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FOTD 07-01-03 (Ghostly Happenings [9])
by Jim Muth 07 Jan '03

07 Jan '03

FOTD -- January 07, 2003 (Rating 9) Fractal visionaries and enthusiasts: The work is quite heavy this morning. With no time for a lengthy discussion, I will let the image speak for itself. This is no problem, for it speaks very well. I really like today's image. The rating of 9 that it was given is no exaggeration. The image earns every bit of its excep- tional rating. I named the picture "Ghostly Happenings", not because there is something spooky about it, but because the image is another of my 'evaporated' images, consisting of all-inside, with the ghost of the vanished material made visible by <bof60> fill. The parent fractal was created by combining negative portions of Z^(-0.75) and Z^(-7.5) before adding (1/C). The fact that one exponent has ten times the value of the other is of no impor- tance. The parent is an indescribable thing that is almost impossible to describe, but it is typical of this class of double-negative fractals. Today's scene is located in a valley in an unlikely area of the northern part of the parent. I call the area unlikely because at first glance it appears to be non-critical and therefore to hold no midgets. But, as today's image shows, the world of fractals, like the real world, sometimes holds the unexpected. The render time of 12 minutes is quite reasonable for such a quality image. And as always, the completed GIF file is available on Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather here at Fractal Central on Monday was partly cloudy with a temperature of 34F 1C and occasional flurries of snow. The dynamic cats, who dislike snow, spent the day sleeping by the warmest radiators they could find. I don't know what has come over the once truly dynamic pair. The older they get, the more they sleep. It seems like 10 years since they last chased each other up and down the stairs. As for myself, I have a bit of work to chase down and finish before starting my search for a fractal that equals or exceeds today's. I probably will fail to find one -- such images are not easy to find -- but check tomorrow to see how close I come. Until then, take care, and good things sometimes come to those who wait, but if they wait too long, they sometimes miss the fractal boat. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Ghostly_Happenings { ; time=0:12:36.98--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.49916201924092700/+2.289316930073352\ 00/1.336895e+007/1/85/-5.98323907294306956e-008 params=-2/-0.75/-9/-7.5/0/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=0006Qa3Qc5Oe7Mg8LhAJjBIkDGmEFnGDpHCqJAsK9tM\ 7vN6wO9uPCsQFqQIoRLmSOkTRiTUhUXfV_dWbbWe`XhZYkXZnV\ ZpUluMyzFvuJspNpkRmfVjaZgXacWd_WfXVhTVjPVmMUoIUqFU\ sESnEQjEOfDMbDKYDIUCGQCEMCDIUEjPFmLFpGGrCGu7Hx3Hz6\ Jx8LvANtCPsFRqHToJVnLWlOYjQ_iSagUceXedZgb`i`bj__ga\ YecWbdU`fRYhPWiNUkLRmJPnGMpEKrCHsAFu8Dv7Iq6Mm5Qi4U\ e4Za3bY2fU1jQ1nM3kK4hJ6eH7cG9`EAYDCVBDTAFQ8GN7HL6N\ J7SI7YH7bG7gE7mD7rC7wB7dBENBL5BS5BR5CP5CO4DM4DL4EJ\ 4EI3EH3FF3FE3GC2GB2H92H82H73KB4NF5QJ6TN7WQ8ZU8aY9d\ aAgdBjhCmlDppDrsCsrCsqBspBsoAtnAtm9tl9tl9uk8uj8ui7\ uh7vg6vf6ve6ve5ub5t_5tYwsVwsSwrQwrNwqLwpIwpFmzDzzc\ zn7zn5wm2zm0mf6c_CUTHXNNdGSk9Yr3bj2`b2ZV2XN2VG2UK4\ XO6ZS7`W9b_BdcCfgEhjFjhDcgBXe9Rd8Kb6Ea47`31c8FeDTS\ 9ME6G13A77CCAEHDFNGHSJJXMKYNLZOM_PNzQzzRzzSzzTzzUz\ zVzdWUeXVfYWgZXh_Yh_ZeYVcXS`WPZUMWTJUSFRQCPP9MO6KN\ 3JL9JKFJJLJIRIHXIGbIFh9Q_ } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 06-01-03 (Siegel Mandelbrot [4])
by Jim Muth 06 Jan '03

06 Jan '03

FOTD -- November 06, 2003 (Rating 4) Fractal visionaries and enthusiasts: Two days ago I posted a FOTD that illustrates what I assume to be almost-Siegel Disks, or about as close as is possible to come to Siegel Disks this side of infinity. Then, yesterday, I began wondering about the appearance of the Mandelbrot set at a point so close to the Siegel-boundary. The area was extremely easy to find, but its maxiter of over 1-million made the rendering quite slow. What I found was an area of thin, wiry arms, so jagged that it is difficult to determine the direction from which they are coming. The coloring shows that the arm in the upper right part of the image is the lowest-iteration feature in the frame, but the tan-colored arm in the left half of the frame could just as easily be entering from the top as from the bottom. It actually enters from the top. I also noticed that the midgets are very plentiful this deep in the M-set. At least 30 become visible in the frame when the color mode is toggled. I assume that the smaller ones are surrounded by even wirier and more jagged arms in addition to taking even longer to render. Curiously, at this extreme location of the M-set, the normal 2-4-8... pattern has all but vanished. The pattern might be there, but if it is, it is so distorted as to be virtually beyond detection. I am also curious about the appearance of the odd planes and oblique slices of the Julibrot at this point, but without Fractint's fast Mandelbrot formula to speed up the rendering, such images would be extremely slow. Still, I might investigate this aspect in the near future, and if the results show anything unusual, it will appear as a FOTD. Like the Siegel Disk image of two days ago, the interest of today's image lies mostly in the mathematical aspect, and like the earlier image, it also rates a 4. I named the image "Siegel Mandelbrot" as a simple description. With its render time of almost 1-1/2 hours, the image is a very slow one, I recommend downloading it from one of the following two web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> But before going for the download, give Paul and Scott a chance to render and post the image. Snow fell all day Sunday here at Fractal Central, piling up 5in 12cm by nightfall. The snow, combined with a temperature of 30F -1C, kept the dynamic fractal cats housebound. They put on their best pouts to let me know of their unhappiness, but knowing them as I do, I realized that their displeasure was mostly a show. It's another threatening day today, with talk of several more inches of snow by this evening. (We still measure length in inches, and temperature in degrees Fahrenheit here in the best educated ;-) nation in the world.) The cats were saddened by the news of still more snow. As for me, I've got enough supplies stocked and enough graphic work waiting that I have no time to be sad and no need to venture out on treacherous roads. The next glorious fractal will appear in only 24 hours. Until then, take care, and if you lift too much heavy snow, you might hurt a Siegel Disk. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Siegel_Mandelbrot { ; time=1:22:52.63--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-0.3905\ 4756291390700/-0.58679532300884950/442757.7/1/102.\ 5/-2.48215537707041634e-009 params=0/0 float=y maxiter=1200000 inside=0 logmap=905 periodicity=10 colors=0008pe5rf7pg8ng9mhAkhBiiChiEfjFdjGckHakI_lJ\ ZlKXmMVmNUnOSnPQoQPoRNpTLpUKqVIqWGrXFrYDsYBuZCs_Cr\ _Cq`Cp`CoaCnaCmbDlbDjcDidDhdDgeDfeDefEdfEcgEagE`hE\ _iEZiEYjFXjFWkFVkFTlFSlFRmFQmGPnGOoGNoGMpGKpGJqGIq\ HHrHGrHFsHEtHDtHBuHAuI9vI8vI7wI6wI5xI4xI3tH7qGAnFD\ kEGgDJdDMaCPZBSVAWS9ZP8aM8dI7gF6jC5m94p53t64s75r86\ q97pA7oB8oC9nDAmEAlEBkFCjGDjHDiIEhJFgKGfLGfMHeNIdN\ JcOJbPKaQLaRM`SM_TNZUOYVPYWQXWQWXRVYSUZTT_TT`USaVR\ bWQcWPdXPdYOeZNfZMg_Lh`KiaKjaJkbIlcHmdGohCmdGk`KiY\ NgUReQVcNYaJa_FeYChW8lV5oU6pT6pS6pS7pR7pQ7pQ7pP8qO\ 8qO8qN8qM9qL9qL9qK9qJArJArIArHArHBrGBrFBrEAsFBrFCr\ FCrFDrFDrGEqGEqGFqGGqGGqHHpHHpHIpHIpHJpIKpIKoILoIL\ oIMoJMoJNnJOnJOnJPnKPnKQnKQmKRmKSmLSmLTmLTlLUlLUlM\ VlMWlMWkMXkMXkNYkNYkNZkN_jN_jO`jO`jOajOaiObiPciPci\ PdiPdiPehQehQfhQghQghQhgRhgRigRigRjgRjgSihThhTghUf\ hUehVehVdhWchWbhXahBpaApc } END PARAMETER FILE=========================================

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FOTD 05-01-03 (The Forest [4])
by Jim Muth 05 Jan '03

05 Jan '03

FOTD -- January 05, 2003 (Rating 4) Fractal visionaries and enthusiasts: Today's image rates a somewhat-below-average 4. As is true with all my ratings, this rating is totally subjective and exists 'in my opinion'. I found the midget easily enough, and decided that its ghost would make a better image soon enough. I determined quickly enough that the <bof61> inside fill would do the best job of revealing the ghost, and the final image rendered fast enough. At that point I was expecting an image worthy of a rating of at least a 6. But then I began coloring the image, and soon found that nothing seemed to work. I ended up with an image that I feel had a rating of at least 6 in it, but which failed to live up to its potential. The disappointment might be due to my clumsy attempts at coloring, or it might be due to an inherent diffi- culty in coloring such images. Regardless, I could rate the final result no higher than a humdrum 4. I named the picture "The Forest" because, with much imagination, one might see an exotic forest in the image. The formula behind the image combines portions of Z^(-1.4) and Z^(-9.6), and adds (1/C) instead of plain C. The parent fractal, before it is evaporated, somewhat resembles a caterpil- lar. Today's scene is located in a tiny valley on the southwest shore of the largest circular bay. As is the case with all fractals of this double-negative class, (indeed with all frac- tals of any nature), other areas of the parent hold an infinity of other scenes that will never be discovered. The 9-minute render time can be avoided by downloading the com- pleted GIF image file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Saturday was fractal-like here at F.C. -- some sun, some clouds, some wind, and a temperature of 36F 2C. Being frac- tal in nature, the cats checked the weather, ventured briefly into the yard, then retired to their resting places to pass the day. As one can easily see, the lives of aging fractal cats are not very exciting. And this morning, light snow is falling. The dynamic duo will likely have another less-than-exciting day. The nature of my day is yet to be determined, as is the quality of tomorrow's FOTD. Check back then to see what happens. Until next FOTD, take care, and the FOTD-CD will be coming soon. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Forest { ; time=0:09:15.79 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.37047999988935450/-0.627083448737120\ 20/25184.95/1/42.5000000000153761/6.43986378112693\ 103e-010 params=5.9/-1.4/10.4/-9.6/0/1e+100 float=y maxiter=1600 inside=bof61 logmap=yes colors=0000sJ0q`0mo0kz0iz4gzAezGezJdzPdzVbzZbzd`zi\ ZzoZzsXzxXzzVzzVzxTxoTxeTvXTvNTvETu4Tu0Tu0`k2ed4kX\ 8qPAvHCzAzCqzAmz8iz8ev6bs6Zo4Vk4Rg2Nd2J`0GX0CT08P0\ 4L00J00E6A8EL2LX0Tg0`s0gz0oz0vz0sz0oz0mz8ixGeqNdkX\ `ddXXkVRZLHNEAC42000800G00L00T00`00e02m02u04z04z06\ z06z0Az0Cz0Ez0Gz0Jz0Lz0Nz0Pz0Rz0Vz0Xz0Zz0`z0bz0Vx0\ No0Hd4AVC2JJ0AR00Z00d00`00Z00X00V04T06P0AO0CL0GJ0H\ H0LE0000RA0T82V62`4Ae4Hk2Pq2Xu0bz0iz0qz0xz0zz0zRbs\ zozzkzu8zm2ze0zi0zR0zJ0zC0z40z00z40zC0zJ0zR4zcCzZE\ zZEuZEiZEZZENZEEVJ8TP4PV0N`0Le0Hk0Gq0Eu0Jk0Px0Vx0`\ z0ez0kr0qz0vz0zz0zz0zz0zz0qz0ez0Xz0Lz0Cz00u40z8zXG\ voPubZsVgqVqoVzmVzkVziVzT0zE0iJ0eP0bV0``0Xe0Ti0Re0\ Ld0H`0CZ08V02T00P00N00L00G00CA08K04X00e00q40z60zA0\ zC0zA0zA0zA0x82m86m8Ag8Eb6HX6JR6NL6RG4VA4Z44`04d06\ e08g0Ak0Cm0Co0Eq0Gu0Hv0Jx0Jz0Lz0Nz0Pz0Rz0Rg0zb0xX0\ qR4kLEdHLZCTR4q00u00x00u4 } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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investigations#3.1
by jos hendriks 04 Jan '03

04 Jan '03

Dear reader Intro It was Jim Muth, who gave me the inspiration to contribute now and then to the list. I transport his pars to a file specially called muth.par . About once a week I render some of them. Often I like the pictures. It is also quite funny to compare his rating with the one I should give. Most o the time they differ considerable. For instance the last one I rendered, the one 31-12-2002 named:"so let it be", I would rate an 8 at least. It reminds me of a (intricate) staircase. And because it's never ending I should have call it "staircase to heaven". Ismand In the documentation (helpfile) of fractint you can find under "formula" that it's possible to use the predefined variable ismand to create formulas with witch you can toggle between mandel and Julia frm's. But how? A few weeks ago I run into the demo from Sylvie Gallet, so know I know. But it might be a good idea to put some information about the use of ismand in the documentation itself. The formula frm:Jh_square {;Jos Hendriks,2002 if (ismand) z = 0 , c = pixel else z = pixel , c = p1 endif : a=real(z),b=imag(z) z=a*a+flip(b*b)+c real(z)<p2 && imag(z)<p2 } This time, again, a simple and at first look nothing promising, formula: f(x,y)=(x^2,y^2)+c. I don't think there exist a ( simple) complex equivalent. The Mandelbrotset is a square (not hard to see) with corners (-2,-2) and (0.25,0.25) (witch is more difficult to see). So that gives really nothing. Nevertheless Juliasets can give nice images (although then nothing of the Juliaset itself is to be seen). Sometimes with fractal features. Below are two pars. I called the pictures: "looking at the block of flats at the opposite of the street and "looking out of the window to the windows at the opposite of the street." They render in seconds, even on a slow machine. frm:Jh_square {;Jos Hendriks,2002 if (ismand) z = 0 , c = pixel else z = pixel , c = p1 endif : a=real(z),b=imag(z) z=a*a+flip(b*b)+c real(z)<p2 && imag(z)<p2 } block_of_flats { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=fractint.frm formulaname=jh_square ismand=n passes=1 center-mag=-0.77118865717993890/+0.78113466887094510/227799/0.6848 params=-2.522474238758866/-2.5106260160601/4/0 float=y colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zV\ V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0\ S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKK\ S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3\ >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G\ 8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBG\ GBFGBDGBCG000<6>000 } windows { ; Jos Hendriks ,2002 reset=2000 type=formula formulafile=fractint.frm formulaname=jh_square ismand=n passes=1 center-mag=-1.64e-006/2.205e-006/0.5706675 params=-2.016863584518433/0.3288808465003967/3/0 float=y colors=000z0zc0cz00c00zz0cc00z00c000z00c0zz0cc000000zzzccc<238>ccc }

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FOTD 04-01-03 (Siegel Disk Fractal [5])
by Jim Muth 04 Jan '03

04 Jan '03

FOTD -- January 04, 2003 (Rating 5) Fractal visionaries and enthusiasts: For quite some time I have been hearing rumors of the existence of fractal things known as Siegel Disks. When I first started hearing these rumors, I had no idea what Siegel Disks were supposed to be. I supposed they were some type of Julia set, but why were they called disks? I wondered about the problem a day or two, then forgot it. Then, a few months later, I found that a Siegel Disk is a feature that appears in Julia sets with a C-value that lies on the exact boundary of the Mandelbrot set. And there appears to be a particular Julia set, the one with a C-value of -0.390541,-0.586788i, that lies on the boundary and is considered to be the 'Siegel Fractal'. At that point, I lost interest in Siegel Disks, but yesterday, I decided that I would like to see exactly what a Siegel disk looks like, so I calculated the Julia set that corresponds to the above value of C. The result was a Julia set like many I had seen and ignored before. Why, I wondered, was this fractal called a 'disk'. I raised the maxiter from my usual exploration value of 1200 to 500,000 and recalculated the fractal. Other than going somewhat slower, the image remained unchanged. But I did not give up. Doing further investigation, I changed the value of C to -0.390547-0.586796i, a value that corresponds to a point lying a tiny bit inland on the M-set, and recalculated the fractal. To be sure the calculation did not skip over any near-periodic points, I set the periodicity to 12. Now, things started to happen. As the image developed, I saw that the fractal was not empty, but was filled with disk-like rings of extreme maxiter value. Here at last were my Siegel Disks. They are not the true Siegel Disks, which would have a maxiter of infinity and be totally flat and featureless. These would be impossible to draw. My disks are close enough to be called pseudo-siegel-disks however, and they have a huge advantage in that they are possible to calculate within the time that the universe will continue to exist. When all my exploration was finished, I named the resulting image "Siegel Disk Fractal" and rated it at a 5. The rating is mostly for the mathematical interest of the image. Artistically, it rates no more than a 3 or 4. Despite its extreme maxiter, the image draws in only 15 minutes on my tired old Pentium 200mhz machine. Most machines, being faster, will draw it faster. And as always, the completed GIF image is available on the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Now that I have a way of controlling the flood of spam that could result, I also might soon resume posting the FOTD images to: <alt.binaries.pictures.fractals> But don't go there yet. I have not yet made the decision. It rained and rained Friday here at F.C. -- a 34F 1C ice-cold rain that did good to neither man nor cats. The man passed the time accomplishing some useful work. The cats passed the time sulking like the mature cats they are. Whatever became of the happy, playful kittens they were 10 years ago? Today is starting cloudy, but a clearing is on the horizon, and I expect the day will turn out far better. And I have only a modicum of work to finish, which should make the day a good one by the time it ends. Until the next FOTD appears in 24 hours, take care, and I wonder how much data a Siegel disk can hold. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SiegelDisk_Fractal { ; time=0:15:25.16--SF5 on a P200 reset=2002 type=julia passes=1 center-mag=0/0/0.97\ 12963 params=-0.390547/-0.586796 float=y inside=255 maxiter=500000 logmap=yes symmetry=origin periodicity=12 colors=0000000000000000000000000000000000000000000\ 000000000000000000000000000300600AI0EC0I60K00O00S0\ 0W00_00c00g03k0Co0Ks0Uz6ezEozNzzWzzezzozzvzvzzkzz_\ zzNzzEzz3zv0zs0zo0zo0zb0zR0zE0z30k00_00K0080000000\ 000000Kz0No0NR0N30R00R00R00_00e00o00v00z0Cz0Rz0ez0\ vz0zz0zz0zz0zz0sz0ok0kb0eR6bIC_8IU0NR0UN0_I0eE0kC0\ s80z30k00b00R00I0080000C00K00I0CE0_C0z00z00z00z00z\ 00z00z00z08z0Kz0Wz0hv0vv0zz0zz0zz0zz0zz0zz0zz0zv0z\ o0vh0vb0sW0sR0oK0oE0k80k30o00s00s00v00v00z00z00z00\ z00v00o00h30b80WC0UI0NN0IU0C_06b03h00o00v00z00z30z\ 63z8RzCszEzzIzzKzzKzzKzzKkvKWoKKkEEhC8e83b30_00W00\ U00R00N00K00I00E00C0080080000000000000003608C30UI0\ kW0zU0zR0zR0zN0zN0zK3zK8zIEzEKzERzC_zCez8kz8sz6zz6\ zz0zz0zv0zk0zb0zU0zK0zC0z36z0_z0zzzzzzzzzzzzzzzzzz\ zzzoz0_zIRz_UzRUzIWz8Wz0_z0_z0kz0vz0zz0zz3zz6zsCzz\ Ezz8zz3zz0zz0zz0vz0kz0ez0 } END PARAMETER FILE=========================================

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FOTD 03-01-03 (Negative [5])
by Jim Muth 03 Jan '03

03 Jan '03

FOTD -- January 03, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's image is another 'evaporated' one that consists entirely of inside fill. It strongly resembles yesterday's image, which consisted of FMOD inside fill, but today's image is made of bof60 fill. While studying the image, searching for a suitable name, I could not shake the impression that I was looking at a negative. I finally settled on the name "Negative". This name has nothing to do with my opinion of the image's worth, which is average -- it refers solely to the appearance. The image was created by adding 1 part of Z^(-6.66) to 7 parts of Z^(-1.75) before adding (1/C). The variety in the fractals created by combining negative powers of Z appears nearly inexhaustible. I have been exploring these fractals for a year or so, and have not yet scratched the surface. The 12-minute render time can be avoided by downloading from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The clouds hung around all day Thursday here at Fractal Central. With a temperature of 39F 4C, it was far too unpleasant outdoors for the dynamic duo, who spent the day sleeping by the heat and occasionally asking for food. Today is starting just as unpleasantly, and it is raining as well. I fear the cats will remain unhappy. I now find myself with quite a bit of work to do and a limited time in which to do it. So until next FOTD, take care and think positive when the world is negative. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Negative { ; time=0:12:47.20--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.20995120647748890/+0.778751248577170\ 40/18264.3/1/-42.5/-3.61434354667622415e-011 params=7/-1.75/1/-6.66/0/1e+100 float=y maxiter=1500 inside=bof60 logmap=yes periodicity=10 colors=000uwztwzswMrwNqwPpvQouUntXms`lrckqfjpaioY`\ gUU`QMTMFLI8EE7FD7FC7FB7GA7GA7G97H87H77H76JB6LE6NH\ 6PK6RO5TR5VU5XX5Z`5`c4bg4dkXfo`irekufmukovqqzNjfRd\ `V_VYVQ_XR`ZRa`RbbRddRefRfhRgiRikSjmSkoSlqSnsSouSp\ wSqwS050lsUipUgnVdlVbiW_gWYeXVbYT`YQZZOWZLU_JS_MUc\ PVgSWkUXnXYr_Zva_ycavectgeqigokimlkjnmhpofrqctsauu\ _pvYkvXfwVbwUYwSTwROwQKwOFwNAwL5wK1wJ5wN9tRDqUHnYL\ k`PhdTegXbk`_ndXrgVuhXthYsh_rh`qhbpicoienifmihliik\ gemebnc_oaWp_TqZQrXNsVJtTGuRDvQAwREtRHrRKpROmRRkSU\ iSYfS`dScbSf`SeYSeWSeUSdSSdQSdOSdMScKScIScGSbESbCS\ bASb8TaCT`GT_JT_NTZQUYUUXXUX`UWcUVgVUjVUnVTqVSuVSx\ YUv`WubYte_sgardbqacpZdoWenTfmQglOhkLijIjiFkhClg9m\ f6ne4oe5kg5hi5ek5bm5Zo5Wq5Ts5QtBPoHPkNPgTPcZP_dPWj\ PSpPOuPKtQLsRMrSNqSNpTOoUPnVQmVQlWRkXSjYTiYTQHuMMt\ JQtFUsCZs8br5fr7gm8gi9geAgaBgXCgTEhPFhLGhGHhCIh8Jh\ 4Ke6Kc8Ka9LZBLXCLVELTFMQH } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Fractal Calendar 2005
by Fractal Forum 02 Jan '03

02 Jan '03

This is an open call for you to submit your fractal artwork for consideration for inclusion in the Fractal Universe ® Calendar 2005. All the information you will need is detailed on the following website: http://www.fractalforum.com Please make your submissions and any additional enquires you may have via the contact form on the above website. This message has been posted to some of the fractal art newsgroups, mailing lists, and forums. If you think it may be of interest to others please feel free to forward it, as it is written here, to other 'net sites where fractal artists meet to share and discuss fractals. Thanks and good luck! Linda Allison and Tina Oloyede xxxxxxxxxxxxxxxxxxxxxxxxxxx Fractal Forum http://www.fractalforum.com xxxxxxxxxxxxxxxxxxxxxxxxxxx

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FOTD 02-01-03 (Jellyfish [8])
by Jim Muth 02 Jan '03

02 Jan '03

FOTD -- January 02, 2003 (Rating 8) Fractal visionaries and enthusiasts: For the second day of the second year of the third millennium we have a fractal image that rates a much-above-average 8. It is one of my 'evaporated' scenes, where I take an image that contains a negative power of Z, find something interesting, and then raise the bailout radius to one-googol, which causes the screen to go blank. Next, I apply one of the non-flat inside fills to the image, which now consists totally of 'inside' points. Sometimes, nothing much happens, but usually, the inside fill reveals the 'ghost' of the scene that originally was there. Thus, today's image is a ghost, a thing which in the world of fractals certainly does exist. I was a bit puzzled when the time came to give a name to the image. It reminded me of something...but what? Then, after pondering for several minutes, I thought of a jellyfish. This was it. The image, with its appearance of transparency, reminds me of a jellyfish drifting gently in a warm ocean current. Of course, no real jellyfish is so symmetrical. It is the effect of transparent elements before an infinite blue background that earns the name. The warhorse MandelbrotMix4 formula calculated a critical plane of the expression 45Z^(-0.8)-36Z^(-0.9)+(1/C) to create the parent fractal of today's image. When calculated with the default bailout radius, this parent is little more than a circle filled with great blobs of fractal glop. But a small bud of Mandel-material lies on the X-axis, and today's image is located at the tip of a filament stretching from a sub-bud of this bud into an open area, where it finally dies out. The 37-minute render time of the attached parameter file is slow. Those with other things to do as the normal work routine resumes will want to download the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> With the temperature hanging in the middle 40'sF (around 6C), it rained steadily all day Wednesday here at Fractal Central, some- times quite heavily with occasional claps of thunder. Some minor flooding was reported around the area, but F.C. remained dry. The dynamic cats were very depressed however as they sat at their window, watching the rain and wishing they could go out. An evening treat of tuna helped ease their depression, but they still ended the day in a sullen mood. Though today is starting cloudy, at least the rain has ended, which is a good sign. Now, if the mud in the yard would dry, the dynamic ones might have a pleasant day. It will take more than a dry yard to make my day pleasant however. This will not happen until the design work is finished, and it will not be finished until I begin. So until tomorrow, take care, and be kind to your fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Jellyfish { ; time=0:30:23.25--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=t center-mag=-0.4004091333751482/+0.0215282924423132\ /3.080974e+007/1/80/-1.5530640837951859e-007 params=45/-0.8/-36/-0.9/0/1e+100 float=y logmap=yes maxiter=1200 inside=fmod proximity=1 periodicity=10 colors=000UPqUQpURnUSlUTjUUhUVfUXeUYdWZcY_b_a`ab_c\ cZedYfeWgeVfeUfeTeeSefQdfPdeOceNcfLbfKbfJafIafHZeK\ XdMVcNTbPQaQO`RM_TK_UHZVFYXDXYBWY8V_6U`4Ta2Tb1S`1S\ _1SZ1SX1SW1SW1SV1RV1RV1RU1RU1RV1RV1RW1QX1QX1QY1QZ1\ QZ1Q_1Q`2R_2RZ3SY3SX4TX4TW4UV5UU5VU6VT6WS7WR7XQ7XQ\ 8YP8YO9ZN9ZNA_MA_LA`KBaJBbJCcICdHDdGDfGDfFEgEEgDFh\ CFiCGjBGjAGk9Hl9Hm8In7Io6Io6Hn8HmAGmBGlDFlEFlGEkHE\ jJDjKDiMCiNCiPBhQBgSAgUAgV9eX9eY8e_8d`7cb7cc6be6bf\ 5ah5ai6`g6_e6Zd6Yb7Xa7W_7VZ7UX7TV8SU8RS8QR8PP8OO9N\ M9MK9LJ9KHAJGAIEAHDAGBAF9BE8BD6BC5BB3BB2BB2BC2BC2B\ D2BD2HQ5Mb8RoAQnCQmEQlFPkHPjIPiKPhMOgNOfPOeQOdSNcT\ NbVNaXN`YM__MZ`PYbUYcZagcejhimmmqrrtwwwzzzwxtrtnmp\ hhmbcfVZ`NaUSbEWcA_gBShBLfCEbC7ZC0YE1XG2WH3VJ4UK5T\ M6SN7RP8RQ9PP9NO9KNAIMAGLAEKAFJFGJKGJOHJTIJYIJaJJf\ KJkKJoLHpLGpLFpLEpLDpLCqLBqLAqL9qL8qL7rL6rL5rL4rL3\ rP7pTAoXDn`GmdJlhMklPjpSi } frm:MandelbrotMix4 {; 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, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Best concise definition of fractal ?
by Anna Baron 02 Jan '03

02 Jan '03

Hi folks! Grateful for all your answers which I've enjoyed - all of them interesting attempts to reduce such a complex subject to a simple definition. Special thanks to Jos H.'s for having been particularly entertaining, giving me enough food for reflection :) Cheers all! Anna __________________________________________________ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com

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FOTD 01-01-03 (Broken Symmetry [7])
by Jim Muth 01 Jan '03

01 Jan '03

FOTD -- January 01, 2003 (Rating 7) Fractal visionaries and enthusiasts: It's a new year here at Fractal Central, and we start it off with a sudden switch to an optimistic outlook and a trip to the Z^(sqrt(2))*(0.6(C))+C fractal to find an image that rates a 7. The parent fractal was drawn by the JimsCompMand formula, which is simply a generalization of the cmplxmarksmand formula of Fractint. The strange little midget in the image lies in the East Valley area of the largest midget on the main stem of the Z^(1.4142)+C Mandeloid. Yes, I can already hear the voices telling me that the Z*(1.4142)+C Mandeloid has no main stem, that the stem vanishes as the exponent of Z is dropped to a value less than 2. This is true, but the parent Mandeloid of today's image is not exactly the Z*(1.4142)+C figure. In the JimsCompMand formula, Z^(1.4142) was multiplied by 0.6(C) before (C) was added. This multiplication causes the fractal to split apart along the negative X-axis, and this splitting causes the non-existent negative stem to emerge from never-land into the world of fractal reality, where it can be examined as though it had never vanished. The prominent midget is still there on the revealed stem, grossly distorted of course, with its East Valley still easily recognizable. The stem itself still zig-zags down into the center of the valley, and it still has midgets strung along it, though at such a low power of Z, the midgets are rather difficult to pick out along the zig-zagging and branching stem filament. Today's scene lies quite deep, so deep in fact that it actually shows signs of breaking up, and needed the mathtolerance reset to /1 to reach the magnitude. I have included the mathtolerance setting in the parameter file so that the image will draw at the correct magnitude at all resolutions. I named the image "Broken Symmetry" because of the spectacular discontinuity that, along with the coloring, spoils (or makes) it. This is the one of the greatest degrees of disorder that I have yet come upon, though undoubtedly an infinity of midgets with even more disorder do exist and are waiting to be found. The 13-minute render time is a bit trying, and may be avoided by visiting Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and downloading the completely rendered image from there. The weather was much improved Tuesday here at F.C., with mostly sunny skies, light breezes, and a temperature of 55F 13C. The small amount of dampness remaining in the yard did not deter the dynamic ones from enjoying a 2-hour romp, which helped their moods immensely. In fact, they ended the day in such a pleasant mood that they were satisfied with their normal diet. But today is rainy, and I doubt that their pleasant moods can weather the storm. Check tomorrow to see how they make out. As for me, I'll probably do little more than watch football on the TV. Until next FOTD, take care, and here we go again with another whole year to get through. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Broken_Symmetry { ; time=0:13:24.99--SF5 on a P200 reset=2002 type=formula formulafile=jim.frm formulaname=JimsCompMand passes=1 mathtolerance=/1 center-mag=-1.36389419716712900/+0.671782211838532\ 70/1.326342e+013/1/102.501354055520352/3.885780586\ 18804789e-016 params=1.4142/0/0.6/0/0/0 float=y maxiter=5400 inside=0 logmap=285 periodicity=10 colors=000DaZEc`FebGgdHifIkhJmjKolLqnMrpNvrOztTmmY\ fga_afTVkMPoGJpIIpKIpMHpOHpQHpSGpUGpWFpYFpZFl`HibJ\ edKbfMZhOWiPTkRPmTMoUIqWFsYCtZGhSKYLOMESB7W01Z57aA\ DdFJgJPjOVmT`pYfsakp_imZgjXfhWdeUbbTa_R_YQYVOXSNVQ\ MUOMWMMXLMZJM_IMaGMbEMcDMeBMfAMh8Mi7MjDHbJCWP7OV3H\ R8JNDKKILGNMCSN9XO5aP2eQ4gT6iW7jY9l`AmbCoeEqhFrjHt\ mIuoOI`QJaSKaULbVMbXNbZOc`PcaQdcRdeSdgTehUejVflWfm\ XfQX1PW2PW3OV4OV4NU5NU6MT7MT7SQBXOEaMHfKKkINpGQuET\ tCWsBYr9_q8ap7do5fn4hn3jh8mbCoXGrRKtMOvOQsPSqQUnRW\ lSXjTZgU`eWbbXd`YeZZgW_iU`kRamPbnNVeHNYBFQ57I08J69\ KCAKHBLNCLTDMYEMcFNiFNnKOkOPhSQfWQc_RadSZhSWlTUpUR\ tUPrTNqSMpRLnQJmPIlPHjOFiNEhMDfLBeLAdK9bJ7aI6`H5_H\ 4YG6XF8VEAUDBWCDYBF_AGa9Ic8Ke7Mg6Ni5Pk4Rm4So7PqIXt\ TYwc_zcazcczaez_gzYizYkzYmzYozYpzXqzXrzXszXtzXuzXv\ zXwzXxzUyzVzzVzzVzzVzzVzzVzzjzzizzhzzgzzgzzfzzezzd\ zzdzzczzbzzbzzazz`zz7zz7z } frm:JimsCompMand {; Jim Muth z=c=pixel: z=z^p1*(c^p2)+c, |z| <= p3+100 } END 20.0 PAR-FORMULA FILE==================================

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