally chaotic effect, or too broad, giving too many boringly flat areas. The way to see the full craziness is to muster your patience and run the included parameter file, or to try the FOTD web site at: <http://www.Nahee.com/FOTD/> Even with a mild temperature of 59F 15C, the heavy clouds and steady rain here at Fractal Central on Tuesday made things less than ideal for both man and cats. The cats missed their sun, while the man wanted the work finished. The cats got no sun, though, with some help from FL, the man did manage to get the work finished. The FOTD fractal soon followed. And speaking of fractals, the next one will be posted in 24 hours. Until then, take care, and give homage where it is due. I leave it to the individual to decide where homage is due. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Seahorse_Elephants { ; time=0:11:33.63-SF5 on P4-2000 reset=2004 type=mandel center-mag=+0.2985719666032\ 641/-0.01848742793131565/7.471066e+009/1/142.5/0 params=0.3101057985168/0.8009060914945 float=y maxiter=12000 inside=0 outside=tdis periodicity=6 colors=000gzehzdizckzblzamz`nz`kzaizbgzcezdczeaxf_\ vfYtgWrhUpiSnjQlkOjlMhlKfmIdnGboE`pCZqAXr8WrEXpJYo\ OYmTZlYZkc_ih`hm`fraewadv`eu`ft`gs_hr_ir_jqZkpZloZ\ m50B50C50D50E50F50H50I50I60K70K70K70N60P50Q40R31S2\ 2O11N02L02K53OA4RF6UJ7YO9`SBcVDhZElbHpeJtfMrfNqfPp\ gPngRlgRjhThhUfhVdhWbiX`iYZiZWj_Uj`SjaQjaOkbMkbKkc\ IlcGldEldCleAkfBjgBihBhjBglCgnCfpCerGdtKcvPcxUhzZm\ zcmzemzgmzivzkzzmzzozzqzzszzuzzsrzrhzqZzpPyoMvnmsm\ cplmnkcljmjichjUfkcdlcbmZ`mZemcmpUgtUbsUerSXrQXqOW\ pMWpKVnIVmGUlEUkCUjATiATgATfBSeCSdCRcDRbER`EQ_FQZF\ QYGPXHPWHOUIOTJOSJNRKNQKNPMeGLdHLcIKbJKbKJaLJ`MJ_N\ I_OIZPHYQHXRGXSGWTGVUFUVFUWETXESYESZGT_IT`KUaLUbNU\ cPVcQVdSWeUWfWWgXXgZXh`XiaYjcYkeZkgZlhZmj_nl_om_oY\ XdJVUMUVOTVQTVSSVVSVXRWZRW`QWcPWePWgOXiOXlNXnNXpMX\ rMXiNP`OHSP9JQ2KR3KR3KR4KR4KR5KS5KS6KS6KS7KS7KS7JS\ 7JS8JS8IS8IS8HS80S9Yv_Yu_ } END PARAMETER FILE=========================================

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FOTD 30-11-10 (Fractal Boogie-Woogie [6])
by Jim Muth 30 Nov '10

30 Nov '10

FOTD -- November 30, 2010 (Rating 6) Fractal visionaries and enthusiasts: With more than average graphic design work to be done on Monday, today's discussion will have fewer than the average number of words. Today's 6-rated image is part of the same 'fan' that produced yesterday's 8-rated image. The scene is located on the fringe curving out from the bottom right edge of the fan. The name "Fractal Boogie-Woogie" came to me when something about the image reminded me of that 8/4 rhythm. If I had had more time to work on the colors, the image might have earned a higher rating. As it is, the rating of a 6 will have to suffice. The image is rather slow, taking over 23 minutes to finish. Those who have too little time to spare may try checking the FOTD web site at: <http://www.Nahee.com/FOTD/> to see if it is up to date yet. A mixture of sun and clouds, with a temperature that rose from 21F -6C to 46F +8C made Monday notably fall-like here at Fractal Central. The cats of the fractal variety, (as all cats are), spent most of the afternoon on their window shelf, stretching out when the sun appeared and curling up when it went behind a cloud. My day was busier than average. (There's been a lot of that going around lately.) The next FOTD will be posted in 24 hours. Until then, take care, and this is the one and only genuine FOTD. Accept no substitutes. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= FractlBoogieWoogie { ; time=0:23:20.60-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.5902872895/-2.3048310835/37539.65/1/\ 170.2/0 params=-22/-1.1/-5.5/-11/0/574/0/0 float=y maxiter=18000 inside=0 logmap=794 periodicity=6 colors=00095CD7EGAFKEHNIIRLKUPLYTM`WOd_PgcRkfSnjUr\ nVuqWttXtrXspXsnXrlXrjXqhXqfXpdXpbXo`XoZXnXXnVXmTX\ mRXlPXlNXkLXkJXjKYiKYhKYgLZfLZeLZdLZeK_fJ`gIahHbiG\ cjFdkFelEfmDgnChnBioAjp9kq8lr7ms6nt5ou4pv3qw2rw1rs\ 0np0jm2fj4ch6bf7be9bcAbbCb`DbZEaYGaWHaVJaTKaSLaQN`\ OO`NQ`LR`KT`IU`GV_FX_DY_C__A`_9a_EU`JN`NFaS8aW1aZ2\ Y`4Tb6Pd8Kg9GiBBkD7mE3lC6kB9jACi9Fh8Ig6Lf5Oe4Rd3Uc\ 2Xb3Ua4R`5P_6MZ7KY8HX9EWACVB9UC7TD4TE2RG5QI7PKAOMC\ MOFLQHKSKJTMHVPGXRFZUE`WXEQzy`zyczyezTjzEoz0sz1kz2\ cz3Xz4Pz5Hz5Az6Ez7Hz7Kz8Nr8QU9Tz9WzAZzBazBdzCgzCj`\ DmaDpZEYTEXcKocQicTccTXcTRcTLaTKWJJWYzUYzVYzVYzVYz\ VYzVYzVYzVYzWYzWYzWYzWYzWYzWYzWYzWbzZbz`bzbbzdbzfb\ zhbzibzjbzjbzkbzkbzlbzlbzmbzmbzhozcoz_ozVozQozMozH\ ozCoz8oz8oz8oz8oz8oz7oz7oz7ozmtzmtzmtzmtzmtzmtzmtz\ mtzutzutzutzutzutzutzutzutzztzztzztzztzztzztzztzzt\ zztzztzztzztzztzztzztzztz } 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 29-11-10 (Fanning Out [8])
by Jim Muth 29 Nov '10

29 Nov '10

FOTD -- November 29, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today we stay with the same fan that appeared in the image of two days ago, but instead of delving into the edge of the blade, we have checked the handle. What we find there is a curious kind of bud with a filament extending into a kind of 'star'. Today's image lies near the point where the filament terminates at the center of the star. I named the image "Fanning Out" because instead of concentrating on the fan blade, we are broadening our horizon to include the handle of the fan. The rating of an 8 shows that by broadening our horizon we have found a better image. The calculation time of under 5 minutes is slower that what I consider ideal, but the image that will appear makes it all worth the effort. And if Paul is still on the road to recovery, the finished image will soon be available on the FOTD web site at: <http://www.Nahee.com/FOTD/> Morning clouds, afternoon sun and a temperature of 43F +6C made Sunday a rather pleasant day here at Fractal Central. The fractal cats, being cats, passed the sunny afternoon on their shelf in the southwest window, keeping comfortably warm. My day was uneventful. The next FOTD will be posted in 24 hours. Until then, take care, and I hear that in 50 years, technology will have solved all our problems, including global warming. If anyone doubts this, all they need do is ask those in snowbound Europe how worried they are about global warming right now. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Fanning_Out { ; time=0:04:52.92-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.235409017246/-0.00349153665/5.6e+008\ /1/141/0 params=-22/-1.1/-5.5/-11/0/525/0/0 float=y maxiter=3600 inside=0 logmap=-560 periodicity=6 colors=000000HE7ED7BB88A958A37A59C7AD9BFBCGDCIFCJH\ DLJDMLDONEQPFSRGUTHWXFY`9_c3_jF_nR_qbQwnGwz7sv8qs8\ gp8gm9fi9ff9ecAe`AdXAdUBcRBcOAhNAmMArMAoMAlMAiIAfF\ AcCAa9A_4AY0AX3AT6AQ8AO9JMAGLBKN1OQFKWIFaOBgU6mW2r\ Y6vZAz`EvaIrcSmdchfrcgvZizUjzPmzKozIrzFuzIxzMzzPzz\ RzTTzzUzTmwzXtTZqz_nUakzbjUNYP6L0EN0LP0SR0_T0mVqrX\ svZuzYszYrzXqzXozXnrWmjWliWjgVifVheVfcUebUdaUcXV_S\ WWOXSJYOEZKAZGEcIHhJLmKOqLWfMcWNjMOrBPy1Pz4Uz7VzAY\ zD_zGbzJezMgzPjzSmzVozYrz`uzcwvcvrcvncvkhvgivcjv`k\ vXlvTmvQnvMovIpvFqvHorJmoLklNjhPheRfbSe_UcWWaTY_Q_\ ZMaXJcVGdUDhYIlaMpdQleThfVegYah_ZiaVidSjfOkhLlkHmm\ EmoHnmKolNpjQqiSrgVsfYte`uccvbew`hx_kyYnzXpzWozVoz\ VozVozVozVozVozVozUozUozUozUozUozUozUozUmzWkzYiz_h\ zafzcdzdczfazh_zjZzlXzmVzoUzqSzsQzuPzwqzxnzylzzjzz\ hzzezzczzazz_zzXzzVzzTzzRzzSzzUzzWzzXzzZzz`zzazzcz\ zdzzazzZzzWzzTzzQzzNzzKzz } 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 28-11-10 (Near the Optimum [7])
by Jim Muth 27 Nov '10

27 Nov '10

FOTD -- November 28, 2010 (Rating 7) Fractal visionaries and enthusiasts: Yesterday's image showed one of the frequently mentioned but rarely seen fractal 'fans' that exist in fractals of the type (-n*(Z^-n))+(-n*(Z^-n))+(1/C). Today we check one of the minibrots that exist around the edges of such fans. In today's image we doubled the (Z) portions of the FOTD of November 23. The resulting parent fractal closely resembles the earlier image, though its size is slightly smaller. Today's image is located on the right edge of the 'fan' that was featured in yesterday's image. The overall effect is of a minibrot in one of the higher-order 'stars' of the Mandelbrot set. There are also minibrots all over the flat 'blade' of the parent fan, though it takes a bit of searching to find them. The name "Near the Optimum" is misleading. I see nothing in the image to imply that something in it is near optimum. In fact, I doubt that anything in fractals can be considered at optimum, except perhaps for a critical value for initial Z in certain fractals. The rating of only a 7 means that calculation time of 16-1/2 minutes will be more effort than the result will be worth. The finished image is or soon will be posted on the FOTD web site at: <http://www.Nahee.com/FOTD/> If the image is not yet posted, be patient. Paul is doing his best to get the FOTD site caught up, but he is still recovering, and it might be a while before things are completely back to normal. Saturday brought snow flurries, but with some afternoon sun, and a temperature of 39F +4C to Fractal Central. The snow flakes brought the fractal cats to the window, but they soon grew bored and returned to warmer spots. My day was average. The next FOTD will be posted in 24 hours. Until then, take care, and if we could change the past, would we know the future? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Near_the_Optimum { ; time=0:16:32.05-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+1.934869010826633/-1.863451620247872/\ 1.059113e+010/1/-167.5/0 params=-22/-1.1/-5.5/-11\ /0/525/0/0 maxiter=12000 inside=255 logmap=2000 periodicity=6 colors=000UGVXKSZOP`RMcVJeTGgXDiVBa_PUWbMSoPUmRVlU\ WjWXiZYh`Zfc_ee`chabjYamc_cQZmWXcUWgYV9APD0dH0bL4`\ P8ZTDYXHW`MUdQShVRlZPkcNjYLiXKiTMhYMhTMhYMcYMZYMUY\ MPYMKYMFYMRXGbRBH0FSP1bHIbJZRCnPBlNAkLAiJ9hH9fF8eD\ 7cB7b96`76_89a8Bc9De9Fg9HiCIgFJeHKdKKbNLaPM_SMZUNX\ XOW_OUaPTdQRfQQgRRgRRhSRhSRiTRiTRjURjURkVRkVRlWRlW\ RmXRmXRbVRSTRTRVTQYTOaUNdUMhUKkVJoVHrVGvVFyUCYUA79\ UwBSvCQvDOuEMuFKtGItHGtJEsKCsLArM8rN6qO4qP2qhL6eN7\ cP8aR9VIJPASQBRRCQSDPTEOUFNVGMWGLXHKYIJZJI_KH`LGaL\ FVGDPBBI69C27D6AGACJEFKIHMJKOLMPOPVmRXbUZgW`lZbq`b\ vbakd`_e_RfZIgZAhWCgTEgSGgQIgPKgNMgMOgRQeWTc`VaeY_\ j`YubczeUxgSwiOvkLzzItnFzsCrzzzz6pwcztzlqEznGhlzzk\ LTdzpjNbigjhSZgUffXVeZXfcWgbWhbWibWjbVkbVlaVmaVmaU\ maUmaUmaUm`Tm`Tm`Tm`Tm`CmoDmnEmzFmzGmzHmzImzJmzKmz\ PmzUmzZmzcmzhmzmmzmmzmmzmmzmmzmrzmrzmrzmrzmrzmrzmr\ zmrzmrzmrzmrzmrzmrzmrzzzz } 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 27-11-10 (The Great Fan [7])
by Jim Muth 27 Nov '10

27 Nov '10

FOTD -- November 27, 2010 (Rating 7) Fractal visionaries and enthusiasts: In many fractals of today's double-negative type, I tell of a prominent 'fan' in the parent fractal. Until now however, I have been pretty much ignoring this 'fan'. In today's image this oversight has been corrected. The image shows one of these 'fans' in its full glory. The handle of the fan is at the origin of the fractal, while the blade points directly east. Today's image has been rotated 90 degrees, so that the blade points straight up instead of to the right. Minibrots abound in these fans, especially along the edges, though sometimes they are difficult to find. Quite a few mini- brots are buried in today's image, and I just might find a few of them and turn them into the FOTD's of the next few days. The name "The Great Fan" says it all. The rating of a 7 makes the task of running the parameter file a minor one, especially since the image finishes in a lightning-fast 23 seconds. The finished image is or soon will be available on the FOTD web site at: <http://www.Nahee.com/FOTD/> Morning clouds cleared away for afternoon sun here at Fractal Central on Friday. The temperature of 39F +4C and brisk winds kept things chilly, but were nothing that would be considered exceptional in late November. The fractal cats kept snug on their shelf in the strong afternoon sun. With the work caught up and the holiday past, my day was relax- ing. The next FOTD will be posted in 24 hours. Until then, take care, and when the truth shines through the fog, will it be recognized even if it proves to be irrational, or is irrational truth an absurdity? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= The_Great_Fan { ; time=0:00:23.12-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=1.578/0/0.4/1/90/0 params=-22/-1.1/-5.5\ /-11/0/525/0/0 maxiter=1500 inside=0 periodicity=6 colors=0009BcCAc98bU6b95bc3bA2bcDc88dmFd6DerKf3Ifv\ Pg3OhzWh6Tiz_j4Yjzak2clzcl3dkzej0dizeh0dgyef0dexed\ 0dcwfc0ebuha0gasj`0i_qk_0kaolb0mcmndKofipgcqherics\ katl_umYvnWwpUxqSyrQzsOvpMrmLnjJjgHfdGbaEZZDVWBRT9\ OQBQQDSRFURHWSJYSL_TNaTPeUSgUViVYkV`mWcoXfqYhsWhtT\ hsQhrNirKiqHipEipBjoAjnAjnAjmAkmAklAklAkkAkkAkkAUj\ CBhDAfE9dF8bG8`H7ZI6XJ6VK5UL4SM4QN3OO2MP2KQ1IR0GS0\ FTDJPPNLaRHmVDyZ9wYAuXBsWCrVDpVEnUFmTGkSHiSIhRJfQK\ dPLcPMbRObSPaTQaUR`VS`WT_XU_YVZZWZ_XY`YYaZYb_Va`Ta\ `R``P``N_aL_aIZaGZaEYbCYbAXb8Xb6Xb5Vd5Tf4Sg4Qi3Ok3\ Nl7RmAUmEXmH_mLbmOemShmVkmZnmaqmWefRV`MJVH8PH8PG8O\ G8OG8OF8NF8NF8MF8ME8ME8LE8LD8LD8KD8KA8HC8KC8JC8JB8\ JB8IB8IA8IA8HA8HGdVFcUFcUFbUFbUFaUFaTF`TF`TF_TF_TF\ ZSFZSEZSEYSEYSEXREXREWREWREVREVQEUQEUQEUQDTQDTPDSP\ DSPDRPDRPDQODQODPODPODOODOOCONCNNCNNCMNCMNCLMCLMCK\ MCKMCJMCJLCJLBILBILBHLBHK } 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 26-11-10 (Spiral for the Ages [7])
by Jim Muth 26 Nov '10

26 Nov '10

FOTD -- November 26, 2010 (Rating 7) Fractal visionaries and enthusiasts: Things were rather busy here at FC on Thursday, which was the holiday on which we give thanks for something I'm not quite sure of. But despite the activity I found time to locate a worthy fractal. I took the parent fractal of three days ago and cut the portions in half. The effect was to do little more than double the size of the parent. Instead of lying in a valley at the southern edge of the 'fan' of the parent, today's scene lies in a spiralling filament extending from a twisted minibrot on the southeastern edge of the fan. The name "Spiral for the Ages" is admittedly overblown. The chief feature in the image is the minibrot, not a spiral. The rating of a 7 is about what the scene is worth. If I had more time, I might have improved the colors and raised the rating a half point or so. The image calculates in just one minute -- in the super-fast category. No time will have been wasted if disappointment prevails after the minute. And the image is always available on the FOTD web site at: <http://www.Nahee.com/FOTD/> Thursday began with snow and sleet here at Fractal Central. For a while it looked like a white Thanksgiving was in store, but by late morning it all changed to rain and within an hour the centi- meter or so of snow that had piled up was gone. The fractal cats kept careful watch on the big floppy flakes for an hour or so, then decided to ask for food. The temperature rose during the day from 32F 0C at daybreak to 39F +4C at nightfall. My day was pleasant enough. FL kept the two guests who were expected well supplied with food, while the foul weather kept any unexpected visitors from dropping by. The next FOTD will be posted in 24 hours. Until then, take care, and what will the next media-manufactured crisis be? It's already got me worried. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Spiral_for_theAges { ; time=0:01:03.44-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+4.21799657059/-4.05052923939/1.92e+007\ /1/100/0 params=-5.5/-1.1/-0.55/-11/0/525/0/0 maxiter=1500 inside=0 logmap=135 periodicity=6 colors=000dsmbtmcrm`umZtmYvmVvmTwmRymTxmUwmWvmXumY\ tm_sm`rmaqmcpmdomfnmgmmaUmjkm_SmlimYQjifmWOgfckUMd\ c`iSKa_YhQIZWUfOGWSQcMETOM_KCQKIXIANGEVEBKCAPA8H86\ F04F02050A40C30B20D10F50IA0HF0GK4EP8CUCAZDAcEAhFAm\ FArKAvPAwUCwZEwZGwZGwcGwhFwhEwmGwmHwrJwrKwwLwwNssO\ ptQmpRjlSggUddVccWc_YcTZcU`cVacWbcXdeYefZfdZeb_d`_\ cZ_bX_bV_aT_`R__P__N_ZL_YJ_XH_XF_WD_VB_U9_U7_T5_S3\ _R2_R6YL9WGCUAFS5IQ0HO4HN8GMBGLFFLIFLMFLPJUQM_QP`Q\ SXQVZQYVQ`WQcSQfUQiVQlWQoXQrYQp_Sn`TlaUjTVhVWfWXeX\ YcY_a_`_`aYabWbcUcdTceRcgPchNciLcjJckHclGcmEcoCZpA\ Zq8Zr6Zs4Zt3Zu2Zs2Zr2Wq2Ro2Jn2Bm23l64m95nC6oF6pJ7q\ M9rP9rSBsWCtZDuaEvdGwgGwhJxhKxiMxiNxjPxjQxjSxkTxkV\ xlWxlXxlZxm_xmaxnbyndyoeyogyohypiypkzqlzqnzqozrqzr\ rzsszstzsuztvzuwzvxzwyzxzzyzzzzzzzzzzzzzzzzzzzzzzz\ 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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FOTD 25-11-10 (Mount Mountain [7])
by Jim Muth 25 Nov '10

25 Nov '10

FOTD -- November 25, 2010 (Rating 7) Fractal visionaries and enthusiasts: The FOTD is late. The reason -- I was too busy with other things on Wednesday Nov. 24 to do a proper search for the image for Nov. 25. Today's image is named "Mount Mountain", a fine name for a fractal mountain if ever there was one. The mountain exists mostly in the human mind, though partly in the parent fractal that is created when the formula Z^(1.1)+C is iterated 11 levels up the multi-dimensional complex logarithmic hyperladder with no function applied to the works. I rated the image at a 7, which is not too bad for a fractal mountain with a touch of snow on its peak. The calculation time of 12-3/4 minutes is admittedly slow, but then good things are worth waiting for, and the calculation can always be bypassed by going direct to the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Sun in the morning gave way to clouds in the afternoon here at Fractal Central on Wednesday, while the temperature reached no higher than a chilly 45F +7C. The fractal cats spent most of the day watching their television, which is what they see on the other side of the window when they sit on their shelf. My day was occupied getting the work caught up before the big holiday. FL busied herself picking up the goodies for the Thanksgiving feast. If we're lucky, only two guests will show up; if we're not, it could be six. The next FOTD will be posted in 24 hours, possibly as little as 14 hours. Until whenever, take care, and what will be the next big breakthrough? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Mount_Mountain { ; time=0:12:49.73-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=t center-mag=-0.0853596/0.776714/7.814454/1/-142.5/0 params=1.1/0/11/525 float=y maxiter=32767 inside=253 logmap=63 periodicity=6 colors=000QGaQH`QH_PIYPJXOKWOLVOMTNNSKORHOQHPOHQNG\ RMGSLGYJFUIFVHFVGGWHGRIHRIHRJIRKIRKJWLJWLJWMKWNKWN\ LWOLRPMRPMRQNRQNRRNRSORSORTPRTPRUQRVQRVRRWRRXRRXSR\ YNRYORZOR_PR_PR`OT_PS`PR`QQaQQaQPbRObRNcRNcSMdSLdN\ _eOZeOYfOXfPXgPWgPVgQUhQUhQTiRSiRSjRRjSQkSPkSPlbOl\ bNmbNmcMncLncKndKodJodIpeHpeHqeGqfFrfFrfEsgDsgCrgC\ mhBhhAccFZZKUUPTPUKKZFFcEAcE5cE3bE3aE4`E4`E4dE4cD4\ bD4bD5aD5`D5`D5_D5ZD5YD5YC6XC6WC6VC6VC6UC6TC7SC7SC\ 7RB7QB7QB7PB7OB8NB8NB8MB8LB8KA8KA9KA9KAUcAUKAmKAUc\ AmKAUK9Uc9mK9UK8UK8mK8Uc8UK7mK7UK7Uc6zE6cD6zD6cD5c\ D5zD5cD5cD4zD4cD4cD3zD3cD3cC3zC2cC2cC2cC1cC1cC1cC1\ cC0cC0cC0cC0cJ4cP7IWBMaEPhIQgHRgHSfHSfHTeGUeGVdGVd\ GWdGXcFYcFYbFZbF_aE_aE``Ea`Eb`Em_Dm_DmZDmZDmYCmYCm\ YCmXCmXCmWBmWBmVBmVBmUAmUAmUAmmAmmAmm9mm9mmzmmzmmz\ mmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmm\ zmmzmmzmmzmmzmmz00ammzmmz } 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 24-11-10 (Busy-body Blueness [5])
by Jim Muth 24 Nov '10

24 Nov '10

FOTD -- November 24, 2010 (Rating 5) Fractal visionaries and enthusiasts: As I said in yesterday's FOTD, I have grown bored with the odd slices of the Julibrot, and have decided to return to the old familiar routine images a week early. Today's image lies in a remote valley of the strange parent fractal that results when the formula Z^sqrt(2)+C is iterated 41.3 levels up the complex logarithmic ladded with no function applied. The minibrot at the center is a square-root-of-2 thing. With exponents of Z in this range, parent fractals and their mini- brots can take any shape whatever, which is not surprising, since the complex logarithm is multi-valued. The name "Busy-body Blueness" is one of the most unjustified I can remember. Very few blue tints are in the image, which is more of a sickly olive-green and orange than anything else. I have no idea what the 'busybody' is supposed to refer to. The rating of a 5 might have been higher if I had put a bit more effort into the coloring. The calculation time of 5-1/4 minutes is asking a bit much from the casual viewer to see a 5-rated image, but those who decline to view it will never know what they have missed. Running the included parameter file may not be necessary. The finished image is likely posted on the FOTD web site at: <http://www.Nahee.com/FOTD/> Clouds prevailed all day Tuesday here at Fractal Central, but they broke in the west just before sunset, leading to a spectac- ular light show. The temperature reached a pleasant 57F 14C. The fractal cats took things easy until late afternoon, when they began agitating for food. My day was a very boring average, but then who needs excitement all the time. The next FOTD will be posted in 24 hours. Until then, take care, and the fractals will keep coming until the supply is exhausted. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Busy-body_Blueness { ; time=0:05:14.45-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.09186130753/+1.498879230002/2387775/\ 1/110/0 params=1.4142/0/41.3/0 float=y maxiter=8400 inside=0 logmap=362 periodicity=6 colors=000qPLqPLqPMqPNqPOqPPqPPpPQpPRpPSpPSpPTpPUp\ PVpPVoQWoRXoSYoTYoUZoV_oW`oXboY`mZ_k_Yh`XfaWdbUacT\ _dRYeQVfPTfNReMOdKMcJJdJKcILcHLbGMbFMaFN`ENZDOYCOX\ CPdBPcAQa9Q`9RZ8RY7vW6vV6vU5vS4vR3vP3vO2sM1pL0mK0j\ M2gN4dO6aP8ZQAXRCYSEYTGYUHYVJYWLYYNYZPZ_RZ`TZaVZbW\ ZcYZd__ea_fc_ge_ig_ji_kj_ll`mn`np`or`pt`qv`rx`sy_q\ wZpvZouYnsYmrXlqXkoWinVhmVgkUfjUeiTdgTcfSaeR`dR_bQ\ ZaQY`PXZPWYOUXNTVNSUMRTMQRLPQLOPKMOJKMJILIGKIEIHCH\ HBGG9EF8DF7CE6AE59D48D37E58F78FA9GC9HE9HHAIIAIJAJL\ BKMBKNBLPCLQCMRCNTDNUDOVDOXEPYEQZEQ`FRaFRbFQ`KQ_UP\ ZcPXjOWcOVUNUKNSCMRCMQCLOCLLBKJBKHBJFBJDAICAIBAIBA\ HD9GF8GI8FK7FL6EO6EQ5DS4CV4CW3BY2Be2Af1Ag1lh2li3lj\ 4lk5ll6lm7ln8lo9qpAqqBqrCqsDqtEquFqvGqwHqxIqyJqzKq\ zLqzMvzNvzOvzPvzQvzRvzSvzTvzUzzVzzWzzXzzYzzzzzzzzz\ 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 23-11-10 (Minibrot in Bloom [8])
by Jim Muth 23 Nov '10

23 Nov '10

FOTD -- November 23, 2010 (Rating 8) Fractal visionaries and enthusiasts: I had intended November to be exclusively a month of odd slices of the Z^2+C Julibrot, and here we are 3/4 of the way through the month, with quite a few interesting odd-slice scenes to show for the effort. While searching for an odd Julibrot slice today however, I came up blank, but the workhorse MandAutoCritInZ formula rescued me in the nick of time. The image shows a minibrot in a valley at the southern edge of the superb fan of the parent fractal, which was created when I combined 11 negative parts of Z^(-1.1) with one negative part of Z^(-11), and added (1/C). I rated the image at an 8, including a full point for the extra coloring effort. I named the image "Minibrot in Bloom" when I noticed FL raking leaves out in the back-yard garden. The calculation time of 3-1/4 minutes is well within reason for an image that rates an 8. Viewing the image already calculated on the FOTD web site is even more reasonable. The web site may be accessed at: <http://www.Nahee.com/FOTD/> Morning clouds gave way to afternoon sun here at Fractal Central on Monday, while the temperature reached a pleasant 57F 14C. The fractal cats occupied themselves for an hour or so chasing the laser beam up and down the hallway. After the work- out they were too exhausted to do much but sleep and ask for food. My day was rather slow. In the afternoon I spotted FL raking leaves in the garden, but she finished before I could go out and help. The next FOTD will be ready in 24 hours. Watch for it then in this same spot. Until next time, take care, and I'll tell you how if you tell me why. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Minibrot_in_Bloom { ; time=0:03:14.93-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.302856921705854/-2.971635012449411/\ 3.859e+009/1/150/0 params=-11/-1.1/-1/-11/0/100/0/0 float=y maxiter=2400 inside=0 logmap=290 periodicity=6 colors=000H0OD0L90J50G10D00A00800C00F31H62J83L64HC\ 3PA3MH2VF1PA1TG0UF0fE1gb2lh3onDgrW`ufRypmzzzzwzysm\ xpcwlCvkCtjDrgEpfFneFncGnaHn`InZInXJnWKnULnTLjRNgQ\ PcNR`MTXKUUJWQHYNG_JE`GDbCBd9Af69g7Hi8Ol9WnAbqAisK\ XhTLZb8Pk0FhAKeNOb`T_mX_i__eb_ad_Zg_Vi_Rl_Nn_Kq_Gs\ _Cv_9x`BuaCssPqbFnrglcHjmLUbPbbTZbXVb`RizzbhJrTz03\ 20760BA0EE0II0LL1PP1ST2WX3_`3bc4fg4ik5mo5pr7mp9jnB\ glCdjEahGZgIWeJTcLQaNN_OKZLPXJTVHXTF`RDdPBhNEeRGbU\ I_YKX`MVdOSgQPkSMnUKqQHkNFfKDaHBXE9SA7N75I43D11800\ 30GJ0WZ0km7eoE`qLWrTRt_MvfHwdQpcYjaed`mZai`bfbcbcq\ lzeWgfTheVieWidYjdZju`kcakYbdTcYOdRIcLDcE8c73b14b4\ 4b74bA4bD4bG4bJ4bM5bP5cS5dV5eY5f`5gc5gf5gh4hi4ii4i\ j3jj3jj3kk2kk2ll2ll1ml1mm1nm0nn0on0on7qoEtpLwqSzrZ\ zsWztTzuQzvSzwTzxUzyVzzWzzWzzmzzmzzmzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzzmzzmzzmzzzz5zz7zz9zzBzzzzzzzzzzz\ 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, esc=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < esc } END PARAMETER FILE=========================================

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Postings to Mailing List
by Roger Alexander 22 Nov '10

22 Nov '10

Because of lots of busy-ness at Action Central postings to the mailing list may be a little sparse for the next few days. Best regards, Roger Alexander

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FOTD 22-11-10 (Feeling the Blues [7])
by Jim Muth 22 Nov '10

22 Nov '10

FOTD -- November 22, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows a curious minibrot, (if this is the proper name for such creatures), that lies on what remains of the main stem of the Mandelbrot set when the Julibrot is sliced at an angle oriented 20 degrees from the Oblate toward the Elliptic direction. To bring the image to reasonable proportions, I stretched it about 4 times in the horizontal direction, which is a little excessive, but makes the best effect. In my opinion the image is worth a rating of a 7, not the least of it due to the coloring, which brings blue to a new extreme. The name "Feeling the Blues" describes the mood of the scene. The calculation time of 23 seconds will pass in half a flash, as also will the trip to the FOTD web site at: <http://www.Nahee.com/FOTD/> to see the pre-calculated finished image. A mixture of sun and clouds and a temperature of 50F 10C kept everyone happy here at Fractal Central on Sunday. In the evening, Cassie, the smaller fractal cat, started growling at something in the yard, but we could see nothing. Nicholas, the large cat, assured her that all was well, and after a few minutes, whatever had her concerned moved on. Meanwhile, my day was average. The next FOTD will be posted in 24 hours. Until then, take care, and sometimes a person needs light to see the light. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Feeling_the_Blues { ; time=0:00:23.29-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=-1.575725778\ /0/75.37224/3.9228 params=70/0/20/0/0/0/0/0 float=y maxiter=3200 inside=0 logmap=29 periodicity=6 colors=00000600800A00D00F00I00K00N00Q00R00S01T02U0\ 3V04W05X06Y07Z08_09`0Aa0Bb0Cc0Dd0Ee0Ff0Fg0Fh0Fi0Fj\ 0Fk0Fl0Fm0Fn0Fo1Fp2Fq3Fr4Fs6Ft7Fu8Fv9FwAFxBFyCFzDF\ zAGz8HzAIzCJzEKzGKzIKzKKzMLzOMzQOzSQzUSzWUzYWz_Yza\ ZzcZzeZzg_zh`ziazjbzkczldzmeymfxmhwmivmjumktmlsmms\ mmsnmsomspmsqmsrmssmssmstmstmsumsumsvmsvmswmswmswm\ swmswmsvmsumstmssmsqmsqmsqmsqmsqmtsmtumuwmusmvsmws\ mxrmyrmzrmzrmzqmzqmzqmzqmzpmzpmzpmzpmzpmzomynmxmmw\ lmvkmujmtimshmrgnqfooeondomcplbpkapj`picpzcpzcpzcp\ zcpzcpzcqzcqzcqzcqzcqzcqzcqzcqzcqzcqzmrcmrcmrcmrcm\ rcmrcmrcmrcmrcmrcmscmscmscmscmscmscwscwscwscwscwtc\ wtcwtcwtcwtdwtewtfwtgwthwtiwujwtkwtlwtmwsnwsowspwr\ qwrrwrswqtwquwqvwpwwpxwpywozwozzzzzzzzzzzzzzzzzzzz\ 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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FOTD 21-11-10 (By Sherry [Unrated])
by Jim Muth 21 Nov '10

21 Nov '10

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

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

19 Nov '10

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

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

19 Nov '10

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

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Mandelbrot Newtons
by Roger Alexander 18 Nov '10

18 Nov '10

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

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

18 Nov '10

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

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

17 Nov '10

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

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

16 Nov '10

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

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

16 Nov '10

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

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

16 Nov '10

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

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Henon_JKO
by Mike Frazier 15 Nov '10

15 Nov '10

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

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FOTD 15-11-10 (Troubled Julia Set [7])
by Jim Muth 15 Nov '10

15 Nov '10

FOTD -- November 15, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image is an almost Julia set of the 4th valley beyond Seahorse Valley out the main spike of the Mandelbrot set. I call it an *almost* Julia set because its orientation is rotated 0.4 degree toward the Rectangular direction. The valley itself appears as the open stripe down the center of the image. The north and south branches of the valley are seen edge-on, and appear as the brilliant blue-white areas flanking the open area and filling the outer Julia shape. The name "Troubled Julia Set" indicates that the Julia set is askew. This close to the over-extended Julia orientation of the Julibrot, a small rotation makes a big difference. The rating of a 7 might not fully justify the calculation time of just under 6 minutes, but the image is still an interesting one. The finished image might be posted on the FOTD web site at: <http://www.Nahee.com/FOTD/> but I am not sure Paul has the site up-to-date quite yet. Sunday turned into a perfect day here at Fractal Central. The blue sky, mare's-tails cirrus and temperature of 61F 16C kept both cats and humans happy. I passed some time walking to the nearby Susquehanna River, where a large number of Canada geese were resting on the water before flying south. FL kept busy doing other things. The next FOTD will be posted in 24 hours. Until then, take care, and old age is the time when a person has the money to do what he always wanted to do but is no longer able to do it. (Hey, don't tell me my attitude is negative. That's the way I see it and I'm not the one who designed it.) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Troubled_Julia_Set { ; time=0:05:58.08-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=0/0/26.83367\ /1.0692 params=90/0/89.6/90/-1.3996313761/0/0/0 float=y maxiter=250000 inside=0 logmap=35 symmetry=yaxis periodicity=6 colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\ OziPygQxeRwcSvaTu_UtYVqWWnUXkSYiQZfOZcMYaKXZIWWGVU\ EURCTOASM8RJ6QG4PE5OF5NF5MF5LF5KG5KG5KG5KG6KH6KH6K\ H6KH6KI6KI6KI6KI8KH9KGALGBNFDQEESEFUDGWDIZCJ`BKbBL\ dAMfAQbET_IWXMZUQbQTeNXhK`kHdnEgoFfoFepFdpGdqGcqGb\ rGarHasH`sH_sH_uL`vO`wR`xVayYaz`azaYzaUzbRzbNzcKzc\ GzdDzd9zd5zdFzdPzeZyecxehwfhvfduectdbscarb`qa_p`Zo\ _YnZWmYVmXUmWTmVSmURmTQmTPmXOm`OmdNmdNmdRlcCkcDjcC\ icChcCgcCfcCecBdcBccBcbBcbBcbBcbAcaAcaAcaAc`Ac`Ac_\ Cc_DcZEcZFcYHcYIZXJUXKPWMKWNFVOAVP5UR3SS3RT3RU3SW3\ TX4VY4V`4Wc4Wh4Xm4Xr4Zv4`z4az5dz5ez5gz5iz5jz5jz5lz\ 5mz5nz3pz5qz6qz8rz9rzBrzCszDszFszGtzItzJtzKuzMuzNu\ zPvzQvzSvzTwzUwzWwzXwzZwz_wz_wzaxzbxzcxzdxzexzfyzh\ yziyzjzzkzzlzzmzzozzpzzqzzqzzqzzqzzqzzrzzrzzrzzrzz\ szztzzuzzvzzwzzvzzuzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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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FOTD 12-11-10 (Deep-Blue Computer [!])
by Jim Muth 15 Nov '10

15 Nov '10

FOTD -- November 12, 2010 (Rating !) Fractal visionaries and enthusiasts: Today's image is a slice through the Julibrot oriented halfway between the Mandelbrot and Julia directions. It is not the one- and-only halfway slice. There is no single slice. The Julibrot is four-dimensional, and today's slice is but one of an infinity of slices oriented halfway between the M and J directions. Today's image is actually the entire parent fractal of the past two days' FOTD's. With minor tweaking, I have used basically the same colors on all three images. I named the image "Deep-Blue Computer". I think this is the name of the computer than beat a grand master at chess a number of years ago. I rated the image with an exclamation mark. (Called a 'bang' in the printing trade.) I surprised myself when I tried the 'real' option on the 'outside' parts. The calculation time of 5 seconds makes whatever comes up worth the effort. But all effort may be eliminated by checking the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> I usually avoid discussing politics, but today I must make an exception. While FL and I were taking a break watching the news at lunch time on Thursday, they showed a 10-second clip of a certain un-named congressman declaring that something must be done about the country's out-of-control financial deficit. A few minutes later, when some effective but painful actions were suggested, the same congressman declared that the suggestions were unacceptable, unworkable and totally out of the question. The resulting laugh from FL made my day. The Thursday weather here at Fractal Central was a repeat of Wednesday's, with a slight drop in temperature to 57F 14C. The fractal cats spent the afternoon basking in the sun on their window shelf. My day was quite busy but still acceptable. The next FOTD will be posted in 24 hours. Until then, take care, and does anyone know how to reduce the deficit without raising taxes or cutting benefits? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Deep-Blue_Computer { ; time=0:00:05.05-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=-0.000556425\ /0/0.6726457 params=45/0/-45/0/-0.75/0/0/0 float=y maxiter=1000 inside=0 outside=real symmetry=xaxis colors=00075H76I77K78M79P7AR7BT7CW7DY7E_7Fb7Gd7Hf6\ Ii6Jk6Jm6Jp6Kr6Kt6Lw6Ly6Lz6Oz6Qz6Sz8Uz9VzAUzBSzCQz\ DRzERzGSzHTyITxJUxKVwLVvMWuOXtPXsQYrRZqSZpT_oU`nV`\ nSZoQ_pO`pMaqJbrHcrFcsDctBct8cu6cv4cv2cw0cw2cx3cy4\ cz5cz6cz7cz8cz9czAczBczCczbcz_czYczWczUczSczQczOcz\ MczKczJczHizGszLozQlzTczVczXczZcz`czbczfcziczmczpc\ ztczwczzcz0cz1cz1cz1cz1kzAizJhzRgzTjzUlzWnzXpzYrzT\ ozPlzKizGfzBcz7`z3YzIazXdzjgzjfzjfzjezjezjdzjdzjcz\ jczcYzXSzQMzJGzDBzOIzYOzhUzr_zfYzVWzJUz8Tz9Pz9Lz9H\ zADzA9zA5zA2zH9zOFzULz`SzgYzmczkfziizhlzfnzeqzctzb\ vzLWz36zELzOZzYlzgzzavzWrzQozKkzEhz8dz2az7XzBTzFPz\ JKzNGzRCzV8zRKzNWzJgzJfzIezIdzIczIbzIbzIbzIbzIbzIb\ zIbzIbzIbzIbzKazLazNazOazQazSazTazVczXezYgz_iz`kzd\ mzhozmqzrszvszzzzzzzzzzzzzzzzvuzrwzmyzhzzZozUezPVz\ KLzGAzCAzB8zB6zB4zB3zB3zA4zA4zA5zA6zA6zA7z97z98z98\ z99z9Az9Az8Bz8Bz8Cz8Cz8Dz } 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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<Paul> I hope you're feeling better, Paul.
by Hal Lane 14 Nov '10

14 Nov '10

I hope you're feeling better, Paul. - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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Newtonish Mandelbrot
by Roger Alexander 14 Nov '10

14 Nov '10

According to the formula writer this formula is a newton mandelbrot mash-up. Regular bailouts, inverse bailouts it can be so confusing at times. Pre-rendered at the usual http://maxitersfractalfollies.blogspot.com And finally welcome back Paul, keeper of the FOTD! Newtonish Mandelbrot { ;fract515.gif a minibrot ; blank ; calctime 0:34:08.17 ; created Nov 13, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=_m.frm formulaname=man-newt-man center-mag=-0.78353162878688400/+0.06835193132850351/2185.907/1/44.99999\ 99999986215/-4.14705769724577067e-012 params=0/0 float=y maxiter=1500 inside=0 logmap=42 colors=0Sm000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } frm:man-newt-man {; Sylvie Gallet [101324,3444], 1995 +R.B. ; tiny mod on original Mandel-Newton by Sylvie ; tweaked brainlessly by Robin Bussell ; to give a hybrid mandel-newton fractal z = pixel, c = z, iter = 1, test1 = 1 rad = 3.1, center = (1.0,0.1) pix = (10*pixel+(5.0,-3.4))*(-0.1,-0.95) zn = center+rad/(pix-center) limit = real(p1), b1 = 16, b2 = 0.0001 : test1 = (1-test1), test2=(iter!=limit) z = (z-zn)*test2 + zn z2 = z*z, z4 = z2*z2, z1 = (z4*z-1)/(4*z4) z = (z2+c)*test1 + (z-z1)*(1-test1) iter = iter+1 ((|z| <= b1) * test1) || ((|z1| >= b2) * (1-test1)) ;SOURCE: forummsg.frm } Roger Alexander

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Re: [Fractint] FOTD 06-11-10 (Almighty Spiral [6])
by Paul.N.Lee＠att.net 14 Nov '10

14 Nov '10

Lloyd Garrick (JackOfTradeZ) wrote: > > I dont see any FOTD posted after Oct 27 2010? > Is there a problem or did the site move again?? > Sorry for the delay in getting these uploaded, but it seems that old age is not what it is cracked up to be (or maybe it is a matter of way too many cracks). Anyway, I got admitted to Emergency unexpectedly, and am just now getting caught back up with my emails, and other issues. Mike Frazier wrote: > > I made a 1200x900 pixel image with 5x5 > anti-aliasing which can be downloaded.... > Very nice example of what Jim's FOTDs have within them, especially when one takes the time to explore and render at such larger image sizes. The details in the lower portion sure stand out much better. Sincerely, P.N.L. -------------------------------------- http://www.Nahee.com/PNL/Fractals.html http://www.Nahee.com/Fractals/

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FOTD 14-11-10 (Glimmer of Hope [8])
by Jim Muth 14 Nov '10

14 Nov '10

FOTD -- November 14, 2010 (Rating 8) Fractal visionaries and enthusiasts: Today's image is not exactly a slice of the Z^2+C Julibrot, but it is certainly a slice of some other Julibrot, and at least in my opinion, it is well worth being declared FOTD for November 14. The rating of an 8 includes 2 full points for the coloring, which creates most of the effect of the image. But I cannot take too much credit for the colors. They were created by the Fractint program with a random strike of the <enter> key. The brilliant spot at the center of the image is a point of anti- bifurcation, or as I call such things, an anti-minibrot. While naming the image I was undecided between "Light at the End of the Tunnel" and "Glimmer of Hope". I finally decided on the latter name, since it was the one that fit in the allotted space in the parameter file. The image is a super fast one, finishing in a speedy 36 seconds. The way to avoid the calculation might be to check the FOTD web site at: <http://www.Nahee.com/FOTD/> I say 'might be' because I have not heard from Paul for a week or so, and the last I checked, the web site was not yet up to date. If for some reason, Paul is unable to continue with the FOTD web site, I could probably take it over myself. We are also considering setting up our own web site here at FC. Maybe we could incorporate the FOTD web site into our own site. After a chilly start, Saturday here at glorious Fractal Central turned into another near-perfect day, with a temperature of 61F 16C. Only a few delicate streaks of cirrus marred the unbroken blueness of the sky, while the strong sun in the southwest window gave the fractal cats all the pleasure they needed while the humans were away antiquing. Our day was occupied by the antiquing trip to Richfield. Maybe I'm going soft, because these trips are actually starting to become rather enjoyable. The next FOTD will be posted in some- thing like 12 hours. Until then, take care, and if the best has not already happened, it is yet to come. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Glimmer_of_Hope { ; time=0:00:36.30-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=-0.7352361863561826/+0.2917224444576193\ /5293406/1/82.5/0 params=7/100000000000.0/0/0 float=y maxiter=1500 inside=0 periodicity=6 colors=000VULTSKRQIOOHMLFKJEIHCFFADD9BA79866644432\ 21000hhOddM``KXXIUUGQQEMMCIIAFF8BB6774332647A23E6C\ HCGjsKhqJgpIfnIemHckHbjGahG`gFZeFYdEXbEWaDU_DTZCSX\ CRWBPUBOTANSAzzzzzzzzzzzzzvzzrzzozylzxivwervbouZlt\ UisPfrJcqEbp9ao5`n0_m0Zl0Yk0Xj0Wi1Vh1Ug1Tf1Se1Rd1Q\ c1Pb1Oa1N`1M_1LZ1KY1JW1IV1HU1HT1GS1FR1FQ1EP0EO0DN0\ DM0CL0BK0BJ0AI0AG09F08E08D07C07B06A059058047046035\ 024023c12b11a0D`4CZ3CY3BX3BW3BV3AU3AT39S39R29Q28P2\ 8N28M27L27K26J26I26H15G15F14E14D14B13A139138027026\ 0150140130020010oTqiQkdNf_K`VHWQERKBLF8GA5A5254_93\ Z83Y83Y83X83W83W83V73U73U73T73S73S73R62Q62Q62P62O6\ 2O62N52M52M52L52K52K52J42I42I41H4BXrAYsAYtAYuDXsGW\ qJVoMUnPTlSSjVRhXRgWQfVPeVPdUOcTObTNaSN`RM_RM_QLZP\ LYPKXOJWOJVNJVNIUMITLHTLHSKGRJGQJFPIFOHENHEMGDMFCL\ FCKEBJDBIDAHCAGB9FB9EA8E98D97C87B76A75965854754743\ 6335324223112111000_ZPXWN } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Thermal Emission
by Roger Alexander 13 Nov '10

13 Nov '10

The map suggests heat and flame. Fire-along with air,earth, and water one of four elements to the ancients. Ready made at http://maxitersfractalfollies.blogspot.com. Thermal Emission { ; fract510.gif ; blank ; calctime 0:02:00.94 ; created Nov 12, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=range-y-3_jul center-mag=0.127469/0.618401/13.64778 params=0.5/0.5/4/1/1/1 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=000000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } frm:range-y-3_jul { ; Kerry Mitchell 23jan98 ; ; colors Julia set by real part of iterate, only when ; imaginary part of iterate falls in certain range; ; range specified in terms of c ; use decomp=256 ; ; p1 = Julia parameter ; real(p2) = bailout (try 4) ; imag(p2) = decomposition scale factor (try 16) ; real(p3) = center of range (try 1) ; imag(p3) = width of range (try 0.1) ; center of range is multiplied by imag(sqr(sqr(c)+c)+c) ; calculation done on variable zc, z used for coloring ; zc=pixel, c=p1, maxr=real(p2), scale=imag(p2), iter=1 angle=0, fac=imag(sqr(sqr(c)+c)+c) lo=(real(p3)-imag(p3)/2)*fac, hi=(real(p3)+imag(p3)/2)*fac if (hi<lo) temp=lo, lo=hi, hi=temp end if : ; ; iteration ; if imaginary part of iterate falls into range, ; scale real part into decomp angle ; iter=iter+1, zc=sqr(zc)+c, r=imag(zc) if ((r>lo)&&(r<hi)) angle=scale*real(zc) end if ; ; bailout--escape and maximum iterations treated the same ; set "iteration done" flag (iter=-1) ; decomposition method will color according to last time ; imaginary part of iterate was within range ; if iterate was never in range, angle was initially set ; to 0, so decomp with use color 0 ; if ((|zc|>maxr)||(iter==maxit)) iter=-1 z=cos(angle)+flip(sin(angle)) end if iter>0 } Roger Alexander

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FOTD 13-11-10 (Juliptic Minibrot [6])
by Jim Muth 13 Nov '10

13 Nov '10

FOTD -- November 13, 2010 (Rating 6) Fractal visionaries and enthusiasts: As the name of today's image -- "Juliptic Minibrot" -- implies, today's image lies in an orientation half way between the Elliptic and Julia directions. The center of the slice is the origin of the Julibrot. The image lies just east of a larger minibrot on a kind of main spike of the parent fractal, which is shaped the same as the minibrot in today's image. Quite a bit of trickery was necessary to bring today's image to a reasonable proportion. It was necessary to expand the X-axis direction to nearly ten-thousand times its normal size. The unexpanded view of the same area is only a series of vertical stripes. A minor coloring trick -- rendering the scene with the outside set to 'tdis' -- brought just enough extra oomph to the image to qualify it as FOTD for the day. The rating of a 6 is based more on mathematical curiosity than artistic value. The calculation time of 5-1/2 minutes is slow for an image that rates only a 6. I recommend viewing the image in finished form on the FOTD web site at: <http://www.Nahee.com/FOTD/> Hopefully Paul is well enough to bring the site is up to date. The last time I checked, the last posted FOTD was November 2. Thursday began with fog here at Fractal Central, but by 9am the sun broke through, and for the rest of the day total sun prevailed, with a temperature of 57F 14C. The fractal cats made the most of the sun, which at its low angle, comes in their window quite strongly. My day was occupied with wrapping up the week's work. The next FOTD is due in 24 hours, but if it is late, an antiquing trip most likely arose on Saturday. Until whenever, take care, and be ready to sacrifice. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Juliptic_Minibrot { ; time=0:05:31.15-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=-2.474863995\ 1095/0/915153/9451 params=90/0/45/0/0/0/0/0 float=y symmetry=xaxis maxiter=15000 inside=0 outside=tdis colors=000zm0KgGIkIHnKCjU7fc3cl9`hEZeJWaOUZURVZPSc\ MOhKLlGWpCet8ow4yU6STAVSEXRH_RLaQPdPSfOWiOZk97_ois\ llbjoMhr6bhFY_OTRXOIeJ9mavGUDGVHEWLCXPAYT9ZX7_`5`d\ 3`g2RbIHZX7IY6DZ6DUAAUA7UA5UA6UA6UA6NACVAIbFNjKTrH\ YzKUtNQnQNiTJcWFYZCTa8Nd5IeKTzYcelnzzyzrqzzinbapWU\ sOMvGEx97r8Cm7Gh6Lc6PZ5UU4YP4aM6KJ8`G9KDB`ADK8E`9G\ K9HcAJKAKfBLKBNiCOjCPkFUgHYdKa`MeYOiURmRTqNVuKXzQz\ rWZza`pgazmznsazpaln`zk`ji_zfzhdZgazg_YfXYeVXdSXcQ\ WbNWaLWaJx`VyYVx_Qx`MxbIwcEweAwf6wg2ue5tc7sa9q`CpZ\ EoXGmVJlULkSNiQQhOSgNU_TWTYXMcZEh_7na0sbLpaemazkav\ icsgepffldhicifakb`l_ZnXYoa_nf`mkalpbkucjl`ccZYWWR\ NULERE6P88OD9NHBNMCMQDLUFLZGKbHKfwmNsnPpoRmpSjqUgr\ WcrX`sZYt_VuaSvcOvdLwfIxhFyiCzk9zlBvjDshEofGldIhbJ\ e`HbZF`YEYXCWWBTV9RU7PS6MR4KQ3HP1FO0DN2GQ4IT6LW8NZ\ APaCSdEUfGXiIZlK`oMcrOeuPgwQfuResSdrTcpUbnVamW`kX`\ jQZlKXnDVp7Tr1Rt7SsQYAO`C } 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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Blue Swirls
by Roger Alexander 12 Nov '10

12 Nov '10

A presentation of blue swirls. Ready made at http://maxitersfractalfollies.blogspot.com Blue Swirls { ; fract504.gif noodle-ish ; blank ; calctime 0:04:06.84 ; created Nov 11, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=conic.frm formulaname=km_08 center-mag=-0.894769/0.249144/2.693612/1/180 params=-0.2698141422772912/-0.1384014404736473/-0.195287942136906/0.3802\ 30109561449/0.1877803888058107/0.9158909878841517/-0.9793694875942259/0.\ 6154667806024354 float=y maxiter=1500 inside=0 outside=atan decomp=128 colors=atubuvcwwdxxfzzfzzeyydyydxxcwxbvwavwauv`tv_tuZsuYrtYqtXqsWpsVorVo\ rUnqTmpSlpRloRkoQjnPjnOimOhmNglMglLfkLekKejJdjIciHbhHbhGagF`gE`fE_fDZeCY\ eBYdAXdAWc9Wc8Vb7Ub7Ta6Ta5S`4R_3Q_2PZ2PZ1OY0NX1NX2OY3PY4QZ5R_6R_7S`8Ta9U\ aAVbCWcDXcEYdFZeG_eH_fI`gJagKbhLciMdiNejOfkPgkQhlRhmSimTjnUkoVloXmpYnqZo\ q_pr`qsaqsbrtcsudtueuvfvwgwxhxxiyykzzjyyixyhwxgwxfvweuvdtvcsubrtart`qs_p\ sZorYnqXmqWmpVloUkoTjnSinRhmQhlPglOfkNekMdjLciKciJbhIagH`gG_fFZfEZeDYdCX\ dBWcAVb9Ub8Ua7Ta6S`5R`4R_3QZ2PZ1OY0NX1NX2OY3PY4QZ5R_6S`7T`8Ua9VbAWcBXcCY\ dDZeE_fF`fGagHbhJciKdiLejMfkNglOhlPimQjnRkoSloTmpUnqVorWprXqsYrtZsu_tu`u\ vavwbwxcxxbwxavw`uvZtuYrtXqtWpsUorTnqSmpRkoPjnOimNhmMglKfkJdjIciHbhFagE`\ fD_fCYeAXd9Wc8Vb7Ta5S`4R_3QZ2PY0NX1OX2PY3QZ4RZ6S_7T`8Ua9VbAXbBYcDZdE_eF`\ fGafHbgIchKdiLejMfjNgkOhlPimRjnSlnTmoUnpVoqWprYqrZrs_st } frm:km_08 { ; Kerry Mitchell 11may98 ; originally conic-near_jul16 ; tweaked by rjr 2k04 to allow user to directly input ; julia parameters previously hardcoded to 0.2882,0.0106 cc=p4, zc=pixel, maxr=1e12, minr=maxr, iter=1 a=real(p1), b=imag(p1), c=real(p2), d=imag(p2) e=real(p3), f=imag(p3): iter=iter+1, zc=sqr(zc)+cc, x=real(zc), y=imag(zc) conic=|x*(a*x+b)+y*(c*y+d)+e*x*y+f| if (conic<minr) minr=conic end if if ((|zc|>maxr)||(iter==maxit)) iter=-1 t=log(minr) z=cos(t)+flip(sin(t)) end if iter>0 } Roger Alexander

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FOTD 11-11-10 (Not a Julia Thing [8])
by Jim Muth 11 Nov '10

11 Nov '10

FOTD -- November 11, 2010 (Rating 8) Fractal visionaries and enthusiasts: A busy day means a late FOTD. Wednesday was unusually busy here at Fractal central, so the FOTD is late. Today's image lies in the parent fractal of yesterday's image. It is located in the Seahorse Valley of a distorted minibrot on the main stem of the parent, very near the point where the stem joins the main body of the Julibrot fractal. I named the image "Not a Julia Thing". On the surface it resembles an everyday Julia set, but it actually lies in an orientation rotated halfway toward the Mandelbrot direction, making it something for sure, but not a pure Julia set. The rating of an 8 includes a full point for the extra effort I put into coloring the image. The coloring creates the better part of the overall effect. The calculation time of over 1-1/2 hours that is listed in the parameter file is some kind of timing bug that sometimes appears in the fractal computer after I run the ancient 'WordPerfect 5.1 for DOS' program, which I still use after all these years. The actual calculation time is around 2-1/2 minutes. It's too bad the bug doesn't make the fractals calculate as fast as it makes the clock run. (While the bug was in effect, the calculation time for an hour-long fractal was listed as 'a very long time'!) The finished image may be seen by running the included *2-1/2* minute parameter file or by viewing it on the FOTD web site at: <http://www.Nahee.com/FOTD/> Total sun and an unexpectedly warm temperature of 61F 16C kept nearly everyone happy here at Fractal Central on Wednesday. The fractal cats actually had a bit too much sun in the afternoon, and retired to the bookshelves in the hallway. My day was quite busy, yet satisfactory, which is all I could hope for. The next FOTD will probably be posted in 12 hours. Until then, take care, and when all those predicted technolog- ical wonders finally arrive, will they be for everyone, or only for the wealthy? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Not_a_Julia_Thing { ; time=1:31:02.06-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=-0.944342858\ 62/+0.000172719906/4812174/1/-40/0 params=45/0/-45\ /0/-0.75/0/0/0 float=y maxiter=5000 inside=0 logmap=614 periodicity=6 colors=00000B00D00F00I00K00N00P00S00V00Y00_01b02d0\ 3f04h05j06l07n08o09p0Aq0Br0Cs0Ds0Es0Fs0Gs0Hs0Is0Js\ 0Ks0Js0Ks0Ls0Ls1Ms2Ns3Ns4Os6Pr7Pq8Qp9RoARnBSmCTlDT\ lASm8TnAUnCVoEWpGXpIXqKXrMXrOYsQYsSYsUYsWZsYZs_Zsa\ _sc_se_sg_sh_si_sj_sk_sl_sm`sm`sm`sm`sm`sm`sm`smas\ masnasobspfsqfsrgssgssestfstgsuhsujsvksvlswmswnswo\ swpswqsvrsurstrssrsqrsqrsqssqtsqutsvtuwuwxusxvszws\ zxrzyrzzrzzrzzqzzqzzqzzqzzpzzpzzpzzpzzpzzpzzpzzpzz\ pzzmzzozznzzmzzmzzmzzmxznxzmxzlxzkxzkxzkxzkxzkxzkx\ zkxzkxzjxzjxzjvzivzhuzgvzftzetzdrzcqzarz_qzYpzWqzU\ qzQpzMpzIpzGqzGrzGsyFtxEvw8uv2su0rt0ms0is0es0as0Zn\ 0Wi0Td0Q_0NV0KQ0HL1EI1CI0AI08L09P0CT0EX0I_0Lc0Og0R\ m0To0Vq0Xs0Ys2Ys3Zs5Zs6Zs8ZsAZsBZsD`sFbsGdsIfsJhsN\ jsRlsWns`psdpshwshwshwshwshwsdrs`tsWvsRwsHlsCbs7Ss\ 2Is0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs0B\ s0Bs0Bs0Bs0Bs0Bs0Bs0Bs0Bs } 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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Steel Blue Curves
by Roger Alexander 11 Nov '10

11 Nov '10

Another Kerry Mitchell formula fractal. Gif and jpg at the usual http://maxitersfractalfollies.blogspot.com Steel Blue Curves { ; fract283.gif ; blank ; calctime 0:14:50.83 ; created Jun 30, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=kerrym.frm formulaname=km_12 center-mag=0.639399/0.290604/1.173709/1/15.0000000000000018/-3.778227730\ 67748585e-014 params=-1.596484267708365/-0.3024384289071322/1.072847682119205/0.015808\ 58790856655/-0.5392010254219184/-0.1369060335093234/-0.2313303018280587/\ 0.7412945951719717 float=y maxiter=1500 inside=0 invert=0.644093142490921/-0.0506912442396313/-0.962157048249763 decomp=256 periodicity=0 colors=ELLFLLFMMGMMGNNHNNHOOIOOIPPJPPJPPKQQKQQLRRLRRMSSMSSNTTNTTOTTOUUPU\ UPVVQVVQWWRWWRXXSXXSXXTYYTYYUZZUZZV__V__W``W``W``XaaXaaYaaYaaYbbYbbZbbZb\ b_cc_cc`dd`ddaddaeebeebffcffcffdggdggehhehhfiifiigiigjjhjjhkkikkikkjlljl\ lkmmkmmlnnlnnmnnmoonoonppoppopppqqpqqqrrqrrrrrrssssssttttttuuuuuuuuvvvvv\ vwwwwwwwwwxxxxxxyyyyyyyyyxxxxxxwwwwwwvvvvvvuvvuuutuutttsttsttrssrssqrrqr\ rprrpqqoqqoppnppnoomoomoolnnlnnlmmkmmkmmjlljllikkikkhkkhjjgjjgiifiifiieh\ hehhdggdggcggcffbffbeeaeeaeeadd`dd`cc_cc_ccZbbZbbYaaYaaXaaX``W``W__V__VZ\ ZUZZUZZTYYTYYSXXSXXRXXRWWQWWQVVQVVPVVPUUOUUOTTNTTNTTMSSMSSLRRLRRKRRKQQJQ\ QJPPIPPIPPHOOHOOGNNGNNFNNFMMFMMELLELLDLLDKKCKKCJJBJJBIIAIIAII9HH9HH8GG8G\ G7GG7FF6FF6EE5EE5EE4DD4DD3CC3CC3CC2BB1BB1AA0AA0AA1BB1BB2CC2CC3DD3DD4DD4E\ E5EE5FF6FF6FF7GG7GG8HH8HH9HH9IIAIIAJJBJJBJJCKKCKKDLLDLL } frm:km_12 { ; Kerry Mitchell 11may98 ;originally conic-near_jul2 ;tweaked so user can directly input ; julia parameters (cc=p4) originally ; hardcoded to -2 cc=p4, zc=pixel, maxr=1e12, minr=maxr, iter=1 a=real(p1), b=imag(p1), c=real(p2), d=imag(p2) e=real(p3), f=imag(p3): iter=iter+1, zc=sqr(zc)+cc, x=real(zc), y=imag(zc) conic=|x*(a*x+b)+y*(c*y+d)+e*x*y+f| if (conic<minr) minr=conic end if if ((|zc|>maxr)||(iter==maxit)) iter=-1 t=log(minr) z=cos(t)+flip(sin(t)) end if iter>0 } Roger Alexander

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Re: [Fractint] FOTD 06-11-10 (Almighty Spiral [6])
by Roger Alexander 10 Nov '10

10 Nov '10

A very impressive fractal Jim. The design is vivid. Roger Alexander

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FOTD 10-11-10 (The Mystical Donut [7])
by Jim Muth 10 Nov '10

10 Nov '10

FOTD -- November 10, 2010 (Rating 7) Fractal visionaries and enthusiasts: Like all images in the month of November, today's image lies in an unfamiliar slice of the Z^2+C Julibrot. I'll not try to describe the location or orientation of the parent-fractal slice, other than reporting that it is centered on Seahorse Valley and is double-rotated halfway between the Mandelbrot and Julia orientations. This is little help, since in the 4-D Julibrot there are countless orientations halfway between the M and J directions. Today's scene is located on the rudimentary main stem of the parent slice. I named the image "The Mystical Donut". I know it's a rather silly name. There is little of a mystical nature in a donut. But I can't help it if I saw a donut in the image. Most of the image's detail was created by rendering it with the outside set to 'real'. The 'imag' and 'summ' options work almost as well. The rating of a 7 makes the image worth the minute required to run the parameter file. Those with over-qualified machines can hopefully find the eye- ball-ready image posted to the FOTD web site at: <http://www.Nahee.com/FOTD/> A mixture of sun and clouds prevailed here at Fractal Central on Tuesday, with the clouds predominating. The temperature of 55F 13C was just a bit too chilly for maximum comfort, though it was about normal for early November. The fractal cats enjoyed the sun when it appeared and sought comfort by the heat when it went behind the clouds. My day was average. Isn't that boring? The next FOTD will be posted in 24 hours. Until then, take care, and do we exist even when we are unconscious? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= The_Mystical_Donut { ; time=0:01:03.50-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=-1.41420407/\ 0/724383.1/1.5564/-90/0 params=45/0/-45/0/-0.75/0\ /0/0 float=y maxiter=1400 inside=0 outside=real colors=000JffIeeIddIccIbbIbaIb`Ib_IbZIbYIbXIbWIbVI\ bUKaTLaSNaROaQQaPSaOTaNVcMXeLYgK_iK`kKdmKhoKmqKrsK\ vs2zz2zzzzzzzzzzzzvuzrw2my2hz2ZoCUeMPVWKLfGApCAzB8\ vB6tB4rB3oB3mA4kA4iA5gA6eA6dA7c97b98a98`99_9AZ9AY8\ BX8BW8CV8CU8DT8DS7ER7EQ7FP7FO7FN7GM7GL7GN7HP7HS7IU\ 7IW6IZ6J`6Jb6Je6Kg6Ki6Ll6Ln6Lp6Ms6Mu6Mw8Nv9OuAPtBP\ sCQrDRqERpGSoHTnITmJUmKVlLVkMWjOXiPXhQYgRZfSZeT_dU\ `cV`cSZdQYeOXeMWfJVgHUgFThDRiBQi8Pj6Ok4Nk2Ml0Ll2Nh\ 3Od4Pa5QY6RU7SR8TN9UJAVGBWCCX8DY5BaDAeL9iT8l`AmaBm\ bDmcEmdGmeHnfJngKnhMniNnjOnkQolRomTonUooWopXpqZpr_\ psaptbpucpuensflrgkqhipigojfnldlmcknajo_ipZhqXgrWf\ n_djbcffabi`Zm_VpYRtXOwWNtVMqVLoVKlVJjUIgUHeUGbUF_\ UEYTDVTCTTBQTAOTCPUDQUERUFSUGTUHUVIVVJWVKXVLYVNZWO\ _WP`WQaWRbWScXTdXUeXVfXWgXVeUVcSVbQV`OV_MVYKUXIUVG\ UUEUSCURAUP8UO6SSDQWKP_QNcXMgbKkiJnoKnpKnpKnpKnpKn\ oKnnKmmKllKkkKjjKiiJhhJgg } frm:SliceJulibrot2 {; draws all 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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Field Line Variations
by Roger Alexander 09 Nov '10

09 Nov '10

Today's blog post of Fractint compatible gifs and anti-aliased jpgs is of two versions of the field4_jul formula by Kerry Mitchell. They are identical except for the imaginary P2 values. I calculated with values of 0 and 12. Available at http://maxitersfractalfollies.blogspot.com I've posted only one version of the par file, just vary imag(P2) if regenerating. Field Line Variations { ; fract506.gif ; blank ; calctime 0:03:55.63 ; created Nov 08, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=*.frm formulaname=field4_jul center-mag=0.048197/0.607759/3.404629 params=0.375/0.375/1000000/0 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=00101211312412413523624724825935936A36B37C47D48E48F49F59G5AH5AI5B\ J6BK6CK6CL6DM7DN7EO7EP7FP8FQ8GR8GS9HT9HU9IUAIVAJWAJXBKXBKYBLYCLZCMZCM_DN\ `DN`DOaDOaEPbEPbEQcFQcFRdFReGReGSfGSfHTgHTgHUhIUiIViIVjIWjJWkJXkJXlKYlKY\ mLZnLZnM_oM_oM`oN`pNapOaqObqPbrPcrPcrQdrQdsResRetRftSftSgtTguThuUhuUivVi\ vVjvVjvWkwXkwYlwYlwZmxZmx_nx_nx`ox`oxapyapybqybqycrydryesyeszftzgtzhuzhu\ zivzjvzkwzmwznxzpxzqyzryzuzzuzzuzzryzqyzoxznxzmwzkwzjvzivziuzhuzgtzftzfs\ zesydrycrybqybqyapyapy`ox_ox_nxZnxZmxYmwYlwXlwXkwWkwVjvVjvVivVivUhvUhuTg\ uTguSfuSftRetQesQdsQdrPcrPcrObqObqOapNapN`oN`oM_nM_nMZmLZmLYlLYlKYlKXkJX\ kJWjJWjIViIViIUhHUhHTgHTgGSfGSfFRfFReFQdFQcEPcEPbEObDOaDNaDN`CM_CM_BLZBL\ ZBKYAKYAJXAJWAIV9IU9HU9HT8GS8GR8FR8FQ7EP7EO7DN7DM6CL6CL6BK6BJ5AI5AH59G59\ G48F48E47D37C36B36A35A259248247236135124124113012001000 } frm:field4_jul { ; Kerry Mitchell 20jan98 ; ; Colors Julia sets by nearest approach to ; period 4 field lines ; ; use decomp=256 ; p1 = Julia parameter ; real(p2) = bailout (try 1e12) ; imag(p2) = number of field line to use: 0 - 15 ; 4 iterations per pixel ; variable zc used for calculation, z for coloring ; zc=pixel, c=p1, maxr=real(p2), minr=maxr, iter=1 fieldangle=tan(imag(p2)*2*pi/15): ; ; iteration ; compare tangent of polar angle with desired ; field line angle, update minimum if needed ; iter=iter+4, zc=sqr(zc)+c, zc=sqr(zc)+c, zc=sqr(zc)+c zc=sqr(zc)+c, rzc=|zc|, tanangle=imag(zc)/real(zc), r=cabs(fieldangle-tanangle) if (r<minr) minr=r end if ; ; bailout ; set "iteration done" flag (iter=-1) ; use log of minimum difference of angles as ; decomposition angle ; if ((rzc>maxr)||(iter>=maxit)) iter=-1 angle=log(minr) z=cos(angle)+flip(sin(angle)) end if iter>0 } Roger Alexander

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FOTD 09-11-10 (Hourglass Spirals [7])
by Jim Muth 09 Nov '10

09 Nov '10

FOTD -- November 09, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image is (no guarantee) the last of the series of near- Julia Mandelbrot valley images. This one shows the valley of the north bud of the large minibrot on the west branch of the filament that extends from the north bud of the Mandelbrot set. The effect is much the same as the previous images, though there is more decoration around the almost-Julia set. The name "Hour- glass Spirals" refers to the hourglass-like shape of the two spirals on either side of the center. It is tempting to think of these fractal spirals as 3-D things such as short curved lengths of string. But they are actually 2-D slices of 3-D spaces that curve and twist in 4-D space. As with all 4-D stuff, the entirety of the spirals is impossible to visualize. As mere humans, our consciousness is limited to the 3-D experience. I decided to give today's image, which is likely the last of the series, a rating of a 7. We have been mired in this series longer than I had intended, and there are many unusual slices of the Julibrot that we have not yet checked. Tomorrow's image will begin the exploration of these. Today's image calculates in under 7 minutes, not fireball fast, but certainly faster than some FOTD's, which have taken days to complete. The last I heard, Paul was still in the hospital, recovering from an infection. He has enough access to the FOTD web site to post the FOTD discussions. But since he is using a new-fangled laptop machine running Vista, which panics as the sight of the Fractint program, he cannot run the parameter files. I am send- ing the finished GIF images to him while he is in the hospital, from where he can post them to the FOTD web site. Hopefully, the web site will be up to date shortly. As always, the site may be accessed at: <http://www.Nahee.com/FOTD/> A few too many clouds and a bit too little sunshine here at Fractal central on Monday kept the fractal cats from reaching maximum contentment. The temperature of 54F 12C was just about normal. My day was normal also. The next FOTD will be posted in 24 hours. Until then, take care, and I hear that within 25 years everyone will have their own private autogyro for their daily commute. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Hourglass_Spirals { ; time=0:06:51.18-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=0/0\ /11.7/1/87/0 params=89.9/0/89.9/52.5/-0.15436/\ 1.0371225/0/0 float=y maxiter=40000 inside=0 logmap=8 periodicity=6 colors=000CKVDLUEMSFNWGOTHPRIQOJRMJSJKTIMUJNVIOWIQ\ XHTYGVZGY`F_aFabEdcDfeDifCkgCnhBpjAskAul9wm9zlCzlE\ zlHzlJxlMvlOtlRtlTslWslYsl`rlbrlerlgqljqllqlnokmnj\ lmikkijjhiifhgdhfegedfcbecadcaccaccabcbacc`cc_ccZc\ cZccYccXccWccVccUcbUcaYc`acZecXicWmcVqcUpcUpcUpdUp\ dUpdUpeUpeUoeUofUofUofUogUogUogUnhUnhUnhUniUniUnjU\ nkUmlUlmUkmUjmUimUhmUhmUgmUfmUemUfmUgmUhmUhmUimUjm\ UjmUkmUlmUlmUmmUnmUnmUomUpmUpmUpmUqmUrmUsmUtmUumUv\ mUwmUxmUymUxmUxmUxmTxmSxmRwmQwmPwmOwmNwmMwmLvmKvmJ\ vmIvmHvmGumFumEumDumCumBuiEteHtaKsYNsUQrSRrQSrOTsM\ UsKUsIVsGVsEWtCWtAXt8Xt6Yt4Zu2_u0`u0bz0dz0ez0ez0fz\ 0fz0gz0hz0hz0hz0iz1jz3jz4kz5kz7kz8qzArzBrzCszEszFs\ zHuzIuzKuzLuzMuzOuzPuzRuzSuzSuzUzzVzzWzzXzzYzzZzz`\ zzazzbzzczzdzzezzgzzhzzizzizzzzzzzzzzzzzzzzzzzzzzz\ 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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Re: [Fractint] Fractint Digest, Vol 93, Issue 4
by JackOfTradeZ＠comcast.net 08 Nov '10

08 Nov '10

. can someone tell me why i can not see the FOTD image post after Oct 27? is it my problem or something with the site - has it moved? thanx .

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FOTD 08-11-10 (Be Forever Fractal [No Rating])
by Jim Muth 08 Nov '10

08 Nov '10

FOTD -- November 08, 2010 (No Rating) Fractal visionaries and enthusiasts: Today's image is what happened when I tried the almost-Julia- valley trick on the valley leading to the large sub-bud on the northwest shore line of the large period-2 bud of the Mandelbrot set. Like the recent images, there are some similarities and some differences. The greatest difference in today's image is the fact that it is only the central part of the entire parent almost-Julia set. I have cropped off a good part of the out- lying areas, but the part that remains is interesting enough. We have the same spirals and the same grossly enlarged view of the Mandelbrot aspect of the valley. Once again I used mostly the same color palette, though in today's image I cut the values and intensity of the stronger hues. I could hardly give just another valley scene a proper rating, though I did name it "Be Forever Fractal", a name that sounds a bit more meaningful than it actually is. The calculation time of only 3 minutes is blessedly brief. (I gave it the blessing myself.) I haven't heard how Paul at the FOTD web site is coming, but the last I heard he was recovering, so it might be worth a look to see if the FOTD web site at: <http://www.Nahee.com/FOTD/> is up to date yet. FL and I managed the shift from daylight time to standard in fine shape here at Fractal central on Sunday. We simply arose an hour earlier. The cats never noticed the change, except in the evening, when they had to wait an hour longer for their treats. A mixture of sun and clouds hung above Fractal Central all day. The fractal cats enjoyed the sun while it was out and the house heat when the sun failed them. The temperature of 45F +7C was chilly for both man and cat. The next FOTD will be posted in 24 hours. There is no escaping the delay. Until then, take care, and resistance is futile. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Be_Forever_Fractal { ; time=0:03:07.19-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 periodicity=6 center-mag=0/0/2.16/1/47.5/0 float=y maxiter=42000 params=88.7/0/88.7/77.5/-1.12542/0.21722/0/0 inside=0 logmap=yes colors=00086a97bA8cB9dCAeDBfECgFDhGEiHFjIGkJHlKImL\ JnMKoNMnOOmPQlQSkRUjSVgTWdUXaSY_QZXOZUMYSKXQIWOGVN\ EULCTJASH8RE6QB4P95OA5NA5MA5LA5KB5KB5KB5KB6KC6KC6K\ C6KC6KD6KD6KD6KD8KC9KBALBBNADQ9ES9FU8GW8IZ7J`6Kb6L\ d5Mf5Qb9T_DUXHUULUQOUNSUKWUH_UEbUFaUF`UF_UG_UGZUGY\ UGXUHXUHWUHVUHVULWUOWURWUVXUYXU`XUaTUaPSbMQbIOcFQc\ BSd8Ud4Wd0YdA_dKaeUceZceccfccf_ceZcdYccX`cWZcVWcUT\ cTQcRNcQLcPIcOFcNCcM9cL7cKEcJLcJScIZcIccMMc7Oc8Mc7\ Lc7Mc7Nc7O`7PY6QV6SU6UU6WU6YU6_U5aU5cU5cU5cU5cU5cU\ 7cU8cU9cUAcUCcUDZUEUUFPUHKUIFUJAUK5UM3UN3UO3UP3UR3\ US4VT4WW4YZ4Zc4`h4am4cq4ev4fw5ix5jy5lz5nz5oz5oz5pz\ 5pz5qz3rz5rz6rz8sz9tzBtzCuzDuzFuzGvzIwzJwzKxzMxzNx\ zPzzQzzSzzTzzUzzWzzXzzZzz_zz_zzazzbzzczzdzzezzfzzh\ zzizzjzzkzzlzzmzzozzpzzqzzqzzqzzqzzqzzrzzrzzrzzrzz\ rzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrzzrz\ zrzzrzzrzzrzzrzzrzzrzzrzz } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 07-11-10 (Home of the Spiral [No Rating])
by Jim Muth 07 Nov '10

07 Nov '10

FOTD -- November 07, 2010 (No Rating) Fractal visionaries and enthusiasts: The lateness of today's image is due to a not-so-surprise antiquing expedition that arose not-so-unexpectedly on Saturday. But better late than never. Today's FOTD is the parent fractal of yesterday's 'Almighty Spiral' fractal. The actual spiral that filled yesterday's image lies humbly at the right edge of today's scene. Many other spirals fill the upper half of the image, which lies on the bud side of the Mandelbrot valley that is visible as the two brilliant wedges jutting across the center of the outer shape. The lower half of the image, which is the main-bay side, has no spirals at all. Today's image is not a Julia set, but it comes very close. It is double-rotated 0.04 and 0.04 degrees from the actual Julia orientation. (Double rotation is a mathematical abstraction most difficult to comprehend. Nothing at all like it exists in three-dimensional space.) But the orientation of today's image produces many Julia characteristics and also shows the position of the hairline spirals in relation to the Mandelbrot aspect of the area. With today's image being a near-repeat of yesterday's, I could give it no rating. The name "Home of the Spiral" needs no expla- nation however. The calculation time of almost 10 minutes will need to be endured in nail-biting impatience. I hear that Paul Lee has been in the hospital for over a week, and has been unable to update the FOTD web site. Fortunately, he appears to be on the road to recovery. But a trip to the FOTD web site that he has maintained for over 13 years and that holds the past FOTD images is always a lot of fun. The web site may be accessed at: <http://www.Nahee.com/FOTD/> Heavy scudding clouds, blustery north winds and a temperature of 43F +6C made Saturday quite brisk here at Fractal Central. The fractal cats had enough heat inside that they never noticed the outside chill. When the antiquing was over and done, my day was reasonably settled. The next FOTD will be posted in 24 hours. Until then, take care, and the answer may lie where least expected. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Home_of_the_Spiral { ; time=0:09:52.49-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=0/0/0.8503401/1/126/0 periodicity=6 params=89.96/0/89.96/0/0.3272613/0.0561252/0/0 float=y maxiter=150000 inside=0 logmap=yes colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\ OziPygQxeRwcSvaTu_UtYVqWWnUXkSYiQZfOZcMYaKXZIWWGVU\ EURCTOASM8RJ6QG4PE5OF5NF5MF5LF5KG5KG5KG5KG6KH6KH6K\ H6KH6KI6KI6KI6KI8KH9KGALGBNFDQEESEFUDGWDIZCJ`BKbBL\ dAMfAQbET_IWXMZUQbQTeNXhK`kHdnEgoFfoFepFdpGdqGcqGb\ rGarHasH`sH_sH_uL`vO`wR`xVayYaz`asaYlaUebRZbNScKLc\ GEdD7d91d5AdFFdPKeZUeccehmfhlfdiecfdbcca`b`Za_W`ZT\ _YQZWNYVLXUIWTFVSCUR9TQ7TPEXOL`OSdNZgNcdRMlCOpDMlC\ LiCMfCNcCO`CPYBQVBSSBUPBWMBYJB_GAaDAcAAc7Ac4Ac1Ac3\ Cc5Dc6Ec8Fc9HcBIZCJUEKPFMKHNFIOAKP5MR3NS3PT3QU3SW3\ TX4VY4W`4Yc4Zh4`m4ar4cv4ez4fz5iz5jz5lz5nz5oz5oz5pz\ 5pz5pz3qz5qz6qz8rz9rzBrzCszDszFszGtzItzJtzKuzMuzNu\ zPvzQvzSvzTwzUwzWwzXwzZwz_wz_wzawzbwzcwzdwzewzfwzh\ wziwzjwzkwzlwzmwzowzpwzqwzqwzqwzqwzqwzrwzrwzrwzrwz\ rwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrw\ zrwzrwzrwzrwzrwzrwzrwzrwz } 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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Yet Another Spiral
by Roger Alexander 07 Nov '10

07 Nov '10

Today's post is a spiral, perhaps not as impressive as Jim Muth's FOTD 06-11-10 but incontestably a spiral. Ready made at http://maxitersfractalfollies.blogspot.com Yet Another Spiral { ; fract502.gif ; blank ; calctime 0:10:07.09 ; created Nov 06, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=km_04 center-mag=0.167019/0.535127/24.2564 params=-0.5/-0.5/-0.6354869228186896/-0.3533127842036195/-0.173558763389\ 996/-0.1402325510422071/0.08810693685720389/-0.7196569719534898 initorbit=0.3/-0.6 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=DHVCGUBET9DS8BR7AQ69P57O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAE\ TBGUCHVDIWFKXGLYHMZIO_JP`KRaLSbMTcOVePWfQXgRZhS_iTajUbkVclXemYfnZgo_ip`j\ qakrbmscntepufqvgrwhtxiuyjvzjvziuyhsxgrwfqvdoucntblsakr`jq_hpZgoYfnWdmVc\ lUbkT`jS_iRYhQXgPWfNUdMTcLSbKQaJP`IN_HMZGLYEJXDIWCHVBFUAET9DS8BR7AQ58P47\ O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAETBGUCHVDIWFKXGLYHMZIO_JP`KRaLS\ bMTcOVePWfQXgRZhS_iTajUbkVclXemYfnZgo_ip`jqakrbmscntepufqvgrwhtxiuyjvzjv\ ziuyhsxgrwfqvdoucntblsakr`jq_hpZgoYfnWdmVclUbkT`jS_iRYhQXgPWfNUdMTcLSbKQ\ aJP`IN_HMZGLYEJXDIWCHVBFUAET9DS8BR7AQ58P47O36N24M13L02K02K13L25M36N47O69\ P7AQ8CR9DSAETBGUCHVDIWFKXGLYHNZIO_JP`KRaLSbMTcOVePWfQYgRZhS_iTajUbkVclXe\ mYfnZho_ip`jqalrbmscntepufqvgswhtxhtxiuyhtxgrwfqveoucntbmsakr`jq_ipZgoYf\ nXdmWclVbkT`iS_hRZgQXfPWeOUdNTcMSbLQaKP`IO_HMZGLYFJXEIW } frm:km_04{; Kerry Mitchell 26aug98 ; tweaked by rjr so user can input julia parameters ; See the end of the formula general_man-2circ for ; Kerry Mitchell's explanation of the "2 circles ; coloring method". ;originally general_jul_test ; "2 general circles" coloring method for Julia sets ; c = Julia parameter, hardcoded originally to (0.65,0.33) ; p1 = x-circle center ; p2 = y-circle center ; real(p3) = x-circle radius ; imag(p3) = y-circle radius ; bailout hardcoded to 10^12 ; use "decomp=256" coloring ; zc=pixel, c=p4, bailout=1e12, iter=1, rmin=1e12 cenx=p1, radx=real(p3), rad2x=radx*radx ceny=p2, rady=imag(p3), rad2y=rady*rady: iter=iter+1, zc=sqr(zc)+c tempx=|zc-cenx|-rad2x tempy=|zc-ceny|-rad2y temp=tempx+flip(tempy), r=|temp| IF (r<rmin) rmin=r, z=temp ENDIF IF ((|zc|>bailout)||(iter==maxit)) iter=-1 ENDIF iter>0 ;SOURCE: 98msg.frm } Roger Alexander

1 0

FOTD 06-11-10 (Almighty Spiral [6])
by Jim Muth 06 Nov '10

06 Nov '10

FOTD -- November 06, 2010 (Rating 6) Fractal visionaries and enthusiasts: Usually, I put little effort into fractal spirals. They're very easy to find and nearly everyone does them. But the spiral in today's image is so unusual that I had to make it a Fractal of the Day. I found the spiral when I tried to extend the trick of the two most recent FOTD's to the valley of the period-10 bud on the northeast shore line of the Mandelbrot set. The trick worked as I thought, producing the anticipated image, but I never expected the image to be filled with such hairline-thin spirals. Today's scene is a blow-up of a small part of the full image, which in itself is quite interesting. (The full image will be the FOTD for tomorrow, November 07.) Actually, images with very fine details such as today's and tomorrow's are improved by anti-aliasing, which helps eliminate the awkward breaks in the finer parts. Because of the fine detail in today's image, I recommend calculating it at the highest resolution available. The name "Almighty Spiral" is overblown. The spiral is not all that great when compared to some that have been found by others, though it is probably the best I have found. If spirals were not so commonplace, I might have rated the image higher. As it is, a rating of a humdrum 6 will have to do. The calculation time of 11 minutes is for a resolution of 640x480. It will be far longer if the image is rendered at a higher resolution than this. But for the true fractal-spiral fan, the result will be worth the wait. The finished image is posted on the FOTD web site at: <http://www.Nahee.com/FOTD/> Sprinkles of rain fell during the morning Friday here at Fractal Central. A few breaks of sun appeared during the afternoon, but not enough to lure the fractal cats to their shelf by the south- west window. The temperature of 52F 11C was about normal for early November. The next FOTD will be posted in 24 hours. Only a surprise antiquing trip could delay it. Until next time, take care, and expect the unexpected. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Almighty_Spiral { ; time=0:11:12.40-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=t periodicity=6 center-mag=-0.448511/-0.894674/9.159484/1/114/0 params=89.96/0/89.96/0/0.3272613/0.0561252/0/0 float=y maxiter=15000 inside=0 logmap=-3 colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\ OziPygQxeRwcSvaTu_UtYVqWWnUXkSYiQZfOZcMYaKXZIWWGVU\ EURCTOASM8RJ6QG4PE5OF5NF5MF5LF5KG5KG5KG5KG6KH6KH6K\ H6KH6KI6KI6KI6KI8KH9KGALGBNFDQEESEFUDGWDIZCJ`BKbBL\ dAMfAQbET_IWXMZUQbQTeNXhK`kHdnEgoFfoFepFdpGdqGcqGb\ rGarHasH`sH_sH_uL`vO`wR`xVayYaz`asaYlaUebRZbNScKLc\ GEdD7d91d5AdFFdPKeZUeccehmfhlfdiecfdbcca`b`Za_W`ZT\ _YQZWNYVLXUIWTFVSCUR9TQ7TPEXOL`OSdNZgNcdRMlCOpDMlC\ LiCMfCNcCO`CPYBQVBSSBUPBWMBYJB_GAaDAcAAc7Ac4Ac1Ac3\ Cc5Dc6Ec8Fc9HcBIZCJUEKPFMKHNFIOAKP5MR3NS3PT3QU3SW3\ TX4VY4W`4Yc4Zh4`m4ar4cv4ez4fz5iz5jz5lz5nz5oz5oz5pz\ 5pz5pz3qz5qz6qz8rz9rzBrzCszDszFszGtzItzJtzKuzMuzNu\ zPvzQvzSvzTwzUwzWwzXwzZwz_wz_wzawzbwzcwzdwzewzfwzh\ wziwzjwzkwzlwzmwzowzpwzqwzqwzqwzqwzqwzrwzrwzrwzrwz\ rwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrw\ zrwzrwzrwzrwzrwzrwzrwzrwz } 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=========================================

3 2

Threaded Julia
by Roger Alexander 05 Nov '10

05 Nov '10

Today's post is another formula by Kerry Mitchell based on the Julia iteration loop. Gif and jpg version available at http://maxitersfractalfollies.blogspot.com Threaded Julia { ; fract499.gif another Julia iteration loop fractal ; blank ; calctime 0:05:22.08 ; created Nov 04, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=km_08 center-mag=-0.730914/0.135225/2.109705 params=0.5243385113071077/0.07968382824182867/-0.8776207770012513/-0.809\ 0762047181616/-0.5746330149235511/0.3112582781456953/-0.8414868617816705\ /0.2847071749015778 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=000734633523422312211101000000100200311411512612723823924A34B35B3\ 5C46D46E46F47G57H58I58J69K69L6AM6AN7BO7BP7BQ8CR8CS8DT9DU9EU9EV9FWAFXAGYA\ GZBH_BH`BHaCIbCIcCJdCJeDKfDKgDLhELiEMjEMkEMlFNlFNmFOnGOoGPpGPqHQrHQsHRtH\ RuISvISwJTwJTwKUwLVwLVwMWwNWwNXwOXwPYwQYwQZwRZxS_xS_xT`xU`xUaxVbxWbxWcxX\ cxYdxZdxZex_ex`fx`fxagxbgxbhxchxdiyejyejyfkygkyglyhlyimyimyjnyknykoyloym\ pynpynqyoqyprypsyqsyrtyrtzsuztuztvzuvzvwzwwzwxzxxzyyzyyzzzzzzzyyzxxzxxzw\ wzvwzvvzuvztuztuzstzrtzqszqszprzorzoqynqympympyloykoyknyjnyimyimyhlyglyg\ kyfkyejyejydiychybhybgyagy`fy`fy_eyZeyZdyYdyXcyXcyWbyVbxVaxUaxT`xT`xS_xR\ _xQZxQZxPYxOYxOXxNXxMWxMWxLVxKUwJTvJTuJTtISsISrIRqIRpHQoHQnHPnGPmGOlGOkF\ NjFNiFNhFMgEMfELeELdDKcDKbDJaCJ`CI_CIZCHYBHYBHXBGWAGVAFUAFTAES9ER9DQ9DP8\ CO8CN8BM7BL7AK7AJ7AI69H69H68G58F57E57D46C46B45A45934834 } frm:km_08 { ; Kerry Mitchell 11may98 ; originally conic-near_jul16 ; tweaked by rjr 2k04 to allow user to directly input ; julia parameters previously hardcoded to 0.2882,0.0106 cc=p4, zc=pixel, maxr=1e12, minr=maxr, iter=1 a=real(p1), b=imag(p1), c=real(p2), d=imag(p2) e=real(p3), f=imag(p3): iter=iter+1, zc=sqr(zc)+cc, x=real(zc), y=imag(zc) conic=|x*(a*x+b)+y*(c*y+d)+e*x*y+f| if (conic<minr) minr=conic end if if ((|zc|>maxr)||(iter==maxit)) iter=-1 t=log(minr) z=cos(t)+flip(sin(t)) end if iter>0 } Roger Alexander

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FOTD 05-11-10 (Order-Three Nonsense [No Rating])
by Jim Muth 05 Nov '10

05 Nov '10

FOTD -- November 05, 2010 (No Rating) Fractal visionaries and enthusiasts: I rather enjoyed the half-and-half view of Seahorse Valley that I posted as the FOTD for yesterday. Today I decided to take it one step further and see what would happen if I calculated the same type of view of North Valley. The result is today's image. The image closely resembles yesterday's, with the outer shape being the familiar Julia set of the area, with the bloated Mandelbrot-valley aspect filling the inside. At first glance, today's image appears to have origin symmetry. A second glance however reveals that it has no symmetry. An even greater change is in the periodicity. In yesterday's image the blunt spirals had two arms; in today's image there are three arms in each spiral. I re-used the same color palette to bring out the similarities in the images. But this makes today's image too much of a repeat for an honest rating. I let it go with no rating. The name "Order-Three Nonsense" refers to the periodicity of the area of the Julibrot pictured in the image. The calculation time of 46 seconds is just about what the image is worth. The most convenient way to view the Julia-Mandelbrot nonsense is to view the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Heavy clouds, steady rain, and a temperature of 46F +8C spoiled outdoor plans here at Fractal Central on Thursday. Luckily, with no outdoor plans, the fractal cats were satisfied indoors, lying by the heat. My day was tranquil enough, which means enough work to keep my thoughts reasonably free of politics, philosophy and personal opinions in general. Now that gardening season has ended, FL found herself with more spare time than she knew what to do with, but a latin soap-opera soon filled the empty time. (I wish I understood Spanish.) The next FOTD, even higher-order nonsense, will be posted in 24 hours. Until then, take care, and will there ever come a day when someone discovers the last fractal? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= OrderThreeNonsense { ; time=0:00:46.52-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 symmetry=none center-mag=-0.0201592/-0.0270368/0.9861933/1/58.5/0 params=87/0/87/58.7/-0.125/0.66/0/0 float=y maxiter=2700 inside=0 logmap=yes periodicity=6 colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\ OziPygQxeRwcSvaTu_UtYVqWWnUXkSYiQZfOZcMYaKXZIWWGVU\ EURCTOASM8RJ6QG4PE5OF5NF5MF5LF5KG5KG5KG5KG6KH6KH6K\ H6KH6KI6KI6KI6KI8KH9KGALGBNFDQEESEFUDGWDIZCJ`BKbBL\ dAMfAQbET_IWXMZUQbQTeNXhK`kHdnEgoFfoFepFdpGdqGcqGb\ rGarHasH`sH_sH_uL`vO`wR`xVayYaz`asaYlaUebRZbNScKLc\ GEdD7d91d5AdFFdPKeZUeccehmfhlfdiecfdbcca`b`Za_W`ZT\ _YQZWNYVLXUIWTFVSCUR9TQ7TPEXOL`OSdNZgNcdRMlCOpDMlC\ LiCMfCNcCO`CPYBQVBSSBUPBWMBYJB_GAaDAcAAc7Ac4Ac1Ac3\ Cc5Dc6Ec8Fc9HcBIZCJUEKPFMKHNFIOAKP5MR3NS3PT3QU3SW3\ TX4VY4W`4Yc4Zh4`m4ar4cv4ez4fz5iz5jz5lz5nz5oz5oz5pz\ 5pz5pz3qz5qz6qz8rz9rzBrzCszDszFszGtzItzJtzKuzMuzNu\ zPvzQvzSvzTwzUwzWwzXwzZwz_wz_wzawzbwzcwzdwzewzfwzh\ wziwzjwzkwzlwzmwzowzpwzqwzqwzqwzqwzqwzrwzrwzrwzrwz\ rwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrw\ zrwzrwzrwzrwzrwzrwzrwzrwz } frm:SliceJulibrot2 {; draws all 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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Re: [Fractint] FOTD?
by JackOfTradeZ＠comcast.net 05 Nov '10

05 Nov '10

. I dont see any FOTD posted after Oct 27 2010. ? Is there a problem or did the site move again?? .

1 0

Yesterday's Post
by Roger Alexander 04 Nov '10

04 Nov '10

Today's fractal is the Nov. 2 formula with a new map and different parameters. And at good ole http://maxitersfractalfollies.blogspot.com is yesterday's post re-sampled. Yesterday's Post { ; fract498.gif ; blank ; calctime 0:13:29.11 ; created Nov 03, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=km_10 center-mag=-0.63921378791777690/+0.42946123624707840/231.2811 params=-0.2080599383526109/1.29938962981048/-0.510940885647145/1.6808160\ 64943388/0.2298806726279488/0.8896145512253182/-0.749626148258919/0.4 float=y maxiter=256 inside=0 outside=atan decomp=256 periodicity=0 cyclerange=0/255 colors=sz8sz8rz8rz8qz8py8py8oy8ny8nx8mx8mx8lx8kx7kw7jw7iw7iw7hv7gv7gv7fv\ 7fv7eu7du7du7cu6bt6bt6at6`t6`s6_s6_s6Zs6Ys6Yr6Xr6Wr5Wr5Vq5Uq5Uq5Tq5Tq5Sp\ 5Rp5Rp5Qp5Po5Po5Oo4No4Nn4Mn4Mn4Ln4Kn4Km4Jm4Im4Im4Hl4Gl3Gl3Fl3Fl3Ek3Dk3Dk\ 3Ck3Bj3Bj3Aj39j39i38i28i27i26i26h25h24h24h23g22g22g21g20f10f10e10e10d10c\ 10c10b10a10a10`10_10_10Z10Z10Y10X10X10W10V10V10U10T10T10S10R10R10Q10Q10P\ 10O10O10N10M10M10L10K10K10J10J10I10H10H10G10F10F10E10D10D10C11B01A009009\ 00A00B00C00C00D00E00F00F00G00H00I00J00J00K00L00M00M00N00O00P00P00Q00R00S\ 00T00T00U00V00W00W00X00Y00Z00_00_00`00a00b00b00c00d00e00f10f11f12f13g14g\ 15g16g17h17h18h19i2Ai2Bi2Ci2Dj2Ej2Fj2Fk2Gk2Hk2Ik3Jl3Kl3Ll3Mm3Nm3Nm3Om3Pn\ 3Qn3Rn4So4To4Uo4Vo4Vp4Wp4Xp4Yp4Zq4_q5`q5ar5br5br5cr5ds5es5fs5gt5ht6it6jt\ 6ju6ku6lu6mv6nv6ov6pv6qw7rw7rw7sx7tx7ux7vx7wy7xy7yy7zz8 } frm:km_10 { ; Kerry Mitchell 11may98 ; originally conic-near_juli ; tweaked so user can directly input ; julia parameters (p4) originally hardcoded ; to 0,1 cc=p4, zc=pixel, maxr=1e12, minr=maxr, iter=1 a=real(p1), b=imag(p1), c=real(p2), d=imag(p2) e=real(p3), f=imag(p3): iter=iter+1, zc=sqr(zc)+cc, x=real(zc), y=imag(zc) conic=|x*(a*x+b)+y*(c*y+d)+e*x*y+f| if (conic<minr) minr=conic end if if ((|zc|>maxr)||(iter==maxit)) iter=-1 t=log(minr) z=cos(t)+flip(sin(t)) end if iter>0 } Roger Alexander

1 0

FOTD 04-11-10 (Seahorse Games [7])
by Jim Muth 04 Nov '10

04 Nov '10

FOTD -- November 04, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image keeps us in Seahorse Valley. The image is centered on the real(X) axis, just west of the valley itself. The orientation of the slice is double rotated 5 and 5 degrees from the actual Julia direction, which is close enough that the outer shape of the Julia set of Seahorse Valley can clearly be recognized. The multi-colored arms thrusting into the outer Julia shape from the sides are part of the Mandelbrot aspect of Seahorse Valley. The open upper half of the fractal is part of the main period-2 Mandelbrot bud; the lower half is part of the main bay. The colorful decorations are stuff that mostly lies in the perturbed Mandelbrot sets. Due to its fancy colors, I rated the image at a 7. The name "Seahorse Games" was inspired by the colorful trimmings, such as might be seen at a birthday party. The calculation time of 14 seconds is a real bargain. The trip to view the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> is equally brief, and more convenient than running the included parameter file. Wednesday began with fog here at Fractal Central, but by 10am the fog cleared off, leading to a day with total sun, just what the fractal cats needed to keep them happy. The temperature rose from a sunrise 28F -2C until it reached a very typical 54F 12C in mid-afternoon. My day was average, which is pleasant enough but leaves little to discuss. FL had a similar day. The next FOTD, a trip to a different part of the Julibrot, will be posted in 24 hours. Until then, take care, and who's behind those wacko conspiracy theories that the radiation emitted by cell phones is unsafe? If the phones were unsafe, the phone companies would be warning us, just like the tobacco companies warned us about the dangers of smoking cigarettes. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Seahorse_Games { ; time=0:00:14.77-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=0/-0.025052/0.85034 params=85/0/85/90/\ -0.764/0/0/0 float=y maxiter=2500 inside=0 logmap=yes symmetry=yaxis periodicity=6 colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\ OziPygQxeRwcSvaTu_UtYVqWWnUXkSYiQZfOZcMYaKXZIWWGVU\ EURCTOASM8RJ6QG4PE5OF5NF5MF5LF5KG5KG5KG5KG6KH6KH6K\ H6KH6KI6KI6KI6KI8KH9KGALGBNFDQEESEFUDGWDIZCJ`BKbBL\ dAMfAQbET_IWXMZUQbQTeNXhK`kHdnEgoFfoFepFdpGdqGcqGb\ rGarHasH`sH_sH_uL`vO`wR`xVayYaz`asaYlaUebRZbNScKLc\ GEdD7d91d5AdFFdPKeZUeccehmfhlfdiecfdbcca`b`Za_W`ZT\ _YQZWNYVLXUIWTFVSCUR9TQ7TPEXOL`OSdNZgNcdRMlCOpDMlC\ LiCMfCNcCO`CPYBQVBSSBUPBWMBYJB_GAaDAcAAc7Ac4Ac1Ac3\ Cc5Dc6Ec8Fc9HcBIZCJUEKPFMKHNFIOAKP5MR3NS3PT3QU3SW3\ TX4VY4W`4Yc4Zh4`m4ar4cv4ez4fz5iz5jz5lz5nz5oz5oz5pz\ 5pz5pz3qz5qz6qz8rz9rzBrzCszDszFszGtzItzJtzKuzMuzNu\ zPvzQvzSvzTwzUwzWwzXwzZwz_wz_wzawzbwzcwzdwzewzfwzh\ wziwzjwzkwzlwzmwzowzpwzqwzqwzqwzqwzqwzrwzrwzrwzrwz\ rwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrwzrw\ zrwzrwzrwzrwzrwzrwzrwzrwz } 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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Spirals of Threads
by Roger Alexander 03 Nov '10

03 Nov '10

Today's post uses a formula using a Julia iteration loop producing a spirals of threads design. Ready made at http://maxitersfractalfollies.blogspot.com Spirals of Threads { ; fract492.gif ; blank ; calctime 0:06:08.77 ; created Nov 02, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=km_10 center-mag=-0.550248/0.349382/6.884776 params=0.1263771477401044/0.1877803888058107/-0.8391064180425428/0.67070\ 52827539903/0.1497543259987182/0.7999206518753624/-0.749626148258919/0.7\ 06839197973571 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=000000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } frm: km_10 { ; Kerry Mitchell 11may98 ; originally conic-near_juli ; tweaked so user can directly input ; julia parameters (p4) originally hardcoded ; to 0,1 cc=p4, zc=pixel, maxr=1e12, minr=maxr, iter=1 a=real(p1), b=imag(p1), c=real(p2), d=imag(p2) e=real(p3), f=imag(p3): iter=iter+1, zc=sqr(zc)+cc, x=real(zc), y=imag(zc) conic=|x*(a*x+b)+y*(c*y+d)+e*x*y+f| if (conic<minr) minr=conic end if if ((|zc|>maxr)||(iter==maxit)) iter=-1 t=log(minr) z=cos(t)+flip(sin(t)) end if iter>0 } Roger Alexander

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FOTD 03-11-10 (Valley of Surprise [5])
by Jim Muth 02 Nov '10

02 Nov '10

FOTD -- November 03, 2010 (Rating 5) Fractal visionaries and enthusiasts: Today we enjoy another image from the Z^2+C Julibrot. The image would normally have been discarded as soon as it appeared, but November is the month of salvation for questionable images from the Julibrot, so I decided to give today's image a chance to show its stuff, or its lack of stuff. The rating of a 5 is right in the middle of the rating scale, which ranges from zero to ten. This leaves it to the individual fractal fan to decide whether the 2-1/3 minute calculation time would be worth the effort. The scene lies in the Seahorse Valley complex of the Julibrot. I have totally lost track of the location and orientation, and of the amount of stretching and skewing I did on the scene, but in the end, I was left with an image of a debris-filled hole with a brilliant white stripe in the background, which on the surface has no resemblance at all to anything normally connected to Seahorse Valley. The name "Valley of Surprise" has something to do with the first impression of the image. If one looks closely enough, however, they will see tiny hints of seahorse activity every- where. Finally, the 2-1/3 minute wait for the image to calculate may be avoided by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> The total sun here at Fractal Central on Tuesday was spoiled by a morning temperature of only 23F -5C and an afternoon high of 48F +9C. The fractal cats, who spent the day in the indoor temperature of 68F 20C fully enjoyed the sun however. My day was average. The next FOTD will be posted in 24 hours. Until then, take care, stay alert, and prepare for a bombshell. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Valley_of_Surprise { ; time=0:02:19.88-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=-0.512268272656399/+0.0732312476231547/\ 164.2885/5.3623/13.0817225561897121/65.54874842\ 92186195 params=0/0/90/0/-0.76/0/0/0 float=y maxiter=15000 inside=255 logmap=142 periodicity=6 colors=000dWteXsfXqgYohZmi_kj`ikaglbfmbencdodcpebq\ farg`sg`sf_sfZsfZsfYsfXrfXqfWpfWocXn`YmZZlX_kW`jUa\ iSbhScgQdfPeeNfcLgaJh_GiYEjWBkV7nU9lTBjSChREfQFdPG\ bOH`NIXMIXLJVKKTJLRIMPHNNHPLIRJJSHKTFKUDKVBKW9KX7M\ X5OX2QX4SX5UW7SW8QWAOWBMXDKXEIWGGVHEUIDTKCSLCSNCRO\ AQQ9PR7PT6PU2SU5RV8RVBQWEPWHNXKMXNLYQKYTIZWHZZH_ZI\ _ZJ_ZKQZLH_MJ`NKaOLcPMdQNeROfSPhTQiURjVSlWTmUUnUVo\ UWpUXpUYoUZmUYkUXiUWgUVeUUcUTaUS_URYUQWVPVVOUVNTUM\ STLRTKQTJPTIOUHNUGMUFLVEKVDJVCKXBKYAKZ9KZ8KZ7KY6KX\ 7KW7LX8LX8LX9LX9LYALYALYALZBL`BMaCMbCMcDMdDMdEMdEM\ dFMeFMeGNeGNeGNfHNfHNfINfINgJNgJNgKOgKOhLOhLOhMOhM\ OiMOiNOiNOiOPjOPjPPjPPjQPkQPkRPkRjzzczzczzczzczzcz\ zczzczzezzdzzdzzczzczzbzzbzzazzazz`zz_zz_zzZzzZzzY\ zzYzzXzzXzzWzzWzzVzzVzzUzzUzzTzzTzzSzzRzzRzzQzzQzz\ PzzPzzOzzOzzNzzNzzMzzMzzLzzLzzKzzJzzJzzIzzIzzHzzHz\ zGzzGzzFzzFzzEzzEzzDzzuzz } frm:SliceJulibrot2 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 02-11-10 (An Undefined Mini [7])
by Jim Muth 02 Nov '10

02 Nov '10

FOTD -- November 02, 2010 (Rating 7) Fractal visionaries and enthusiasts: In my fractal explorations I constantly find interesting and unexpected slices of the Julibrot. Usually I discard these almost as soon as I find them, but now I have decided to make November the month of unexpected slices of the Z^2+C Julibrot, which is the abstract four-dimensional monster that holds the Mandelbrot set as well as all the perturbed Mandelbrot sets and all the Julia sets. Yesterday's image was the first of these slices. At first glance, today's image appears to be a Julia set of Seahorse Valley. But it is not. Seahorse Valley Julia sets have either XY-axis symmetry or origin symmetry. The mini-thing in today's scene has X-axis symmetry, something that is impossible for a Julia set to have. The reason is that it is not a mini-Julia set, it is an Oblate set corresponding to the Seahorse Valley of the large minibrot on the main spike of the Mandelbrot set. The scene of the image is off to the side of the valley in the real(Z) direction at a distance of 0.5477. The entire image has been stretched about 2-3/4 times in the horizontal direction to bring it into what is considered normal relative dimensions. The brilliant line through the center of the image is actually the narrow space between an extension in the real(Z) direction of the two branches of Seahorse Valley of the large minibrot on the main spike of the M-set I put more coloring effort into the image than it deserves, but the effort raises the worth a full point from 6 to 7. The name "An Undefined Mini" means that, as far as I know, there is no generally accepted name for the type of object that appears in today's image. So maybe I'll invent a name. The calculation time of 2 minutes is about what the image is worth. A bargain may be found on the FOTD web site at: <http://www.Nahee.com/FOTD/> where the finished image is posted for near-instant viewing, and if not total, then at least partial satisfaction. The air remained chilly here at Fractal Central on Monday, with a high temperature of only 46F +8C, but the sky was clear and the sun shone strong on the fractal cats' window shelf most all day, keeping them happy as two bedbugs in a flophouse mattress. My day was about average. The next FOTD will be another unexpected slice of the Z^2+C Julibrot. It will be posted in 24 hours, give or take a few. Until then, take care, and our world might be a better place without religion, but what would we replace it with? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= An_Undefined_Mini { ; time=0:02:12.52-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=-0.\ 00030581/0/269/2.763 params=0/0/90/0/-1.7685291540\ 2387/0/0.5477/0/2/0 float=y maxiter=120000 inside=255 logmap=12 symmetry=xaxis periodicity=6 colors=0007Wb7Wc7Vc7Vc7Vc7Ud7Ud7Ud7Ud9VeAVeBVfCWfE\ WgFWgGWhHXhIXiKXiLYjMYjNYjOYkQZkRZlSZlT_mU_mW_nX_n\ Y`oZ`o_`paapbapcaqdbqecrgdrhesifsjgtkhtmiunjuokvpl\ vqmvrmsrmprmnrmkrmirlfrkdsjasiZshXsgUsfSsePseNseKt\ eHteFteCueAve7we5xe2ye0zd0yd0xc0wc0vb0ub0ta0sa0r`0\ q`0p_0o_0nZ0mZ0lY0kY0jX0iX0iW0hW0gV0fV0eU0dU0cT0bT\ 0bS0aS0aS0`R0_R0_Q0_Q0ZP0_P0ZO0ZO0ZN0ZN0YM0ZM0YL0X\ L0XK0WK0UK0TK0TJ0RJ0RI0QI0QH0PH0PG0OG0NG0OF0NE0NE0\ MD0LD0LC0KC0JB0JB0IA0HA0H90G90F80F80E70E70E60E60E5\ 0E50E40E40F30F30F20E20D10C10B00A00A03A06A09A0CA0DA\ 0EA0EB4HC8KDCMEGOFKRGOTHSVIWYJ__KcaLgYNgVPgSRgPTgM\ VfJXfGZfD`fAaf7`eN`db`cq_boZbmYblXbjWbhVbgUbeTacSa\ bRa`QaZRaYSaWTaUUaTV`RW`PX`OY`MZ`K_`J``Ha_Fb_Ec_Ce\ _Ag_9i_7k_5m_4oZ5qZ5sY5uY6wX6xX6yW6zW7yV7xV7wU7wU8\ wT8wT8wT8wV7wW7wX7wZ7w_6w`6wa6wc6wd5we5xf5xh5xi5yj\ 4yl4ym4zn4zo3zq3zr3zs3zt3 } frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Devil Fractal
by Roger Alexander 01 Nov '10

01 Nov '10

Behold a fractal devil. Actually that's the name of the formula, the same one used in the Oct. 2 post. I zoomed in one of the lobes, rotated 90 degrees giving the image a portrait orientation and re-sized. The rotating of the image takes it from simple anti-aliasing to the level of post-processing. To everybody this blogs first post-processed fractal! Go to http://maxitersfractalfollies.blogspot.com for instant gratification. Halloween Devil { ;fract495.gif ; blank ; calctime 0:07:22.81 ; created Oct 31, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=_d.frm formulaname=devil passes=1 center-mag=0.738924/3.33067e-016/3.908693 float=y maxiter=1500 inside=0 colors=000000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } frm:devil {; Copyright (c) Paul W. Carlson, 1998 ; Based on one of Noel Giffin's formulas w = pixel z = iter = wp1 = wp2 = bailout = 0 : old_w = w w = w * w - wp2 wp2 = wp1 wp1 = real(old_w) - flip(imag(old_w)) IF (|w| > 4) bailout = 1 z = 4 * iter + 30 z = z - real(216) * trunc(z / real(216)) ENDIF iter = iter + 1 z = z - iter bailout == 0 ;SOURCE: 98msg.frm } Roger Alexander

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Halloween Minibrot
by Roger Alexander 01 Nov '10

01 Nov '10

A minibrot in Halloween colors. According to Wikipedia "Black and orange are the traditional Halloween colors and represent the darkness of night and the color of bonfires, autumn leaves, and jack-o'-lanterns" Gif and re-sampled jpg. At the usual http://maxitersfractalfollies.blogspot.com Halloween Colors { ; fract493.gif ; blank ; calctime 0:01:56.33 ; created Oct 31, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=mandel center-mag=-0.04428222277847312/-0.98332827545909710/508323.8/1/170.0000\ 00000846683/-9.35095410825592666e-010 params=0/0 float=y maxiter=2300 inside=0 logmap=163 colors=00000000000000000000000000000000000000000000000000000000100100100\ 100100100100100100100100100100100100100100100200200200200200200200200200\ 200200200200200200200200200300300300300300300300300300300300300300300300\ 300300300400400400400400400400400400400400400400400400400400400500500500\ 500500500500500500500500500500500500500500500600600600600600600600600600\ 600600600600600600600600600700700700700700700700700700700700700700700700\ 7007008KF0OG0SI0WK0_M0cO0gQ0kS0kS0kS0kS0lT0lT0lT0mU0mU0mU0nV0nV0nV0oW0oW\ 0oW0pX0pX0pX0pX0qY0qY0qY0rZ0rZ0rZ0s_0s_0s_0t`0t`0t`0ua0ua0ua0ua0vb0vb0vb\ 0wc0wc0wc0oW0oW0oW0oW0ye0ye0zf0zf0zf0zf0ye0ye0ye0xd0xd0xd0wc0wc0wc0vb0vb\ 0vb0ua0ua0ua0ua0t`0t`0t`0s_0s_0s_0rZ0rZ0rZ0qY0qY0qY0pX0pX0pX0pX0oW0oW0oW\ 0nV0nV0nV0mU0mU0mU0lT0lT0lT0kS0gQ0cO0_M0WK0SI0OG0KF0000 } Roger Alexander

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FOTD 01-11-10 (Maximum Credulity [No Rating])
by Jim Muth 01 Nov '10

01 Nov '10

FOTD -- November 01, 2010 (No Rating) Fractal visionaries and enthusiasts: Today's image was created in the same manner as the image of three days ago -- the `Offside' image of October 29 -- though instead of going off from the center of the period-2 bud in the Rectangular direction, we go off in the other perpendicular direction, the Oblate, until we reach the edge of the Julibrot. By some very curious coincidence, in this direction the Julibrot ends on the real(Z) axis at a distance of plus and minus 1.61803...., which strangely enough is the golden ratio. Since today's image was created in the same manner as the earlier image and is a virtual repeat, I declined to give it a rating. The name "Maximum Credulity" came to mind Sunday after- noon while I was watching a skeptical show about the existence (read non-existence) of the supernatural. Perhaps the best feature of today's image is its fireball-fast calculation time of 5-1/2 seconds, which guarantees that virtually no time will have been wasted if the image fails to inspire awe and wonder for natural numbers. Viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> will involve no wishful thinking, and will also guarantee that no time will be wasted if a let-down happens. Blustery conditions, accompanied by dark wind-shredded clouds and a temperature of 54F 12C made Sunday a typical autumn day here at Fractal Central in central Pennsylvania. The fractal cats had their thrill when a pigeon landed on the outside of their lookout window, only inches from Nicholas' hungry jaws. But as soon as Nicholas made his move, the pigeon flew away, leaving Cassie to wonder what all the tail thrashing was about. My day was average, even though the FOTD turned out to be below average. The next FOTD, an improved one to be sure, will be posted in 24 hours. Until then, take care, and only the credu- lous believe in ghosts. Since I do believe in ghosts, I guess that makes me credulous as well as superstitious. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Maximum_Credulity { ; time=0:00:05.32-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=+0.000039265\ 06831894/0/176501/0.0009777 params=0/0/-24.095/0/-\ 1/0/1.61803/0/2/0 float=y maxiter=1500 inside=bof61 periodicity=6 colors=0004_q3Rc2IR19DCAv65TdBXR7MD3BJdO9KC00Z00W0\ 0S01O02L03I04F059066084m61scXmL`zAI0CkBne5PL4CzyZf\ VHL6EC498244otQYaHHJ8RGBKC8D856428qmUjdKVRAFDs_IeR\ DSI9E94h_tUOaFCJG7sC5e83S41EES77E36Bj47V23Fw7Iw2RT\ xmLh`EUP7FCeakSPWECGZW`QORHGI889hZJCE08904407cZ5UQ\ 3KH1A8LM9FG6AB4552s8b`5QI2DEq27R1HKaK_DDO86C4UDcM9\ UF6K73AyS34LR3FK2AD156_rlIRO2ab1ST1JJ099Q7tD3SQPXA\ 3Y72P51H208_jivj5bV3JF16`94O62C3zPjjIZVCNF6BOEr8LZ\ enLLPAd33U22K11A00w2`h1RU1IF09pWbH1dLQOEHG788o4vY2\ bH1Jqlnc_aROPDCCZm4HP2hTqTKNLFHEAB755txleh_SUOEFCX\ XxGGUlCa_9SO6JC39AT`6JO39CTY8EH4TtrESRiwgs2Pf4NW3H\ L2BA15iGNYCHN8BB45smze`jSPVECF80fKkNJoTHsZGvdCic8X\ b4Ka18aG7XV6Si5Nx5IpMRia_bqgjeeqUcxIatOSpUIm_8fL1S\ D2E537yk4dW2KGAkv6Wb3GJBHy7Bd35K4tNRooDQQE9KTwXLhO\ EUG7F8uMbTBJAum5TPaDbJ6JLrdARKUwEKc9AK4v3xg2hT1UE0\ FZypNdZBKHx8XU4GLqfE_S7IE } frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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FOTD 31-10-10 (Shadow of the Wind [6])
by Jim Muth 31 Oct '10

31 Oct '10

FOTD -- October 31, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's rather harmless image lies in a valley of the fractal that results when various negative parts of Z^(-4.5) and Z(-1.7) are mixed together and (1/C) is added. Like most fractals of this double-negative type, this parent fractal cannot be des- cribed, though it may easily be seen by backing out of today's image. I rated the image at a 6. I searched for something to justify a higher rating, but nothing is there. The name "Shadow of the Wind" has nothing to do with an old radio hero who could make himself invisible. It's simply a phrase that came to mind from apparently nowhere. The calculation time of 9 minutes means that the time required to run the parameter file is more than the resulting image is worth. The problem may be eliminated by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Too many clouds and a temperature of 54F 12C kept the fractal cats suppressed here at Fractal Central on Saturday. My day was relaxing enough, though for some reason the Halloween trick-or- treaters were out one evening early. The next FOTD will be posted in 24 hours. Until then, take care, and if a spook spooks you, spook him back. (They do exist, you know. Whether they are real is another question.) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Shadow_of_the_Wind { ; time=0:09:02.88-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+0.56620315067701/+0.03728036351951/\ 8.3e+009/1/2.5/0 params=-0.6/-4.5/-3.6/-1.7/0/0/0/0 maxiter=10000 inside=0 logmap=1140 periodicity=6 colors=000HChCAkF7mE5oE3qD4oD5nC6mC7kB8jB9iAAgABf9\ Ce9Cd9Db8Ea8F`7GZ7GY6IX6JVCHU5LT5LSFHU8JVAIWHGYDGZ\ EF_JEaHDbJCcMBeLBfNAgP9iQ8jR7kS6mU5nW4oQ3kZ2r_1sN3\ iU2mO3gI3aC4V65P05JA7EJ8ASA5`B1bD2cF3dH4fJ5gL6hN7i\ P8kR9lTAmVBnXCpZDq`ErbFsdGufHvhIwjJxkKuiLrgMoeNlcO\ iaPf_QcYR`XRYVSVTTSRUPPVMNWJLXGJYDIYDIdDIkDIrAXm7k\ h4zdCqcJhcQ_bXRbcIaj9aq1ao3`n4_m5_k6Zj7Zi8Yh9XfAXe\ BWdCWcDVaEV`FU_GTZHTXISWJSVKRULRTMQTMQTNP1BF19G8CI\ EEKKGMQIOXKQbMShOUnQVlTWjVWhXWf_WdaWccWdeTefQfhNgi\ LhkIilFjnCkoAbf8VY6MQ4EH26905EA4JK4NU3Sc2Xm2`w4Xr6\ Un7Ri9OeBKaCHXEETFBPEJXDRcDYjLdXSkJEU8KTBPSEVRH_RK\ Vw8RvANvCJuDFuFBuG9qP8mY7if6eoRShkEacH_XKYQNWJQUCT\ S5WR6YX6Zb6_g6`m6arKVhXPZiIPvCGsSGqfGouGgqN`nUTk`M\ ggEdn7au5dm3fe1hY0jQEfTRcWd`ZqY`y8FtIMoRTfYZYddPki\ Gzo8ztAzmBzfCz_DzTEzMFzFBzQ8z_5zi2zsKzr`zrqzrmzliz\ ffz`bzVZzPWzK1zB1zC1zD1zE } 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, esc=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < esc } END PARAMETER FILE=========================================

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Plant Scales
by Roger Alexander 30 Oct '10

30 Oct '10

I let my imagination run wild when I generated today's post and I thought I saw scales on a plant. The Oct. 28 post (Swirly Wallpaper) formula with different parameters. Ready made at http://maxitersfractalfollies.blogspot.com Green Scales { ; fract491.gif ; blank ; calctime 0:00:42.19 ; created Oct 29, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=LKM-quiltm2 function=cos/cosxx center-mag=-0.899274/-0.684337/0.3272439/1/180 params=1.75/-0.875/0.375/-0.375 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=0F00F00F00F00F00G00G00G00G00H00H00H00H00H00I00I00I00I00J00J00J00J\ 00J00K00K00K00K00L00L00L00L00L00M00M00M00M00N00N00N00N00O00O00O00O00O00P\ 00P00P00P00Q00Q00Q00Q00Q00R00R00R00R00S00S00S00S00S00T00T00T00T00U00U00U\ 00U00U00V00V00V00V00W00W00W00W00X00X00X00X00X00Y00Y00Y00Y00Z00Z00Z00Z00Z\ 00_00_00_00_00`00`00`00`00`00a00a00a00a00b00b00b00b00b00c00c00c00c00d00d\ 00d00d00e00e00e00e01e01e01e02e02f02f03f03f03f04f04g05g05g05g06g06g06g07h\ 07h07h08h08h08h09i09i0Ai0Ai0Ai0Bi0Bj0Bj0Cj0Cj0Cj0Dj0Dj0Dk0Ek0Ek0Fk0Fk0Fk\ 0Gl0Gl0Gl0Hl0Hl0Hl0Il0Im0Im0Jm0Jm0Km0Km0Kn0Ln0Ln0Ln0Mn0Mn0Mo0No0No0No0Oo\ 0Oo0Po0Pp0Pp0Qp0Qp0Qp0Rp0Rq0Rq0Sq0Sq0Tq0Tq0Tr0Ur0Ur0Ur0Vr0Vr0Vr0Ws0Ws0Ws\ 0Xs0Xs0Ys0Yt0Yt0Zt0Zt0Zt0_t0_t0_u0`u0`u0`u0au0au0bv0bv0bv0cv0cv0cv0dw0dw\ 0dw0ew0ew0ew0fw0fx0gx0gx0gx0hx0hx0hy0iy0iy0iy0jy0jy0kz0 } frm:LKM-quiltm2 {; Kerry Mitchell ; quilted backgrounds ; uses 2 iterations of 2 mandelbrot variables with different c's ; c1 and c2 are tiled periodically, with different frequencies ; z1 & z2 are multiplied together to add their angles ; use "decomp=256" coloring ; r=bailout=0 for swirly exteriors and no interiors ; real(p1), imag(p1) = x1, y1 frequencies for c1 ; real(p2), imag(p2) = x2, y2 frequencies for c2 ; try different fn1 and fn2 for added joy x=real(pixel), y=imag(pixel) a1=pi*real(p1), b1=pi*imag(p1) a2=pi*real(p2), b2=pi*imag(p2) x1=2*cos(a1*x), y1=2*cos(b1*y) x2=2*sin(a2*x), y2=2*sin(b2*y) c1=x1+flip(y1), c2=x2+flip(y2) z1=c1, z2=c2, r=0: z1=sqr(z1)+c1, z2=sqr(z2)+c2 z=fn1(z1)*fn2(z2) |z| < r ;SOURCE: lkm.frm } Roger Alexander

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FOTD 30-10-10 (Reciprocal World [6])
by Jim Muth 30 Oct '10

30 Oct '10

FOTD -- October 30, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image is an afterthought. On Friday I was exploring the (-Z)^(1.5)+C Mandeloid, with no thought of finding a FOTD there, but when I stumbled upon today's image, it struck me as so unusual that I decided to declare it FOTD for October 30. Actually, what we have here is a scene in the Mandeloid that results when the formula is iterated with Z initialized at -0.5. I named the image "Reciprocal World" because of the apparent negative curvature of the surface at the bottom of the frame. If this were a real planet, it would be in the shape of a pseudo- sphere. The rating of a 6 makes the 4-1/2 minute calculation time barely worth the effort. I recommend viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Friday turned blustery here at Fractal Central, with alternating periods of sun and heavy clouds, and even a few light showers. The temperature of 48F +9C was too chilly for the fractal cats, who grew tired of watching the blowing leaves and spent most of the day sleeping near the heat or asking for their treats. My day was slightly busy, but nothing to get excited about. The next FOTD is due to be posted in 24 hours. But if an unexpected antiquing trip comes up on Saturday, it could be dalayed how- ever. Until whenever, take care, and be filled with wonder. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Reciprocal_World { ; time=0:04:26.88-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=1 float=y center-mag=-0.0079014/+0.7369293/90/1/-72.5/0 params=0/0/0/0/0/0/-0.5/0/1.5/0 maxiter=24000 inside=0 logmap=-120 colors=000KAHKAIKAJKAKKALKBMKCNJDOIENHFMGGLFHKEIKD\ IJCIIBIHCIHAIIDHJEGKEFLFEMFEMHFNJFNLGQNHUPKZRMcSOh\ UQmWSrYUv_VzaWzbWzdWzfXzhXzjXzlXzmXzlYzlZzl_zk`zka\ zkbzkczjdzjezjfzifzigzihziizhjzhkzhlzgmzgnzgozgozh\ pzipzipzjpzkqzkqzlqzmqzmrznrzorzorzpszqszqszrszztz\ ztzztzztzzuzzuzzuzzuzzpzzkzzfzzazzYzzXzzWzzWzzVzzV\ zzUzzTzzTzzSzzSzzRzzQzzQzzPzzPzzOzzNzzNzzMzzMzzLzz\ LzzJzzHzzFzzEzzEzzEzzEzzEzzEzzEzzAzzEzzHzzKzzOzzRz\ zUzzYzz`zzczzgzzjzzmzzqzzszzrzzpzzozznzdmzekzfjzfi\ zggzgfzheziczibzjazj`zkZzlYzlXzmVzmUznTznSzlUzkVzj\ XziYzhZzg`zfazebzddzcezbfzahz`iz_jzZlzYmzXnzWpzVqz\ UrzSqzRqzPpzOpzNozLozKnzJnzHmzGmzFlzDlzCkzBkz9jz8j\ z6kz7jz8jz8jz9jzAjzAizBizCizCizDizEhzEhzFhzGhzGhzH\ hzIgzIgzJgzKgzKgzLfzMfzMfzNfzOfzOfzPfzPgzQgzQgzHdz\ QgzZjzgmzppzxszxqzxpzxnzxmzxkzxjzxhzxgzxfzxdzxczxa\ zx`zxZzxYzxXzuYzsYzqYznYz } frm:SliceJulibrot5 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Swirly Wallpaper
by Roger Alexander 29 Oct '10

29 Oct '10

A Fractint generated fractal with nary a minibrot in sight! Fractint - a little something for everybody. And for those who the whole point of the internet is clicking on links for instant satisfaction try http://maxitersfractalfollies.blogspot.com Swirly Wallpaper { ; fract486.gif ; blank ; calctime 0:00:41.91 ; created Oct 28, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=LKM-quiltm2 function=tan/sinh center-mag=1.33227e-015/-4.44089e-016/0.4644958 params=0.1115146336252937/0.4293343913083285/1.394390697958312/1.4464552\ 75124363 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=05F05F05F16G16G16G16G16G27H27H27H27H27H38I38I38I38I38I49J49J49J49\ J49J5AK5AK5AK5AK5AK6BL6BL6BL6BL7CM7CM7CM7CM7CM8DN8DN8DN8DN8DN9EO9EO9EO9E\ O9EOAFPAFPAFPAFPAFPBGQBGQBGQBGQBGQCHRCHRCHRCHRCHRDISDISDISDISDISEISEJTFJ\ TFKTGKUGLUHLVHMVIMVINWJNWJOWKOXKPXLPYLQYMQYMRZNRZNSZOS_OT_PT_PT`QU`QUaRV\ aRVaSWbSWbTXbTXcUYcUYcVZdVZdW_eW_eX`eX`fYafYafZbgZbg_ch_ch`ch`diadiaeibe\ jbfjcfjcgkdgkdhlehleilfimfjmgjmgknhknhlniloimojmpjmpknpknqloqloqmprmprnq\ snqsorsortpstpstqtuqturuuruvsvvsvwtwwtwwuxxuxxuxxvyyvyywzzvyyvyyuxxtxxtw\ wsvwsvvruvquuqtupstostorsnqsnqrmprlpqloqknpjnpjmoimohlnhkngkmgjmfjleileh\ kdhkcgjcfjbfibeiaeh`dh`cg_cgZbfZbfYaeX`eX`dW_dW_cVZcUYbUYbTXaSWaSW`RV`RV\ _QU_PTZPTZOSYNSYNRXMQXLQWLPWKPVKOVJNUINUIMTHLTGLSGKSFKRFJREIQDIQDHPCHPBG\ OBFOAFN9EN9EM8DM8CL7CL6BK6AK5AJ49J49I38I37H27H16G16G05F } frm:LKM-quiltm2 {; Kerry Mitchell ; quilted backgrounds ; uses 2 iterations of 2 mandelbrot variables with different c's ; c1 and c2 are tiled periodically, with different frequencies ; z1 & z2 are multiplied together to add their angles ; use "decomp=256" coloring ; r=bailout=0 for swirly exteriors and no interiors ; real(p1), imag(p1) = x1, y1 frequencies for c1 ; real(p2), imag(p2) = x2, y2 frequencies for c2 ; try different fn1 and fn2 for added joy x=real(pixel), y=imag(pixel) a1=pi*real(p1), b1=pi*imag(p1) a2=pi*real(p2), b2=pi*imag(p2) x1=2*cos(a1*x), y1=2*cos(b1*y) x2=2*sin(a2*x), y2=2*sin(b2*y) c1=x1+flip(y1), c2=x2+flip(y2) z1=c1, z2=c2, r=0: z1=sqr(z1)+c1, z2=sqr(z2)+c2 z=fn1(z1)*fn2(z2) |z| < r ;SOURCE: lkm.frm } Roger Alexander

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FOTD 29-10-10 (Offside [6])
by Jim Muth 29 Oct '10

29 Oct '10

FOTD -- October 29, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's scene lies off to the side of the large period-2 bud of the Mandelbrot set at an angle of 90 degrees. But since there is a complete 360-degree circle of lines in the Julibrot perpen- dicular to the M-set, we must be more specific. Today's image lies in the direction of the imag(Z) axis, and is centered at the point 0.78615 on that axis. The image is not a perturbed Mandelbrot set. It is rotated at an angle of -19.37 degrees from the Mandelbrot orientation, the angle at which it is tangent to the edge of the Julibrot in the Elliptic orientation. When rendered in the conventional manner, today's image is a rather boring fractal. The Fractint program cures this monotony with its various inside and outside fills. I rendered today's image with the outside set to 'real' and the inside set to 'bof61'. I could rate the image no higher than a 6. It has too much program magic and not enough true fractal stuff for any higher rating. I named the scene "Offside" because it lies off to the side of the large bud on the main stem of the M-set. The calculation time of under 6 seconds is brief enough to hold disappointment at bay if the resulting image is seen as lacking. The easiest way to view the image is to visit the FOTD web site at: <http://www.Nahee.com/FOTD/> where it is posted already calculated and ready to be appreciated at leisure. With a temperature of 68F 20C and sunny skies, Thursday was pleasant enough here at New Fractal Central, though the wind was a bit too blustery for absolute comfort. The fractal cats spent most of their time in the window, watching occasional flurries of leaves that fluttered past on the gusts. My day was uneventful; FL's day was the same. The next FOTD will be posted in 24 hours. Until then, take care, and a month ago my broker told me I could make a pile in the guano market, but I must have done something wrong because I dropped a load. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Offside { ; time=0:00:05.59-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/-0.0000596\ 847054883/272487.8/0.0009874/90/0 params=-19.37/0/\ 0/90/-1/0/0/0.78615/2/0 symmetry=none inside=bof61 float=y outside=real maxiter=1500 periodicity=6 colors=000WuVTtYQt`NtcKsfHsiEskDGyCleAe_8ZU7SO5LIz\ uCzr6xoJrfFhYCXQ9QH6J83d38Y26R25K14D126mzNRzI`mDS`\ 9IP49CTnyPwzLaiIVaEPVAJN7CF367eJdaidU_WMROFIG798Zt\ DNa8BJ4I1cF0YC0SA0M70H50B205AWz8Sr7Oj6Kb5GV3CN28F1\ 47I1OueoaSYJEHhVxaQoWMfPHYJDQC8H648IP3EK2AF17A1350\ YO9MG6B834Xw2Mc1BKcUIGoqYFkYYxTTpPPhLLaHHUCCM88F44\ 7iswWtbGSJeMyRkOLaJGSEAJ9594Lg4AM2bQcXMYRISMEMiTWi\ QXgS_`_m`Zn`Yo`Xn`Wm_VkYUiVRfTQbQO_cMWmPhzWHyVHzbI\ v`IrbImeJhhJcjJZlIUnHPpGRrFYtEcuEanL`hSZaZYWdRRYLN\ RFIK9EDHJHPOLXTPdYTlaX_bONcFAd69c58b47a42SF8SNDSVB\ OQ9KM7GH5CD388144CIR5_e4SX3LP2EG178XorShkObdKWYGQR\ CJK8DD466cdpUUbKKQAADJlUE_M9OF4C7PT8IL6CE46721Q30L\ 20H20D1081040gF_ZCSQ9LH6E837ZZtQQeHHS88ETs9Oi7J`6E\ S49I3491sNGgICXD9M96B43nRdPDKMSLGLFBEA575B`zip3UZ2\ FH15OC3G8184hKHUDBF65cKveQrgWnhajbYeYVaSSYNPUHLQCI\ M6FI1CE9MHHVJOdLWmNbvPZuS } frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Spheres Within Spheres
by Roger Alexander 28 Oct '10

28 Oct '10

Today's fractal is from Fractint's built in formula fn(z*z). The design is of spheres within spheres colored in blue and cyan. Ready made at http://maxitersfractalfollies.blogspot.com Cyan Spheres { ;fract487.gif ; blank ; calctime 0:00:31.09 ; created Oct 28, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=fn(z*z) function=log center-mag=1.56626/-0.0173035/0.7732086/1.0031/90/3.88578058618804789e-0\ 16 maxiter=3000 inside=0 outside=atan cyclerange=0/255 colors=hzzgzzfzzezzdzzczzbzz`zz_zzZzzYzzXzzWzzVzzTzzSzzRzzQzzPzzOzzMzzLz\ zKzzJzzIzzHzzGzzEzzDzzCzzBzzAzz9zz7zz6zz5zz4zz3zz2zz0zz0zz0yz0yz0xz0wz0w\ z0vz0uz0uz0tz0sz0sz0rz0qz0qz0pz0oz0oz0nz0nz0mz0lz0lz0kz0jz0jz0iz0hz0hz0g\ z0fz0fz0ez0dz0dz0cz0bz0bz0az0az0`z0_z0_z0Zz0Yz0Yz0Xz0Wz0Wz0Vz0Uz0Uz0Tz0S\ z0Sz0Rz0Qz0Qz0Pz0Pz0Oz0Nz0Nz0Mz0Lz0Lz0Kz0Jz0Jz0Iz0Hz0Hz0Gz0Fz0Fz0Ez0Dz0D\ z0Cz0Cz0Bz0Az0Az09z08z08z07z06z06z05z04z04z03z02z02z01z00z00z00z00y00y00\ x00x00w00w00v00v00v00u00u00t00t00s00s00r00r00r00q00q00p00p00o00o00n00n00\ n00m00m00l00l00k00k00j00j00j00i00i00h00h00g00g00f00f00f00e00e00d00d00c00\ c00b00b00b00a00a00`00`00_00_00Z00Z00Z00Y00Y00X00X00W00W00V00V00V00U00U00\ T00T00S00S00R00R00R00Q00Q00P00P00O00O00N00N00N00M00M00L00L00K00K00J00J00\ J00I00I00H00H00G00G00F00F00F00E00E00D00D00C00C00B00B00A } Roger Alexander

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FOTD 28-10-10 (Curious Coincidence [No Rating])
by Jim Muth 27 Oct '10

27 Oct '10

FOTD -- October 28, 2010 (No Rating) Fractal visionaries and enthusiasts: Today's image gets no rating. Why? Because it's a virtual repeat of yesterday's image. The difference is that, while yesterday's image was sliced in the Oblate direction, today's is sliced in the Rectangular direction, which consists of the imag(Z) and imag(C) axes of the Julibrot. IMO, what made yesterday's scene so curious is the fact that the fractal terminates on the left and right at values of plus and minus 1.618...., (the golden ratio), while the large valleys meet at plus and minus 0.618...., the reciprocal of the golden ratio). This is curious enough, but when I checked the horizontal terminal points of today's image, I found a value of plus and minus 0.78615.... What an incredible coincidence it is that this is the reciprocal of the square root of the golden ratio. (The two large valleys in today's image meet at plus and minus 0.521555...., though I have yet to find anything significant in this value.) Mathematical interest aside, today's image is simply a variation on yesterday's image, with the same color palette. Those who enjoyed yesterday's will enjoy today's almost as much. Those who thought yesterday's image was boring will be no more impressed by today's. The name "Curious Coincidence" refers to the mathematical aspect of the image. The calculation time of only 3 seconds is mercifully brief. The best way to view the image is to enjoy it already calculated on the FOTD web site at: <http://www.Nahee.com/FOTD/> Wednesday began with clouds here at Fractal Central. But the clouds broke up by midday, leading to a sunny afternoon with a temperature of 72F 22C. These conditions were perfect for the fractal cats, who spent several hours in the sun that streamed in the southwest window. My day was average; FL had a similar day. The next FOTD will be posted in 24 hours, and is likely to be another mathematical curiositiy, though one with far more artistic impact. Until then, take care, and why does the number epsilon equal minus one when it is raised to the power of imag(PI)? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= CuriousCoincidence { ; time=0:00:03.35-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/1.398/1/\ 90/0 params=90/0/0/90/-1/0/0/0/2/0 float=y inside=0 maxiter=300 inside=0 outside=real periodicity=6 colors=000KZzJXwJVsJTpJRmJQjJPgJNeJMbJL`IKYHJVGISF\ HPEGMDFJCDFBBCA8A958GQKJYKMeKPmKUmKZmKcmKhmKmmIrmF\ vmCzjHzhNzeSzcXzbTzaPz`Lz_HzZDzZ9zSCzLFzEHz7Kz1Mz6\ OzAPzFRzJSzNTzSSzXSzaRzfRzhRzjRzlRzmRzoRzqRzrRzzOz\ zLzzIzzFzzKzzOzzTzzXzzVzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Twilight Colors Reprised
by Roger Alexander 27 Oct '10

27 Oct '10

Today's fractal is a remix of my Oct. 24 post. Same formula and palette, different parameters. Like the Oct.24 post ready made at http://maxitersfractalfollies.blogspot.com Twilight Remix { ; fract484.gif ; blank ; calctime 0:17:07.88 ; created Oct 26, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=hermanm_man-polar center-mag=-1.89610111352240000/+0.00222840388810970/9616.574/1/22.49999\ 99999827232/-2.86882184674652763e-011 params=4/2/1/60/3/0 float=y maxiter=1500 inside=0 proximity=1 outside=fmod decomp=256 colors=000302403503504604705805806907A07B08B08C09D1AE1AF1BF1BG1CH1CI1DI1\ EJ1EK1FL1FL1GM1GN1HO2IN2KM2NK2QJ2TH2VG2YE2`D2cB1fA1i81l71n51q41t21w00z03\ z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0jz0nz0rz0vz0zz0xz0vz0tz0rz0pz0nz0lz0jz0h\ z0fz0dz0bz0`z0Zz0Xz0Wz0Uz0Sz0Qz0Oz0Mz0Kz0Iz0Gz0Ez0Cz0Az08z06z04z02z00z00\ y10x20v20u30s40r50p50o61n71l81k91i91hA1gB1eC1dC1bD1aE1_F1ZF1YG1WH1VI1TJ2\ SJ2RK2PL2OM2MM2LN2JO2IM2GJ2EH2CE1AC18916614312000101302503605806A07C19D1\ 9E1AF1AF1BG1BH1CI1DI1DJ1EK1EL1FL1FM1GN1HO2IO2JQ2IS2HV2GX2F_2Da2Cd2Bf2Ah1\ 9k18m17p15r14u13w12z00z20z50z70zA0zC0zF0zH0zK0zM0zP0zR0zU0zX0zZ0za0zc0zf\ 0zh0zk0zm0zp0zr0zu0zw0zz0zw0zu0zr0zo0zl0zj0zg0zd0za0z_0zX0zU0zS0zP0zM0zJ\ 0zH0zE0zB0z80z60z30z00x01v02s03q04n06l07i08g19e1Ab1B`1CY1EW1FT1GR1HO2JN2\ IM2HK2GJ2FH2DG2CE2BD2AB19A18817715514413212000000101201 } frm:hermanm_man-polar { ; Kerry Mitchell 16feb98 ; ; real(p1) = z exponent (use integer >= 2; m=n-1) ; imag(p1) = g exponent (integers) ; real(p2) = alpha magnitude (try 1) ; imag(p2) = alpha polar angle (try integers) ; real(p3) = critical point selector (>0 for positive root) ; imag(p3) = unused (<0 for negative root) ; use decomp=256 ; zero and infinity bailouts hardcoded to 1e-6, 1e6 ; coloring speed hardcoded to 4 ; c=pixel, iter=1, n=real(p1), m=imag(p1), nfac=2*n-1 maxr=1e6, minr=1/maxr, speed=4*pi/128 r=real(p2), t=imag(p2), alpha=r*(cos(t)+flip(sin(t))) oln=1/log(n), fac=log(0.5*log(maxr)) c2=sqr(c), hypnum=sqr(n)+sqr(m), pn=1 hypden=sqr(n-m), hypfac=hypnum/hypden if (real(p3)<0) pn=-1 end if if (real(c2)>hypfac) pn=-pn end if if (imag(c)<0) pn=-pn end if afac=c*n, bfac=c2*(n-m)+(n+m), cfac=c*n d=sqrt(bfac*bfac-4*afac*cfac) z=(bfac+pn*d)/(2*afac) : g=(z-c)/(1-c*z), z=alpha*z^n*g^m iter=iter+1, r=|z| ; ; orbit trap around 0 ; renormalize iteration count via decomp angle ; set "iteration done" flag (iter=-1) ; if (r<minr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed z=cos(angle)+flip(sin(angle)) iter=-1 end if ; ; orbit trap around infinity ; renormalize iteration count via decomp angle ; add pi to angle to separate from 0 orbit trap ; set "iteration done" flag (iter=-1) ; if (r>maxr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed angle=angle+pi z=cos(angle)+flip(sin(angle)) iter=-1 end if iter>0 } Roger Alexander

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FOTD 27-10-10 (A Golden Slice [5])
by Jim Muth 27 Oct '10

27 Oct '10

FOTD -- October 27, 2010 (Rating 7) Fractal visionaries and enthusiasts: The formula behind today's image is Z^2+C, the same formula that creates the Mandelbrot set and all its associated Julia sets. But today's image is obviously not the M-set, nor is it any recognizable Julia set. It is something I call an Oblate set, a hybrid set half-Mandelbrot and half-Julia. The X-axis of the image is the real(Z) axis of the Julibrot, while the Y-axis is the imag(C) axis. The image has a Mandel- brot nature in its vertical direction and a Julia nature in its horizontal direction. The center of the image is the center of the large period-2 bud of the M-set. No shape manipulation such as stretching or skewing was done in the creation of the image, though I did add a bit of life by rendering it with the outside set to 'real'. A most curious relation exists in the location of the elements along the X-axis of the image. The fractal terminates on the left and right at the points plus and minus 1.61803398875.... which of course is the Golden Ratio, while the two major valleys closest to the center meet at plus and minus 0.61803398875.... which is the reciprocal of the Golden Ratio. There must be a logical reason why this is so, though I have not been able to find it. I rated the image at a 7, a good part of which is due to the mathematical interest. Artistically, the image rates a 5 or 6. I named the image "A Golden Slice" because of the appearance of the Golden Ratio in it. Despite all the golden glitter, the image is blazingly fast, finishing on my machine in under 3 seconds, almost as fast as the display can switch to super-VGA mode. The trip to see the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> may not be quite as fast, but it will involve much less set-up work. Rain fell most all Monday night here at Fractal Central. The remaining clouds blocked the sun on Tuesday, but the temperature of 70F 21C was mild enough that the lack of sun was never noticed. The fractal cats spent an hour chasing a mechanical toy mouse we picked up Monday evening. Nicholas finally killed it when its battery went flat. The rest of the day was occupied with routine work. Remembering yesterday, I dared not ask FL what was happening on the Spanish channel. The next FOTD will be posted in 24 hours. It should be no surprise if another odd slice of the Z^2+C Julibrot shows up. Until then, take care, and let your negative side shine through. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= A_Golden_Slice { ; time=0:00:02.85-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/0.7544715 params=0/0/90/0/-1/0/0/0/2/0 float=y maxiter=300 inside=0 outside=real periodicity=6 colors=000KZzJXwJVsJTpJRmJQjJPgJNeJMbJL`IKYHJVGISF\ HPEGMDFJCDFBBCA8A958GQKJYKMeKPmKUmKZmKcmKhmKmmIrmF\ vmCzjHzhNzeSzcXzbTzaPz`Lz_HzZDzZ9zSCzLFzEHz7Kz1Mz6\ OzAPzFRzJSzNTzSSzXSzaRzfRzhRzjRzlRzmRzoRzqRzrRzzOz\ zLzzIzzFzzKzzOzzTzzXzzVzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Benoit Mandelbrot, Mathematician, Dies at 85
by Paul N. Lee 26 Oct '10

26 Oct '10

His death was caused by pancreatic cancer: http://www.nytimes.com/2010/10/17/us/17mandelbrot.html Sincerely, P.N.L. -------------------------------------- http://www.Nahee.com/PNL/Fractals.html http://www.Nahee.com/Fractals/

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FOTD 26-10-10 (Blazing Slices [5])
by Jim Muth 26 Oct '10

26 Oct '10

FOTD -- October 26, 2010 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a view of the western part of the Mandelbrot set rotated so that west is facing up. It is sliced at an angle rotated 66 degrees toward the Oblate orientation. The image is actually a scene in the four-dimensional Z^2+C complex known as the Julibrot, which holds all the perturbed Mandelbrot sets as well as all the Julia sets. Over the years I have stumbled upon countless other Julibrot scenes sliced in odd directions, which look nothing at all like either Julia or Mandelbrot images. Perhaps I'll use some of these odd images as FOTD's before too long. They certainly are interesting enough even though they might not always excel in artistic worth. The spurious buds in today's image are neither Julia nor Mandelbrot things. They exist only at the orientation of today's image. Changing the P1 or P2 parameters will show how critical the orientation is. The name "Blazing Slices" has no connection to an old western comedy movie. It refers to the fiery colors I intentionally gave the image. The calculation time of 10 seconds makes even a 5-rated image such as today's a bargain. The image may also be viewed, this time in finished form, on the FOTD web site at: <http://www.Nahee.com/FOTD/> I made a big mistake Monday afternoon when I caught FL watching one of those mushy latin soap operas and asked her what the show was about. When she described the plot, it went something like this: `that woman loves that man but he doesn't love her and the woman he does love doesn't know that he is her brother. This other woman wants a divorce from her no-good husband, but he has just won a huge lottery and now she doesn't know what to do about the man she really loves. This other man loves the first woman but he has a crippled wife who depends on him.' On and on the convoluted plot description went until, after a few minutes of trying to fathom the intricacies, I dozed off. When I jerked to my senses, I asked FL where does the action fit in. The resulting laughter made my day. A fairly pleasant day passed almost un-noticed here at Fractal Central on Monday. The fractal cats did notice the intermittent periods of sun and the unseasonably warm temperature of 72F 22C, but the humans were involved in other things. The next FOTD will be posted in 24 hours. Until then, take care, and the golden rule is supposed to work both ways. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Blazing_Slices { ; time=0:00:10.10-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/1.10231/\ 1.5/2.0709 params=0/66/0/90/-0.75/0/0/0/2/0 float=y maxiter=450 inside=0 logmap=yes passes=1 colors=00091ZB2_E3`H4aK5bM6cP7cS8cV9cYAc`BccC_fDWj\ ESmFOpFMqEKs9Iv2Jz0KzALzDMvGNsJOpMPpPQpSRpVSpYTp`S\ ocSofSoiRpiRpjQpkQqlQqlPqmPrnOroOroNspNsqNsrMtrMts\ LttLuuLuuKuvKvwJvxJwzKvxJvwJuvJutJtsJtrJspJsoJrnJr\ zJqzJqzJpzJpzJozJozJnzJnzJmzJmzJlzJlzJkzJkzJjzJpzK\ mzJjzJhzIzzzbzzzzzYzzWzzzzzQzzOzzzzzKzzJzzJzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Fractal animal: Fractofusus
by david 25 Oct '10

25 Oct '10

http://en.wikipedia.org/wiki/Fractofusus -- David gnome(a)hawaii.rr.com authenticity, honesty, community

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FOTD 25-10-10 (Seahorse Abomination [6])
by Jim Muth 25 Oct '10

25 Oct '10

FOTD -- October 25, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a "Seahorse Abomination", which is what I named it. Seahorse Valley never deserved to have such things done to it. The valley is a nice little place, a four-dimensional complex, so what have we done to the innocent valley to cause the gross disruption apparent in today's image? To begin, the image is not a Julia set of the familiar Seahorse Valley of the Mandelbrot set. It is a Julia set of Seahorse Valley of the Quaternion Mandelbrot set, which is actually an eight-dimensional Julibrot complex, with a 4-D Mandelbrot aspect and a 4-D Julia aspect. I'll not go into details about the wonders of the eighth dimension; I'm still working on understanding the fourth. But one thing certain is that in 8-D space, 28 two-dimensional planes pass through every point, with every plane perpendicular to all the others. (There is something puzzling about the two quaternion formulas. Today's image was created by the type=quatjul formula, which plots Julia sets. This formula has six variable parameters, all of which are necessary if we are to move off from the screen in the six perpendicular directions. Yet the type=quat formula, which plots Mandelbrot sets, has only two changeable parameters [plus two unused parameters] both of which have the same effect, giving the impression that the quaternion Mandelbrot set is a simple three-dimensional thing that would result from rotating the classic M-set around the X-axis.) Be that as it may, today's image, with its minor mathematical interest and only slightly better artistic worth, rates a 6. The fireball-fast calculation time of under 3 seconds will leave little time to wonder about higher dimensions before the image bursts onto the screen in a blaze of mediocrity. Those who prefer to remain burst-free may see the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Sunday here at Fractal Central featured a mixture of sun and clouds, and a very pleasant temperature of 70F 21C. The fractal cats complained that there was not enough sun then went to sleep on the living room carpet. After my trip back to the nostalgia-infested land of Old Fractal Central on Saturday, Sunday seemed relaxing. (Though I still wish the Phillies had won the NL pennant.) FL occupied herself wondering why I end my FOTD discussions with so many 'silly and unanswerable' comments. The next FOTD will be posted in the generally accepted 24 hours. Until then, take care, and if the belief in God and an afterlife is a defense mechanism evolved to enable us to cope with the awareness of our ultimate mortality, how would society react if it were ever demonstrated beyond all doubt that these things do not exist? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= SeahorseAbomnation { ; time=0:00:02.70-SF5 on P4-2000 reset=2004 type=quatjul center-mag=-0.0300864/0.01\ 38653/1.05286/1/32.5/0 params=-0.75/-0.055/-0.113/\ -0.013/-0.048/-0.134 float=y inside=0 periodicity=0 colors=000KIcLJcMKcNLcOMcPNcQOcTQcWScYUc`WcbYceZch\ `cjbcmebohcrjetffu_dvTawLZwCXs6Uo0Ti1Td3T`5TY6RV6P\ S6NR6JP4EM38H3BB4C56C58E3BG4EI5HK5KM6NO6PR6SU6VX6X\ _6_b6be6ch8ae9ZcBWbCTaDQ_FN_GK_HH_IF`IE`JD`JC`KB`K\ AaL9aL8aM7aM6aJ2eH0hC0c70Z30V51W62W83X94XB5YC6YD7Z\ F9ZGA_IB_JC`LD`MEaNFa7MeANdDNdFNcIOcKObNObPPaSPaUP\ aM0oN1mO5kP8iQCgRFeSJcTMaUQ_x3pr9llEhfJe`OaR0iS3gT\ 7eTCdUGbULaVP_0J46LABNFGOKLQPQSUCpifQdcRb`SaYT_rp0\ nm2ji9feFb`MZXT7efAceCbdEacG`cI_bLYaNX`PW`RV_TUZ_C\ gZEfZFeYGeYHdYJcXKcXLbXMaWNaWP`WQ_VR_VSZ2gm7djBbhF\ `fJZdNXbRV`faRc_TaYVZWWXUYjY0hX0fW4dW9bVDaVI_UMYUR\ WTVUGTVIUVJVVLVVMWVOXVPXVRYVSZDQNFRPHRQIRRKSSMSTNS\ UPSVRTWSTXUTYk03i17g5Be8EcCIaFL_JPYMSWQWJphKpgLofM\ mfMleNjdOhdPgcPecQcbRbaS`aSZ`TY_UW_VUZbfWadX`cX_aX\ Z`YZ_YYYYXXZWVZVUZ8p9OmYPkZQiZQgZRfZRdZSbZT`ZT_ZUY\ ZUWZVUZ_LiZNfYPdXQbWS`f0V } END PARAMETER FILE=========================================

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FOTD 24-10-10 (Elephant Wreath [5])
by Jim Muth 24 Oct '10

24 Oct '10

FOTD -- October 24, 2010 (Rating 5) Fractal visionaries and enthusiasts: Elephants are everywhere in Seahorse Valley of the Mandelbrot set. They come in all sizes, shapes and colors. They also enjoy doing tricks. The elephants in today's image have formed themselves into a wreath, a bit too early for the season to be sure, but decorative just the same. The name "Elephant Wreath" describes the scene well enough. The image is stretched more than 1000 times (1083 to be exact) in the horizontal direction. Such stretching is necessary to correct the natural distortion of the scene, which lies in an orientation rotated 10 degrees from the Rectangular toward the Oblate. The rating of a 5 might be a bit too conservative, but how much can a holiday wreath decorated with elephants be worth? The calculation time of 11-1/2 seconds is fast by any standards. Viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> is equally fast, and could be a lot more fun. A frosty morning gave way to warm sunshine and an afternoon temperature of 64F 18C here at Fractal Central on Saturday. (It reached 73F 23C at Old Fractal Central 150 miles 240km south of here.) The fractal cats slept through most of it. My day, which was occupied with a trip back to Old Fractal Central, was otherwise uneventful. The next FOTD will likely be posted within 12 hours, which will bring the FOTD up to date if it happens. Until next time, take care, and keep alert for that quantum stuff. It's lurking everywhere. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Elephant_Wreath { ; time=0:00:11.52-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=-0.003041525\ 45290287/0/16.30635/1083 params=100/90/0/90/0.265/\ 0/0/0/2/0 float=y maxiter=1500 inside=0 logmap=48 symmetry=xaxis periodicity=6 mathtolerance=0.05/1 colors=000BaMCbODcOEdQFeSGfUHgWIhYJiZKjYMkYOlXQmXS\ nWUoWZrVcuVhxUmzUruVvrVwnVzkWwhWmeWcbWUZXKWWJVVHTV\ EQUCNTAKS9IS8HS7GS6FR5DS4CQ3AO25M10K00K40K70KA0KD0\ KG4PK4UN4ZQ4cT4hW4lX6nY7oY8pZ9rZBs_Ct_Dv`Ew`FxaHub\ IrcKpcLmdNkeOheQffRcgT`gUZhWWiXUiZRj_PkaMkbKhaMe`O\ c_Q`_RYZTWYVTXXRXYOW_LVaJUcGUdDTfBSh8Rj6Rk8ShATfBU\ cDUaFV_GWXIXVKUULVUNWUOXUNYUNYUMYUMXVLXWLXXLWYKWZK\ W_JV`JVaJVbIScIQdHNeHLfGMgGNhGNiGOjGPkGPlV0PX1OY1N\ Z1M_1L`2La2Kb2Jc2Ie3Hf3Hg3Gh3Fi4Ej4Dk4Dl4Cn5Bo5Ap5\ 9q59r68s67t66u66r9BoCGlFLiHQfKVcN_pIZaPcP_mOWhNTcN\ Q_MNVMJRLGMLDIKADK79M9ANBBODCPEDRGESIFTJGULGVNHXOI\ YQJZSK_ULaVMbXNcZNd_OeaPgcQhdRifSjhTjlVkiTkfSkdQka\ Pk_NlXMlUKlSJlPHlNGlKEmHDmFBmCAmA8m77m56l66k76k86j\ 96jA6iB6iC6hD6hE6gF6gG6fG6eH6eI6dJ6dK6cL6cM6bN6bO6\ aP6aQ6`R6`R6_TD_UK_VQZWXZXcZYibVeeSaiPZlMVoJRsGOvD\ KyBHo9DqjdsleunfvT9vpghQY } frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Twilight Minibrot
by Roger Alexander 24 Oct '10

24 Oct '10

Today's post is a minibrot in twilight colors. At the usual http://maxitersfractalfollies.blogspot.com Twilight Minibrot { ; fract483.gif ; blank ; calctime 0:03:23.94 ; created Oct 24, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=hermanm_man-polar center-mag=-2.00319/-0.00306882/27.01637/1/90/3.88578058618804789e-016 params=3/2/1/45/1/0 float=y maxiter=1500 inside=0 outside=atan decomp=256 colors=000302403503504604705805806907A07B08B08C09D1AE1AF1BF1BG1CH1CI1DI1\ EJ1EK1FL1FL1GM1GN1HO2IN2KM2NK2QJ2TH2VG2YE2`D2cB1fA1i81l71n51q41t21w00z03\ z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0jz0nz0rz0vz0zz0xz0vz0tz0rz0pz0nz0lz0jz0h\ z0fz0dz0bz0`z0Zz0Xz0Wz0Uz0Sz0Qz0Oz0Mz0Kz0Iz0Gz0Ez0Cz0Az08z06z04z02z00z00\ y10x20v20u30s40r50p50o61n71l81k91i91hA1gB1eC1dC1bD1aE1_F1ZF1YG1WH1VI1TJ2\ SJ2RK2PL2OM2MM2LN2JO2IM2GJ2EH2CE1AC18916614312000101302503605806A07C19D1\ 9E1AF1AF1BG1BH1CI1DI1DJ1EK1EL1FL1FM1GN1HO2IO2JQ2IS2HV2GX2F_2Da2Cd2Bf2Ah1\ 9k18m17p15r14u13w12z00z20z50z70zA0zC0zF0zH0zK0zM0zP0zR0zU0zX0zZ0za0zc0zf\ 0zh0zk0zm0zp0zr0zu0zw0zz0zw0zu0zr0zo0zl0zj0zg0zd0za0z_0zX0zU0zS0zP0zM0zJ\ 0zH0zE0zB0z80z60z30z00x01v02s03q04n06l07i08g19e1Ab1B`1CY1EW1FT1GR1HO2JN2\ IM2HK2GJ2FH2DG2CE2BD2AB19A18817715514413212000000101201 } frm:hermanm_man-polar { ; Kerry Mitchell 16feb98 ; ; real(p1) = z exponent (use integer >= 2; m=n-1) ; imag(p1) = g exponent (integers) ; real(p2) = alpha magnitude (try 1) ; imag(p2) = alpha polar angle (try integers) ; real(p3) = critical point selector (>0 for positive root) ; imag(p3) = unused (<0 for negative root) ; use decomp=256 ; zero and infinity bailouts hardcoded to 1e-6, 1e6 ; coloring speed hardcoded to 4 ; c=pixel, iter=1, n=real(p1), m=imag(p1), nfac=2*n-1 maxr=1e6, minr=1/maxr, speed=4*pi/128 r=real(p2), t=imag(p2), alpha=r*(cos(t)+flip(sin(t))) oln=1/log(n), fac=log(0.5*log(maxr)) c2=sqr(c), hypnum=sqr(n)+sqr(m), pn=1 hypden=sqr(n-m), hypfac=hypnum/hypden if (real(p3)<0) pn=-1 end if if (real(c2)>hypfac) pn=-pn end if if (imag(c)<0) pn=-pn end if afac=c*n, bfac=c2*(n-m)+(n+m), cfac=c*n d=sqrt(bfac*bfac-4*afac*cfac) z=(bfac+pn*d)/(2*afac) : g=(z-c)/(1-c*z), z=alpha*z^n*g^m iter=iter+1, r=|z| ; ; orbit trap around 0 ; renormalize iteration count via decomp angle ; set "iteration done" flag (iter=-1) ; if (r<minr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed z=cos(angle)+flip(sin(angle)) iter=-1 end if ; ; orbit trap around infinity ; renormalize iteration count via decomp angle ; add pi to angle to separate from 0 orbit trap ; set "iteration done" flag (iter=-1) ; if (r>maxr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed angle=angle+pi z=cos(angle)+flip(sin(angle)) iter=-1 end if iter>0 } Roger Alexander

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Algae
by Roger Alexander 23 Oct '10

23 Oct '10

I usually don't give my posts names but if I did I would call this one "Algae" because it reminds me of algae. Am I consistent or oh so predictable? Pre-calculated at http://maxitersfractalfollies.blogspot.com Algae { ; fract482.gif ; blank ; calctime 0:05:29.50 ; created Oct 22, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=conic-near_man center-mag=+0.00133886277847312/+1.00493995512520900/10743.32 params=-0.5/-0.4000061037018952/0.03488265633106479/0.125/0.557969908749\ 6567/-0.06808679464094974 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=0100200300400500700800900A00B00D00E00F00G00H00J00K00L00M00N00P00Q\ 00R00S00T00V00W00X00Y00Z00`00a00b00c00d00f00g00h00i00k00k01k02k03l04l05l\ 05m06m07m08n09n0An0Bo0Bo0Co0Dp0Ep0Fp0Gp0Hq0Hq0Iq0Jr0Kr0Lr0Ms0Ns0Ns0Ot0Pt\ 0Qt0Ru0Su0Tu0Tu0Uv0Vv0Wv0Xw0Yw0Zw0Zx0_x0`x0ay0by0cy0dz1dz1ez1ez1fz2fz2gz\ 2gz2hz3hz3iz3iz3jz4jz4kz4kz4lz5mz5mz5nz5nz6oz6oz6pz6pz7qz7qz7rz7rz8sz8sz\ 8tz8uz9uz9uz9tz9tz9tz9sz9sz8sz8rz8rz8rz8qz8qz7qz7pz7pz7oz7oz7oz6nz6nz6nz\ 6mz6mz6mz5lz5lz5lz5kz5kz5kz4jz4jz4iz4iz4iz4hz3hz3hz3gz3gz3gz3fz2fz2fz2ez\ 2ez2dz1dz1cz1bz1ay1`y1_y1_x1Zx1Yx1Xw1Ww1Vw1Uv1Uv1Tv1Su1Ru1Qu1Pt1Ot1Ot1Nt\ 1Ms1Ls1Ks1Jr1Ir1Ir1Hq1Gq1Fq1Ep1Dp1Cp1Co1Bo1Ao19n18n17n16m06l06k06j06i06h\ 06g06f05e05d05c05b05a05`05_05Z04Y04X04W04V04U04T04S04R03P03O03N03M03L03K\ 03J03I02H02G02F02E02D02C02B02A0190180170160150140130010 } frm:conic-near_man { ; Kerry Mitchell 11may98 zc=0, cc=pixel, maxr=1e12, minr=maxr, iter=1 a=real(p1), b=imag(p1), c=real(p2), d=imag(p2) e=real(p3), f=imag(p3): iter=iter+1, zc=sqr(zc)+cc, x=real(zc), y=imag(zc) conic=|x*(a*x+b)+y*(c*y+d)+e*x*y+f| if (conic<minr) minr=conic end if if ((|zc|>maxr)||(iter==maxit)) iter=-1 t=log(minr) z=cos(t)+flip(sin(t)) end if iter>0 } Roger Alexander

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FOTD 23-10-10 (Star of the Spike [8])
by Jim Muth 22 Oct '10

22 Oct '10

FOTD -- October 23, 2010 (Rating 8) Fractal visionaries and enthusiasts: The 2-second calculation time of today's image is no mistake. The image is a scene in the best-known fractal of all -- the Mandelbrot set. And on my particular fractal dedicated machine, the Mandelbrot set runs at faster-than-light speed. I originally planned on naming the image "Not Quite Dead Yet" to indicate that the M-set is no tired warhorse on its last lap around the track. It is chock full of interesting and lively scenes, not only of minibrots, but of countless other undiscov- ered wonders. But then I decided that such a name was much too downbeat for such an upbeat image. I finally decided on the name "Star of the Spike", which has a far more positive sound and also indicates the location in the M-set. The image rates an 8. I'm not sure how much of that rating is due to my coloring, but I did work on the colors for well over an hour. The scene lies on a filament extending from the Seahorse Valley of a minibrot located on the main spike of the M-set, not far west of the main body of the set. As I said earlier, the calculation time is an incredibly brief 2 seconds. But there is still the hassle of copying this letter into your parameter file in text mode with a .par extension, hoping that no spurious characters get inserted, then running it as you would any other parameter file. This minor inconvenience may be avoided by going to the FOTD web site at: <http://www.Nahee.com/FOTD/> and viewing the finished image there. A mixture of clouds and sun, a brisk wind from the northwest and a temperature around 52F 12C gave Friday a very autumnal feeling here at Fractal Central. The fractal cats enjoyed the sun when it was shining and the house heat when the clouds prevailed. My day was slow enough to put the extra coloring work on the FOTD. FL had a slightly more active day. I think a trip back to Old Fractal Central, 130 miles (200km) south of here, is coming up on Saturday, so do not be surprised if the FOTD for October 24 is late. Until whenever, take care, and wouldn't it be great if humans had designed the laws of the natural world instead of the great unknown? (But could we have done it with- out fighting?) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Star_of_the_Spike { ; time=0:00:02.11-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.40473711526\ 07/+0.0001010790714/8e+008/1/180 params=0/0 float=y maxiter=5200 inside=0 logmap=538 periodicity=6 colors=0000AL0AM0AN0AO0AP0AQ0AR0AS0AT0AU0AV0AW0AX0\ AY0AZ0A_0A`0Aa0Ab09c08d07e06f07g08h09i0Aj0Bk0Bl0Cm\ 0Dn0Eo0Fp0Gq0Gr0Hs1It2Ju3Kv4Iy5Kv5Ms6Nq6Pn7Ql7Si8T\ g8Vd9Wb9Y_AZYA`VBaTBcQBdOEcQHcSJbUMbVPbXRaZUa`WaaX\ bbXbcXbcXbdXbdYbeYbeYbfYbfYcgZcgZchZchZciZcgZcd_ca\ ZdZYeWXfTWgQVhNUiKUjHUkEUlCUm9Uo6Uq3Us1Ut2Ut3Yt4bu\ 5fu6ju7ov8tv9zz8zvAztBwrCwpDwnEvlGvjHvgIveJvcKvaLu\ _NuYOuWPuTQuRRtPTtNUtLVtJWtHXyA`tFYoJWkOUfSSaXQY`O\ TeMOiKKmILlKLlMMkOMkPYkA_hB`eBbbBc_CeXCfUEgPIhKMiF\ QjAUk6Yk1an9epHhsOluWoxcszevzUWm85cKX1Vx4_t7dq9grC\ ivEmzDrzDqzDovDcmCbaCSVCHRCANJNMQWBkd0zc0qlFejEbiD\ XgDVfCUeCVaAWY9XV7YR6ZN4ZK3T_COoLRkITgGVcEX`C_X9aT\ 7cP5eM3cOCaQK_SSZU_XWgVYoU_wbbskdotfkqkXnpIku4ovOR\ wP2xQ5tI8qAAn3CoBEpIGpPIqXPmTSlNVkGfzzczzazzZzzXzz\ UzzSzzPzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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<David> 4 variables define a 4D space
by Hal Lane 22 Oct '10

22 Oct '10

David, Jim Muth said, "...the formula Z^2+C consists of two complex numbers which have four variables in all. Four variables define a space of four dimensions." Here's as much of one four-dimension fractal as can be seen. I've projected the 4D fractal object to 3D, then put a string of these 3D projections together into a pseudo-4D .gif animation. A different 3D portion of the 4 dimensional fractal object is shown in each frame in the animation: http://home.earthlink.net/~hallane/hals_fractals_n_photos/ - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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FOTD 22-10-10 (Unknown Landscape [6])
by Jim Muth 22 Oct '10

22 Oct '10

FOTD -- October 22, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image takes us back to the 'Patterns in the Mist' image of October 20 -- two days ago. In that discussion I commented that the image had minibrots, but they were not very interest- ing. Since then, I have done further exploring and found that the minibrots are more interesting than I had assumed. I decided that today's image, which shows a minibrot that was hidden in the earlier image, is worth being declared FOTD for October 22. The color palette is basically the same as the one in the earlier image, with only a bit of tweaking to emphasize the hidden patterns. Now, instead of two levels, we have three levels of near-random chaos. The strongly colored highlights are seen to be gathered near the minibrot, with the outlying, more vague features sugges- ting elements of the actual Seahorse Valley location. The rating of a 6 is all I could give today's image, which after all is basically a repeat of the earlier image. The name "Unknown Landscape" is perhaps a bit overdone. The scene does lie in the Seahorse Valley of its parent, so how surprising can it be that the vague patterns resemble the very familiar elements in Seahorse Valley? The calculation time of 3-1/2 minutes is brief enough to make running the included parameter file worth the small effort. The small hassle of setting up and running the parameter file may be avoided by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> A brisk west wind, showers of leaves, a mixture of sun and clouds, and a temperature of 59F 15C made Thursday a typical mid- autumn day here at Fractal Central in central Pennsylvania. The fractal cats were fascinated by the falling leaves, and spent several hours in their window, trying to decide what was happen- ing outside. My day was normal; FL's was the same. The next FOTD will be posted in 24 hours. Until then, take care, and if everything is an illusion in the mind, as some mystics claim, in what then is the mind only an illusion? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Unknown_Landscape { ; time=0:03:33.36-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-0.74125203921/+0.04311355888/633984/1\ /37.5/0 params=-3/10/0/0 float=y maxiter=7500 inside=0 logmap=207 periodicity=6 colors=000HHHmcUUcmcmAmrnwKpmsomsnmsmmrkmqimpgmoem\ ncmmbmc`mcZmcXmcVmcUmcSmcQmcOmUMmUKmUJmUHmUFmUDmUD\ mUAmUAmUAmUAmUAmUAmUAmUAmUAfUAgUAhUAiUAjUAjUAkUAlU\ AmUAnUBoUBpUCqUDqUDmUEjUEgUEdUE`UEYUEVUESUERUDRUDR\ UCH02H52H61G61G71G70L70L80L80K90K90K90KA0KA0K00OB0\ OB0OC0OC0OD0OD0OD0PE0PF0QF0QG0QG0RH0RI0RI1SJ2SJ2TK\ 3TL4TL5UM5UM6UN7VO7VO8VP9WP9WQAXRBXRCXSCYSDYTEYUEZ\ UFZVGZVGYUHXTIXTJWSKWSLVRLUQMUQNTPOTPPSOQSOQRNRQMS\ QMTPLUPLVOKVNJWNJXMIYMIZLH_LH_JFZIEZHDZFCZEAYD9YB8\ YA7Y95X74X63X52X61W71W81V91V91VA1UB1UC1UD1TD1TE1TF\ 1SG1SG1SH1RI1RJ1QK1QK1QL1PM1PN1PO1OO1OP1OQ1NR1NR1N\ Q3OQ4OQ5OQ6OP7OP8OP9OPAOOBOOCOOEPOFPNGPNHPNIPNJPMK\ PMLPMMPMNPLOPLQQLRQLSQKTQKUQKVQK0QJ0QJ0QJ0QJ0QS0bT\ 0bT0cT0dU0dU0eV0eV0fV0fW0gW0gW0hX0hX0iX0jY0jY0kZ0k\ Z0lZ0l_0m_0m_0n`0n`0oa0p`0o`0o`0o`0o`0n_0n_0n_0nO0\ 8Q0AR0DS0FT0IU0KW0NX0QY0S } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 21-10-10 (Man-O-Peace Fractal [5])
by Jim Muth 21 Oct '10

21 Oct '10

FOTD -- October 21, 2010 (Rating 5) Fractal visionaries and enthusiasts: Yes, today's image is late, but here it is in its full glory, better late than never. The image is a scene in the default manowar Mandeloid. I named it "Man-O-Peace Fractal" because I disapprove of violence. With not much going for it, I could give the image a rating of no more than a 5, which indicates an everyday average fractal. The calculation time of 1-1/3 minutes is brief enough to assure that little time will have been wasted if the image lays a rotten egg. The best way to avoid an unwanted omelet is to view the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> After a foggy start, Wednesday turned rather pleasant here at Fractal Central, leading to an afternoon with ample sunshine and a temperature of 63F 17C. The fractal cats, Nicholas and Cassie, spent the afternoon on their shelf in the southwest window, basking in the strong sunlight streaming in. My day was unexpectedly busy, which also explains the lateness of today's FOTD. The next FOTD will be posted in 24 hours, more or less. Until then, take care, and don't get lost in the Z^2+C Julibrot. If you do, you'll never find your way out. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Man-O-PeaceFractal { ; time=0:01:20.14-SF5 on P4-2000 reset=2004 type=manowar center-mag=-0.1384789735/0\ /92456/1/90/0 params=0/0 float=y maxiter=1250 inside=255 logmap=810 colors=000G0OH0PI0QJ0RK0SL0TM0UN0VO0WP0XQ0YR0ZS0_T\ 0`U0aU0bU2cU4dU6eU8fUAgUChUEiUGjUIkUKlTMmSOnRQoQSp\ PUqNWrLYsJ_sK`rLaqMbqNcpOdoPeoQfnRgnShmTilUjlVjkWi\ jWfiVcgU_eTWcSSaQO_OMYMKWKIUIGSGEQFCOEAMC8KB6KA4K9\ 2K82K72K62K52K42K32K66K8AKAEKDIKFMKHQKKUMMYOO`PQbQ\ RcRTdRVeSYfS_gTbhTdiUgjUikVklVijWghXffXdeYbcZaaZ__\ _YZ`YX`XVaWTbWSbYTO_T9`WDaYHb_LbbPcdTdfXdh_biXajV`\ kT_lQYlOXmMWnJVoHUoFRiHPdJN_LKVMIQOGKQDFRBAT95V70W\ A1XD2XG3XJ4XM4XP5YS6YU7YX8Y_8Yb9ZeAZhBZkCZmCZlFXlH\ VlJUkLSkNRkPPjROjTMjVLiXJiZIi`GibFgWGfPGeIGdBGc4GR\ A8FF1X8Mm2en6anAYnDVnHRnLNnOKnPJnQInRInSHnTHnUGnVG\ nWFnXFnYEnZElWNkTWjQdiNmhKueJsbIr`HpYHoWGmTFlQEkOE\ iLDhJCfGBeEBdDEfDGgCJiCLjCOlBQmBToBVpAYrA_sAbu9dv9\ gx9iyMMMKKKIIIHHHFFFUfOPfSKfWFfZAfb5ff0fi3df5cd8bb\ A``C_ZFZXHXVKWSMVQOTORSMTRKWPIYOG`LD_NE_OF_PF_QG_S\ GZTHZUIZVIZXJZYJZZKY_LYaL } END PARAMETER FILE=========================================

2 1

Fmod Minibrot
by Roger Alexander 21 Oct '10

21 Oct '10

Minibrots-if the iteration loop has x^2 + c its got a minibrot! Another pre-calculated nomadic mandelbug at http://maxitersfractalfollies.blogspot.com. Fmod Minibrot { ; fract481.gif ; blank ; calctime 0:17:12.49 ; created Oct 20, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=hermanm_man-cart passes=1 center-mag=+1.10021739445293500/+0.02785688062135686/341530.1/1/-167.500\ 000001965589/7.71297616053434609e-010 params=4/3/1/0/2/0 float=y maxiter=1500 inside=0 proximity=2 outside=fmod logmap=14 colors=00101211312412413523624724825935936A36B37C47D48E48F49F59G5AH5AI5B\ J6BK6CK6CL6DM7DN7EO7EP7FP8FQ8GR8GS9HT9HU9IUAIVAJWAJXBKXBKYBLYCLZCMZCM_DN\ `DN`DOaDOaEPbEPbEQcFQcFRdFReGReGSfGSfHTgHTgHUhIUiIViIVjIWjJWkJXkJXlKYlKY\ mLZnLZnM_oM_oM`oN`pNapOaqObqPbrPcrPcrQdrQdsResRetRftSftSgtTguThuUhuUivVi\ vVjvVjvWkwXkwYlwYlwZmxZmx_nx_nx`ox`oxapyapybqybqycrydryesyeszftzgtzhuzhu\ zivzjvzkwzmwznxzpxzqyzryzuzzuzzuzzryzqyzoxznxzmwzkwzjvzivziuzhuzgtzftzfs\ zesydrycrybqybqyapyapy`ox_ox_nxZnxZmxYmwYlwXlwXkwWkwVjvVjvVivVivUhvUhuTg\ uTguSfuSftRetQesQdsQdrPcrPcrObqObqOapNapN`oN`oM_nM_nMZmLZmLYlLYlKYlKXkJX\ kJWjJWjIViIViIUhHUhHTgHTgGSfGSfFRfFReFQdFQcEPcEPbEObDOaDNaDN`CM_CM_BLZBL\ ZBKYAKYAJXAJWAIV9IU9HU9HT8GS8GR8FR8FQ7EP7EO7DN7DM6CL6CL6BK6BJ5AI5AH59G59\ G48F48E47D37C36B36A35A259248247236135124124113012001000 } frm:hermanm_man-cart { ; Kerry Mitchell 16feb98 ; ; real(p1) = z exponent (use integer >= 2; m=n-1) ; imag(p1) = g exponent (integers) ; p2 = alpha ; real(p3) = critical point selector (>0 for positive root) ; imag(p3) = unused (<0 for negative root) ; use decomp=256 ; zero and infinity bailouts hardcoded to 1e-6, 1e6 ; coloring speed hardcoded to 4 ; c=pixel, iter=1, n=real(p1), m=imag(p1), nfac=2*n-1 maxr=1e6, minr=1/maxr, speed=4*pi/128, alpha=p2 oln=1/log(n), fac=log(0.5*log(maxr)) c2=sqr(c), hypnum=sqr(n)+sqr(m), pn=1 hypden=sqr(n-m), hypfac=hypnum/hypden if (real(p3)<0) pn=-1 end if if (real(c2)>hypfac) pn=-pn end if if (imag(c)<0) pn=-pn end if afac=c*n, bfac=c2*(n-m)+(n+m), cfac=c*n d=sqrt(bfac*bfac-4*afac*cfac) z=(bfac+pn*d)/(2*afac) : g=(z-c)/(1-c*z), z=alpha*z^n*g^m iter=iter+1, r=|z| ; ; orbit trap around 0 ; renormalize iteration count via decomp angle ; set "iteration done" flag (iter=-1) ; if (r<minr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed z=cos(angle)+flip(sin(angle)) iter=-1 end if ; ; orbit trap around infinity ; renormalize iteration count via decomp angle ; add pi to angle to separate from 0 orbit trap ; set "iteration done" flag (iter=-1) ; if (r>maxr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed angle=angle+pi z=cos(angle)+flip(sin(angle)) iter=-1 end if iter>0 } Roger Alexander

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Re: [Fractint] What?
by Jim Muth 20 Oct '10

20 Oct '10

At 09:34 PM 10/19/2010 -0400, D Fisher wrote: >I was going through my fractal files and asked myself a >question to which I don't know the answer: Exactly what am >I seeing when I view a fractal? What is the relationship of >the display to the <z> axis? When a Mandelbrot fractal is viewed, the two C axes are displayed on the screen, while the two Z axes are perpendicular to the plane of the screen. This nonsense is possible because the formula Z^2+C consists of two complex numbers which have four variables in all. Four variables define a space of four dimensions. (In the Julia sets, the Z axes are on the screen, while the C axes are perpendicular.) >Is it possible to rotate any >fractal so that any axis becomes any other axis? Or is the >computed display all there is? Is it possible to begin >parsing with different axes? Yes, any Fractal may be rotated through any orientation in the four-dimensional hyperobject called the Julibrot. The SliceJulibrot4 formula that I frequently use does just this. >Basically, imagine a rectangle the ratios of which (x, y, z) >are 2:4:1 (of any magnitude). Where on, or in, this >rectangle is the position of the fractal? And if it were >observed from the smallest axis (z), what would it look >like? The Mandelbrot set cuts a two-dimensional slice through the center of the Julibrot, though it does not cut the Julibrot apart. The perturbed M-sets cut other slices in the same orientation, though not through the center. The Julia sets cut slices through the same Julibrot in an absolutely perpendicular orientation. When a Mandelbrot set is viewed from the other 2 axes, nothing of the M-set remains but a single point, but we now see new stuff surrounding the point that we call a Julia set. >This has me baffled, and is mind game that is generating a >lot of heat. >Any answer would be appreciated, but especially one I could >understand. >Thx > >David M fisher This is the situation as I see it. Lots of luck understanding it. After 20 years, I'm still not sure I actually understand it. Jim M.

2 1

Patch Level 10
by Roger Alexander 20 Oct '10

20 Oct '10

Posted at http://maxitersfractalfollies.blogspot.com a minibrot ,gif and anti-aliased jpg versions, of the classic Mandelbrot generated with the just released patch level 10 for Fractint 20.04. No problems so far running the new executable under DOSBox in Vista. Fractint 20.04 Patch 10 { ; Fractint 20 04 Patch 10 just released ; fract480.gif ; calctime 0:03:04.88 ; created Oct 19, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=mandel center-mag=+0.41523553474131090/-0.33178413843968140/1.117565e+008/1/90/\ 3.88578058618804789e-016 params=0/0 float=y maxiter=12000 inside=0 logmap=500 colors=000202303505606808A0AB0BD0DE0EG0GI0IJ0JL0LM0MO0OQ0QR0RT0TU0UW0WY0\ YZ0Z`0``0`a0ab0bc0cd0dd0de0ef0fg0gh0hh0hi0ij0jk0kl0lm0mm0mn0no0op0pq0qq0\ qr0rs0st0tu0uu0uv0vw0wx0xy0yz0zy0yw0wv0vt0ts0sq0qp0pn0nm0mk0ki0ih0hf0fe0\ ec0cb0b`0`_0_Y0YW0WV0VT0TS0SQ0QP0PN0NM0MK0KJ0JH0HF0FE0EC0CB0B90980860650\ 530310100100200300500600700800A00B00C00D00F00G00H00I00K00L00M00O00P00Q00\ R00T00U00V00W00Y00Z00_00`00b00c00a12b25c48d5Ae6Df8Gg9JhBLiCOjDRkFUlGWnIZ\ oJapKdqMfrNisPltQouRqvTtwUwxWzzVwyTswRovPktNgsLdqJ`pHXnFTmDPkBMj9Ih7Eg5A\ e36d00b00a00_00Z00X00W00U00S00R00P00O00M00L00J00H00G00E00D00B00900800600\ 5003001100300600900B00E00H00J00M00M00O00Q00S00U00X00Z00a00d00g10k10n10r1\ 0v10z21z21z43z65z87zA9zDBzFDzHFzJHzLJzOLzQNzSPzURzWTzZVzXUzVSzTQzROzPMzM\ KzKIzIGzGEzECzBAz98z76z54z32z00v00o00g00Z00O00D00100100 } Roger Alexander

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What?
by David M Fisher 20 Oct '10

20 Oct '10

I was going through my fractal files and asked myself a question to which I don't know the answer: Exactly what am I seeing when I view a fractal? What is the relationship of the display to the <z> axis? Is it possible to rotate any fractal so that any axis becomes any other axis? Or is the computed display all there is? Is it possible to begin parsing with different axes? Basically, imagine a rectangle the ratios of which (x, y, z) are 2:4:1 (of any magnitude). Where on, or in, this rectangle is the position of the fractal? And if it were observed from the smallest axis (z), what would it look like? This has me baffled, and is mind game that is generating a lot of heat. Any answer would be appreciated, but especially one I could understand. Thx David M fisher

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Re: [Fractint] Fractint version 20.04 patch 10 is now available
by Roger Alexander 20 Oct '10

20 Oct '10

Jonathan Osuch wrote: Fractint version 20.04 patch 10 is now available on the developer's web site So far no problems running it under DOSBox in Vista. Roger Alexander

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FOTD 20-10-10 (Patterns in the Mist [5])
by Jim Muth 20 Oct '10

20 Oct '10

FOTD -- October 20, 2010 (Rating 5) Fractal visionaries and enthusiasts: Today's image rates only a 5, but this is for its artistic aspect, which I admit is not too great. It's mathematical aspect is far more interesting however. While casually rotating the colors of today's scene, and ready to move on to a more promising image, I caught a fleeting glimpse of an unsuspected pattern buried in the chaos that fills the screen. I bit of tweaking revealed that I was not mistaken. The pattern definitely is there -- unlike anything I have seen before. But it takes special coloring to reveal the underground pattern, which is nearly invisible with normal random coloring. The parent fractal consists of a circle with a trapezoidal shape nearly filling it and a large distorted Mandeloid inside the trapezoid. Most of the distortion in the Mandeloid lies in the higher-order buds, which are elongated to ridiculous lengths. Today's scene lies in the northern branch of Seahorse Valley of the Mandeloid. The image is filled with both minibrots and disappointing dry valleys that look like they hold minibrots but go flat before a minibrot appears. I have already checked a few minibrots and found them to be disappointing. This does not mean that no great minibrots lie in the depths, but it is not a good way to start searching. The name "Patterns in the Mist" refers back to the original scene before I began work on the colors, when the dark under- ground pattern was virtually invisible. The calculation time of 2-1/2 minutes will pass in a flash, especially for those who have something else to do while waiting. Those with idle time may avoid impatience by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Tuesday turned out really not too bad here at Fractal Central. The morning fog cleared off by 10am, leading to a sunny day with light winds and a temperature of 63F 17C. For some reason, the fractal cats were active unusually early, and settled into their afternoon naps well before noon. My day was rather busy but satisfying. FL was also busy. The next FOTD will be posted in 24 hours. Until then, take care, and the supernatural does not exist, that is unless we are talking about what the human brain is supposed to do. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= PatternsInTheMist { ; time=0:02:31.61-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=-0.741183021/+0.043160417/3242/1/\ -12.5/0 params=-3/10/0/0 float=y maxiter=7500 inside=0 logmap=68 periodicity=6 colors=000PPPmcUUcmcmAmrnwKpmsomsnmsmmrkmqimpgmoem\ ncmmbmm`mmZmmXmmVmmUmmSmmQmmOmmMmmKmmJmmHmmFmmDmmD\ mmAmmAmmAmmAmmAmmAmmAmmAmmAfmAgmAhmAimAjmAjmAkmAlm\ AmmAnmBomBpmCqmDqmDmmEjmEgmEdmE`mEYmEVmESmERmDRmDR\ mCH02H52H61G61G71G70L70L80L80K90K90K90KA0KA0K00OB0\ OB0OC0OC0OD0OD0OD0PE0PF0QF0QG0QG0RH0RI0RI1SJ2SJ2TK\ 3TL4TL5UM5UM6UN7VO7VO8VP9WP9WQAXRBXRCXSCYSDYTEYUEZ\ UFZVGZVGYUHXTIXTJWSKWSLVRLUQMUQNTPOTPPSOQSOQRNRQMS\ QMTPLUPLVOKVNJWNJXMIYMIZLH_LH_JFZIEZHDZFCZEAYD9YB8\ YA7Y95X74X63X52X61W71W81V91V91VA1UB1UC1UD1TD1TE1TF\ 1SG1SG1SH1RI1RJ1QK1QK1QL1PM1PN1PO1OO1OP1OQ1NR1NR1N\ Q3OQ4OQ5OQ6OP7OP8OP9OPAOOBOOCOOEPOFPNGPNHPNIPNJPMK\ PMLPMMPMNPLOPLQQLRQLSQKTQKUQKVQK0QJ0QJ0QJ0QJ0QS0bT\ 0bT0cT0dU0dU0eV0eV0fV0fW0gW0gW0hX0hX0iX0jY0jY0kZ0k\ Z0lZ0l_0m_0m_0n`0n`0oa0p`0o`0o`0o`0o`0n_0n_0n_0nO0\ 8Q0AR0DS0FT0IU0KW0NX0QY0S } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Re: [Fractint] Fractint version 20.04 patch 10 is now available
by jimmckenzie＠earthlink.net 19 Oct '10

19 Oct '10

Is there a way mto make this run in 64 Bit Win 7? I tried changing the compatibility settings but it doesn't help. -----Original Message----- >From: Jonathan Osuch <osuchj(a)avalon.net> >Sent: Oct 16, 2010 12:06 PM >To: Fractint and General Fractals Discussion <fractint(a)mailman.xmission.com> >Subject: [Fractint] Fractint version 20.04 patch 10 is now available > >Folks, > >Fractint version 20.04 patch 10 is now available on the developer's web >site: > >http://www.fractint.net > >or > >http://www.fractint.org > >What's new: > >Fixed WinFract resetting palette when parameters are changed with the ><X>, <Y>, <Z>, or <G> screens. > >Fixed usage of shift and control keys in Xfractint. > >Added sanity checks in Xfractint parser functions. > >Fixed long standing bug in Xfractint that occurred when a PAR was >invoked from the command line. > >Increased the WinFract maximum image size to 4096x4096 pixels. Your >mileage may vary depending upon how much memory Windows can allocate. >But remember that above 2048x2048 passes=1 is forced. > >Fixed bug in the cvtcentermagbf() routine that was introduced some time >prior to version 19.6. This fixes the problem that was occurring when >rotating ap math images by 90 degrees. > >Fixed buffer overflow in Xfractint that occurred when changing >directories. > >Jonathan > > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

6 10

Moody Blue
by Roger Alexander 19 Oct '10

19 Oct '10

A dark moody palette with a flickering of light. This fractal was generated with a real p1 (bailout) of 20 instead of the suggested 10^12. At the usual http://maxitersfractalfollies.blogspot.com. Moody Blue { ;fract477.gif ; blank ; calctime 0:01:15.85 ; created Oct 17, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=frac_ml.frm formulaname=gaussinttot_man center-mag=-0.864/0.761751/17.83333 params=20/30 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=00101211312412413523624724825935936A36B37C47D48E48F49F59G5AH5AI5B\ J6BK6CK6CL6DM7DN7EO7EP7FP8FQ8GR8GS9HT9HU9IUAIVAJWAJXBKXBKYBLYCLZCMZCM_DN\ `DN`DOaDOaEPbEPbEQcFQcFRdFReGReGSfGSfHTgHTgHUhIUiIViIVjIWjJWkJXkJXlKYlKY\ mLZnLZnM_oM_oM`oN`pNapOaqObqPbrPcrPcrQdrQdsResRetRftSftSgtTguThuUhuUivVi\ vVjvVjvWkwXkwYlwYlwZmxZmx_nx_nx`ox`oxapyapybqybqycrydryesyeszftzgtzhuzhu\ zivzjvzkwzmwznxzpxzqyzryzuzzuzzuzzryzqyzoxznxzmwzkwzjvzivziuzhuzgtzftzfs\ zesydrycrybqybqyapyapy`ox_ox_nxZnxZmxYmwYlwXlwXkwWkwVjvVjvVivVivUhvUhuTg\ uTguSfuSftRetQesQdsQdrPcrPcrObqObqOapNapN`oN`oM_nM_nMZmLZmLYlLYlKYlKXkJX\ kJWjJWjIViIViIUhHUhHTgHTgGSfGSfFRfFReFQdFQcEPcEPbEObDOaDNaDN`CM_CM_BLZBL\ ZBKYAKYAJXAJWAIV9IU9HU9HT8GS8GR8FR8FQ7EP7EO7DN7DM6CL6CL6BK6BJ5AI5AH59G59\ G48F48E47D37C36B36A35A259248247236135124124113012001000 } frm:gaussinttot_man { ; Kerry Mitchell ; ; Gaussian integer coloring of Mandelbrot set ; color by average distance to nearest integer ; inside and outside handled the same way ; ; use decomp=256 ; real(p1) = bailout (try 1e12) ; imag(p1) = scaling factor (try 30) ; variable zc used for calculation; coloring done with z ; zc=0, c=pixel, rmax=real(p1), scale=imag(p1) iter=1, rmin=1, z=zc, tot=0: ; ; iteration ; zr = gaussian integer ; r = distance to zr ; zmin = integer with minimum distance ; tot = running sum of r's ; iter=iter+1, zc=sqr(zc)+c, rzc=|zc| zr=round(zc), r=|zc-zr|, tot=tot+r ; ; bailout ; scale average distance to decomp angle ; set "iteration done" flag (iter=-1) ; if ((rzc>rmax)||(iter==maxit)) angle=scale*tot/(iter-1) z=cos(angle)+flip(sin(angle)) iter=-1 endif iter>0 } Roger Alexander

1 0

FOTD 19-10-10 (Evaporated but Present [6])
by Jim Muth 19 Oct '10

19 Oct '10

FOTD -- October 19, 2010 (Rating 6) Fractal visionaries and enthusiasts: The name of today's image -- "Evaporated but Present" -- gives away the big secret -- the image is an evaporated one. The one- googol value of the imag(p3) parameter is yet another give-away. The scene lies in the same indescribable parent fractal as yesterday's image, though in a different part. In its entirety, this parent is truly indescribable, but it does somewhat resemble a snowman that has toppled over and is lying flat with its head facing east. The rating of a 6 was held back because the colors seem a little washed out, but a rating of a 6 is still above average, and with a calculation time of only 1 minute, what is there to lose. Perhaps the best way to view the finished image is to surf virtually out to the FOTD web site at: <http://www.Nahee.com/FOTD/> and ogle the finished product there. Lots of clouds, occasional sprinkles of rain, and a chilly temperature of 52F 11C spoiled things here at Fractal Central on Monday. The fractal cats spent most of the morning squatted down in the sulk position, so I suppose they got no more enjoy- ment from the conditions than the humans did. Both my day and FL's day went along uneventfully. The next FOTD will be posted in 24 hours. Until then, take care, and if one were to go back in time and shake hands with his younger self, would he remember both sides of the handshake when he returned to the present? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= EvaporatdButPresnt { ; time=0:01:00.67-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=-2.802310377022/+1.013603876431/1e+008\ /1/-135/0 params=4/-1.4/1/-4.4/0/1e+100/0/0 float=y maxiter=1000 inside=bof61 logmap=52 periodicity=6 colors=000000638G8AA7CIDEEBGLGIIFKNKLJLMJONKRWOPPK\ X_BULKXkT_O`eMiXKkkKm_KohKqcKscKucKwcPxcUzzzzzzzzz\ zzzrphrphmphmphhphhphcphcphZphZphUphUrgSphTniUmiUk\ jVjjWhkWglXelYdmZbmZan__o`Zo`XmaWjbUgbTd`RaZPZXNWV\ LTTJQRIMPGJNEGLCDA08A05A04A04LD4NF4QH4SJ4UL4WN4ZO3\ `Q3bS3dU3gW3iY3k_3ma3ob3m`5lZ7jY9iWAgUCfTEdRGcQHbO\ J`ML_LNYJOXHQVGSUEUTDVRFXQGYPHZOI_NJ`MLaLMbzNczOdz\ PezRfzSgzThzUizVjzXkzYlzZmz_nz`ozakzagzbczb`zcXzcT\ zcQzdMzdIzeEzeBzf7zf3zf0zc1za1zZ1zX1zU1zm1zz1zm2zz\ 2zm2zz2zm2zz2zm2zz0zm2zz3zm5zz6zm8zz9zNAzzCzTDzzFz\ ZGzzIzdJzzKziMzzNzoPzzQzuSzzTzzUzzSzzRzzQzzPzzOzzN\ zzMzzLzzKzzJzzIzzHzzMzzQzzVzzUzzUzzUzzTzzTzzUzzTzz\ TzzTzzTzzTzzTzzTzzTzzSzzSzzSzzSozSrzStzSwzSyzSuzRr\ zQozQlzPhzOezObzN_zN`zQ`zSazUazWbzZbz`czbczdezafz_\ gzYizVjzTkzRmzOnzMozKqzHrzFszDmzNgzW`zcazdbzeczfdz\ fezgfzhgzihziIzMJzLKzKLzK } 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, esc=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < esc } END PARAMETER FILE=========================================

1 0

FOTD 18-10-10 (Away on a Dry Wind [6])
by Jim Muth 18 Oct '10

18 Oct '10

FOTD -- October 18, 2010 (Rating 6) Fractal visionaries and enthusiasts: Most of the worth of today's image came about when I rendered it with the inside set to 'bof60' and the outside set to 'tdis'. The image itself consists of about half inside and half outside stuff. The parent fractal is one of those indescribably complex things that result when both exponents of Z have negative values and (1/C) is added. The name "Away on a Dry Wind" came to mind first when I tried to find a name for the image. I can see little connection to the actual image however. The rating of a 6 is just enough above the routine average to make the 3-1/6 minutes required to run the parameter file worth the effort. The finished image is available for instant viewing on the FOTD web site at: <http://www.Nahee.com/FOTD/> and no password is needed. Sunday here at Fractal Central was near perfect. The sunny skies and temperature of 70F 21C brought contentment to humans and cats alike. Being a human, (At least I was the last time I checked), I shared in the contentment. The next FOTD will be posted in 24 hours. Until then, take care, and where did it all go? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Away_on_a_Dry_Wind { ; time=0:03:10.21-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=+1.3713561803/-0.1740601838/29157/1/\ -77.5/0 params=4/-1.4/1/-4.4/0/0/0/0 maxiter=1500 float=y inside=bof60 outside=tdis periodicity=6 colors=000GbBGaBGaAG`AG`9G_9G_9GZ8GY8GY7GX7GX7GW6G\ W6GV5GV5GU5GU4GT4GT3GS3EP0GS3IU6KW9MYBO_EQaHSdJUfM\ WhPYjR_lUanXbpZSkeIfl0nz0mz0lz0jz0hz0fz0dz0bz0`w0Z\ s0Xo0Vk0Rg0Nc0J_0FW0AX05T00KVEITEGQEFOEEMEDOIGPLJR\ PLSSOUWQVZTXbWYeY_i``lbbpecsg`phZmhXjhVhhTehRbhP_h\ NYhLVhJSiHQiFNiDKiBHi9Fi7Ci59i37i4Gj4Pj5Yk5fk2wm5o\ k8hjBaiEUgHNfKGeM9dOBcPDcQEcRGbSHbTJbVKbWMaXOaYPaZ\ R`_S`aU`bV`cX_dY_e__faZgbZidZjeZkgYlhYmjYnlXpmXqoX\ rpXsrWtsWuuWvvWsuYqu_nt`ltbiscgsedsfbrh_rjYqkVqmTp\ nQppOpqNooMomMolLojKohKogJoeIocIobHo`Ho_GoYFoWFoVE\ oTDoRDoQCoOCoNBoLAoJAoI9oG8oE8oD7oB1u67oACiEHcIMYM\ RSQWMU`HXZGWYGVWFVVFUUEUSETRDTQDSOCSNCRMCQKBQJBPIA\ PGAOF9OE9NC8NB8MA8M99N9AO9AO9BP8BP8CQ8DQ8DR8ER7ES7\ FS7GT7GT6HU6HU6IV6JV6JW5KW5KX5LX5MY4MY4NZ4NZ4O_2N`\ 4O_5P_6Q_QMDQLDQLDQNCVQNZUXgTehYdjZcmZcrZbvZazZ`vU\ ZrPWmKThFQcEOcENcEMcEKcEJ } 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, esc=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < esc } END PARAMETER FILE=========================================

1 0

Fractint version 20.04 patch 10 is now available
by Jonathan Osuch 17 Oct '10

17 Oct '10

Folks, Fractint version 20.04 patch 10 is now available on the developer's web site: http://www.fractint.net or http://www.fractint.org What's new: Fixed WinFract resetting palette when parameters are changed with the <X>, <Y>, <Z>, or <G> screens. Fixed usage of shift and control keys in Xfractint. Added sanity checks in Xfractint parser functions. Fixed long standing bug in Xfractint that occurred when a PAR was invoked from the command line. Increased the WinFract maximum image size to 4096x4096 pixels. Your mileage may vary depending upon how much memory Windows can allocate. But remember that above 2048x2048 passes=1 is forced. Fixed bug in the cvtcentermagbf() routine that was introduced some time prior to version 19.6. This fixes the problem that was occurring when rotating ap math images by 90 degrees. Fixed buffer overflow in Xfractint that occurred when changing directories. Jonathan

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FOTD 17-10-10 (Flower of Fertility [7])
by Jim Muth 17 Oct '10

17 Oct '10

FOTD -- October 17, 2010 (Rating 7) Fractal visionaries and enthusiasts: This FOTD is late because I spent too much time on Saturday involved in pondering. I see on the list that Mr. Mandelbrot has moved on to whatever comes after this life for mathematicians. As far as I observed, his passing was little noted in the general news, which as always, seems more concerned with political polls and the con- trived adventures of the current pop celebrities. My thoughts about the event are that if I had designed mankind, I would have given him a few more, no a lot more, prime-of-life years on earth. I have always grumbled that we don't learn how to properly live life on earth until it's too late to benefit from what we have learned. All we can do is try to pass on to our children what we have learned. But what a waste of effort. Today's middling fractal is another one that rates a 7. It's actually an image of an order-7 minibrot in the vicinity of an anti-minibrot. I named it "Flower of Fertility". Who knows why. And I rated it at a 7 because that's what I consider it to be worth. The calculation time of 30 seconds is so brief that even if the result is disappointing, it will have almost been worth the effort. As always, the finished image is available on the FOTD web site at: <http://www.Nahee.com/FOTD/> Near perfect mid-autumn conditions held sway here at Fractal Central on Saturday, with sunny skies and a temperature of 68F 20C. The fractal cats made the most of things by passing the time sleeping, while my day was routine. The next FOTD will be posted in about 12 hours. Until then, take care, and how could a storm chaser be happy in heaven, where there are no storms to disturb the peace and the weather is always perfect? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Flower_of_Fertilty { ; time=0:00:30.75-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinalDivideBrot function=recip float=y center-mag=-1.254120781288623/+0.3826441355303951\ /1.154265e+010/1/125/0 params=7/-5000000000.0/0/0 maxiter=1500 inside=0 logmap=21 periodicity=6 colors=000pdRnaRk_QhYPeWPbUO_SNXPNUNMRLLOJLLHKIFIF\ DHCBF99D77CA9EDAGFCIIDKLFMNGOQIQTJSVLTYMV`OWbPXeRZ\ hS_jT`iU_hV_hVZgWZfXZfXZeYZe_ZdaZccZceZdgZeiZfkZfm\ Zfoafpcfqefrhfsjgvkftlesldrldqlcolbnlbmlall`jl`il_\ hlZglZemYdmXcmXbmW`mV_mVZmUYmTWmTVmSUmRTmRSmRRlRQl\ RPkRPkROkRNjRMjRMiRLiRKiRJhRJhRIhRHgRHgRGfRFfREfRE\ eRDeRCdRBdRBdRAcR9cS7dR9cQAbQBaPC`PD_OEZOGYNHXMIWM\ JVLKVLLUKNTKOSJPRJQQIRPHSOHUNGVMGWLFXLFYKEZJE`IDaH\ CbGCcFBdEBeDAgCAhB9iB9jA8k97l87n76o66p55q45r34s24t\ 25u36v37w48x48y49z5Az5Bz6Cz6Cz6Dz7Ez7Fz8Gz8Gz8Hz9I\ z9JzAJzAKzALzBMzBNzCNzCOzCPzDQzDRzERzESzETzFUzFVzG\ VzGWzGXzHYzHZzIYzHXzHWzGWzGVzFUzFUzFTzESzERzDRzDQz\ CPzCSz9QzBPzCOzENzFLzGKzIJzJIzKHzMFzNEzPDzQCzRBzT9\ zU8zV7zX6zY5zW5zZ5za5zc5zf5zh5zk5zm5zp4zs5zr6zr7zr\ 8zr9zrAzrBzrCzrDzrEzrFzqGzqHzqIzqhzAgzAgz7fzAfzCfz\ EfzHfzJfzLfzOfzQfzSfzVfzX } frm:FinalDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1)+0.00000000000000000001: z=(-b)*(z*z*fn1(z^(a)+b))-c |z| < esc } END PARAMETER FILE=========================================

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Benoit Mandelbrot 1924-2010
by Roger Alexander 17 Oct '10

17 Oct '10

Today's post marks the passing of Benoit Mandelbrot, father of fractal geometry. As a tribute to Benoit Mandelbrot's contribution to the field of fractal geometry today's fractal image is of the default original Mandelbrot set. The plotting does not use the usual inside and outside mappings but rather uses the distance estimator method with a two color map. This plotting method was chosen because I find it enhances the demonstration of the complexity of the basic Mandelbrot set. According to the Fractint manual "The distance estimator method widens very thin "strands" which are part of the "inside" of the set. Instead of hiding invisibly between pixels, these strands are made one pixel wide." At the usual http://maxitersfractalfollies.blogspot.com. Benoit Mandelbrot { ; distance estimator method ; fract474.gif ; calctime 0:01:00.47 ; created Oct 16, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=mandel passes=1 center-mag=-0.5/3.33067e-016/0.837633 params=0/0 float=y maxiter=1500 inside=0 outside=1 distest=1200/71/800/600 colors=0000Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0X\ z0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz0Xz } Roger Alexander

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Halley_JJP
by Mike Frazier 16 Oct '10

16 Oct '10

Here is a fractal I have been using to test improvements to Fracton's 3D Model Export. I switched from a grid based approach to a more sophisticated algorithm that searches for the edges of the fractal. Here is a quick loading web page with a few pictures and a short QuickTime movie that flies through the fractal. http://www.fracton.org/fmlposts/halley_jjp.html If you would like to view the fractal in FractInt, here is the parameter file. The complex parameter p1 is the exponent. halley_jjp { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20101016_1116 passes=1 float=y center-mag=0.4115234375000001/0.002148437499999963\ /0.8533333439999999/1/-90/0 params=7/0/0/0/0/0/0/0/0/0 maxiter=100 proximity=0 colors=UzJ<2>znP<1>B`3<4>H1C<3>i6X<2>znP<237>znP } frm:F_20101016_1116 { ; Type: Halley ; From Computers, Pattern, Chaos, and Beauty by Clifford Pickover ; See p277 for a related image and formula derivation ; Formula and par by Mike Frazier, public domain z=pixel: lz=z, f=z^(p1+1)-z,; Function z(z^p1-1) f1=(p1+1)*z^p1-1,; First derivative f2=(p1+1)*p1*z^(p1-1),; Second derivative z=z-2*f*f1/(2*f1*f1-f2*f), abs(|z|-|lz|)>=0.01 } -- Mike Frazier www.fracton.org

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Benoît Mandelbrot dead at 85 from pancreatic cancer
by Lee H. Skinner 16 Oct '10

16 Oct '10

A sad day for us all. You can google the various news stories. Lee

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Greenery
by Roger Alexander 16 Oct '10

16 Oct '10

More summer greenery reminders. Perhaps I can't face the possibility of frigid winter? At the usual http://maxitersfractalfollies.blogspot.com. fract473.gif { ; green swirls ; blank ; calctime 0:09:38.76 ; created Oct 15, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=kerrym.frm formulaname=ave8triangcount_m center-mag=-0.837046/0.868648/3.081854 params=1000000/0/3/3 float=y maxiter=1500 inside=0 invert=-0.485518967253/-0.217505417035/-0.711050752281 decomp=256 periodicity=0 cyclerange=0/255 colors=Dp1Cp1Co1Bo1Ao19n18n17n16m06l06k06j06i06h06g06f05e05d05c05b05a05`\ 05_05Z04Y04X04W04V04U04T04S04R03P03O03N03M03L03K03J03I02H02G02F02E02D02C\ 02B02A01901801701601501401300100100200300400500700800900A00B00D00E00F00G\ 00H00J00K00L00M00N00P00Q00R00S00T00V00W00X00Y00Z00`00a00b00c00d00f00g00h\ 00i00k00k01k02k03l04l05l05m06m07m08n09n0An0Bo0Bo0Co0Dp0Ep0Fp0Gp0Hq0Hq0Iq\ 0Jr0Kr0Lr0Ms0Ns0Ns0Ot0Pt0Qt0Ru0Su0Tu0Tu0Uv0Vv0Wv0Xw0Yw0Zw0Zx0_x0`x0ay0by\ 0cy0dz1dz1ez1ez1fz2fz2gz2gz2hz3hz3iz3iz3jz4jz4kz4kz4lz5mz5mz5nz5nz6oz6oz\ 6pz6pz7qz7qz7rz7rz8sz8sz8tz8uz9uz9uz9tz9tz9tz9sz9sz8sz8rz8rz8rz8qz8qz7qz\ 7pz7pz7oz7oz7oz6nz6nz6nz6mz6mz6mz5lz5lz5lz5kz5kz5kz4jz4jz4iz4iz4iz4hz3hz\ 3hz3gz3gz3gz3fz2fz2fz2ez2ez2dz1dz1cz1bz1ay1`y1_y1_x1Zx1Yx1Xw1Ww1Vw1Uv1Uv\ 1Tv1Su1Ru1Qu1Pt1Ot1Ot1Nt1Ms1Ls1Ks1Jr1Ir1Ir1Hq1Gq1Fq1Ep1 } frm:ave8triangcount_m {; Kerry Mitchell 12feb98 ; See the end of formula ave8rootcount_j for Kerry Mitchell's ; explanation of his "average" formulas ; real(p1) = bailout (try 1e6) ; imag(p1) = unused ; real(p2) = inner coloring speed (0 for outer only) ; imag(p2) = outer coloring speed (0 for inner only) zc=pixel, c=pixel, rc=cabs(c), r2zc=|zc| iter=1, maxr=real(p1), count=0 b1=maxr, fac=b1^0.125, b2=b1*fac, b3=b2*fac b4=b3*fac, b5=b4*fac, b6=b5*fac, b7=b6*fac, b8=b7*fac iter1=iter2=iter3=iter4=iter5=iter6=iter7=iter8=0 inspeed=real(p2)*pi*255/128 outspeed=imag(p2)*pi*255/128: iter=iter+1, z2=sqr(zc)+c, rz2=cabs(z2) fac=abs(r2zc-rc), q=(rz2-fac)/(r2zc+rc-fac) zc=z2, r2zc=|zc|, count=count+q IF (r2zc>b1) IF (iter1==0) iter1=iter, q1=count/iter ENDIF IF (r2zc>b2) IF (iter2==0) iter2=iter, q2=count/iter ENDIF IF (r2zc>b3) IF (iter3==0) iter3=iter, q3=count/iter ENDIF IF (r2zc>b4) IF (iter4==0) iter4=iter, q4=count/iter ENDIF IF (r2zc>b5) IF (iter5==0) iter5=iter, q5=count/iter ENDIF IF (r2zc>b6) IF (iter6==0) iter6=iter, q6=count/iter ENDIF IF (r2zc>b7) IF (iter7==0) iter7=iter, q7=count/iter ENDIF IF (r2zc>b8) IF (iter8==0) iter8=iter, q8=count/iter ENDIF iter=-1 q=(q1+q2+q3+q4+q5+q6+q7+q8)*0.125 angle=q*outspeed z=cos(angle)+flip(sin(angle)) ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF IF (iter==maxit) q=count/iter angle=q*inspeed z=cos(angle)+flip(sin(angle)) iter=-1 ENDIF iter>0 ;SOURCE: 98msg.frm } Roger Alexander

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FOTD 16-10-10 (Time to Trap a Fly [7])
by Jim Muth 16 Oct '10

16 Oct '10

FOTD -- October 16, 2010 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a ghost of its former self. Actually, it's an evaporated scene in the parent fractal that results when various portions of Z^(-1.4) and Z^(-4.1) are mixed and (1/C) is added on each iteration. The color section of the parameter file is so short because the image uses only 43 colors, but those 43 do the work of a full 255. The active inside fill of 'bof60', is a rather unusual one for me to use. The name "Time to Trap a Fly" came about when something in the image reminded me of a Venus Fly-trap plant. The rating of a 7 makes running the parameter file worth the 2 minutes required to finish. The already finished image may be viewed on the FOTD web site at: <http://www.Nahee.com/FOTD/> Friday passed uneventfully here at Fractal Central, with clouds but no rain, and a temperature of 61F 16C. The fractal cats had an equally uneventful day. The next FOTD will be posted in a matter of hours. Until then, take care, and watch out for the fractal ghosts. They can be hauntingly beautiful Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Time_to_Trap_a_Fly { ; time=0:02:29.62-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.83036955877/-0.09596038543/462548/1/\ 75.5/0 params=4/-1.4/1/-4.1/0/1e+100/0/0 float=y maxiter=1800 inside=bof60 logmap=yes periodicity=6 colors=000zTcxScvRctQcrPcoOclNdjMeiLdhKcgJbeIadH`d\ G_cFZcH`dIbdKddMfdNhePjeRleTnfUpfWrf_tfcuihqlmmnri\ qvetzantdgog`jjXffTbbPYZLSVGMRCHN8BJ000<211>000 } 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, esc=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < esc } END PARAMETER FILE=========================================

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Green Filaments
by Roger Alexander 15 Oct '10

15 Oct '10

Summer is over and fall has started. Today's fractal remembers the green which has not completely faded. Both gif and re-sampled jpg posted at the usual http://maxitersfractalfollies.blogspot.com As promised yesterday's image has been re-sampled and posted. Green Filaments { ; fract470.gif ; blank ; calctime 0:01:44.75 ; created Oct 14, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=kerrym.frm formulaname=field3_jul center-mag=0.0829957/0.59665/2.9036 params=0.375/0.5/100000000/4 float=y maxiter=1500 inside=0 decomp=256 colors=0100200300400500700800900A00B00D00E00F00G00H00J00K00L00M00N00P00Q\ 00R00S00T00V00W00X00Y00Z00`00a00b00c00d00f00g00h00i00k00k01k02k03l04l05l\ 05m06m07m08n09n0An0Bo0Bo0Co0Dp0Ep0Fp0Gp0Hq0Hq0Iq0Jr0Kr0Lr0Ms0Ns0Ns0Ot0Pt\ 0Qt0Ru0Su0Tu0Tu0Uv0Vv0Wv0Xw0Yw0Zw0Zx0_x0`x0ay0by0cy0dz1dz1ez1ez1fz2fz2gz\ 2gz2hz3hz3iz3iz3jz4jz4kz4kz4lz5mz5mz5nz5nz6oz6oz6pz6pz7qz7qz7rz7rz8sz8sz\ 8tz8uz9uz9uz9tz9tz9tz9sz9sz8sz8rz8rz8rz8qz8qz7qz7pz7pz7oz7oz7oz6nz6nz6nz\ 6mz6mz6mz5lz5lz5lz5kz5kz5kz4jz4jz4iz4iz4iz4hz3hz3hz3gz3gz3gz3fz2fz2fz2ez\ 2ez2dz1dz1cz1bz1ay1`y1_y1_x1Zx1Yx1Xw1Ww1Vw1Uv1Uv1Tv1Su1Ru1Qu1Pt1Ot1Ot1Nt\ 1Ms1Ls1Ks1Jr1Ir1Ir1Hq1Gq1Fq1Ep1Dp1Cp1Co1Bo1Ao19n18n17n16m06l06k06j06i06h\ 06g06f05e05d05c05b05a05`05_05Z04Y04X04W04V04U04T04S04R03P03O03N03M03L03K\ 03J03I02H02G02F02E02D02C02B02A0190180170160150140130010 } frm:field3_jul { ; Kerry Mitchell 20jan98 ; ; Colors Julia sets by nearest approach to ; period 3 field lines ; ; use decomp=256 ; p1 = Julia parameter ; real(p2) = bailout (try 1e12) ; imag(p2) = number of field line to use: ; 0, 1, 2, 3, 4, 5, 6, 7 ; 3 iterations per pixel ; variable zc used for calculation, z for coloring ; zc=pixel, c=p1, maxr=real(p2), minr=maxr, iter=1 fieldangle=tan(imag(p2)*2*pi/7): ; ; iteration ; compare tangent of polar angle with desired ; field line angle, update minimum if needed ; iter=iter+3, zc=sqr(zc)+c, zc=sqr(zc)+c, zc=sqr(zc)+c rzc=|zc|, tanangle=imag(zc)/real(zc), r=cabs(fieldangle-tanangle) if (r<minr) minr=r end if ; ; bailout ; set "iteration done" flag (iter=-1) ; use log of minimum difference of angles as ; decomposition angle ; if ((rzc>maxr)||(iter>=maxit)) iter=-1 angle=log(minr) z=cos(angle)+flip(sin(angle)) end if iter>0 } Roger Alexander

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FOTD 15-10-10 (Dancing Lepidoptera [7])
by Jim Muth 15 Oct '10

15 Oct '10

FOTD -- October 15, 2010 (Rating 7) Fractal visionaries and enthusiasts: Once today's image is viewed, the reason for the name "Dancing Lepidoptera" will be obvious. The rating of a 7 is right on the mark. And btw, a lepidoptera is a butterfly. The scene is located in the remains of the northern branch of Seahorse Valley of the decaying large minibrot on the main stem of the parent fractal. This parent is a Mandelbrot set on its surface, but in its depths, it becomes an order-7 Mandeloid. I particularly enjoy the seven totally-separated butterfly-like elements surrounding the central near-perfect order-7 minibrot. The calculation time of 8 seconds is no mistake. The image actually does finish in this brief time span. Of course, setting up this letter as a parameter file for calculation is a minor hassle, but this hassle may be avoided by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Thursday was a most unpleasant day here at Fractal Central. The day began with fog. By 10am a chilly rain had set in, which continued off and on, mostly on, through the day, while the temperature hovered around 48F 9C. The fractal cats avoided the unpleasantness by spending the day near the heat and eating an extra treat of tuna and cheddar. Except for the routine things that pass every day without notice, my day was uneventful. FL kept busy writing a word- search puzzle. The next FOTD will be posted in 24 hours. Until then, take care, and bad things happen to good people for the same reason that good things happen to bad people. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= DancingLepidoptera { ; time=0:00:08.01-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=-1.763845130568216/+0.00640222373378594\ /2.281007e+010/1/-75/0 params=7/1000000/0/0 float=y maxiter=400 inside=0 logmap=12 periodicity=6 colors=0001Ic5Jc9KcDLcHMcLNcROcWPc_QcbRceScgTcgUcg\ TchSchRchQcAAA000KHKTLNXPQ_TScXUf`XjdZmh`qlctpeztg\ zrcup_znWtlSzjOzhKzfGqdCzeBzfAzg9hh8zi7zj6zj5_k4zl\ 3Vm2Tn1Ro0Po0Qi4Rd8SZCTUGUOKUJOIwqMhsPVuTGwW2x_5ub\ 8seBqhDolGmoJkrMiuOgoPijQjeRk`SmWTnRUoMVqHWrCXsEan\ GejIieJmaMl_OlYQlXSkVVkUXkSZjR`jPcjNeiMgiKiiJlhHnh\ GphErhDhdKZ`RQYYGUd7RjDTeIUaNVYSWUXYPaZLf_Hk`Di_Gg\ _JeZMcZOaYR`YUZXXXXZVXaTWdSWgQViOVlMUoKUrJUtK`uLfu\ MmuMsuLoqKlmKiiJffJcbI`ZHXVHUSGROGOKFLGFIDHGEIFFJE\ FKCGMBHNAHO8IP7JR6JS4KT3LU2LV9QWGUXMYYTaZ_e_ei`lma\ sqbyudureqpfnnhjligijcgl`emXcnU`pQZqNXrJVsGTtKStOR\ tSRuWQu_QubPufPvjOvnOvrNvuNsrPppRmnTklUhiWegYbe_`c\ `_bb_bdZafZahZaiY`kY`mX_oX_pX_rWZtWZvWZwXYuYYsZYr_\ Xp`XoaXmbWlcWjdWieVgfVfgVdhUciUaiU`EEUBUX8hZEdXJaV\ OYTTVRYRPcONhKLmHJrDHwAGtCFrDFoEFmFFjHFhIFfJFcKEaL\ EZNEXOE6KY6MY6NY6PY6QY6SY } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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Re: [Fractint] 1 day, 21 hours, 20 minutes, 32 seconds, but worth it :-)
by JackOfTradeZ＠comcast.net 14 Oct '10

14 Oct '10

. how did you go from 8 seconds to 2 days ?? .

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Circles and Curls
by Roger Alexander 14 Oct '10

14 Oct '10

This fractal will definitely be re-sampled soon, hopefully in tomorrow's post. Posting re-sampled images is a great benefit of my blog. The convenience of pre-calculated pars and anti-aliased gifs, who can argue with that? Speaking of blogs go to http://maxitersfractalfollies.blogspot.com to check things out. Circles and Curls { ; needs re-sampling ; fract469.gif ; calctime 0:10:48.62 ; created Oct 13, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=2circles.frm formulaname=cenx=ceny_jul center-mag=-0.545532/-0.10771/17.1126 params=-0.8416089358195745/-0.2229987487411115/0.125/0.3681142612994781/\ 0.5048982207708976/-0.5791192358165227 float=y maxiter=1500 decomp=256 periodicity=0 cyclerange=0/255 colors=DHVCGUBET9DS8BR7AQ69P57O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAE\ TBGUCHVDIWFKXGLYHMZIO_JP`KRaLSbMTcOVePWfQXgRZhS_iTajUbkVclXemYfnZgo_ip`j\ qakrbmscntepufqvgrwhtxiuyjvzjvziuyhsxgrwfqvdoucntblsakr`jq_hpZgoYfnWdmVc\ lUbkT`jS_iRYhQXgPWfNUdMTcLSbKQaJP`IN_HMZGLYEJXDIWCHVBFUAET9DS8BR7AQ58P47\ O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAETBGUCHVDIWFKXGLYHMZIO_JP`KRaLS\ bMTcOVePWfQXgRZhS_iTajUbkVclXemYfnZgo_ip`jqakrbmscntepufqvgrwhtxiuyjvzjv\ ziuyhsxgrwfqvdoucntblsakr`jq_hpZgoYfnWdmVclUbkT`jS_iRYhQXgPWfNUdMTcLSbKQ\ aJP`IN_HMZGLYEJXDIWCHVBFUAET9DS8BR7AQ58P47O36N24M13L02K02K13L25M36N47O69\ P7AQ8CR9DSAETBGUCHVDIWFKXGLYHNZIO_JP`KRaLSbMTcOVePWfQYgRZhS_iTajUbkVclXe\ mYfnZho_ip`jqalrbmscntepufqvgswhtxhtxiuyhtxgrwfqveoucntbmsakr`jq_ipZgoYf\ nXdmWclVbkT`iS_hRZgQXfPWeOUdNTcMSbLQaKP`IO_HMZGLYFJXEIW } frm:cenx=ceny_jul {; Kerry Mitchell 26aug98 ; ; See the end of the formula general_man-2circ for ; Kerry Mitchell's explanation of the "2 circles ; coloring method". ; ; "2 concentric circles" coloring method for Julia sets ; p1 = c = Julia parameter ; p2 = (both) circle center ; real(p3) = x-circle radius ; imag(p3) = y-circle radius ; bailout hardcoded to 10^12 ; use "decomp=256" coloring ; zc=pixel, c=p1, bailout=1e12, iter=1, rmin=1e12 cenx=p2, radx=real(p3), rad2x=radx*radx ceny=cenx, rady=imag(p3), rad2y=rady*rady: iter=iter+1, zc=sqr(zc)+c tempx=|zc-cenx|-rad2x tempy=|zc-ceny|-rad2y temp=tempx+flip(tempy), r=|temp| IF (r<rmin) rmin=r, z=temp ENDIF IF ((|zc|>bailout)||(iter==maxit)) iter=-1 ENDIF iter>0 ;SOURCE: 98msg.frm } Roger Alexander

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FOTD 14-10-10 (Sparkling Waters [7])
by Jim Muth 14 Oct '10

14 Oct '10

FOTD -- October 14, 2010 (Rating 7) Fractal visionaries and enthusiasts: While viewing the image that Roger posted to the list Tuesday evening, I became so interested in the curious formula that I checked to see what I might be able to do with it. Returning to the default parameters of 0,0 and magnitude of 0.67, I found today's scene in one of the vague bud valleys of the Mandel-like parent. I have never seen anything quite like the image I came up with. When rendered at a very high resolution, it almost looks like a true-color image, though the standard 640x480x256 rendering creates a rather gritty but still notable scene. The scene itself is apparently a minibrot in the East Valley area of a larger minibrot. The parent fractal however consists of only the western half of a Mandelbrot set, with no East Valley, so today's image must lie in the East Valley area of a minibrot on the filament extending from the largest bud. I named the image "Sparkling Waters". Something about it reminds me of a just-opened bottle of soda water. The rating of a 7 seems about right. The calculation time of a mere 2-1/4 minutes actually seems a bit too brief for such a detailed image, but that's the way fractals are. The image may be viewed by saving this entire letter in DOS text mode with a .par extension, copying it into your Fractint directory, and running it as you would any other parameter file. Or all this work may be avoidved by going to the FOTD web site at: <http://www.Nahee.com/FOTD/> and viewing the finished image posted there. Near perfect though slightly chilly conditions prevailed here at Fractal Central on Wednesday, with cloudless skies and a tempera- ture of 61F 16C. The fractal cats slept in the sun to ward off the slight chill. My day was average, which is the way I like things. The next FOTD will be posted in 24 hours. Until then, take care, and the here and now is but an infinitesimal hyperplane sliced from the infinity of spacetime. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Sparkling_Waters { ; time=0:02:16.87-SF5 on P4-2000 reset=2004 type=formula formulafile=shells.frm formulaname=NovenaM2 passes=1 center-mag=+0.384602701512/-0.621157851044/2409632\ /1/-132.5/0 params=0/0/0/0 float=y maxiter=32000 inside=255 periodicity=0 colors=000mzzmxzrwzquzpszoqznozmmzlkzkizggzcez_czW\ azS_nOYnLViIReFMaCIY9DT69N34J00E01A02A02A03I04I04I\ 0BI0HIJNIHTIFZII_GK`FMaEPbDRcCTcBWdAYe9_f8bg7dh6fh\ 5YeGQbRI``AYk2WuJuONkPRbPVUPZUz_UzaUz_Uz`UzbUzcUzd\ WzfZzg`zhcmj`mkcmqecnhctjczzzzwzzzmzwzzzmzwRzmPvkN\ vjKviIviGvhEvgCvgAreCndDkbEgaFd_G`ZHXXIUWJQUKNTLJR\ MGQNLPQQOTVNWZNZcM`hLclLfqKivJlzJnyFpxCqx9sw6tw3ur\ 5rn7oj8leAiaCfYDcTF`PHYLIVGKSCMP8NNAPLCRJDTHFVFGXD\ IZBK`9Lb7Nd5Of3Qh1Rj0Sk3Sk5Sk7TlATlCTlETmHUmJUmLUn\ OUnQVnSVoVVoXVoZ21V74UB7TFASJDRNFQRIPVLOZONbRMfTLb\ SP_SSWSVTSYQS`MSdJSgFSjCSm9SpBUnCVlDWjEXhFYfHZdI_b\ J``KaZLbXNcVOdTPeRQfPRgNShMSgQSgTSgXSg_SgcSgfVThYE\ j`0lY4jW7iUBhREgPIfNLeTSiZZlcdoiksorvtxyolmk`bgPSc\ DH_LLWTPS_SOgWKo_HvbWjhiZmwNrvOmvPhvQcsVfp_hnckkhm\ iloknklpgmrcnt_ovWpwTfqYYkaOeeF_i6Um5Ydzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzmmm } frm:NovenaM2 {; Another Mandelbrot-like set for Novena. ; The Nova Formulae, discovered by PGD. ; Freely distributable but may not be sold. z=-0.5+(-1.75)^(0.5) c=pixel: z2=z*z z3=z*z2 func=z3+z-2 der=3*z2+1 oz=z z=z-(func/der)+c |oz-z|>p2 } END PARAMETER FILE=========================================

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Blue Shells
by Roger Alexander 13 Oct '10

13 Oct '10

This image suggests sea shells on the shore of some distant planet. At the usual http://maxitersfractalfollies.blogspot.com Yesterday was the Canadian Thanksgiving holiday. As a matter of trivia, in Lithuania Canadian Thanksgiving is almost as popular as Festivus! Blue Shells { ; fract468.gif ; blank ; calctime 0:29:13.10 ; created Oct 12, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_n.frm formulaname=NovenaM2 center-mag=+0.31907977426182810/-0.55275782073055070/172.6108 params=0/0/1e-006/0 float=y maxiter=1500 inside=0 proximity=1 outside=fmod periodicity=0 colors=hzzgzzfzzezzdzzczzbzz`zz_zzZzzYzzXzzWzzVzzTzzSzzRzzQzzPzzOzzMzzLz\ zKzzJzzIzzHzzGzzEzzDzzCzzBzzAzz9zz7zz6zz5zz4zz3zz2zz0zz0zz0yz0yz0xz0wz0w\ z0vz0uz0uz0tz0sz0sz0rz0qz0qz0pz0oz0oz0nz0nz0mz0lz0lz0kz0jz0jz0iz0hz0hz0g\ z0fz0fz0ez0dz0dz0cz0bz0bz0az0az0`z0_z0_z0Zz0Yz0Yz0Xz0Wz0Wz0Vz0Uz0Uz0Tz0S\ z0Sz0Rz0Qz0Qz0Pz0Pz0Oz0Nz0Nz0Mz0Lz0Lz0Kz0Jz0Jz0Iz0Hz0Hz0Gz0Fz0Fz0Ez0Dz0D\ z0Cz0Cz0Bz0Az0Az09z08z08z07z06z06z05z04z04z03z02z02z01z00z00z00z00y00y00\ x00x00w00w00v00v00v00u00u00t00t00s00s00r00r00r00q00q00p00p00o00o00n00n00\ n00m00m00l00l00k00k00j00j00j00i00i00h00h00g00g00f00f00f00e00e00d00d00c00\ c00b00b00b00a00a00`00`00_00_00Z00Z00Z00Y00Y00X00X00W00W00V00V00V00U00U00\ T00T00S00S00R00R00R00Q00Q00P00P00O00O00N00N00N00M00M00L00L00K00K00J00J00\ J00I00I00H00H00G00G00F00F00F00E00E00D00D00C00C00B00B00A } frm:NovenaM2 {; Another Mandelbrot-like set for Novena. ; P2 is an inverse bailout, ; set this to a small nonzero value and use ; floating point. E.g. 0.0000001. ; The Nova Formulae, discovered by PGD. ; Freely distributable but may not be sold. z=-0.5+(-1.75)^(0.5) c=pixel: z2=z*z z3=z*z2 func=z3+z-2 der=3*z2+1 oz=z z=z-(func/der)+c |oz-z|>p2 ;SOURCE: nova.frm } Roger Alexander

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FOTD 13-10-10 (The Fastest Way There [No Rating])
by Jim Muth 13 Oct '10

13 Oct '10

FOTD -- October 13, 2010 (No Rating) Fractal visionaries and enthusiasts: Today's lightning fast image is a Julia view of yesterday's tortured Rectangular scene, which itself is a different view of the Mandelbrot image of October 10. Today's FOTD image is a near exact repeat of the October 10 image, with a circular hole at the center rather than a Mandel- oid minibrot. This is why I could give it no rating. But there is a tremendous unseen difference between the images. The Octo- ber 10 image has a magnitude of 4*(10^011), while the magnitude of today's view is 8*(10^004). The Julia aspect is 5,000,000 times as large as the Mandelbrot aspect. This size disparity is the reason the Rectangular view of yesterday, which uses parts of both the Mandelbrot and Julia views, is so tortured. To preserve the colors of the first image, I kept the same color palette, though I did add a few new highlights to hold boredom at bay. The name "The Fastest Way There" refers to the speed of today's Julia aspect, which, with its calculation time of only 20 seconds is faster than even the Mandelbrot aspect. All this time confusion may be avoided however by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> The overnight showers moved out early here at Fractal Central on Tuesday, leading to a pleasant, partly cloudy afternoon with a temperature of 72F 22C. The fractal cats approved heartily. My day was typical -- occupied with the kind of routine things that are forgotten almost as soon as they happen. I think FL is about finished with gardening for this season, though a few minor chores still remain to be finished. The next FOTD will be posted in 24 hours. Until then, take care, and the future is but the reciprocal of the past. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= TheFastestWayThere { ; time=0:00:20.65-SF5 on P4-2000 reset=2004 type=julia center-mag=0/0/84415/1/45/0 params=-1.779820675627452/3.688441016998832e-011 float=y maxiter=40000 inside=255 logmap=-4416 periodicity=0 colors=000QWtQVsPUsOSrORrNQqNPqMOpLMpLLoKKoJJoJInI\ GnIFmHEmGDlGClFAkE9kE8jD7jD6jC5hC5gB5eB5dB5cA4aA4`\ 94Z94Y94X84V83U83T73R73Q63O63N62M52K52J42H42G41F31\ D20231C31B219218106105104002001000zzzzzzvwprtgmqdi\ ocfmbckaai`_g_YeZWcYUaXS`WQ_VOZUMYUKXTIWSGVREUQCTP\ ASO8RN6QM4PL2OK0NJ0MI0LH0KG0JF0IF0GE0ED0DC0BB09A08\ 9058027006005004003002001000FUHESGDRFDQFCPECODBNDA\ LCAKB9JB9IA8H98G97F86D76C75B65A54954943932A32F21K1\ 1P10U0KZBcWAhU9mS8rQ8vO7zL6zJ6hH58F47D46A358236224\ 1120x9ut8rq8on7lk7ih6fe6cb5`_5YX4VU4TR4QO3NL3KI2HF\ 2EC1B918605302z6ez5dz5cz5bz5bz5az5`z5`z5_z5Zz5Zz4Y\ z4Xz4Xz4WzUVzUVzUUzUTzUTzUSzURzURzUQzUPzUPzUOzUNzc\ NzcMzcLzcLzcKzcJzcIzcIzcHzcGzcGzcFzcEzcEzcDzcCzcCz\ cBzcAzcAzc9zc8zc8zm7zm6zm6zm5zm4zm4zm3zm2zm2zm1zm0\ zz8zz7zz7zz7zz7zz7zz7zz6zz6zm6zm6zm6zm6zm6zm5zm5zm\ 5zm5zm5zm5zm4zm4zm4zm4zzz } END PARAMETER FILE=========================================

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1 day, 21 hours, 20 minutes, 32 seconds, but worth it :-)
by Richard 12 Oct '10

12 Oct '10

FOTD for August 26th, 2010 "Second-Hand Seahorse" 3x antialiasing 1600x1200 <http://www.xmission.com/~legalize/fractals/fotd/2010/08/2010.08.25-SecondHa…> -- "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download <http://legalizeadulthood.wordpress.com/the-direct3d-graphics-pipeline/> Legalize Adulthood! <http://legalizeadulthood.wordpress.com>

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FOTD 12-10-10 (Z Squared Plus C [6])
by Jim Muth 12 Oct '10

12 Oct '10

FOTD -- October 12, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's tortured image is another aspect of the little Mandel- brot minibrot that appeared two days ago as the FOTD of October 10. That image was unmistakably a Mandelbrot-plane scene, but today's image is sliced in the Rectangular direction, which leaves little but the same colors to recognize. I wanted to do something more with the original image. My first impulse was to check the same scene in the Julia direction. The resulting circular hole was not very interesting however. So I tried the Rectangular direction, and look at what happened. To begin, the calculation time increased nearly 100 times to 45 minutes, which shows the efficiency of the type=mandel formula of Fractint. The original 2-lobed basin has been twisted and stretched to a point where it is almost painful to look at. The central minibrot is stretched into a slit so narrow that it has virtually vanished. I did tweak the colors a bit, though not enough to give myself extra points. The name "Z Squared Plus C" implies that the generating formula is the same; only the orientation has been changed. The rating of a 6 seems about right. The calculation time of 45 minutes will definitely not pass in a flash, which is why I recommend viewing the image already calculated on the FOTD web site at: <http://www.Nahee.com/FOTD/> Monday began well enough here at Fractal Central, with lots of sun and a temperature of 79F 26C, but at 4pm the sky clouded over and a minor thundershower moved in, dropping the tempera- ture to 64F 18C. The fractal cats took all this in stride, more concerned about food than the weather. My day was about average. Most likely tomorrow will be the same. The next FOTD will be posted in 24 hours. Until then, take care, and where did we go wrong? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Z_Squared_Plus_C { ; time=0:45:08.14-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=Rectangular center-mag=+0.000000000001\ 01005/-0.00000000000148829/2.16213e+011/0.04251/\ -114.506625219024372/-84.326593494906632 params=-1.779820675627452/3.6884410169988e-011/-1.\ 779820675627452/3.6884410169988e-011 float=y maxiter=40000 inside=255 logmap=-9114 periodicity=6 mathtolerance=0.05/1 colors=000QVtQUsPTsOSrORrNQqNPqMOpLMpLLoKKoJJoJInI\ GnIFmHEmGDlGClFAkE9kE8jD7jD6jC5hC5gB5eB5dB5cA4aA4`\ 94Z94Y94X84V83U83T73R73Q63O63N62M52K52J42H42G41F31\ D20231C31B219218106105104002001000zzwyzwxwwutprqjo\ pgmodknbim`gl_ekZcjYaiX_hWYgVXeUWcUVbTUaST`RS_QRYP\ QWOPUNOSMNRLMQLLQLKQLJPLIPLHPLGPKENICKGAIE9GC8EA7D\ 96B85A7496385274153042031020FUHESGDRFDQFCPECODBNDA\ LCAKB9JB9IA8H98G97F86D76C75B65A5495484363253242131\ 121010KZBIWAHU9GS8FQ8DO7CL6BJ6AH58F47D46A358236224\ 1120x9ut8rq8on7lk7ih6fe6cb5`_5YX4VU4TR4QO3NL3KI2HF\ 2EC1B918605302z6ez5dz5cz5bz5bz5az5`z5`z5_z5Zz5Zz4Y\ z4Xz4Xz4WzUVzUVzUUzUTzUTzUSzURzURzUQzUPzUPzUOzUNzc\ NzcMzcLzcLzcKzcJzcIzcIzcHzcGzcGzcFzcEzcEzcDzcCzcCz\ cBzcAzcAzc9zc8zc8zm7zm6zm6zm5zm4zm4zm3zm2zm2zm1zm0\ zz8zz7zz7zz7zz7zz7zz7zz6zz6zm6zm6zm6zm6zm6zm5zm5zm\ 5zm5zm5zm5zm4zm4zm4zm4zzz } 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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