June 2005 - Fractint - mailman.xmission.com

FOTD 09-06-05 (Daisies in the Field [6])
by Jim Muth 09 Jun '05

09 Jun '05

FOTD -- June 09, 2005 (Rating 6) Fractal visionaries and enthusiasts: Alert: the next paragraph is non-fractal in nature. The fractal fun starts in the paragraph after the next. When I opened my e-mail this morning, I noticed a letter from Earthlink, my ISP, informing me that my password had been changed and I would not be allowed to access my e-mail until I checked in at their web site and re-entered my info. Curiously, if this were actually the case, I never would have been able to access my mailbox to read the letter telling me that I could not access my e-mail. And what right does Earthlink have to change my password? I thought it was up to me to decide if and when to change it. I get so many of these fraudulent letters that I am beginning to suspect we have a new industry emerging. At least none of them complain about the hot weather. I named today's fractal image "Daisies in the Field" because that's what it reminds me of. The image is a pleasant diversion from the world of winning phony lotteries, phishing scams, and hot weather. It is a picture of an invisible midget. Yes, such things actually do exist, and we have one at the center of today's frame. To see the invisible midget in all its non-glory, simply change the inside fill to 'numb' and re-calculate the fractal. Don't wait too long, for nothing will appear but a blank screen. The midget and the whole parent fractal as well have become invisible. Everything has evaporated. Sometimes these 'evaporated' versions are better than anything done in the normal manner. At other times they are worthless. In today's case, the evaporated version is one of the better ones, though several other versions are good enough that they could have been chosen instead. The formula combines Z^(-1.4) and Z^(-4.1) before adding (1/C) to produce a typical 'inside-out' parent fractal. The rating of 6 and render time of under 5 minutes make it all marginally worth the effort. The completed image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A temperature of 93F 34C on Wednesday here at Fractal Central kept the cats in the coolest spot they could find, which happened to be their window shelf, from where they could watch birds and keep cool at the same time. I kept my cool by finishing some work and not worrying about global warming. Today is starting the same, so the duo will likely have another day by the window. The next FOTD will appear as always in 24 hours. Until then, take care, and wait for the new age. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= DaisiesInTheField { ; time=0:04:47.81--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.22664453241798800/-1.722164951309734\ 00/7704166/1/-57.5/-8.9860445882036788e-006 params=-1/-1.4/-0.4/-4.1/0/1e+100 float=y maxiter=1000 inside=bof61 periodicity=10 colors=000Hi5Fi5Gb4HW4IQ3JJ3KC2L62QM7V`B_oF`jI`fK`\ bM`ZORVWTTjVSxZUpbWifYbj_Wn`PerNbgL`XJYMINV5KV5HV5\ DU5AU57U54U5Ynk`m8WiHRfPNcXI`dEYlESiEMfFNbGOZHPWIQ\ SJROKSLN`VQhcHNS92H8CM8MQ8WVleZmoczxgco_sgTGZLIREK\ J7OHASGCWFE_DGcCIgBKhDViFziHzrMzoJzmHzjFkhDhfBec9b\ a7__5XeJckXiqjpwxvlgfbRSVOQNLPGIO8FN1CM6GRBJVFN_KQ\ cPUhTXlS_eRb_QdUPgOOiINlCNn6ToBZoGdpLipPoqUuqZzqby\ lcyhdycey_eVSU1KJ3LP5MU6MZ8NdAOiBOnYKhtGboN`jT_fZY\ aeXYkVTqUPwTPvQPvNPvLPvIPvGPvDPvBKlIFbOATV5J`19fcc\ 1UyjOqcJjXEcQ9XKDQMGJOJCPC6E614955C96FD7IG8LK9OOAR\ SBUVBWZAXa9Ze7_h6al5bo4ak3ah3ad3aa3aZ3aV3aS3aO3aL3\ aI3aE3aB3a83ZB9XDEVGKTIPRKUON_MPdKRiIUoGWtEYyXlpoz\ glzeizcgzbdz`bz__zYXzWVzVSzTQzSLoUHeVDVW9LY5AZ10_8\ 3WE5SK7PO8QR9RU9SYAT`BUcBUfCVjDWmDXpEYsEYmKXgPWbUW\ aSXaRXaQXaOXaNYaMYaLY`JY`IY`HZ`FZ`EZ`DZ`CZcBYeAWhA\ UPZTPaNPcHPfBPh6Ni5Li5Ji5 } 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 PARAMETER FILE=========================================

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FOTD 08-06-05 (Fractalville [7])
by Jim Muth 08 Jun '05

08 Jun '05

FOTD -- June 08, 2004 (Rating 7) Fractal visionaries and enthusiasts: Alert: the topic of the next three paragraphs is political rather than fractal. Those who are bored with politics should skip ahead. The day started with fractal lady complaining of the heat, telling me that global warming is getting bad, and they had better do something about it before drought kills the crops and we all starve. I tried to convince her that she is complaining of a temporary localized hot spell in the Mid-Atlantic region of North America, not a permanent world-wide rise in temperature, but being a proper liberal thinker, she knows that the current heat is caused by the evil big greedy corporations that care only about their profits and not one bit about the environment or the poor people who work for them. I ended the conversation by telling her that liberals (whatever they are) mean well, but they had best get their facts straight before offering irrelevant solutions to monumental problems. Catastrophic global warming is a real possibility, but a single early summer warm spell in Maryland is not a sign that it is happening. The real problem is that the human population is suffering runaway inflation and under-developed countries are starting to develop. Forcing the big corporations to care about the environment and pay their workers more money, as she would like the government to do, would not end the population explo- sion. It certainly would cause prices to rise and inflict more hardship on the poor however. The most effective means of controlling population growth is economic development, but the planet has too few resources to bring its present population of 6,200,000,000 to the economic level now enjoyed in the U.S. Mankind is most likely as doomed as F. Lady fears, but from unavoidable over-population rather than a global warming that might or might not be in progress. What better way to cure a downer of a morning than with a good fractal. And today's image is well above average. (At least IMO.) Today's image is actually beyond the range of resolution, but with such a naturally broken-up image, the slight extra break-up caused by the math failure is hardly noticeable. The 'mathtolerance' entry that permits such a magnitude to be reached is now automatically included in the Fractint parameter files. To find today's very slow image, I went to the southern shoreline of the broadened East Valley of the large midget on the negative stem of the Z^2.0001+C Mandeloid, and examined an unusually fragmented area. What I found there is worth being chosen FOTD for June 8. For some forgotten reason, I named the image "Fractalville", not to be confused with Frackville, an old coal-mining town in central Pennsylvania. Then I rated the scene at a 7, which might be a bit of a gift. Unfortunately, the image is an unusually slow one, taking almost two hours to complete on my old machine. Fortunately, I have sent the completed image on ahead to Paul at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is posted, ready for download. A high temperature of 88F 31C on Tuesday kept the fractal cats on the shady porch all afternoon, where they stretched out to take it easy. They must have had a thoroughly satisfactory afternoon, for when they came in, they asked for no tuna. My day was average. Today is starting even warmer; I expect similarly lazy cats. The next FOTD will appear right here in 24 hours, more or less. Until that apocalyptic moment, take care, and if the end comes, can a new beginning be far behind? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fractalville { ; time=1:57:50.12--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotVE-VP passes=1 center-mag=-1.74990797821024600/-0.000452782810913\ 32/2.790644e+013/1/82.5/-0.0271040593762201867 params=2.0001/0/0/0/0/0/2/0 float=y maxiter=32767 inside=0 periodicity=10 mathtolerance=0.05/1 colors=0003vL4vK4uJ5uI5uH6tG6tG7tF7tE8sD8sC9sB9rAA\ r9Ar9Br8Bq7Cq6Cq5Dp4Dp3Ep2Ep2Go1In1Jn1Lm1Ml1Ol1Pk1\ Rk1Sj1Ui1Vi0Xh0Yg0_g0`f0bf0ce0ed0fd0hc0ic0jb2kb3kb\ 4lb5lb6ma7ma8na9naAoaBp`Dp`Eq`Fq`Gr`Hr_Is_Js_Kt_Lt\ _MqZPoZRmZUkZWiZYgZ`eZbbYd`YgZYiXYkVYnTYpRYrP_oO`l\ MbiLcfKedIfaHhZFiWEkTDlRBnOAoL8qI7rF6sD6pE6mE6jF6h\ F6eF6bG6_G6YG6VG6SF6PE6NE6KD6HD6EE6CE69E65F65FA4FK\ 9HP3IU7KXAL_EMbHPeMQhQSkVUnZWq`Yte_wi`zmcypdzsezpb\ xm_vkXvhUueRtcOs`MrYJpUGoQDjNAeJ7eH5iFBmIHqNNpTToY\ Ynacmiilqokstirqhlnfkleiicdfbcd`ba_aZY`XX_UVZRUYPS\ XMRWJPVHOUEMTBLS9RWBX_DbcFhgHnkJtoLzrNyoJylFxiBxf8\ vdAucCsbEraFp`Ho_JnYLlXMkWOiVQhUSgTThVShXShYSh_Rha\ RhbRhdQhfQhgQhiQikPilPinPipOiqOisOiuNivNixNiyNixPi\ xRixTixVixXixZix`ixbixdiwfiwhiwjiwliwniwpiwriwtiwu\ jusktqlsomrmnqkooipngqmerlcskatj`pibmhdjgfgghdfjae\ lZdnWdobSWhFDeJEcMEaPE_SE } frm:MandelbrotVE-VP {; Jim M. variable escape and power a=p1, z=p2, c=pixel+p3, b=sqr(real(p4)): z=z^(a)+c, |z| < b } END PARAMETER FILE=========================================

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FOTD 07-06-05 (Twisted Donuts [7])
by Jim Muth 07 Jun '05

07 Jun '05

FOTD -- June 07, 2005 (Rating 7) Fractal visionaries and enthusiasts: Who ever thought that twisted donuts could be found in a fractal? Certainly not me. I expect to find twisted donuts in a bakery. But something about today's image reminds me of twisted cinnamon donuts, so I named it "Twisted Donuts". Donuts are not the healthiest food available. I eat them because they taste good, and not to be healthy. Fractals on a computer screen are rather useless, but I enjoy them anyway, because they are fun and they supply the adventure that it is now both too late and too early to enjoy otherwise. Today's image is a scene near the tip of the main stem of the Mandelbrot set. But it is not really the Mandelbrot set we are examining; it is only a look-alike. The iterated expression is Z^2.0000000003+C, which produces a fractal virtually indistin- guishable from the M-set, except along the negative stem, which is where today's image lies. A couple outzooms will reveal that the main stem, which at the angle of today's image runs northwest-southeast, has split into two, and that today's scene lies between the two. The area is filled with features never before seen (at least by me) in the M-set. It is this kind of thing that I was searching for in yesterday's simple image, but never found. I really could have spent a bit more time on the coloring, so the rating of a 7 seems justified. The render time of under 2 minutes is plenty fast, at least for those with Fractint-ready machines. Those with Fractint-deprived units can still see the image by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is, or soon will be, posted. The Monday high temperature of 91F 33C was a bit much for the fractal cats, who cut their outdoor time to under 30 minutes before asking to come inside. A lively thunder-shower came up at 7pm and sent Thomas scurrying for cover. Tippy braved the action on the window shelf. Today is starting almost as hot. I expect the cats will have a similar day. For me, the day promises to be just another one to be forgotten as soon as it has ended -- except for the trip to the local donut shop, that is. The day's FOTD will live on however. And the next in the endless series of FOTD images will appear in 24 hours. Until then, take care and be iterative, but don't eat too many donuts. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Twisted_Donuts { ; time=0:01:52.82--SF5 on a P200 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotVE-VP passes=1 center-mag=-1.99994352213414000/-0.000000000515175\ 04/5.741663e+009/1/-50/-4.15090305853904606e-005 params=2.0000000003/0/0/0/0/0/2.01/0 float=y maxiter=600 inside=0 periodicity=10 colors=000AA9EAEI9IM8NQ8RPNaP`kPnuLmrImoFllCli9kf6\ kc3j`0jZ7eWE`TLXQQVUUTYZSabQegPikNmoMqrKkuJexI`sHc\ oGfkFigElbDoZCrVBuRAwQ9wQ8wQ7wQ7wgSuylsootfqtYstPu\ tGwtKvlOudStYWsQ_rIbrBVgEAPzAKzAAzAAyAAxAAwAAvAAuA\ AtAAsAArAAqAApAAoAAnAAmAAlAAkAAiAAgAAeAAcAAaAA_AAY\ AAWAAUAASAAQAAOAAM97K73IG4GO5DW6Ac77k75lE4mK4nQ4oX\ 3pb3qh3rk8smDtpIurNutRllNceJWZGNRCEK86D5ACCEBIHAOL\ 9UP8`S7fW6lZ5rW8sUBsREsPGtMJtKMtIOtLJoNFjPBeR7`T3W\ cJPmZJwmDukIsiN`PKI4IHBFHIDGPAGW8Fb5Fi3un6teCsYHsQ\ NrISqAYq2bm2gi2lf2pi7lkChmGeoLaqPZjSWcUTYWRSRZMNfG\ InAEuTGYkHAjGEiGIiFMhFQgEUgEYjFXmFXoGXrGXtHXwHXyHX\ jRSX`NZXK_UI`QGaNDbJBcG9XTRRehLryOUkXSaeRSnPIvO9qY\ ElfIgoNcxRrOcjOfcOiWOkPOnIOpGUrEZtCcvAhw`cgWWbROZM\ GVH8RcZMyxImpJahJQaJEUJ2NJ6SG9XED`CGeAJi8OhESgKXfQ\ `eWddaicgmbmqasrdqrfprhorkmrmlroksnnsmqtmttlwtlytk\ utjqtinthjthgnaaAI31C06B5 } frm:MandelbrotVE-VP {; Jim Muth real(c),imag(c) a=p1, z=p2, c=pixel+p3, b=sqr(real(p4)): z=z^(a)+c, |z| < b } END PARAMETER FILE=========================================

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Re: FOTD 01-06-05 (Hexa-Something [5])
by Jim Muth 06 Jun '05

06 Jun '05

At 02:18 PM 6/4/05 -0400, Hal Lane wrote: >How does one view 'invisible' midgets? Were you >able to apply a certain rendering method to render >them visible? Or does 'invisible' in this context >just mean that they are too small to be seen at the >scale of the Hexa-Something fractal? Although there are such things as invisible midgets that need special rendering to make them visible, the midgets I referred to are simply too small to be seen at the scale of the FOTD fractal. >Also, are you using the phrase 'quintic midget' to > refer to: > - a midget that has five lobes, > - one that has five-fold symmetry around it (the way > Hexa-Something has six-fold symmetry) or > - one generated by an equation with a variable raised to the fifth power? By a 'quintic midget' I mean a midget that is generated by an iterated fifth-power expression such as Z^5+C. These midgets have four lobes and five-way symmetry. Jim M.

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FOTD 06-06-05 (Simply Simple [4])
by Jim Muth 06 Jun '05

06 Jun '05

FOTD -- June 06, 2005 (Rating 4) Fractal visionaries and enthusiasts: Today's image is not the ultimate goal of Sunday's fractal adventure, but it is an interesting scene that appeared on the way. The ultimate goal will appear as the FOTD for June 07. Since I have not yet reached that goal, I have little idea of what I will find there. I know only that it should be interesting. The formula is a new one that calculates Mandelbrot fractals with both variable escape radii and powers of Z. I might make a few speed-up changes in it before making it permanent, but it works well enough as it is for today's image. The name "Simply Simple" means nothing other than what it implies. Of course, there is nothing simple about fractals, which are some of the most complex things found in nature, if indeed nature is where fractals exist. (They might exist only in the mind.) The rating of a 4 is below average. Since the image is only a way-station, I could rate it no higher. The below-average rating is made up for however by the render time, which is a sizzling 35 seconds. For the convenience of those with handicapped (challenged in PC language) computers, the completed image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 88-degree (31C) heat and high humidity kept the fractal cats confined to the shade of the holly thicket on Sunday. But at least they were outside, which is all that cats of the fractal variety need to keep them happy. Today is starting even warmer and more humid. I expect more of the same. The next FOTD will be ready in 24 hours. Until then, take care, and don't sweat it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Simply_Simple { ; time=0:00:35.26--SF5 on a P200 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotVE-VP center-mag=-1.99998588087103100/+0.000000000314646\ 81/1.730527e+010/1/-145/0.00152484032409423709 params=2.0000000001/0/0/0/0/0/2/0 float=y maxiter=600 inside=0 outside=summ periodicity=10 colors=000GoSCqO8rK4tG0uC8oGGjJOdNV_QbUUjPXrJ`yEcw\ B`u9Zt7Xr5Vp3To1RG14M6CRBKVGHYLFaQDdUBhZ8kc6oh4rl2\ ki7dfBZdFSaJLZOFXS8UW2S_JLTZFMn9FjBEgDDcFCXHBUAAPA\ 9AA8`TJjYUtbctx0mv4ft8`sBUqFNoJHnMJjKKfJMbHNZGOVFL\ VIIVLGVODVRAVU8VX5V_3VbAYeH`hObkVenahqgjtaduWZvQUw\ KOxEIy9DzW_fruNVjU8_`PPbdEcaCa_A_Y8ZW7XU5VS3UQ1SO0\ RK1VH2YE3`A4c75f46i8R1CgBGxLMpRRiWXbaaWfgPllIqqBvk\ GqeKm_OiUSdOW`I_XCcTGfVKiWOlYSnZWq`_tacvbdrZenWfjT\ gfQhbMiZJjVGkSDjXDjaDifDikDhpDhtDZdOPPYG9gG8fF7fE6\ fD5fD4eC3eB2eB1eC2cC2bC3aC3`C4_C4YC5XC5WC5VDDAC6UC\ 6SC7RC7QD8PD8OD9ND9LD9KDAJDAIDBHDBFDCEDCDDDCDDBM3r\ L4oL4mK5kK5iJ6gJ6eJ7cI7`I8ZH8XH9VG9TGARGAPFBMFBKEC\ IECGDDEDDCjQjiPihPhhPhgPgfOffOfeOeeOddNdcNccNbbNbb\ MaaM``M``M__MZ_LZZLYYLXYLXXKWXKVWKVVKUVJTUJTUJSTJR\ SJRSIQRIPQIPQIOPHNPHNOHMNHLNGLMGKMGJLGJKGIKFHJFHJF\ GIFFHEFHEEGEDGEDFDCEDBLmX } frm:MandelbrotVE-VP {; variable escape and power a=p1, z=p2, c=pixel+p3, b=sqr(real(p4)): z=z^(a)+c, |z| < b } END PARAMETER FILE=========================================

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FOTD 05-06-05 (Pink Armadillos [6])
by Jim Muth 05 Jun '05

05 Jun '05

FOTD -- June 05, 2005 (Rating 6) Fractal visionaries and enthusiasts: Are armadillos found in Mexico? Yes. Are armadillos found in fractals? One can find anything they wish in fractals. I found pink armadillos in today's image, and I found them without having a single thing to drink. The parent fractal is the Z^2.00000005+C near-Mandelbrot set. The location of the scene is on the main stem, in the East Valley of a small midget just west of the large midget. When the image is seen, the reason I named it "Pink Armadillos" will be apparent. The rating of a 6 is not quite enough to justify the 27 minutes required to render the image, but the image is certainly worth the minute or two required to download it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The clouds slowly cleared away during the day on Saturday here at Fractal Central, letting the temperature rise to 77F 25C and keeping the cays happy. Today is starting sunny and quite warm. The cats should be pleased. For me it looks like a slow day. The next FOTD will appear in 24 hours. Until then, take care, and be lucky. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pink_Armadillos { ; time=0:27:26.23--SF5 on a P200 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotN center-mag=-1.78577221928100200/+0.000000508068675\ 42/4.308652e+009/1/180 params=2.00000005/0/0/0/0/0 float=y maxiter=18000 inside=0 periodicity=10 colors=000kljmkjokirkitkhvkhpiakgWeeP`eJVdCQd6Le0V\ fBdjLnoWwnevnbvi_ucYuZVsUTqQSoNQmKPhHNcDL_AKY7JX4I\ O1IG7KIENFLPJSSNZVReXVl_Zs`YsaYobYkcYhdYdeX_fXVgXS\ hXOiXLjWIkWGlWDmWAnW7oW5pY7k_9gaBccDZeEVgGRiIMkKIm\ MEnNAFhEKfLPdSTbYY`da_jDxNHtQKpSNmURiWUeYXb__ZacVd\ fSfiOhlKjpHlsDnv9py6roDlfJgXQbOWYMKgK8qLEjMJcMOYNU\ ROZKOcEQbDSbDUaDVaDXaDZ`D_`Ca_Cc_Cd_CfZChZCiZCjZCk\ _Ck_Cl_Cm_Cm_ClZDlZDlZDlZDlZDlZEbZQlZElZElZEkZEkZF\ kZFkZFkZFkZFkZGkZGkZGjZGjZGjZGjZHjZHjZHjYHjYHjYIiY\ IiYIiYIiYIiYJiYJiYJiYJiYJiYJhYKhYKhYKhYKhYKhYLhYLh\ YLhYLgYLgYMgYMgXMgXMgXMgXNgXNgXNfXNfXNfXNfXOfXOfXO\ fXOfXOfXPeXPeXPeXPeXPeXQeXQeXQeXQeXQnsOmrPmrPmrPmq\ PmqPmqPmpPmpPlpPloPloPloPloPlnPlnPlnPkmPkmPkmPklPk\ lPklPklPkkPkkPjkPjjPjjPjjPjiPjiPjiPjiPihPihPihPigP\ igPigQifQifQifQheQheQheQheQhdQhdQhdQhcQgcQgcQgbQgb\ QgbQgbQgaQgaQgaQf`Qflkhlk } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FW: [philofractal] FOTD 02-06-05 (Fourth of July [7])
by Hal Lane 04 Jun '05

04 Jun '05

Jim, Your FOTD 02-06-05 (Fourth of July [7]) is a very nice fractal. - Hal Lane ######################### # hallane(a)earthlink.net <mailto:hallane@earthlink.net> # ######################### >-----Original Message----- >From: Jim Muth [mailto:jamth@mindspring.com] >Sent: Thursday, June 02, 2005 12:07 PM >To: fractint(a)mailman.xmission.com >Cc: philofractal(a)lists.fractalus.com >Subject: [philofractal] FOTD 02-06-05 (Fourth of July [7]) > >FOTD -- June 02, 2005 (Rating 7) > >Fractal visionaries and enthusiasts: > >Yes, I know the July 4th holiday is still one month away, but >today's fractal reminds me so much of a fireworks display that I >could not resist naming it "Fourth of July". > >The parent fractal is the Z^4.000001+C almost-quartic Mandeloid. >The scene is located in the east valley of the large midget on >the negative real axis. Just as in the Z^2.000001+C almost- >Mandelbrot set, the area resembles an explosion in a railroad >switching yard. > >The rating of a 7 seems justified, at least to me. The render >time is short enough to make the task almost a pleasure. But >there are some machines out there that dislike the Fractint >program and its crusty old video modes. Those with such new- >fangled machines may download the completed image from the FOTD >web site at: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > >The near-perfect weather conditions here at Fractal Central on >Wednesday delighted the fractal cats, who spent the entire >afternoon lounging in the shade of the holly trees. The trees >have lost a lot of their leaves since last year at this time, >when they were covered with 17-year cicadas who love to deposit >their twig-killing eggs in holly trees, but they still give >enough shade to keep the cats cool on 79F 26C days such as >Wednesday. This morning, the clouds in advance of the next rain >system are moving in, but the rain is expected to hold off until >sunset. It will probably be a good day for the cats. > >For me, it will likely be another reasonable day. The next >fractal will appear in 24 hours. Until then, take care, and >search for the reason. > > >Jim Muth >jamth(a)mindspring.com >jimmuth(a)aol.com > > >START PARAMETER FILE======================================= > >Fourth_of_July { ; time=0:02:23.63--SF5 on a P200 > reset=2004 type=formula formulafile=slices.frm > formulaname=MandelbrotN passes=1 > center-mag=-1.21883450232609400/+0.000001179804919\ > 48/5.071115e+010/1/152.5/-5.20667307325056727e-006 > params=4.000001/0/0/0/0/0 float=y maxiter=15000 > inside=0 logmap=81 periodicity=10 > colors=000NBKMCKLDKKEKJFKIGKHHKGIKFJKFJLEKMDKNCLOB\ > MPBMQANR9NS8OT8OTAQUCRWETYGU_IVaKXcMYeN_gPaiUckZem\ > cgohjqmnsrruuwwwzzzzzzzzzzzzzzzzzzzzzzzZzbwzXwzRwz\ > L5zG`zjZzhYzfWzdVwbUt`SqZRoXPmWOkUNiSLgQKeOIcMHaKG\ > `JI_MJ_PK`RL`UMaXOaZPbaQbdRcfSciUdlVdnWeqXetYevWcq\ > VbmU`iT_dSY`QXXPVTOUONSKMRGLQCaRLUQSMQYEQcMwdJtbHr\ > `FoZDmXBkV9hT7fR5cP3aN1_L3YK5XK7WK9VJAUJCTJESIGRIH\ > QIGRKGSLFTMFUNEVOEWPDXQDYRDYSG_QJaPMcOPdNSfLVhKXiJ\ > _kIbmGenFhpEkrDmsCjoEhkGfhHddJb`L`YMZUOXRPVNRTJTRG\ > UPCWN9X`NWm_VlaXkcZkd`lc_mc_BRJBROBQTAPYAPbAOgAOlB\ > RjBUhCXfCZdCacDdaDf_EiYElXEnVFqTFtRFvQJvSNvTRvUVvV\ > ZvWbvXevYfrXgnXhkXigWjcWk`WlXVmUVnQVoMUpJUqFUrBTs8\ > Tt4Tt1Tq3Pn4Ll6Hi7Dg99dA5bB1_E3YG5WI7TK9RMBPODMRFK\ > THIVJFXLDZNB`P9bQB`TCZWEXYFW`HUcISeKRhLPjNNmOMpQKr\ > RIuSHwRKqQMlPOfOQaNSXMURLWMKYHJ_BIa6Hc1LY5OS8SNBVH\ > EZBHa6Kb9LcBLcEMdGMeJNeLN } > >frm:MandelbrotN {; Jim Muth >b=p1, z=p2, c=p3+pixel: >z=z^(b)+c, >|z| <= 16 } > >END PARAMETER FILE========================================= -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.323 / Virus Database: 267.6.1 - Release Date: 6/3/05

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Jim, Q. re [philofractal] FOTD 01-06-05 (Hexa-Something [5])
by Hal Lane 04 Jun '05

04 Jun '05

############################################################## Jim, I enjoyed your 'hexic' fractal (below): [ FOTD 01-06-05 (Hexa-Something [5]) ] but while zooming out until I could see the entire fractal I did not immediately see anything that had obvious three, four or five-fold symmetry along the way (though I'm afraid I was zooming out pretty rapidly): > Even more unexpected are the much smaller and near-perfect > quadratic, cubic and quintic midgets scattered invisibly through > the scene. How does one view 'invisible' midgets? Were you able to apply a certain rendering method to render them visible? Or does 'invisible' in this context just mean that they are too small to be seen at the scale of the Hexa-Something fractal? Also, are you using the phrase 'quintic midget' to refer to: - a midget that has five lobes, - one that has five-fold symmetry around it (the way Hexa-Something has six-fold symmetry) or - one generated by an equation with a variable raised to the fifth power? - Hal Lane ######################### # hallane(a)earthlink.net <mailto:hallane@earthlink.net> # ######################### >-----Original Message----- >From: Jim Muth [mailto:jamth@mindspring.com] >Sent: Wednesday, June 01, 2005 10:07 AM >To: fractint(a)mailman.xmission.com >Cc: philofractal(a)lists.fractalus.com >Subject: [philofractal] FOTD 01-06-05 (Hexa-Something [5]) > >FOTD -- June 01, 2005 (Rating 5) > >Fractal visionaries and enthusiasts: > >We start June with an enigma of the fractal variety. > >The thing at the center of today's image is a puzzle. It shows >all signs of being a hexic object, if that's the proper name for >equations of the 6th degree. But the parent fractal was created >by a combination of Z^3 and Z^5. Its formula contains not a >hint of Z^6. I guess that's how fractals are -- always doing >the unexpected. > >Even more unexpected are the much smaller and near-perfect >quadratic, cubic and quintic midgets scattered invisibly through >the scene. I will check further into this situation later >today. When the suspected unexpected is found to exist, can the >unsuspected unexpected be far behind. > >All this talk of mysterious things does not make a great fractal >however. Despite its mystery, today's image rates only an >average 5. I named the image "Hexa-Something" because, despite >the numerical confusion, there is something 6-ish about it. > >The render time of 2-3/4 minutes is true on the 10-year-old >computer with the balky fan, which I have dedicated to fractals. >On a more modern unit, the image will render in less than a >minute. But regardless of the speed of your computer, if you >can get onto the internet, you can download the completed image >from the FOTD web site at: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > >With a high temperature of 77F 25C and full sun, Tuesday turned >out to be one of the all time best days for the fractal cat duo. >They went out before noon and stayed out until after 8pm. As >far as I know, nothing disturbed their peaceful day in the holly >thicket. Today is starting with a few more clouds and a bit >cooler. After yesterday, the cats can't complain. > >For me it's work before play. The next FOTD fractal will appear >in 24 hours. Until then, take care, and do we place too little >or too much faith in the scientific method? > > >Jim Muth >jamth(a)mindspring.com >jimmuth(a)aol.com > > >START PARAMETER FILE======================================= > >Hexa-Something { ; time=0:02:45.16--SF5 on a P200 > reset=2004 type=formula formulafile=allinone.frm > formulaname=MandelbrotMix4 function=ident passes=1 > center-mag=-0.73359310668167350/+0.000008397796090\ > 92/1462787/1/-72.5/4.36410307197432346e-009 > params=1/3/-0.2/5/-0.15/0 float=y maxiter=5000 > inside=0 logmap=29 periodicity=10 > colors=000URzSUzPXzM_zJbzHezKgzMizOkzQmzTozVqzXszZ\ > uzThzNXzHLcC95z5Jn7Mc9PWARSCUNDWJFZFG`dP3cCh`QWYcJ\ > Wp7StBOzFKzzGzzDpRHhQKaPNVOQNNTGMW9M`BKdCIiDGmFFrG\ > DvHBzIAvKFrMJnONjQRfSVbUZZVbDVxk5fTXTAcFFfMJVTOG_S\ > 2fT9_UGUVNNWUHX`AYf4`d6ba8e_BgYDjVFmTIoQKrOMtMOpLR\ > mLUjLXgK_dKaaKdZKgWJjTJmQJoNIrKIuHIxEIzGLyINxJQxLS\ > wMVwOXvP_vRauTdtUftWisXksZnr_prasqbuqatm`tj_tgZsdY\ > saXsZWrWVrTUrPTqMSqJRqGQpDPpAOp7Np4LoFJnQIm`KlkMku\ > OhrQioSkmUmjWohYqe_scau`cvZewWgxUiySkzQlzOmzMnzKoz\ > IpzGqzErzCszBtzBuzAvzAwz9xz9yz8zz8zz8zz7zz7zz6zz6z\ > z5zz5zz5zzCzzJzzQzzXzzczzjzzhzzgzzfzzdzzczzbzz`zz_\ > zzZzzXzzWzzVzzTzzSzzRzzQzzPzzPzzOzzOzzOzzjzzgzzczz\ > _zzXzzUzzRzzOzzLzzJzzBzz4zzBzzIzzPzzWzzbzzizzpzzmz\ > zkzzhzzfzzYzz`zzczzfzzizzlzznzzmzzmzzlzzlzzmzznzzo\ > zzpzzqzzqzzrzzrzzszzszztzztzzuzzuzzuzzrzzozzlzzizz\ > gzzdzzazzZzzWzzUzzYzzCzzE } > >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 PARAMETER FILE========================================= ############################################################## -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.323 / Virus Database: 267.6.1 - Release Date: 6/3/05

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FOTD 04-06-05 (Just-Under Brot [7])
by Jim Muth 04 Jun '05

04 Jun '05

FOTD -- June 04, 2005 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal takes the 'just under 2' theme of yesterday,s FOTD several steps further. The exponent of Z in today's fractal is 1.999999; the exponent of the extra C is 0.000001, resulting in a fractal that on the surface cannot be distinguished from the Mandelbrot set. But a close examination of the exposed negative stem reveals that things are not as they should be. What at first appears to be a single negative stem, turns out to be many. The splitting is not as chaotic as it is in fractals with exponents slightly greater than 2, but there are still many new scenes to be investigated in the area, especially in the East Valley area of the large main-stem midget, which is where today's scene was found. I have named today's image "Just-Under Brot" because its parent fractal is so close to being the Mandelbrot set, yet falls such a tiny bit short. The rating of a 7 is mostly due to the coloring, which I put some extra effort into. The render time of 3-1/2 minutes is fast enough for all but the most impatient fractalist, if there are such things as impatient fractalists, that is. The finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Rain fell most all day Friday here at Fractal Central, keeping the cats well ensconced indoors, where they passed the day on their window shelf, watching birds. A little extra tuna kept them from becoming too unhappy. Today is starting cloudy but dry, and it is warmer. The cats should approve. The next FOTD will appear in 24 hours. Until then, take care, and never stop searching for the universal fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Just-Under-Brot { ; time=0:03:35.58--SF5 on a P200 reset=2004 type=formula formulafile=jim.frm formulaname=JimsCompMand center-mag=-1.74965828584687500/+0.000001348290590\ 31/1.002694e+008/1/167.5/-6.57347995682011632e-007 params=1.999999/0/1e-006/0/0/0 float=y maxiter=2000 inside=0 logmap=223 periodicity=10 colors=000H4HGBFHHE6KD2UC3UJ3UP3UW3Ua3Uh3Un3St6Rs9\ PrBNqELpHJoJHnMFmODmKHhHKdDN_AQW6TR3WN5aQ6fS8kU9pW\ HmTPjQXgNddKlaHt_EoYIkXMfVQbUUYTYURaPQeLPhIOgGOgDO\ gBOf8Of6Of4OfERdOUcXXaf_`oa_MxlKxgJxcIx_GxWFxSExOF\ oSFfVGYYGPaHGdH7gPEjXKlcQokWqsatzgvvfkseaodSlbIl_F\ hVCdRAbM7`H4VD2_C9dCGiCNnCUrC_hER_GIRIATMDUQGVTJWX\ MX`PYcRUdOQeMMfKJgHFhFBiD8jBFcFLYJRSMXLQbFUh9XcGUZ\ MSVSPQZNMdKHjIDpGMr7EZW7GsDHmIHgOHaTIWZIQcIKhIFeTJ\ bbN_lQYjQWiQUgQSfQ9me8meCigFeiIajLYlOUmRQoUMqXIr_E\ tbBu_DrXEpUFnRGkPHiMJzJKvGLkDM`BNZEMWHMTJMQMLOOLLR\ LITLGSKKRJORISQIWQH_PGcOFgOFkNEoNDsMCwMCzQBpUBfYAX\ aANe9Di93kKHmVVoehpoulpsipqfpocpm`pkYpiVqgSqePqcMq\ aJq_GqYDqXZlSsgNrhMqhMqiMpiMojMojMnjMmkMmkMllMklMl\ lMmkPmjRmjTmiVmhYmh_mgamhcmiekjdikcglbemacn`ao__pZ\ YqYWrXUsWStVQuUPvTQwSPxUOyWNzXMzZLz_KzaJzbJzdIzeHz\ gGzhFzjEzkDzmDznJzoJzFKzG } frm:JimsCompMand {; Jim Muth z=c=pixel: z=z^p1*(c^p2)+c, |z| <= p3+100 } END PARAMETER FILE=========================================

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FOTD 03-06-05 (Broccoli [5])
by Jim Muth 03 Jun '05

03 Jun '05

FOTD -- June 03, 2005 (Rating 5) Fractal visionaries and enthusiasts: I have recently done several studies of what happens in the main stem area of the M-set when the exponent of Z is increased very slightly. For today's fractal however, I checked what happens when the exponent is reduced. A problem immediately arose, since the main stem of the M-set vanishes when the exponent of Z is less than 2. Luckily, I have a formula, JimsCompMand, that can pull the vanished stem from its hiding place and place it in the full light of day, ready to be checked. The new formula is a generalization of the formula 'cmplxmarksmand', which has been in Fractint for many years. To produce today's image, I set the exponent of Z at 1.9 and the exponent of the extra C at 0.09, which brings the main stem barely out of hiding. Then I checked the East Valley area of the large stem midget. Instead of the explosion in a switching yard effect, I found large disconnected chunks scattered around the scene in a near chaotic arrangement. Today's FOTD image is typical of the situation in the area. I named today's picture "Broccoli", which is a vegetable I can't get too much of. I'm not quite sure why I gave it this name. There must be something suggestive of broccoli somewhere in the image, though at the moment I seem to have lost sight of it. Despite being named after my favorite vegetable, today's FOTD rates only an average 5, but its render time of a minute or so makes up for the lack of superior quality. Those who dislike both broccoli and rendering fractals can see the image by down- loading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The rain held off until after dark on Thursday here at Fractal Central. The temperature of 66F 19C was cool for the season, but the cats didn't seem to mind as they passed the afternoon in the holly thicket. At one point another neighborhood cat roamed into the yard, but when Tippy advanced on him ready to fight, the intruder beat a hasty retreat. Unfortunately, today is starting with rain in the area. This is bad for cats, but good for me, for it will give me a chance to catch up on some work that is starting to back up. The next FOTD, which will appear in 24 hours, will probably be an improve- ment over today's, but check back to be sure. Until then, take care, and why is global warming always worse when it is summer in the northern hemisphere? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Broccoli { ; time=0:01:22.39--SF5 on a P200 reset=2004 type=formula formulafile=jim.frm formulaname=JimsCompMand center-mag=-1.73970084521555300/+0.045170357407869\ 22/1992095/1/25/-1.00643305703251862e-008 params=1.9/0/0.09/0/0/0 float=y maxiter=1500 inside=0 logmap=59 periodicity=10 colors=000KAKK7MKCOKHPKMKKRJKVFKdKKnP7gW6aa5Vg4Pm3\ Js2Hn2Gi1Ed1D`1CW0AR09M08Izp0uk5qf9maDiXHeSLbWR`_W\ Zc`WgeUkjSooaaiZ_lXYnVWpTVrRTtPRvNQxRRrVRlYSfaS`dT\ VzTPzTUZULMVM9WNDL`GBmJ1zejTtHXpFVlDThCRdAQ`8OX7MT\ 5KP4JT9IWDHZIHbMGeRFhVFdz3gzDizNleXnZfqSpsMzkLtcKn\ WKhOJbGJX8IR1IMBLKKOJTRHbUGkXEt_DsaPsc`selsgwkaxdW\ xYQyQKyJEzC8zJEuQKpXQkcWgjabfgYchRIiKHjKGkJFkJFlJE\ mJDmJCnICoIBoIApICpIEoHGoHIoHKnHMnHOnHQnHSmHUmHWmH\ YmH_mHanHcnHenHgnHioGknGmoGooGqnGsnGunGwnGwmGwmGwm\ GwlGwlGwlGwkGwkFwkFwkFwjFwjFwjFwiFwiFwiFwjFwkFwlFw\ mFwnFwoFwpEuqErrEosEltEitEftEctEZtEYtEYuEYvEZwEZxE\ _yE_zD`zD`zD`zDazDazDbzDbzDczDczDczDdzDhzDmzDrzDvz\ JzzIzzHzzGzzFzzEzzDzzPzzOzzOzzOzzOzzOzzNzzNzzNzzNz\ zNzzMzzMzzMzzMzzMzzLzzLzzLzzLzzLzzKzzKzzKzzKzzKzzJ\ zzJzzJzzJzzJzzIzzIzzIzzIzzIzzHzzHzzHzzHzzHzzGzzGzz\ GzzGzzGzzFzzFzzFzzFzzFzzV } frm:JimsCompMand {; Jim Muth z=c=pixel: z=z^p1*(c^p2)+c, |z| <= p3+100 } END PARAMETER FILE=========================================

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