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FOTD 24-05-11 (Bubbles in Numbers [6])
by Jim Muth 23 May '11

23 May '11

FOTD -- May 24, 2011 (Rating 6) Fractal visionaries and enthusiasts: When certain people have trouble sleeping, they sometimes count sheep. When I can't sleep however, I begin mentally exploring an imaginary four-dimensional world. My imaginary world is truly four-dimensional; the problem is that I can mentally ex- plore it only one 3-D slice at a time. As our planet earth has a curved two-dimensional surface, my 4-D world has a curved three-dimensional hypersurface. On earth, two coordinates, latitude and longitude, are necessary to posi- tion a point; on my 4-D world, latitude, longitude and lithi- tude, (my own invention), are required. Moving in the lithi- tude direction does not take us into the sky or underground; it moves us in the third dimension, flat along the hypersurface. To reach a given location on this 4-D world, we start at the zero-zero-zero point on the equator, which is a great circle that circles the planet just as earth's equator does, and from there we travel until we reach the correct longitude. Now we find ourselves with a problem. Before we can set off toward the pole, we need to determine in which direction to go. On earth there are two directions, north and south, leading toward the two polar points; on my 4-D world there is a full 360- degree circle of directions extending from the equator, each direction leading to a distinct point on the polar circle. The direction in which we must travel away from the equator is the lithitude. Once we have chosen the lithitude, we need the lati- tude coordinate, which tells us how far to go toward the polar circle in the direction we are traveling before we reach our destination. But even stranger things than this happen on my planet. There is also the matter of rotation. On earth, rotation is a simple thing -- the planet rotates on its axis, a line that extends through the globe from pole to pole. But on my 4-D planet, the axis of rotation is a plane that cuts the hypersurface along the polar circle, a curiosity that causes complications. The problem arises because the polar plane exists in two dimen- sions that are stationary even as the planet rotates around it. The polar plane is therefore free to rotate on itself, with the equator as the axis of its rotation. And in a universe with 4-D gravity, it is unlikely in the extreme that the polar plane does not have at least some degree of rotation. The 4-D planet is subject to two independent rotations at the same time. Every point on the hypersurface as well as every point within the planet is tracing out what is known as a surface of double revol- ution, a kind of 4-D donut. Things on the surface of my planet move in paths resembling spirals, which curve back on themselves into closed loops. This means that the stars in the hypersky must move in helixes. What fun it must be to set up camp in some dark spot on the hypersur- face of my hyperplanet and point a hypertelescope at the hyper- stars and hyperplanets. The hypertelescopic clock-drive would be a complex device, but I'm sure that it could be made. If the two rotations are equal, things get even more complica- ted, but this is a story for another day. For now, we have a fractal to investigate. Today's image lies in the parent fractal that comes about when Z^(1.25) is subtracted from Z^(-1.75) before (1/C) is added on each iteration. This parent is more a field of debris with two large Mandeloids than a single object. Today's scene is located in some debris lying between the two largest Mandeloids. There is not much to be said about the fractal, so I'll let it speak for itself in visual terms. The name "Bubbles in Numbers" refers to the bubbly shapes in today's image and also to the fact that fractals are made of numbers. The rating of a 6 indicates that the image has room for improvement. To view the image, either run the included parameter file or go to the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version of the image 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/> There were too many clouds at Fractal Central on Monday for the day to be considered a good one. The temperature of 75F 24C was fair enough however. The fractal cats spent the day plotting mischief, but fell asleep before they could put their plot into action. In the afternoon a tornado warning came over the radio, but the storm passed over with only a strong wind squall and a torrential rain. The day of the humans was one more in an unending series of similar days. But the older one grows, the more such uneventful days are appreciated. The next in the unending series of FOTD fractals will be posted in 24 hours. Until then, take care, and when do we get to see the all of fourth spatial dimension in one moment of time? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Bubbles_in_Numbers { ; time=0:00:30.04-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+0.03748573643483764/-0.655971033500649\ /1.5667e+010/1/-35/0 params=-1/1.25/1/-1.75/0/0/0/0 maxiter=500 inside=0 logmap=57 periodicity=6 colors=0000440650962C74F86I9AL7DO5HV4Kd2Nl1cu2tz2h\ ZPK35Q46X47b48h59n5AuKBzPBsKGk8Lc9QXAVjBnkGelKYmOQ\ nSIoWAp_2sWLvSbyOtv`atlJqfMnaOkXQhRTeMVbHXaMa`Qe_V\ iZZmYcqXguXky`lndmdgnVkoLnoBLCIF_J9wKLaUXHceMjmRqu\ WxrSppOimKbkGWhCPf8Id5Bc6Eb7Ha8K`9M_APZBSYBUdjo_il\ WijRigNieIicEi`9iZ5iXPVfgGpz1yy2xx3wx4wvAutGtsLrqR\ qpWonanmfmkiqjlthowgqzajpXdgRZYMTPHNGVVNgbUti`neai\ aacZaZVaTRaOOaIKaDHaDGbDFbDEcDDcHCdLCdPBdTBdXBdYAc\ Z9cZ9cSCaLF_EIY7LW0NV4TS8YQCbNFgLJlINqGQvEMbCIJAF0\ 8E62TGJXLL`QMcVOg_PkdRniSrnUurVqrUmrTksYitagueevic\ wmbxq`toZqnXnlWkkUgjSdhQagPZfPYeQXcQWbQW`QVZQUYRTW\ RTVRSTRRSRQQRQPTOQVMQXKRZIR`GSbESdCSfATh8Tj6Ul4Um2\ Uj5Vh8WfBWcEXaHY_KYXNZVQZTT_QW`OZ`MaaKdaUH0`IDVH2W\ H3XH5YH6ZH8_H9`HBDSaHQYKPVNNSQMPTLLWJIZIFRx_StYTqW\ UnUVkTVhRWePXbOYZMZWKZTI_QH`NFaKD5Qd8PaBO_ENXGNVJM\ SMLQPKORKLUJJUTeOWXJZNDaD } 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 23-05-11 (The Original Tree [No Rating])
by Jim Muth 23 May '11

23 May '11

FOTD -- May 23, 2011 (No Rating) Fractal visionaries and enthusiasts: Today, with time at a premium, it's back to fractals-101. When I booted the first version of Fractint that had the ability to calculate fractional powers of Z, the first formula I tried was the type=manzpower, and the second thing I did was check the Julia set of the point on the negative X-axis where the western shore line of the main bay lies. What I found was a fractal that rather resembles one of those extinct marine animals known as trilobites. But an animal that once oozed through prehistoric sea-floor slime makes a poor model for a fractal. Luckily however, the trilobite was surroun- ded by a ring of graceful though stylized fractal trees. One of these trees appeared as one of the very first FOTD images, though that image was calculated at a much lower maxiter than today's version. The original version cut off the deep spirals that engulf the sides of the crown of the tree. I could not give a rating to today's image. I put relatively little coloring effort into it, and it must be about the eighth fractal tree in FOTD history. The name "The Original Tree" simply reminds the viewer that such a tree was the first of the infinity of fractal trees that I stumbled upon. Actually, this fractal tree stuff is quite common in the fractals created with fractional exponents, and can be turned into several other rather convincing things such as fractal landscapes on alien planets. The finished image is posted, already calculated, at: <http://www.crosscanpuzzles.com/Archives.html> The hi-def version of the finished image is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic original FOTD web site is at: <http://www.Nahee.com/FOTD/> Saturday turned into the most pleasant day in over a week here at Fractal Central, with partly cloudy skies and a temperature of 81F 27C. A few showers were scattered around the area, but they all missed FC. Sunday was not so pleasant. The sky was totally cloudy and the temperature reached only 73F 23C. The fractal cats had two uneventful days, spent mostly sleeping. The next FOTD will be posted in 24 hours. Until then, take care, and do well in your endeavor. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Original_Tree { ; time=0:00:32.35-SF5 on P4-2000 reset=2004 type=julzpower center-mag=0.238352/0.49\ 311/6.45945/1/-1.5/0 params=-0.1964/0/1.5/0 float=y maxiter=1500 bailout=25 inside=0 periodicity=6 colors=000ci__haXgbTfcPecMdcIccEbcBac7`c4__0ZY0YZ3\ XZ3WY3VX3UX3TW2SV2RU2QT2PS2OR2OQ2OO4OQ6PS8QTARVBSX\ DTZFU`HVaIWcKXeMYfOZgR_dU``ZaTcbLgcDid6ie8ffAcgC`h\ EYhFZgH_eJ`cLaaNb_PcYRdVTeSVfPVfMVfJVbIUZHSVGQRFNN\ ELKDJGCHCBE8AC49A188397597797997B97DA7FA7HA7JA7LA7\ NB7PB7RB7TB7VB7XB7ZFC_IG`MKbPOcTSdWWf__gbchfgjikkm\ olpsmswXqkUmlRilPemMbmKZmHVnFSnCOoAKo7Ho5Dp29p06p3\ Bn6Fl9KjCOhFTfIXdHYaGY_GYYFYWFYUEYREYPDYNDYLCYJCYG\ BYEBYCAYAAY88TL9SOARRBQTCPWDOYEN`FMbGLeHKgIJjJJlKQ\ cLXWMcONjGOq8Px0Zj9gXIqJRz5_yIbyUexfhxrkvrhtrfsrdq\ rbor`nrZlrXjrUirSgrQerOdrMbrKarIarHbrGcqFdqEeqDepC\ fpBgoAho9io8in7jn6kn5lm4mm3mm3nl4nl4nl4nl4nk5nk5nk\ 5nk5nk6nj6nj6oj6oj7vRSoi7oi7oi7oi8oi8oh8oh8oh8oh9o\ g9pg9pg9pgApgApfApfApfBpfBpeBpeBpeCpeCqeCqdCqdDqdD\ qdDqdDqcDqcEqcEqcEqbErbFrbFrbFrbFraGraGraGraGr`Hr`\ HdZco_Wy_Ou`Qq`SnaUjaWfbY } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 21-05-11 (Minibrot for the Ages [8])
by Hal Lane 22 May '11

22 May '11

Brian, Thanks for sharing these images. I like them a lot. Great images, and super coloring. The shrimp-like shapes in your "c" image below remind me of the extinct anomalocaris: http://bygonebeasts.wordpress.com/2010/10/26/anomalocaris/ - Hal Lane ######################### # hallane(a)earthlink.net # ######################### > -----Original Message----- > From: Brian Prentice [mailto:bprentice@webenet.net] > Sent: Sunday, May 22, 2011 1:26 PM > To: Hal Lane > Subject: Re: [Fractint] FOTD 21-05-11 (Minibrot for the Ages [8]) > > > Thanks Hal, I've just posted two more beautiful details: > > http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06c.png > http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06d.png > > Brian >

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Re: [Fractint] FOTD 21-05-11 (Minibrot for the Ages [8])
by Hal Lane 22 May '11

22 May '11

Brian, Nice images -- and coloring. - Hal Lane ######################### (\__/) # hallane(a)earthlink.net # (='.'=) ######################### (")_(") > 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] 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 20 May '11

20 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 20 May '11

20 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 19 May '11

19 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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