May 2011 - Fractint - mailman.xmission.com

Re: [Fractint] FOTD 21-05-11 (Minibrot for the Ages [8])
by Brian Prentice 21 May '11

21 May '11

Jim, I've been exploring your fascinating fractal for today. If you change the real value of parameter 1 from 1.08 to 1.078, draw the midget corresponding to the one you posted today and then look at the south east side of the hook, you will find an area with an infinite number of midgets or holes. Here is a picture of that area: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06a.png and here is a detail of one of the midgets or holes: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06b.png Brian Prentice

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Re: [Fractint] How do I plug screen coordinates into a julia type?
by Jim Muth 21 May '11

21 May '11

At 12:51 AM 5/19/2011 -0600, Jay Litwyn wrote: >MandelBroh { ; What can you do with this, Jim? > ; This is all I can figure for a parser formula >that does Julia types. > ; It requires plugging screen coordinates into >P4. >z=fn1(pixel) +P2, c=fn2(pixel) +P3: > >if(ismand) > z=z^real(P1) +c >else > z=z^real(P1) +P4 >endif > >|z| <= imag(P1) Jay: It looks to me as though you are trying to write a formula that will automatically switch between the Mandelbrot and Julia aspects of a fractal by toggling 'ismand' on and off. To get the formula to work as you intend, with the screen coordinates automatically entered into the P4 parameter, would probably require new parser code. But many of the formulas hard coded into Fractint already do just this. With a Mandelbrot image on the screen, (try the manzpower formula), strike the space bar. A marker will appear at the center of the screen. Move the marker to the area of the Mandelbrot scene that you would like to see the Julia set of, and strike the space bar again. The Julia set will instantly be calculated. Striking the space bar again will return to the Mandelbrot set. JIM

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FOTD 21-05-11 (Minibrot for the Ages [8])
by Jim Muth 21 May '11

21 May '11

FOTD -- May 21, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is titled "Minibrot for the Ages". This is admit- tedly an exaggeration, but the minibrot actually is the most impressive I have yet found in a Mandeloid with an exponent of Z less than sqrt(2). In today's image the exponent is a lowly 1.08. The parent fractal was calculated 16 levels up the complex- logarithmic hyperladder with the 'recip' function applied. Using this function probably defeats the original purpose of the formula, which was to create an animation of the different fractals that can be created from the different values of the multi-valued complex logarithm. This parent is shaped much like the minibrot in the image, though it lacks the prominent hook, and has a 'nose' on what would be the upper right side of its main bay. Today's minibrot is very large. In fact it is actually visible on the northeast shore line of its parent with only the slight- est magnification. The rating of an 8 might have been higher if I had devoted more effort to the coloring, which I admit is a bit haphazard. The image calculates is an unremarkable 3 minutes. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> and in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site is at: <http://www.Nahee.com/FOTD/> Periods of sun interspersed with occasional thunder-showers made Friday an interesting day here at Fractal Central. The tempera- ture of 70F 14C was mild enough by winter standards, but rather chilly for late May in central Pennsylvania. The fractal cats had a typical day, though I think a bit of bad feelings arose between them in the afternoon. FL and I sometimes think of screening the back porch, adding shelves for the duo to leap onto, and making the entire porch into a catarium, where they can climb around and watch the world from their high, safe perches. The fractal cats appear to be ready for it. The humans had a frustrating day. We got word that one of our biggest customers will no longer be using our design services. This will leave more time for work on fractals, but less money for other things. Luckily, fractals are free and the supply of them is infinite. The next fractal will be posted in 24 hours. Until then, take care, and don't waste your energy worrying about things that have no chance of happening. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= MinibrotForTheAges { ; time=0:03:00.39-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip center-mag=+0.106891367/+1.163747143/147.5/1/\ -178.25/0 params=1.08/0/16/525 float=y maxiter=12000 inside=0 logmap=158 periodicity=6 colors=000cKQaLPZMPWOOUPORRNOSNMTMJVMGWL6ZD9YGCYIE\ YLHZNK`PMaSPcUSdXUfZXh`_jcakedmhgojipljoijofjodkna\ kn_knXlmVlmSmlSmlRmlRlkQkjQiiQhhPfgPefXdeUcdSbcPbb\ N_YKYTIVOFSJDQEAG98A46mKzkFyj3ui5rh7ogDlWScLZUNdKP\ c4Rb9TaDVZIYWM_TRaQVcQXdPYePZfP`hQbkRdmSfoSgqRgsRg\ oTgkUegWccXb_Z`W_ZSaXObWKdUGeSAeS6eTDfRJgQPgPVhOai\ NgiMmjLskKykJubErV9nM4kE0gD5dDA`DFYDKUDPRCUNCZKCcG\ ChDCm93vACqALmAThAadAj_FyUDvVCtVArW9pW8nX6lX5jY2kX\ 3jY3iY4hY4gY5fZ5eZ5dZ6cZ6b_7a_7`_3Ep5MjATdK__UfUcm\ OmzEctJUpOQkSMgXQbaUZeYUjTPlaQniQopFqqLpqQprWor`os\ enskntpmyzzvwztuzqszoqzlovjmpgkceiVbgR`eOYcLWaIY_6\ U_FR_ON_WK_dH_lJZiLYgNYeOXcQXaSW_UWYVVWXVUZUSXQP_U\ QaXRc_SebTgfTiiUklVmoWorWkoXhmYzkzbhz_fzzezThzQkzz\ nzKqzHtzzwz4zz7zzzzzBzzCzzzzzDzzDzzEzzEzz0zzEzzRzz\ czzqzzpzzszzrzzqzzpzzozznzzmzzlzzkzzjzzizzhzzgzzfz\ zezzezzgzzizzkzzlzzizzfzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 20-05-11 (Celestial Banquet [9.5])
by Jim Muth 20 May '11

20 May '11

FOTD -- May 20, 2011 (Rating 9.5) Fractal visionaries and enthusiasts: Today's image is not new. It is an updated version of a FOTD that I first posted over 10 years ago. For the image's second appearance, I did a slight outzoom and slightly intensified the colors. The result rates a 9.5, (at least IMO), with the extra half point honoring the coloring effort. The parent fractal is more a scattering of bits and pieces than a single large bay surrounded by interesting details. But there is one prominent element, and today's image lies in a valley of a bud in this large element. The name "Celestial Banquet" was inspired by the heavenly effect of the turquoise surroundings, where the angels are almost visible dancing on the gossamer clouds. I guess the saints are watching from the sidelines. The spiky arms shooting off in all directions give just enough impression of gateways to infinity to complete the transcendental experience. Actually, such a heaven, at least IMO, would be more of a hell than a reward. What could be worse than being stuck in a boring church service that would never end, lacking even the ability to escape into sleep. I have heard it said that when Casanova, having lived a life of sin, finally arrived at the golden gates, he was met by Saint Peter, who took no time in consigning him to the other place. Hearing the expected bad news, Casanova turned and saw before him two doors, one leading to a very solemn church service where the saved souls were forever praising God, singing unending hymns and listening to unending sermons; the other leading to a place of unending fun feast and sinful frolic, where the con- demned souls were wallowing in their own debauchery, eating and frolicking without the need to ever take a rest break. "It's not as bad as I feared," Casanova said as he turned toward the door leading to the place of debauchery. But before he could reach the door, Saint Peter called out and warned him that he had made a mistake and was going toward the wrong door. The 3-1/2 minute wait while the image cooks may be avoided by visiting the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and viewing the image, already calculated, there. The high-definition version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Heavy clouds and occasional rain prevailed here at Fractal Central on Thursday, with occasional rumbles of thunder thrown in for good measure. The temperature of 63F 17C kept thoughts of imminent summer far away. The fractal cats seemed not to notice the outdoor conditions. They were more concerned with being properly fed. The humans had an average day with the usual frustrations. The next FOTD will be posted in 24 hours. Until then, take care, and why look to the sky for the light when the light may lie at your feet? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Celestial_Banquet { ; time=0:03:31.68-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.par formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.1110932127946931/+0.0666019942450076\ /2.9199e+012/1/-52.5/0 params=1.1/-5/-1.1/1/0/0/0/0 float=y maxiter=3000 bailout=25 inside=0 logmap=405 periodicity=10 mathtolerance=0.05/1 colors=0009biAbhCckDdiEdlGfjHfjJhkKhkLilNjlOjmPjmR\ knSknTkoVloWlpYmpZmq_mqanrbnrdnrensfnshotiotjotkpt\ kptkptlptlptmptmptmptnqtnqtortortpstqstrttstttutuu\ tvvtwwtxxtyzzzzzzzzzzzzztzzzzzzzzzzzzzzzzzznlrgiq`\ epUbnNZmGVl7Rl8RlARkBRkDRjERjFSiHSiIShKShLSgNSgOSg\ PSfRSfSSeUSeVTdWTdYTcZTc`TbaTbbTbdUceTafTahTaiT`jT\ `hUZgWWeXUcYRa_P``MZaKYcHWdFUemTfURg8cu2Qh6SXAUKEa\ 5F_7GY9IXBJWEKVGLUINTKORMPQOQPRSNTTMVULXVKZXK`YJcZ\ Ie_HhaGjbFmdFoeErhDtmCwrByvAyzAyz6mV2cE4MG5NH6OI7P\ J9RLASMBTNCUODVPEWQFXRGYSI_UJ`VKaWLbXMcYOe_Pf`QgaR\ hbSicWncUkcSgcPddN`dLYdIUdGRdEOdCLmAHz8EzDDzHDYMCV\ QBRVBNZAKcAGm9Dz1AzmAzHA`PAYXAVdAWn0WmAXlKXkUYkcXj\ bWjaWi`Vi_Vi_UhZTiYTiXSiWRhVRhVQhUQgTPfSOeRNcQNbPM\ aOLbNLbNKaMJaLJaKIaJIbJHcKHdMGfNIhPLjQOlSRnTUoUXpW\ _qXbrZes_htakubnvdqwetxfwyhzzizzkzzlzzmzznzzczzUzz\ KzzHzzJzzKzzLzzMzzNzzOzzY } 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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How do I plug screen coordinates into a julia type?
by Jay Litwyn 19 May '11

19 May '11

MandelBroh { ; What can you do with this, Jim? ; This is all I can figure for a parser formula that does Julia types. ; It requires plugging screen coordinates into P4. z=fn1(pixel) +P2, c=fn2(pixel) +P3: if(ismand) z=z^real(P1) +c else z=z^real(P1) +P4 endif |z| <= imag(P1) }

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FOTD 19-05-11 (Twenty to the Clock [7])
by Jim Muth 19 May '11

19 May '11

FOTD -- May 19, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us to the parent fractal that results when six parts of Z^(-2) are combined with ten parts of Z^(-10) on each iteration before (1/C) is added. This parent fractal resembles a 3-leaf clover with a prominent bud on the edge of the eastern leaf. Today's image is located on a minor filament extending inland from the shore of this bud. In an effort to make something of the original nothing image, I half evaporated it, then rendered the result with the remaining outside parts set to 'mult' and the newly-exposed inside set to 'bof60'. The result rates a 7. I named the image "Twenty to the Clock", partly for fun and partly because of the twenty converging arms inside each element. The image calculates in 2-1/3 minutes, but this time may be saved by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version of the image is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The venerable original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Lots of threatening clouds hung around Fractal Central all day Wednesday, but once again little rain fell. The temperature of 70F 21C was pleasant enough. Only the lack of sun could be complained about. The fractal cats passed the day wondering what life in the great forbidden outdoor world would be like. I passed the day thinking about cleaning out the spare room, and ending up doing nothing. FL spent the afternoon working in the garden, with me giving occasional moral support. The next FOTD will be posted in 24 hours. Until then, take care, and be of stout heart but lean body. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Twenty_to_theClock { ; time=0:02:20.01-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.10412374889474/-0.07981491857980604\ /1.116e+011/1/92.5/0 params=6/-2/10/-10/0/10000/0/0 float=y maxiter=1500 inside=bof60 outside=mult colors=000mczqttptootkotfntbntZkqeholelsbjzcmvcosc\ qoctlcvhcxeczbfyciyclycnycqxdtxdwxdyxduohqfknZnjQq\ fHtc9wWOxPaxIoxJnoJmfJlY6DsFUmNigPefQbfR_fTXeUUeVR\ eSW`Q`WOeRMiMKnHIsCGw7PqGXkOdeWai2_d5`_7ZV9XQBTLDR\ GFMBHF7D000ILODRQ8YS3cU8dTDeSIfSUWXdMaoBfz1kw5lu9m\ lsg000vsgusgttgstgrugqugpvgowfnwfmxflxfkyfjyfizfiz\ fjvcjr`jnYkjVkgTkcQl_NlWKlTImPFmLCmH9mE7nH6oK6oM6p\ P6pS6qU6qX6r_6ra6sd6sg6ti6tl6uo6uq6lk8ceAW_BNUDEOF\ 6IGBNEFRDKVCOZBTbAXf9aj8en7jr6nv5rz4rv6rr7ro8rkArh\ BrdCr`ErYFrUGrRHqQJpPLnNOmMQlLSkKUiIXhHZgG`fFbdDec\ CgbBiaAkYKnUUqQctMmwIwyRiu_WrgIogNjgRegWag_XgcTh`W\ iYZjV`jSckPflMhlJkmGmnDpnAso7up4xp2zk3xf4wa4vX5tT5\ sO6rJ6pE7oA7nBBdCFVDJLENBFQ2HR3IR4KS5LS6NT7OT8QT8R\ U9mmAUVzmcCXWDZWE_WEYmzXTJWSMVROUPRTOTSNWRMYQK`PJb\ OIeNHgMFjLElKDoJCqNFpQHpTKoWMoZPnaRndUmgWmbViYVeTV\ aOUYJUVEUR9TN4TJ0TGdfKbcK } 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] A meaning for scalemap=0/0/0/0/0/0/0/0/0/0/0/0; silence.
by Jay Litwyn 19 May '11

19 May '11

Okay, so zero is a valid number in this assignment: frequency = reference * 2 ^ (1/12) ^ 0 In that, 2 ^ (1/12) ^ 0 = 1, so a scalemapping of zero translates to the reference frequency: reference over one, which, if your reference frequency is 440Hz, 220Hz, 110Hz, or 55Hz, is a 12-TET Ay. FracTint will use zeros if you enter them manually. It will also save them. I won't load them from parameter files. It should not be treated as it is, though, because that means two Ays are possible in a scalemapping: Zero and Twelve. I've been using zero to reprezent silence for over ten years. That's what M$ QBASIC does. It was a bit tricky to get a neat zero in my synthesizer, when I decided that the PC speaker didn't offer quite enough in the way of parallel harmonics and neat sine waves. If I want to change it, I guess the easiest way is to read the code myself, splice in a special case for zero, where all of the Cs, one of which would normally be at about 65.4Hz, become silent: compile it in, and offer it on the developers mailing list when it works. _______ http://ecn.ab.ca/~brewhaha/Sound/

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FOTD 18-05-11 (Questioned Reality [?])
by Jim Muth 18 May '11

18 May '11

FOTD -- May 18, 2011 (Rating ?) Fractal visionaries and enthusiasts: The version of today's discussion that appears on the FOTD web site includes material that may be offensive to certain sensitive individuals and has been omitted from this fractal- topic version. I gave today's extreme-magnitude image no rating. How could I rate it when I'm not even sure it's real? Oh, the image itself is real enough, but is it an actual fractal or just an artifact of mathematical imprecision? In the end, it doesn't really matter whether the image is real or an artifact. If it's an artifact, it's a real artifact, and with its ever-increasing series of rings, it makes a rather interesting figure. The image is located inside the usually-empty bay of a minibrot in the Seahorse Valley area of the Mandelbrot set. Those who doubt this may back out of the scene and prepare for a surprise. The name "Questioned Reality" refers to the questionable reality of the entire image, and also to the questionable reality of what we call the 'real' world. The calculation time of 5-3/4 minutes may be bypassed by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition image is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Heavy clouds and continued intermittent light rain prevailed again here at Fractal central on Tuesday. The fractal cats kept dry indoors, but wished the outdoor temperature could have gone above the actual high of 63F 17C. The humans kept busy doing other things. The next FOTD will be posted in 24 hours. Until then, take care, and does it take a brain to make a mind or a mind to make a brain? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Questioned_Reality { ; time=0:05:47.01-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-0.75836030827917080/+0.076845311784048\ 33/1.790637e+013/1/-56/0 params=0/0/0/0/0.77/0/\ 1e-100/0 float=y maxiter=1600 periodicity=0 inside=0 logmap=1008 mathtolerance=0.05/1 colors=000B48C37C36D35D24E23E22E21K89JHHIQPHZXGZdF\ _aNYgUXcSYaRX_PVZOSXMOWLLUPIPKAKA5A0002Sc1Rg0Rk8Qm\ FPoMOpUNr`MsgLunKvkNqiQmfTidWebZa`XbZVcXUcVSdTQeRP\ ePNfNQfNUeMceLmeKpeLqeMncMiaNd_O_YOWWSZZWa`_dcbgef\ jgjmjnpmrsrvvvzzzB8j98h78f58d38b18`08ZABTKENTHHmQB\ kP5jK9jFCiBGi8Jh4Nh1Q_CPRMOJWOAeN2oNBcHKSBTG5`40b9\ 5dDAfIFhMKjQPebT`nWiPZr0ar3dr6fr8irBkrEnrGprJsrLuj\ m3fVkiSilQhoOgrLfuJewHdsKcpNclQbiSbfVbbYa_`aXbaWdX\ VfTVhPUjKTlGTmCQpPNs`KvmIyyPwxVux`txgrwmqwsowynwum\ prlinkbkkWgjPdiIaiCUhRMgeEgtFfpFfmFeiFefFecFd_FdXF\ dUJZVNUWRPXVKYYFY`GTbHPeIKgJGjKBlL7nM3RgWO_VLTVIMV\ GFVIIUJLULOUMRTOUTPXTQZTUUQYQNaLKeHIiDFm8Cq49t07s9\ 6sH6sQ5rY5rf4rn4emETlNGkWCnQ9pL6sG3uB0w67sE6jS5beF\ ZdOVcYScfOboLblQajV`h_`fd_dh_aia_ibXjcVjdb`hjRlqIo\ nFqkDshBte8vb6w_4yY2zQ3lI3ZA4L2486JBAYEEkGFhKGfNHd\ QIbUJ`XKZ_LXbMVfet7mw7UW8 } 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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bunny.par
by Jay Litwyn 17 May '11

17 May '11

Exp_Div { ; Formula z=fn1(pixel), exponent=real(P1): z=z^exponent -fn2(z) +P3 exponent=exponent / P2 |z| <= imag(P1) } Bunny { ; http://ecn.ab.ca/~brewhaha/img/Bunny.jpg ; 0:00:20.71/megapixel on a 3.2GhzP4 reset=2004 type=formula formulafile=bunny.par formulaname=exp_div function=ident/conj passes=t center-mag=1/0/0.2089479/1.4289 params=2/8/1/0/-0.5/0 float=y maxiter=255 inside=0 invert=1.07576482623806/1.125/0 symmetry=xaxis periodicity=0 colors=(a)rainboh.map }

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FOTD 17-05-11 (String of Numbers [8.5])
by Jim Muth 17 May '11

17 May '11

FOTD -- May 17, 2011 (Rating 8.5) Fractal visionaries and enthusiasts: With today's image we return to that warhorse formula, the MandAutoCritInZ, where we subtract 1.4 parts of Z^(1.5) from Z^(3.5) before adding straight C. This rather routine combina- tion creates a parent fractal resembling a violin with ears. Today's image is located in a blunt valley jutting into the northern ear. A good part of the image consists of dead 'inside' stuff, brought to life by the 'bof61' inside fill. The other active inside fills create different effects and are worth a try. I named the image "String of Numbers", which is really no name at all, since all fractals are strings of numbers. But this is what came to mind when I studied the image, and this will for- ever be its name. The rating of an 8 might be a bit over-estimated. That's no problem. If 8 is what I think it was worth when I rated it, then 8 is what it's worth. The extra half-point is an after- thought, a self-reward for the coloring. The calculation time of 8-1/4 minutes is too long, but may be avoided by viewing and enjoying the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The discussion on the web site will often differ from the version posted to the list. I consider the web site to be more an omnibus blog than a fractal forum, a blog where all topics are fair game, especially science, religion, and philosophy. High definition fans will find their dreams fulfilled at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where today's image is posted in hi-def. The original FOTD web site, with all images prior to November 2010, is available at: <http://www.Nahee.com/FOTD/> Lots of clouds, only a little rain, and a temperature of 68F 20C made Monday a nondescript day here at the self-proclaimed Fractal Central. After a lively tussle Sunday evening, when oversized Nicholas knocked petite Cassie off the footstool, the fractal cats made up for their spat Monday morning and lived peacefully the rest of the day. The humans had another typical day, with nothing out of the ordinary happening. Unlike Lake Wobegon, where something happens even when nothing happens, when nothing happens at FC, there is nothing to tell. The next FOTD will be posted in 24 hours, and that definitely is something to tell. So until then, take care, and I found a Higgs particle on my desk this morning, but before I could put it in a safe place, it vanished. Once again, worldwide fame and recognition have eluded me. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= String_of_Numbers { ; time=0:08:16.55-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.5921467994425457/+0.2897262397443035\ /2.758e+011/1/137.5/0 params=1/3.5/-1.4/1.5/0/0/0/0 float=y maxiter=3600 inside=bof61 periodicity=6 colors=000VPVVQVVRVVTVVUVVVVVXVVYVVZVV`VVaVVbVVdVV\ eVVfVVhVViVVjVVlVVmVVnVSgSQ`Q000LNLJGIH9GF3EE4DE4C\ E4CE4BE4BE4AE49D49D48D48D47D46D46D45C45C44C43C43C4\ 2C42C41C41G57K6DO6IS7OW8U_8Zc9df9ic8f`7dY6bV5_S4YP\ 3WM2TJ1RG0PE2VC4`B6f98j7Am6Br5Ak5Aj5Ai49h48k48n37u\ 37t36u26v25w25x2By7CzCOzGLzLXzPWzUgzZfzbpzgpzmtzms\ wprtoosrmtrkusivugwvexwdyubxt`wsZwrXvqWvoUunSumQtl\ PtkNsjLshJrgIrfGqeEqdCpcBpeAmfAkhAhi9fk9cl9ahAbeBb\ bBc_CcXDcTDdQEdNFdKFeHGeEGewXUmwJhwIcwHZwHUwGPwFKw\ FFwEGwEHwDJwCKwCMwBNwBPwAQw9Rw9Tw8Uw8Ww7Xw6Zv6_v5`\ v5auBbuGcuMduRduXetaftggtlhtrhtwfpvemvcjubgu`ct_`t\ ZYsXVsWSrUOrTLqRIqQFp000RBnSAlT9jU8hV7fX6dY5bZ4`_3\ Z`3XZ6ZX8_WB`UDaTGbRIcQLdONfMQgLShJViIXjG_kFalG`jG\ `hG`fH_dH_cH_aI__IZYIZWJZVJZTIYRIYPHYNGYMJVKMSIPQG\ TNETFCVHBXE9YC7_A5`73a52a73`94ZB5ZD5WF6VH7SI7QK8PM\ 9NOAMQAQSBQKUPKVPKWQMVQNV } 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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