March 2008 - Fractint - mailman.xmission.com

FOTD 31-03-08 (Time for Flatworms [7])
by Jim Muth 30 Mar '08

30 Mar '08

FOTD -- March 31, 2008 (Rating 7) Fractal visionaries and enthusiasts: Something is wrong with the following scenario, which I read many years ago, but I have never found the apparent flaw in the reasoning. In a certain town lying on the border between Mexico and the United States, a peculiar currency situation exists. In Mexico, ten U.S. dollars are worth only nine Mexican dollars, while in the U.S., the value of ten Mexican dollars is only nine U.S. dollars. One day a cowhand strolls into a Mexican cantina and orders a one-dollar beer. He pays for it with a Mexican ten- dollar bill and receives in change a ten-dollar U.S. bill, which is worth only nine dollars in Mexico. After drinking his beer he strolls across the border to an American saloon and orders another beer. This he pays for with the American ten-dollar bill, receiving a Mexican ten-dollar bill for change. He takes this back to the Mexican cantina and repeats the process, drink- ing beer merrily all day and ending up as rich as he started, with a ten-dollar bill. The question: Who paid for the beer. The moral: Forget about working and visit sunny Mexico. The conclusion: You can't get something for nothing . . . maybe. The solution: (IMO) Such an exchange rate is irrational. (But what if it actually existed?) And speaking of something for nothing, the same is true of fractals. The cost of today's image is 10 minutes calculation on a fast machine. The result is an image that must be seen rather than described. The holes in the diagonal blue background 'object' remind me of flatworms, which is why I named the image "Time for Flatworms". The rating of a 7 is close to correct. And don't be deceived by the apparent X-axis symmetry of the parent fractal. It breaks down on closer examination. Finally, if fractal calculation is not your cup of tea, visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the finished image posted there. Sunday dawned clear but unusually cold here at Fractal Central, with a temperature of 23F -5C. But by afternoon the strong sun warmed it to 50F 10C, making things quite pleasant. The fractal cats spent most of the time by the heat. My day was slow and lazy, which leads to weird thinking, but things are due to perk up tomorrow. The next FOTD will be posted in 24 hours. Until then, take care, and where are those multiple universes when you need one? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Time_for_Flatworms { ; time=0:09:59.62-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.01019/0.00203573/18.69511/1/35/0 params=-0.5/-1.1/-0.5/-1.9/0/0/0/0 float=y maxiter=25000 inside=0 logmap=8 periodicity=10 colors=000wkYwjYviYvhYugYufYteYteYsdYscYsbYraYr`Yq\ _YqZYpZYpYYoXYoWYnVYnUYnTYmSYmSYlRYlQYkPYkOYjNYjMY\ jMYgOZdPZbQZ_SZYTZVUZTVZQXZOYZLZZG`XJ_ZMZ`OYaRXcTW\ eWWfYVh`UjbTkeSmhQpgRogSngSmfTmfTlfUkeUkeVjeVidWid\ WhdXgcXgcYfcZebZeb_db_ca`ba`baaa`a``b``b__cZ_cZ_dY\ ZeXZeXZfWYfVYgVYgUXhTXhTXiSWiRWjQWjQVkPVlOVlOUmNUm\ MUnMTnLToKToKSpJSpISqIRqHRrGSsERrFRrGRrHQqIQqJQqKP\ pLPpMPpMPoNOoOOoPOnQNnRNnSNmTMmTMmUMlVMlWLlXLkYLkZ\ Kk_Kk_Kj`JjaJjbJicJidIieIhfIhgHhgHghHgiGgjGfkGflGf\ mFenFenFeoEdpEdqEdrDcsDctDcuDcuDbvDavD`vD_vDZvDYwD\ XwDWwDVw8YyBWxDVwFUvHSuJRuMQtOOsQNrSMqVKqULqULqUMq\ UMqUNqUNqUOqTOqTOqTPqTPqTQqTQqTRqSRqSRqSSqSSqSTqST\ qSUqSUqRUqRVqRVqRWqRWqRXqRXqQXqQYqQYqQZqQZqQ_qQ_qQ\ _qR_rR_sS_tSauTcvUewUgxViyVkzWmzWmzXmzYmzYmzZmzZmz\ _mz_mz`mzamzamzbmzbmzcmzdmzdmzemzemzfmzfmzgmzhmzhm\ zimzimzjmzjmzkmzlmzlmzmmz } 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 30-03-08 (On The Trail [7])
by Jim Muth 29 Mar '08

29 Mar '08

FOTD -- March 30, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's scene lies in the fractal that results when 0.5 part of Z^(-1.9) is subtracted from 0.5 part of Z^(-1.1) and (1/C) is added. I'll not try to describe this parent fractal, which is quite typical of this family of fractals and is easily created by the MandAutoCritInZ formula. The scene is located in a small valley on the shore line of one of the circular bays of the parent. If the fractal is evapora- ted and the 'bof61' inside fill applied to the resulting blank screen, the result is an image virtually identical to the actual image. The rating of a 7 indicates average satisfaction. The name "On The Trail" can imply anything the viewer wishes. The calcula- tion time of 4 minutes is average. The next FOTD will be posted in a near-average time of 24 hours. The finished image is posted for viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunny but unseasonably cold weather made Saturday a mixed blessing here at Fractal Central. A sunrise temperature of 25F -4C was anything but springlike, but when the strong sun raised the temperature to 50F 10C in the afternoon, it felt almost like spring. The fractal cats ignored the weather outside, and spent the day by the heat, My day was notably average, and I made the most of it by being notably lazy. The next FOTD will be posted in 24 hours. Until then, take care, and did you hear about the ship carrying a cargo of yoyos? It got caught in a storm and sank 27 times. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= On_The_Trail { ; time=0:04:04.32-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-0.2886299468294951/+1.132653355152376/\ 1.150575e+008/1/-107/0 params=0.5/-1.1/-0.5/-1.9/\ 0/0/0/0 float=y maxiter=5000 inside=0 logmap=-430 periodicity=10 colors=000MMJOPIQRGSUFUXEWZCXaBYdAPP9Xc7Wa6W_5VY4V\ W3UU2US1WW6X_AZcE_fIajNbmRdrVquZtwVzwRtwNmmJccFWUB\ UK7S93R30QEAQOK605A19D2CG3FJ3IM4LPXOSsRVsUYpX`m_Nj\ g9gnBbkDaiFYgGVdISbKP`LNZJK`KGXAAS00N00NZX_ikcdYi`\ LobKncJmdIleHlgGkhFjiEijDiiChiBghAfh9eg8dg7cXI`MTZ\ NRVOQQQOMRNHSLDTK9SSIRZRRe_VfbZfebggfgjjhmnhorirui\ tnekhabaYUWULxkXxjWxiVxhUwgTwfSweRwdQwcPwbOwaOxQPu\ STrTWoU_lVbiWffYicZm`_pY`tVawTcxRdyPezOgzMhzKizIkz\ HlzFmzDozBpzAqz8sz6tz4uz3vz5uz7tz8tzAszBs_DtaEucGv\ eIwgJxjLylMznzzpzzrzzozzlzzjzzgzzezzazzZzzWzzTzzQz\ zMzzJzzGzzDzzAzz7zz5zz4zz2zz1zz0zzDzzQzzbzz4zzJzzJ\ zzJzzJzzJzzJzzJzzJzzJzzJzzJzzJzzJbzJczJdzJdzJczScz\ `cziczqgzkkzeoz_rzUqz`pzfozlnzrmzxkzwizwhzvfzvdzuc\ zuazt_ztZzsXzsVzrUzrSzqQzqPzqVzj_zddzYizSZzaOzkEzu\ FztGzsHzrIzqJzpKzoKznLzmMzlNzkOzjPziPzhNziMzjLzjJz\ kIzlGzmFzmWzUUzRRzOPzMQzK } 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 29-03-08 (Not Quite There [6])
by Jim Muth 28 Mar '08

28 Mar '08

FOTD -- March 29, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal began with great promise, but by the time the finished product was ready, the promise had all but vanished. I'm not quite sure what's wrong with the image. Maybe it's the colors, of perhaps the overly busy appearance. Maybe it's that the minibrot too closely resembles those in the more remote valleys of the classic M-set. But whatever it is, I could rate the image no higher than a 6. The name "Not Quite There" shows my disappointment. The formula of the parent fractal subtracts 1/2 part of Z^(-2) from 1/2 part of Z^2 and adds C. The parent itself consists of a scattering of Mandeloids, with today's scene located in a valley on the south side of the largest bud of the largest Mandeloid. In an attempt to add interest, I rendered the image with the outside set to 'tdis', which is the setting I use almost as frequently as the standard equal-iteration bands. The result was not all that I had hoped. The calculation time of 9 minutes could be faster, but it also could be slower. All calculation problems may be bypassed however by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Friday started rainy here at Fractal Central, but by mid-morning the rain ended and by mid-afternoon the sun appeared. When the temperature reached 48F 9C, the day actually became quite pleasant. The fractal cats enjoyed the sun when it finally broke through. My day was notably average. The next FOTD will make its initial appearance in 24 hours more or less. Until then, take care, and be true to your fractals or they'll be false to you. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Not_Quite_There { ; time=0:09:20.96-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.56188992602/-1.56422169664/5.5e+007/\ 1/-37.5/0 params=0.5/2/-0.5/-2/0/0/0/0 float=y maxiter=5500 inside=0 outside=tdis periodicity=10 colors=000wnuwmuwktwitvhsvfsvdrvcrvaqv`qx`nqWhkSbd\ NXZJSSFMMAGF6A925B36D46F47G57I58K68M69N79P8AR8AT9B\ U9BWACYAC_BD`BDaAFb9Hb8Jc8Kc7Md6Oe5Qe5Rf4Tf3Vg2Xh2\ Yh1_i0ai0bb3eX6hQ9jKCmDFK7IK1LKU0`cezEGAGGFIGKKFPK\ FULFULFUIIUGKUENWCPYAR_9Sa8Ud7Vg6Xj5Yl8WmBVnEUoHSp\ JRqMQrPOsSNtVMuXLvVOrUQoTSlSVhRXeQZbPaZOcWMeTLhPKj\ MJlJIoFHqCGs9Fu6It9LsBNsDQrGTrIVqKYqM`pPbpReoTgoVd\ lYai_ZfaWccU`fRYhOWjLTlIQnGNqDKsAHu7Ew5Cy9DtDEoHEj\ KFeOF`SGWVHRZHMbIHeIDYEOQBZJ8hOBiSDiWGi_IicKigNikP\ ioSisUiwWipZdja`cdXYgTRjOLmKEpG8rCCqFFpHJpJMoMQoOT\ nQXnT_mVcmXfl_jlamkcqkftjhwjjvkkulltlltmmsmmrnnqon\ qooppooppnqpnrqmrqlsrlsrhqndpk`nhYmeUkaQjZMhWJgTZf\ _meekfbig`ghYzzWzzTzzRmzPmzMmzKUnHSoFRoDTjEUeFW`FX\ WGZRG_MHaHIbCId7Je2Jb5I`7IY9HWCHUEG_7_f5gd7hc8hbAh\ `Bh_DhZEhXGhWHhVJhUKhXOj_SkaVmdZngapieqliroltqputs\ wzzzyzyxxxxvxxuwxswxqvwpv } 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 28-03-08 (In a Soiled M-brot [8.5])
by Jim Muth 27 Mar '08

27 Mar '08

FOTD -- March 28, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: One of the reasons I am fascinated with fractals is because they are four-dimensional things, and I waste no end of time futilely trying to visualize a four-dimensional anything. Many phenomena in 4-D hyperspace have similar things in our familiar 3-D space, which help us to understand hyperspace. But there is at least one thing in 4-D space (I am sure many others exist.) that is totally unlike anything in our 3-D space. That thing is the motion called double rotation. In 3-D space an object rotates about a line as its axis, and due to the gyroscopic effect, that line will retain its orientation. But in 4-D space a 4-D object rotates about a plane as its axis, which makes the situation more complex. In a simple 3-D type of rotation, the points of a 4-D object describe a circle, while an entire plane of the object remains fixed in place as its points turn on themselves. And just as in 3-D space, the gyroscopic effect will keep the object rotating in the same direction. But what of that axis plane, where the points remain stationary, while turning in place? This is the weird thing. Since the axis-points are not moving, they are not subject to the gyrosco- pic effect, and the entire axis-plane can turn on itself around its center point, carrying the entire 4-D object with it, while the entire object continues to rotate in the first direction. The object is now in a state of double rotation, a motion totally alien to our familiar 3-D objects. While fantasizing a walk on a 4-D hyperplanet recently, and trying to imagine the apparent motion of the heavenly bodies, I realized that I was perilously close to visualizing double rotation, (as projected into 3-D space of course.) What I imagined is extremely difficult to put into words, but I'll give it a try in a near-future FOTD discussion. As for today's image, it lies in the parent fractal that results when 0.01 part of Z^(-2) is subtracted from the classic Mandelbrot set. This fractal is a distorted M-set, filled with debris. Today's image is located in the East Valley area of the remains of the large minibrot on the negative X-axis of the M-set. I named the image "In a Soiled M-brot", which the parent fractal most certainly is. I rated it at an 8-1/2 -- 8 points for the underlying fractal, 1/2 point for my coloring work. The calculation time of only 49 seconds means that no one will be disappointed with the result. Some may prefer to avoid the calculation however, so for convenience, the finished image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Good weather in early spring never lasts long in Central Pennsylvania, so we were not too disappointed here at Fractal Central when Thursday turned out cloudy, chilly and drizzly. The temperature of 45F 7C kept people well wrapped, while the drizzly mist kept the rain gear handy. The fractal cats kept cozy near the heat. My day was on the busy side, though not too busy to affect the fractal. The next FOTD will appear in 24 hours. Until then, take care, and there is more to empty space than meets the eye. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= In_a_Soiled_M-brot { ; time=0:00:49.43-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=-1.230634995848692/-0.488602834129332/\ 1.201185e+011/1/140/0 params=1/2/-0.01/-2/0/0/0/0 maxiter=1500 inside=0 symmetry=none periodicity=10 colors=000WJLVIJUHITFGSEFRDDQtCPrAMp9Mn7MlkMjhMheM\ fbMd_MaYMZVMWSMSPMPMMMKMJHMGEMDBMA8aEKZDIXCGVBESAC\ Q9AO88dhkjGbgF_eEXcDU`CRZBOXBLVAIS9FQ8CO799aiAZeoo\ rmiskcsjYthStfMueHucPsbWracq`jp_roZynHWXJYVL_UNaTP\ cRQdQSfPUhNWjMXkLZmJ`oIbqHcrGanF`kEM87_hEZeDYbCWZC\ VWBUTATQASN9QJ8PG8OD7NA6nsA`dh_aeZ_cYY`XWZWUWVSUUQ\ RTOPSLNRJKQHIPFFODDNBAM98qrcoo`mlZkiXifVgcTe`RcYPa\ VN_SKYPIWMGUJESGCQDAOA8NKTMIQMHOMGMMEJMDHMCFMACM9A\ M88f3mb4e_5Z4c`4c`4aZ4_X6YV7WT8URASPBQNCOLDMJFJHGH\ FHFDJDBKB9L97zzzwwwsssooohfhc`aZXYXUUVSSTQQQOOOMMM\ KKKDCKA9z6gw7cs7`o7Yk7Vg7Td7Rb7P`7NZ7KX7IV7GT7ER7C\ M7AJ78zUKrOAgI9XC7sTHnQFjNEfKCbIBYFAUC8Q97Lr_MnYMk\ WMhUMeSMbQMZOMWMMTKMQIMNGMJEMGCMDAMA8bmz`hzZdzX`zW\ WzUSzSOzRJzPFHNBBDxNErLFlJGfHH`FIVDJPBKJ9LD7zyKwwK\ rrVmhYhcUbYQ_TMWNITIEPCAzqHmaD_M9TVESTDRRCRPCQNBQL\ APJAPI9OG9OE8NC7NA7M86YLN } 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 27-03-08 (Going Ever Deeper [8.5])
by Jim Muth 26 Mar '08

26 Mar '08

FOTD -- March 27, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: A rating of 8-1/2 for a fractal that takes 16 minutes to calculate is pretty unusual, but today's image is unusual enough to earn it. The name "Going Ever Deeper" refers to the magnitude of today's image, which at close to 3*10^13 goes beyond the limit of perfect resolution. The mathtolerance entry assures that the image will be calculated at the correct magnitude. The scene of today's action lies in the same area of the same parent fractal that gave us yesterday's image. The tiny minibrot at the center, which is beyond resolution, was most difficult to find. Nothing but pure instinct led me to it. To see the difficulty, reset the logmap to zero and return to the parent fractal. There is almost no clue at all that the minibrot exists. The calculation time of 16 minutes is admittedly slow, so I recommend visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoying the fully rendered image there. With bright sun, puffy clouds and temperature of 61F 16C, Wednesday turned out to be the best day so far this spring here at Fractal Central. The local fractal cats must have agreed, for they spent the better part of the afternoon gazing at the outdoors that they never get to visit. My day was busy but made satisfying by the better-than-average fractal of the day. Tomorrow will likely be less busy. I have no comment about the next FOTD fractal, which will be posted in 24 hours. Until that semi-glorious moment, take care, and stop to wonder why fractals exist at all. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Going_Ever_Deeper { ; time=0:16:03.45-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.23410086762640360/+0.069182405395851\ 56/2.761998e+013/1.0001/-85/0.026873983727 inside=0 params=2/1.25/1/2.5/0/0/0/0 float=y maxiter=5000 logmap=2030 periodicity=10 mathtolerance=0.05/1 colors=000JAJy2Lz0Lo9ilEfiJefNbbQa_UZXZXUbUQeTNiQK\ nOCsJHpNKnQOkTRhWWeZZbaaadeZfhWilTloQosNrvLtyJwzFz\ zCzz9zz5zz4zz2zz2zz2zz2yz1vz1sw1pv1ns0kp0hn0el0bi0\ _f0Xe0Ub0R_0OX0Lk0Jv0Fk0Cf09L05JH2ZE0b00X00X00N40R\ 90WE0_J0dN0hR0lW0p_0td0yh0zl0zi0zh0zf0zd0zb0ya0yZ0\ yX0yW0yT0yR0zQ0zN0zL0zK0zH0wF0uE0sA0q90o70m40l21k1\ 1j01i01h01g00f00d01c02c05c07c09c1Ac2Ec4Fb5HX7Kf9Le\ ANdCObERaFT_HUZJXXKZWL_UNaTOdRQeQRfTLkORhLXeJbbFha\ ClZ9rW5wU2zR0zO0zN1zR5zW9z_EzbHyfLvkOsoTprWnv_kzdk\ zbhzbfzaezadzabz_az__zZZzZXzZUzXTzXRzWQzWOzWNzULzU\ KzXHzUJzTJzRKyQKsOLnNLhKNbJNXHORFOLEQFER7CQ9CQACQC\ CQCCkzCQzCkzAkzAOzAOJAOKAOLAONAONAOO9NQ9NQ9NR9NT9N\ T9NU9NW5JK7LQ9NW9OaAQfARlCTrFZzCUwAQr9Ll7Jf5Ea29U1\ 5O01J00C005007207427757997CC7FF7HJ7KL7LO7OR7RU7TW9\ WZ9Xa9_d9bf9di9fl9ho9kr9nt9ow9rz9rz5sz7sz9tz9tzAtz\ CvzCvzEvzFwzFwzHwzJyzJyzK } 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 26-03-08 (Only a Minibrot [7.5])
by Jim Muth 25 Mar '08

25 Mar '08

FOTD -- March 26, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image takes the same parent fractal that held yesterday's image and doubles the portions of both Z^1.25 and Z^2.5. In the resulting fractal, the two M-sets are no longer partially merged, but are now well separated, connected by only a narrow 'inside' N-S band centered symmetrically on the X-axis. Today's scene is located very near the point where this band intersects the X-axis. When rendered in the usual manner, the scene is rather dull and lifeless. So to add some life I rendered the image with the outside set to 'tdis' and the inside set to 'fmod'. The proximity factor of 11 was a mistake, but it worked so well that I decided to keep it. When the time came to rate the day's effort, I found enough pizazz in the image to rate it at a 7.5, giving myself a generous half-point for the coloring. The name "Only a Minibrot" refers back to yesterday's image, which held a gaping hole and an impressive spiral in addition to the minibrot, while today's image has only the minibrot. With a calculation time of just under 6 minutes, the parameter file borders on the slow side, but IMO, the small effort is worth it. And for instant gratification, the finished image may be accessed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Near perfect 50F 10C early spring weather continued at Fractal Central on Tuesday, and the fractal cats continued to enjoy the sun. My day was unusually busy, but never beyond control. The next in the near-endless string of FOTD fractal images will be posted in 24 hours. Until then, take care, and dwell in peace in hyperspace, where I might soon take a tour of a hypersphere. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Only_a_Minibrot { ; time=0:05:54.49-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=mandautocritinz function=ident passes=1 center-mag=+0.233227944685145/+0.0082092285206308/\ 1.051e+007/1/-148.75/0 params=2/1.25/1/2.5/0/0/0/0 float=y maxiter=10000 inside=fmod proximity=11 outside=tdis symmetry=none periodicity=10 colors=000CszHkzNezT`uZVodPigTdkXZo`TsbPveJziEzr0z\ o4PH00000040CAUPPHdLRsR`zX000qzguzbvzXxzTzzNzzJzzE\ zzAzz4zz0zz0zz0zz6meL`H`P0oN8uLJxLXzJgzHuzHzzCzz8z\ z4zv0zq0zi0zd0zZ0zN0zE2z46z0Az0Cz0Cu0Em0Ee0EZ0GR0G\ J0GC0H40H00H00A602N00b00X20R80LG0GL0AR04Z00d00k00q\ 00v00q40m80iC0eG0`J0XN0TR0PV0JZ0Gb0Cd08e0Ae0Ce0Ee2\ Ge6He8JeALgH6gN0eL0dL6bLC`LJZLPXJXVJbTJiRJqPJvNHzL\ HzJHzHHzGHzGHzLNzRTqXZV`bAid8qe6xg4zi4zk2zm0zo0ze0\ zW0zO0z00u00e00T20GA080200020460AA0EE0JH0PL0TP0ZT0\ dX0g`0md0sx0ke0vP2z86z00z08z0Ez0Lz0Rz0Zz0dz0kz0qz0\ xz0zy0zx0zw0zv0zuAzuJzuRzu_uqfolnihkddibbl`bqZbpZb\ qXbpV`oT`pT`oR`oP`mN_kN_kL_iJ_vNjiJdZHTNGHC82CE8CJ\ CCPGCVLCZPCcTCcZCcbCceCckCcoCcsCcxCczCcz6cq0cd0cR0\ cE0c00c04cm8cmAcmCcmEcmGcmHcmLcmNcmPcmRcmTcmUcmVcm\ Zci`cebcbdc`ebXgZTiTR`czZcvZsqXqkXoeVm`VkVTiPTgJTe\ ERgLPiTNk`LmgJmmHouGqzEsz } 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 25-03-08 (Hole-Spiral-Midget [6.5])
by Jim Muth 24 Mar '08

24 Mar '08

FOTD -- March 25, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Holes, spirals and minibrots -- today's image has them all. And there are layers also -- not artificial human-created layers, but real layers, created by the numbers themselves. All this, and the result rates only a 6.5. I'm not quite sure what the image lacks, maybe it is a well- defined focus of attention, but despite all the fractal goodies, I could bring myself to rate the image no higher than a 6-1/2. The slightly oversized parent fractal was created by the formula Z^1.25+0.5(Z^2.5)+C, and is shaped like two M-sets, one facing NNW and the other facing SSW, loosely connected along their main bays. Smaller minibrots lie just beyond the main buds of the two M-sets. Today's scene lies between the northern minibrot and the main bud there. I named the image "Hole-Spiral-Midget", the three things vying for attention in the scene. The calculation time of 4 minutes could be faster, but it also could be slower. All calculation may be avoided however by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Near ideal early spring weather prevailed here at Fractal Central on Easter Saturday, Sunday and Monday, with lots of sun and a temperature near 50F 10C each day. The fractal cats enjoyed the sun in their sunny window. I managed to survive the holiday with only a little annoyance. But the work for tomorrow looks to be heavier than usual, which could affect the FOTD. Regardless of the work however, the next FOTD, in glorious RGB color, will be posted in 24 hours. Until then, take care, and wonder about the things worth wondering about. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Hole-Spiral-Midget { ; time=0:04:00.62-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.78157556/+1.91021611/363.0164/1/-85/\ 5.219991e-013 params=1/1.25/0.5/2.5/0/0/0/0 float=y maxiter=5000 inside=0 logmap=40 periodicity=10 colors=000nI0c00Z00c00m00tL0m00c00U00U00U00U00U00U\ 00z00Y00Y00z00Y00Y00z00Y00Y00zU0Z00Z00m00Z00Z00Z00\ Z00ZNmZJlYFlZGkZHjZHiZIiZJh_Jg_Kf_Kf_Le_Md`Mc`Nc`O\ b`Oa`P``P`aQ_aRZaQYaQYaQXbPWbPVbPVbTUgUTgUScVScTRc\ TQcUP`ULcUPfSThRXiP`jNdkQfjQgjRgiNgjOhiOhjQhjQijRi\ jRiiSiiSjhTjhTjhTkgTkhTkgUlgUlfUlgUlgUmfUmgUmfUnfU\ neUneUneUodUodUocUpcUpbUpbUqbUqaUqaUq`Ur`Ur_Ur_Us_\ UsZUsZUsYUtYUtXUtXUuXUuWUuWUvVUvVUvUUvUUwUUwTUwTUx\ SUxSUxSUxRUyRUyRUyRUyRUyRUyRUyRUzRUzRUzRUzRUzRUzRU\ zRUzRUzQUzQUzQUvQUzQUzQUzQUzQUzQUzQUzQTzQSzQRzQQzQ\ PzQOzPNzQMzRLzRKzSJzSIzTGzUFzUEzVFzVGzWHzWIzXJzYKz\ YLzZMzZNz_Oz_Pz`QzaRzaSzbTzbUzcVzdWzdXzeYzeZzf_zf`\ zgazhbzhczidziezjfzkgzkgzkhzkhzkizkizkjzkjzkkzkkzk\ lzllzlmzlmzlmzlmzlmzlmzlmzmmzmmzmmzmmzmmzmnzmozmpz\ nqznrznszntznuzovzpwzqxzryzszztzzuzzvzzwzzxzzyzzzz\ 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 22-03-08 (Satiny Satin [8])
by Jim Muth 21 Mar '08

21 Mar '08

FOTD -- March 22, 2008 (Rating 8) Fractal visionaries and enthusiasts: DUE TO THE SPRING HOLIDAYS THERE WILL BE NO FOTD ON MARCH 23 AND 24. THE NEXT FOTD WILL APPEAR ON MARCH 25. Today's image lies in the fractal created when 1/2 part of Z^3 is combined with Z^1.5 and C is added. The parent fractal consists of two Mandelbrot sets connected like siamese twins into a single N-S stretched fractal with X-axis symmetry. Smaller disconnected M-sets lie N and S of the main fractal. Today's scene lies in the East valley area of the disconnected M-set on the northern side of the main fractal. When I saw the image with its crumpled, satiny interior, I had no choice but to name it "Satiny Satin". I would have given myself an extra half point for producing the satin effect, but it was the program, not I, that created the colors. Still, the rating of an 8 makes the 1-3/4 minute calculation time almost a bargain. Another bargain may be found at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image can be seen already calculated. Except for late afternoon clouds, the Friday weather was near perfect here at Fractal Central. With little wind and full sun, the temperature of 46F 8C felt just about right for the start of spring. The fractal cats agreed. My day was quite busy; the next two days will be busy also. The next FOTD will be posted in 72 hours. Until then, take care, and have a happy fertility festival. (Eggs and rabbits, as well as resurrections, are symbols of fertility and new life.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Satiny_Satin { ; time=0:01:45.36-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.2127364819281549/+2.181650197032898/\ 2.3169e+010/1/-45/0 params=1/1.5/0.5/3/0/0/0/0 float=y maxiter=1800 inside=0 outside=tdis periodicity=10 mathtolerance=0.05/1 colors=000zizzkzzlzzlztizfgkRfXBdI0b20a00f00i04n0B\ q2Jw6Qz9YzDdzGizInzIszIxzIzzJzzJzzJzzJzzIzzIwzIpzI\ izIbzIXzI_zQbzYfzfgtnknwngzpbzxLiz2Gz00z40wN0nd0fw\ 0Yz0dx2kiEqVQxGaz1lz0ws09x8NzXYzsizllzfpz_szTtzNxz\ Gzz9zQ98N06RENXXarzzmzzbzzdxzfxyfxx_xxTrxNnxGix9bx\ 2Yx0Rx0NxkILgDRf9Yd6da2i_0pY0wX0zR0zO2zL8zIBzEGzBL\ z8Qz4TzBVwIXlOYbV_TaaIgb8nd0sd0kV0dL0YD0R20L00E00L\ 01R09X6IbDQiJYnQftXnzbtqVkiObaIVTBNL4ED06400806B0D\ D0LG0RI0YQ1QXBIdL9kV1qb0kd4fdGafRXfbRgnNgzIgz9dp2a\ X0YD0V0OO0z00zE1zzBzzzzzTz0az0kw0ss0pp8nnJlkTkgdgf\ pfbzdazbf00iD0lY0ps0bD1YT9TiGOzNJzTOTGT04990QO1fb6\ wpBkb9_R9OG9D49109001000000000100600B00G00N00R10X1\ 0a20f20k20f40a60X80R80N90JzzOzwTzpXzkazdfz_kzTpzOt\ zIxzDszGpzIlxLgqNdiOabRYXTTOVQIYN9_I2aE0dB0f80gG0a\ N0VV6OaEJgNDpV6wb0zi0zg1zf6zdBzbGzbLTVROiDJx0Ot6Tq\ EYnNalTfiakfindpqfttgxxiz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 21-03-08 (In a Secret Garden [5.5])
by Jim Muth 20 Mar '08

20 Mar '08

FOTD -- March 21, 2008 (Rating 5.5) Fractal visionaries and enthusiasts: Today's image rates only a 5.5, but that's how it goes when I have no time to work on the coloring, which turned out quite a bit too purplish for my taste. The name "In a Secret garden" sounds more like the title of a cheap bodice-busting romance novel than the name of a fractal. The image lies near the negative X-axis of the parent fractal that results when 0.5 part of Z^3 is combined with Z^1.5 and C is added. To try to make something from nothing, the image was rendered with the inside set to 'fmod'. The result is hardly worth the 8 minutes required to run the included parameter file. I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is or soon will be posted for instant viewing. The first day of spring turned out rather blustery and chilly here at Fractal Central, with more clouds than sun and a tempera- ture of only 39F 4C. The local cats took advantage of the few minutes of sun, and stayed by the heat the rest of the time. Due to the upcoming holiday, my day was unusually and unexpec- tedly busy. But holiday, holy day, or not, the next FOTD will be made public in 24 hours. Until then, take care, and what's it all about anyway? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= In_a_Secret_Garden { ; time=0:08:03.67-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.30956628123146/+0.03096772886562/\ 202890.6/1/7.5/0 params=1/1.5/0.5/3/0/0/0/0 float=y maxiter=5000 inside=fmod proximity=0.7 periodicity=10 colors=000poplPUdWYYcaQjeIriBymGroLlpQfqU`rS_mR_hQ\ _cP_ZO_UN_PM_KPYORXSUWVWVZZUb`TebNicImdCqe7uf2yd7o\ bCf`GYZLPXPGRUOMZVHbaCgi7lp2pwAauINs6jYamUboObqIbs\ Dbu7bv2_nBXgJVaGTWERRBPL9NF6LA4OH5RO6UU6X`7_g8bj8e\ k9gh9daJaST_JaXIYUJVRPRPUOP_KUdHZjDcoAhpFmqJrrOvrS\ zsXvt`mtdcmaXg_Q`XLVVGPTEIQCCOB6MGCPLHSQMVURXWOYYL\ Z_I_aG`cDaeAbg8cbDeZHfULhQPiTQgWQeYQd`QbbQaeQ_gQZk\ YYndYqkXtrXNScMO0GV6BaC6hI1oN6mJAkFEiBIg7Id8Ia9JYA\ JVBKRCvh2ll3bo4Us5Kv6By6HsJNnVThgYcsP_hHWZ9SO1PE5c\ R8rcFshMtlTuq_vuewydvpdugduZctQcsHcs9Q`PDIdrIYo_Yl\ qXem_ZicSdgL`jEXn7SrMRr`PrpNqmNrjOsgPtdQuaRvZSwZ9n\ _Cj`FfaHcaK_bMXcPTcRQi_LnhGtqByz6oqAeiDWaHMUKDMNGQ\ QIUSLXUN`WQdZSg`VkbXndUheRbfOXgLRgNSfOTePUdQVcRVbK\ ShEQn7Nt1Lz5Pt8TnBXiE`cHdYKhTNlNQpILfFGXCBN97D7FD7\ OD6XD5dD5mD4lZviUqfQmcMi`IeYEa`AYeJUlOKoVBu_2rX9nT\ GkPM000dF_aKedMhgOjjSjhRj } 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 20-03-08 (Darkest Terraces [7])
by Jim Muth 19 Mar '08

19 Mar '08

FOTD -- March 20, 2008 (Rating 7) Fractal visionaries and enthusiasts: I often see TV shows about true-believing psychics who know that psychic powers do exist, and I see TV shows about true-disbelie- ving skeptics who know that such powers are not real, and both sides are adamant in their opposing convictions. My opinion is that both sides are correct. Psychic powers are not real but they do exist. (Don't ask for an explanation, just add this paradox to the long list of other paradoxes uncovered by our old friend, 'modern science'.) The dispute is as silly and meaning- less as debating whether fractals exist. Fractals are not real, but they do exist -- just like ghosts and bigfoots. Take today's fractal image for example. Run the included para- meter file and a minute later you will see the image on your screen. There is no doubt of it, fractals do exist, for you can see one with your own eyes, and what you see most certainly does not exist only in your mind (whatever that means). But now try to find the physical object that was photographed to produce the image on the screen. No matter where or how far you search, you will never find the actual physical object. No such object exists. When we imply the fullest meaning of the word 'real', fractals do not quite measure up. Today's image lies in the parent fractal that comes about when various portions of Z^3 and Z^5 are combined and 1.038i is added to initial Z. I think this is the first time I have used the ability of the MandAutoCritInZ formula to vary the automatically preset value of initial Z. The result appears a lot more like a critical fractal than the one the formula calculates automati- cally when imag(p4) is left at zero. But the resulting fractal is not exactly critical. Today's image shows a 'dry valley', which is a sure sign that a fractal is not exactly critical. To add interest I rendered the image with the outside set to 'tdis' and the inside set to 'fmod'. The result reminds me of vaguely threatening terraces, so I named the image "Darkest Terraces". The calculation time of 1-2/3 minutes will pass like lightning for the true fractal fan. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image will also pass like lightning. With a temperature of 48F 9C, it was not too chilly here at F.C. on Wednesday, but thick clouds, fog, and near continuous showers kept it far from being pleasant. The fractal DSH cats agreed, and spent the day sleeping on the couch. My day was uneventful; the work was finished by 3pm. If the next 24 hours are just as uneventful, the FOTD for March 21 will appear at the end of that period. Until then, take care, and where was the Mandelbrot set 100 years ago? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Darkest_Terraces { ; time=0:01:38.10-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.002723103650706/+1.392157872857252/\ 91400.53/1/62.5/0 params=1.3/3/0.67/5/0/0/0/1.038 float=y maxiter=1500 inside=fmod proximity=0.001 outside=tdis logmap=yes periodicity=10 colors=000REibGgaHe_IcZKaXL_WNYUPWTSURUSRWSQYSQWTP\ VTPUTPSRQQPQOORMMRLKRKJQIHPHFNEEMCCK9AK79MCAOJAQMA\ OPBOSBQVBSZCUcCWhCYlCXiBXgBXeAXcAWaAW_9WX9WV9WT8VR\ 8VP7VN7VK7VI6UG6UE6UC5UA5U85S98QABOBEMCHKDKIENGFQE\ GTDGVEFTFFSFFRGEQHEPHEOIENJDMJDLKDKLDJLCHMCGNCFNCE\ OBDPBCPBBQBARA9RA8SA7SA6TB6TC6TD6TE6TF6TG6TG6TH6TI\ 6TJ6TK6TL6TM6TM69okBpiCpgEpfFpdGpcIpaJp`KpZMpYNpWO\ pVQpTRpSSpQUpPVpNWpMYpKZpJ_pHapGbpEcpD4_65a76b77c7\ 7d88f89g89h9Ai9Bk9Bl9CmADnAEpAEqBFrBGsBGuCHvCIwCIx\ CKwDLwEMwFOwGPwHQwHRwITwJUwKVwLXvLYvMZvN_vOavPbvPc\ vQevRfvSgvThvTfsUeqVdoWclWbjXahY`fY_cZZb_Ya_X``V_a\ U_bTZbSZeR_jQ_oP_tO`xNazMazLazKazJazJazIazIavIarHa\ mHahH`cG_cGZbFYbFXaFWaEW`EW`EW_DW_DXZDYZDX_DW_DV_D\ U_DT_DS_DS_DR`DQ`DP`DO`DN`DM`DM`ER_EV_EZ_FcZFgZFkZ\ GgWGdUG`SGYQGUNGRLGNJGKHGHFJKGMNHOPHRSITVIWXJY_J`b\ KcdLegLhjMjlMmoNoqNjoRemV } 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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