June 2008 - Fractint - mailman.xmission.com

FOTD 30-06-08 (Haste Makes Waste [7])
by Jim Muth 30 Jun '08

30 Jun '08

FOTD -- June 30, 2008 (Rating 7) Fractal visionaries and enthusiasts: Due to too much time spent pondering irrelevant other-worldly things, I find myself running behind in the FOTD schedule. But I'll cut today's discussion short and get right to the point, hopefully quickly getting caught up once the point is made. After years of searching for something attractive in the higher order Mandeloids, I think I have finally found a way to create higher-order attractiveness. Today's image lies on the main spike of its parent pseudo-Mandel- brot set, in the remains of the Scepter Valley of the largest minibrot between the main minibrot on the spike and the body of the set itself. This minibrot is quite a sight, caught as it is in the act of changing from a quadratic minibrot to a minibrot of order-7. Actually the image is quite attractive. The order-7 minibrot at the center sparkles with gold trim, and the smaller surrounding minibrots are of all shapes and sizes, making each of them inter- esting in a different way. I named the image "Haste Makes Waste" when trying to find an excuse for my recent tardiness. I rated it at a 7, which might be a bit of an exaggeration. One thing not exaggerated however is the lightning speed of the included parameter file, which with a running time of an incred- ible 19-3/4 seconds, is one of the fastest ever. But we must never forget the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted, making the task of running a parameter file totally unnecessary. Sunday turned out unusually muggy here at Fractal Central, though with a temperature of 84F 29C, not unusually warm. The mugginess led to a series of torrential showers in the afternoon and evening, which squashed any thoughts of outside activity. The fractal cats disliked all the water on the other side of their window, but soon went back to sleep. My day was quite relaxing for a change. Tomorrow, when the next FOTD is due, will probably be busier. Until then, take care, and don't think about reality too much. You might find that it's not there. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Haste_Makes_Waste { ; time=0:00:19.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot4 center-mag=-24.47168928461\ /0/157925.5 params=7/15/1500/0 float=y maxiter=1500 inside=0 logmap=44 symmetry=xaxis periodicity=10 colors=0000AQ0AS0AU0AW0AY0A_0Ac0Ag0Fk0Ko0Ps0Uw0Zq0\ cm5hi6ed7b`7`X8YS9VOASKBPFCMBCI7LM8TU8a`8im8rr8zz8\ soAzcBzUDoKEfCFZEGRGHNJIJLIGNJCQK8SL5UL4PM4LM4HN4C\ N48O44O40OBBRIMTPWVWfXbpZYeVTVSPLPUMNYNMbNLfOKkPJo\ PImTHkWHiZHhaGfdGdhGbkGanF_qFYtFXwF_sJbpMelQgiTjeX\ mb_o_blZajZ`hY`fY_dXZaXZ_WYYWXWVXUVWRUVPUVNTULTTJT\ TKVQLXOMZLM`JNbGOdEOeCywS40c65_8AW9FSBKPDPLEUHGZDH\ cAGSSGGi8khElbJmXOmRTnLYoFbo9XmASkBNiCHgCzhDzmEzrE\ zvKzZPzXUzVZzTczRhzQmzTkzWjzZiz`kzamzcnzdpzeqz`izW\ azzVzzNzzGzzMzzdzzwzzpzzjzzdzzZzzTzzUzzVzzWzzXzzYz\ zYzzUzzZzzczzhzzmzzrzzvzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzpzMgzHYzCPz7MzKJz\ XTzNazDjz3az5Tz6Kz7Cz8BzEBzJBzPBzUAzZAzdAziAznlzJl\ zLlzNlzOlzQlzRezQ_zPUzP8zy7zt7zo6zk6zf6za5zY5zT5zP\ 9zICzCFz6JzJNzWRzhszBjzSbzgdzafzWhzRjzLlzFnzAPzV0z\ o4zq7zsAztEzvHzwKzyNzzQzt } frm:DivideBrot4 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 29-06-08 (Five Strikes and You're Out [6])
by Jim Muth 29 Jun '08

29 Jun '08

FOTD -- June 29, 2008 (Rating 6) Fractal visionaries and enthusiasts: I'm not sure whether this borderline stuff is exactly on topic, but fractals certainly hold higher-dimensions, so why not our so-called 'real' world. I recently claimed to have experienced precognitive dreams. But this does not mean that I believe it is possible for Madam Zucchini, who runs a fortune-telling shop down on the corner, to know the future. If it were possible to do so, she would not need to run such a questionable business. She would merely need to buy a lottery ticket. She would know the winning number by using her occult powers. What such fortune-tellers do is known as cold reading, where they fish information from their patrons by clever questioning. It's a technique known to every aspiring magician, which in- volves nothing more than a bit of everyday psychology and a bit of good old common-sense. Spiritualist mediums run their busi- nesses pretty much the same way. But at the same time, I do not claim that it is impossible for information about the future to get into the past. In the case of my precognitive dreams I did not at any time *know* the future. After the attack happened, I realized that information from the future had somehow gone back into the past and in some manner had affected my dreams. But this in itself is incredible. It is even more paranormal than so-called communication with spirits of the dead, where all that would be needed would be for spirits of the dead to actually exist and to be able to communicate with the living, two perfectly intuitive, if not apparent, things. By contrast, there appears to be no possible way for information to now exist about an event that does not yet exist. In fact, if such backwards causality were ever shown to be true, we would need to adjust the entire philosophical foundation of science. The only way out of the situation that I am aware of is to claim that such intense precognitive dreams such as mine are one of those extremely unlikely coincidences, which against all odds, sometimes happen -- perhaps a one-in-a-googol chance. In comparison with precognition, I am firmly convinced that there are no space aliens visiting earth in their UFO space ships. The distances involved are far too vast and worm holes are unlikely in the extreme. Also, no clear pictures of UFO's have ever been obtained even with the ever-increasing number of video cameras and cell-phone cameras, which now are almost everywhere. In my opinion, aliens in UFO's are an example of suggestibility combined with wishful thinking. Yet despite this disbelief of most 'borderline' things, I must still face the fact that information somehow now exists about events that do not yet exist, and this pre-information actually can affect peoples' minds. If I do not accept an impossibly unlikely coincidence, I must accept that the outer world has hidden dimensions, (which physicists also claim), or the human mind has hidden dimensions, (which occultists claim), or perhaps both. One thing for certain however, which can be demonstrated at will, is that fractals have hidden dimensions. In fact, this might be why I enjoy them so. Today's image is a perfect example of a hidden dimension. Inside the parent fractal, which appears as a Mandelbrot set, lies a whole hidden quintic world. The image shows one of the quintic minibrots in the parent's depths. It is located in the East Valley of the largest mini- brot on the filament complex extending from the large period-3 north bud of its parent Mandelbrot set. I rated the image at a 6. It's a little too mundane to be worth more. I named it "Five Strikes and You're Out" when I recalled what the Ednor Gardens Eagles used to yell at the umpire when we thought he was too generous with the opposing batters. The calculation time of 2-1/4 minutes is well within reason even if getting information from the future is not. And as always, the finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A muggy day here at Fractal Central on Saturday, with a tempera- ture of 88F 31C, was climaxed by an exciting thunder-storm at 10pm, which dropped to temperature to 72F 22, making the fractal cats as well as the local humans very comfortable for the night. I totally avoided work during the day, which made both myself and FL very happy. The next FOTD fractal will be posted in 24 hours. Until then, take care, and truth is elusive. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FiveStrikesAndOut { ; time=0:02:15.93-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot4 passes=1 center-mag=-1.544312331880741/+10.29436557667572/\ 1.202258e+012/1/-97.5/0 params=5/10/525/0 float=y maxiter=5000 inside=0 logmap=244 periodicity=10 mathtolerance=0.05/1 colors=000KCQKDSKGUKIWKKYKM_KOaKQcKSfKUhKWjKYlK_mJ\ anIatI`zIbzKbzMazOczQezSgzTizUkzXiz_kzamzdozfqzWtz\ MwzCze1z54zG7zR9z`CzkEyuLuoSqiZmcejY`bWXWUSOSOHQJ9\ OF2NSEScPXo_auZ_zYYvV_rT`nRajPbfNcbLdZJeWHfZIaaJXd\ KTgKOmLKmMFmMBmLFmKJmJNhJRfIVdHZbGbaGfYEaUDXQCSMAN\ I9IP8EZAChCBrNAvS9zU8wTFtRLmLRcMYUKUQKUMKUFKU9n921\ PzobvmYrlTnjOjiJfhEbf9Ze4Wd0c`KjYbhXcgWceVddUdbTda\ Se_ReZReXTgVUiTVkSWmWXnZXobYpeYpQRwMPXJN7FURB`jLB2\ ML9NUFNcLOlROuXUjf__odaihbcmcYqeSvfMzgGudJpaLkZOfW\ QaTTXRVSPXRRZRZ`UcbcldmtezzTzzGmd4wjKufNscQq`TpXVn\ UYlR`kObfLYaJTYHPTFKODFKBBF96B72IAAPDHVGPaJWgMcnPj\ tRqqWko_fmc`khWilQgpLcqN_rPWsRSsSztUzuWzvXzwczxj`y\ qgzxizZkz9nzGpzMrzTtzZvzdWzeXzgYziZzj_zl`znazobzqb\ zr_zkYzeWz_UzUSzOUzTWzYYza_zfazkczogzgjz`mzUpzMszF\ vz8yz1tz8pzFlzMhzTdzZczWczTczQczNczLczKbzJbzHbzGbz\ FazEazDazC`zA`z9mzLjzPfzT } frm:DivideBrot4 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 28-06-08 (No Fault Lines [7])
by Jim Muth 28 Jun '08

28 Jun '08

FOTD -- June 28, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's formula, DivideBrot4, is another new one -- the final version of the DivideBrot series. The only change from DivideBrot3 of the series is in the real(p1) parameter, where the number 2 is subtracted from the entered value before iteration begins. This change permits the order of the minibrots to be directly defined by the value entered as real(p1). The real(p2) parameter defines the escape radius. The imag(p2) parameter is not used. The imag(p1) parameter controls the prominence of the higher-order elements in the resulting fractal. A smaller value of imag(p1) results in a greater prominence of the higher-order elements. A larger value gives more prominence to the underlying order-2 Mandelbrot set, while at the same time enlarging the size of the fractal, which makes the real(p2) parameter necessary to expand the bailout radius so that the entire fractal fits within it. Today's image is named "No Fault Lines". I gave it this name because the central minibrot is of the order 3.5 and such fractional-order minibrots are always surrounded by discontinui- ties, which spoil the surrounding patterns of the minibrots. Today's minibrot however is a horse of a different color. Its surrounding pattern consists of seven elements, and these elements are intact. Seven, of course, equals two times 3.5, the order of the minibrot. The name refers to the lack of discontinuities. The image is located on the west side of the northern branch of the Seahorse Valley of the oversized Mandelbrot set that is its parent fractal. The Seahorse Valley characteristics are very prominent throughout the image. The order-3.5 characteristics are obvious only in the shape of the minibrot. I rated the image at a 7. It consists of too much mathematics and not enough artistic value for a higher value. Rendering the scene with the outside set to 'tdis' helped a little, but not enough to grant the image a rating of 8. With its calculation time of 1-3/4 minutes, the job of running the included parameter file should offend no one. But in this modern day and age, some computers have forgotten the old ways and don't know what to do with DOS programs such as Fractint. Those with such new-fangled instruments may still see the image however by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing it there. Warm temperatures, high humidity and showers prevailed here at Fractal Central on Friday. The fractal cats dislike a tempera- ture of 86F 30C, so they were not too happy with the conditions. But cats are cats, and before long the feline duo had found a cooler place in which to sleep. My day was kept busy by a customer of the worst kind -- one who needs his job at once, but doesn't know what he wants, and as a result, keeps calling in changes. In the end, common sense won out. I refused to answer the phone after the fifth call. The last I heard, he was satisfied. The next FOTD fractal will be posted in 24 hours. Until then, take care, and look up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= No_Fault_Lines { ; time=0:01:44.21-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot4 passes=1 center-mag=-7.662916327120194/+1.181354355289796/\ 3.256997e+007/1/-98.25/0 params=3.5/10/1000/0 float=y maxiter=5000 inside=0 outside=tdis logmap=110 periodicity=10 colors=000JP3UgDP0DK99FH65zX7mN9`DhsH_kDRcAIW6NwsH\ rbFjUDcLBWCW8Nor4ah3OZ331vtV3My`IlPE`EnHocJbULRKNF\ xjg`ZpUWcNUSGRFIeXEXIGwHKVhGTVDRH3Wj5U_7SP9QEToyOh\ jJaWEVHrStcRbPQLY91SD2MH2GL3lXV_ULNRCbluTrxOtXJu6J\ iGJYPJMYXHfiCov7wsAhpCVmFGkH2_aJPv_`dblNd2126THAsV\ BXcCAlT4LYWNbwPPfECR4rEPWKE47X6CP7GI9LAOQJHPBveti`\ fYXUMTG4iC6c97Z79U52LPKFtFKU`wQUnKNeEGX8SYENVBJT8E\ R58H99K7AN5AyTrUAfS8WR6LQ4ROvMPhIPVEPHnH3UL3GbhEYV\ CTHDf6BY4eWPYUJQSEIQ8DMICNEBOAAP6oa7aX5OT4QaEIV8JT\ `GRPDQEh3LXBFLI9MaJGVBBp4Ai3Ab3AW3S4p9TLASGARCAQ7t\ YLhVGXTCLR7NLxINdEOMWE6HsRFkLDcFBW9WHEOKAHN6SJVJMH\ XpTLbG7sCcfBWa9PY7HT5p5naCZOJJdbQPWEK6yHBjFGWCLHQM\ 4IO3H42FA3DF3BK3O3HJBCEI7Z4JMhz8csDYmCVfBRG6EX8KIt\ LDhI9PL6XCTPHKHLBBMvANhAOVAPHKeFBadAXSATFERCCQ7AI5\ Ac4Ac4Ac34cR6mJ8mBOmr4m36m3zz3zzuzzgzzUzzGzzRzzFzz\ jzzWzzHzzezzWzzMzzCzz2zz3 } frm:DivideBrot4 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 27-06-08 (Order Septemdecem [6])
by Jim Muth 27 Jun '08

27 Jun '08

FOTD -- June 27, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's image was created with the third version of the DivideBrot formula, which is notably faster and more intuitive than version 2, the version I have been using until now. I will probably make a few more changes before finalizing the formula as DivideBrot4. Today's image shows an order-17 minibrot lying on the negative spike of the parent Mandelbrot set, very near the escape radius. I know that it's impossible to have order-17 minibrots in a fractal that on the surface appears exactly like the classic Mandelbrot set, but I suppose something in the formula never got the message, for this is what we have in today's image. The image was spiced up a little by rendering it with the outside set to 'tdis'. Everything else comes from the numbers themselves. I could have used a little more time to work on the coloring, which explains the rating of only a 6. The name of the image "Order Septemdecem" is simply a fancy way of saying 'order-17'. The calculation time of today's image is an astoundingly brief 13 seconds. So why not take a moment to run the included parameter file. Those with machines that get a case of indigestion when faced with Fractint may go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the finished image in its full semi-glory there. Thursday began with heavy clouds and light rain here at Fractal Central. But the rain ended at 10am and the sun appeared around noon, leading to an afternoon that was hazy, warm and humid, with a temperature of 86F 30C. The fractal cats enjoyed the sun when it first appeared, but sought cooler spots when it got too warm. I spent my free time working on the new formula and responding to an e-mail on the Fractint list. I'll probably make a few more changes in the formula before I have a final version. The next FOTD will appear in 24 hours. Until then, take care, and seek the elusive fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Order_Septemdecem { ; time=0:00:13.42-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot3 center-mag=-23.99999459284184000/0/6.080533e+011/1 params=15/12/485/0 float=y maxiter=15000 inside=0 outside=tdis symmetry=xaxis periodicity=10 mathtolerance=0.05/1 colors=000kiMjkJegHacGY_FTWDPSCLOBGK9CG88D79IC_0mA\ SLAXQBaUBfZBjbEeZH`WKWSNRPQMLTHIVCFU8Fa9HiAJpBKlKO\ iTSfaWcj_dgVeeQfcLfaGg_BhY6hW1PWVZcVWKHYOJ_SLaWNb_\ PdcRfgThF0gM7gTDgZJgeP06_MRXjohineimchmahlZgkXtYJo\ bNkgRdgNehPfiRgjT51XA7WFDWKJWPPWUVVZ`VcfVyjgskbmkZ\ lqjjofinbhlZZkl4GmALjGQgMUdRZbXb_bgXr0Op6PoCQmIRlO\ SkUTi_UheVEZMMbPKbWJcZOfUSiPWlK`oFdrAhu6atDWsJQrPK\ qWEpa8pg7mh6ji6gj5dk5bk4_l3Xm3Un2Ro2Po3Wl3aj3gh5_c\ 7TZ9LUBEPC7K9JS6V_4ff5_b6U_7OX7IU8CR96O90LE5NJ9OOE\ PTIRYNSbRTgWVl_WqdXvhYlfScdMUbGL`AC_5AY78W96UA4SC2\ QE0OF4QI8RLBTNFUQIWTMXVPZYT__Wab_bebdgfejifljdjkbh\ kagl_emYdmXbnVaoT_oSZpQXpPWnRXlSXkTXiUXhVXfWYeXYcY\ YbZY`_Y_`YYZWXXUWVTVURUSQTQOSONRNLQLKPJIOHHNGFMEEL\ CCKBBX8Ch5Dt3Dq5E_0ml9EjBEgCEeEEbGE`IEYJEWLETNERPE\ PQEXSLcURkWYrYcnb`kgYglVdqS`vPYzN_wOatPbrQdoRfmSgj\ TihUkeVlcWn`XoZYnaVmdSlfP } frm:DivideBrot3 { ; Jim Muth z=0, c=pixel, a=real(p1), b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 26-06-08 (A Higher Reality [8])
by Jim Muth 26 Jun '08

26 Jun '08

At 12:20 AM 6/26/08 -0400, Michael Traynor wrote: >And if only you'd posted about these before 9/11, you'd have >something, but you didn't and there's no way now to check the >extent to which your later knowledge coloured your memory of >the dreams. Consider how unreliable eyewitnesses are when it >comes to demonstrable events and how suggestible eyewitnesses >are and you might understand the skepticism and maybe even >apply some of it to your own recollections. Mike: You are right! If I had posted my dreams on the seven consecutive days, (Sep 4 to Sep 10), before Sep 11, I would have made a much stronger case for something like precognition. However I did not realize the significance of the dreams until after 9-11, when it was too late to post them beforehand. But the point of telling of the dreams now is not to supply proof that will convince skeptics. Probably nothing but personal experience could do that. The point is to tell that I am convinced that at least one of the so-called impossible things considered paranormal does in fact exist. And if precognition does exist, the iron wall of denial has been breached. How many more claims of the paranormal are also true? (BTW, when I say things like this, I feel almost like a traitor to the cause. The skeptics' fight against the flood of irrationality and superstition is difficult enough as it is, even without those like myself going over to the other side.) But I experienced what I experienced, and I know what I experienced because I described the dreams in my dream journal on the mornings after they happened. I know the power of suggestion and wishful thinking. I realize the existence of human credulity and gullibility. If, before I experienced my own dreams, someone else had told me of similar precognitive dreams, I would have said he was either lying or unconsciously adjusting the dream memories to fit the later events, and called it a harmless fantasy. But in my case, I wrote of dreams of crashing planes, horrendous explosions, fire, smoke, and falling buildings on seven cunsecutive days before the event. I have computer files dated before Sep 11 '01 to prove this to myself, but it is still possible to change the dates of computer files, so this is no scientific proof either. (After all, extraordinary claims require extraordinary proof.) The main point of all this is that after 9-11, I became very interested in occultism and the paranormal. I read every serious book I could find, and I am still doing so. I still consider most popular stuff like astrology and UFO aliens to be entertaining fantasies. But I found that there is a serious aspect to the paranormal, which I had previously been casting aside as foolish nonsense not worth wasting time on. I now wonder whether skeptics are doing us a service or a dis- service. Are they saving us from drowning in superstition or denying us a realization of greater realities beyond anyone's wildest fantasies. JIM (still skeptical of some things) M.

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FOTD 26-06-08 (A Higher Reality [8])
by Jim Muth 26 Jun '08

26 Jun '08

FOTD -- June 26, 2008 (Rating 8) Fractal visionaries and enthusiasts: My thoughts today are rambling, but here goes: Today's image introduces us to a higher fractal reality. Yes, I know that skeptics amd materialists grow uncomfortable when the subject turns to metaphysical philosophy, which they distrust. But I am fascinated by metaphysical things, particularly the things commonly known as paranormal, some of which I have discovered in recent years to be true. This interest in the paranormal goes back to the seven days immediately preceding 9-11-01, when I had seven consecutive precognitive dreams that changed me from a questioner to a believer, or more accurately, a knower.) The TV channels are filled with not-too-convincing shows about paranormal things such as Astrology, ghosts and fortune telling etc., but where are the shows about fractals -- things that do not exist in the normally accepted way, yet can still be object- ively pictured with the correct equipment? I can remember only one or two TV shows devoted entirely to fractals, and they were aired many years ago. Perhaps people are now more concerned with alien space ships and getting a message from the recently departed uncle George than with that dull mathematical stuff. Or maybe things are not so bad, and there actually are a few hard science channels that I have yet to hear of which actually program real rational science. Of course, if all the paranormal stuff is for real, which it very well might be, then it is the hard-core science channels that are behind the times when they try to explain everything in a common-sense rational way. Now back to the fractal at hand. I named today's image "A Higher Reality" in recognition of the higher realities that visionaries, including the fractal variety, sometimes experience, and also the fact that the minibrot in today's image is of an unusually high order. And yes, get those skeptical knees jerking in disbelief. By higher realities I do mean higher spiritual planes as depicted in occult lore. Today's image lies on the main spike of the parent fractal, which on the surface resembles a Mandelbrot set but deep inside has order-12 characteristics. It is located a short distance east of the large main-spike minibrot, which must be seen to be believed. With the DivideBrot2 formula, the order of the deep minibrots is the sum of the absolute values of the real and imaginary parts of the p1 parameter. I rated the image at an 8, since it's just about the best order-12 minibrot I have ever seen. The calculation time of 42 seconds is one of the briefest of all time. Of course, nothing could be briefer than the few seconds required to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. Another near perfect day prevailed here at Fractal Central on Wednesday. I knew the day was near perfect when it earned the seal of approval of the fractal cats, who enjoy lots of sun and a temperature around 82F 28C. In my departmant the day was suitably busy. Tomorrow will not only likely be the same, but it will also bring another FOTD. Until then, take care, and I have found that it is indeed possible to enjoy rational science, which can demonstrate the truth of its statements, and at the same time know that some claims of the paranormal, which are scientifically impossible, are true nevertheless. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Higher_Reality { ; time=0:00:42.08-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot2 center-mag=-17.30747127039\ 474/0/9.789325e+011/1 params=2/-10/10/1500 float=y maxiter=5000 inside=0 logmap=139 symmetry=xaxis periodicity=10 mathtolerance=0.05/1 colors=0009FWAFYBGZCH_DI`EIbFJcGKdHLeILgJLiKLkKLmN\ KoQJpSIpVHqXGp_GpaLpdQqgVqi_sldsnitqnusszvxzxzzszz\ zzzzzzzzzbzzZzzVxzRszNszIszEszAsz6sz2sz9szGszNoPUn\ U`m_gldnkiujnhp`WvNIz7Jz9KyALvBMrCNoDOlFPhGQeHRbIS\ ZJTWLUTMVPNWMOWJPWJPXJQXJQXIRXIRYISYISYHSZHTZHTZHU\ ZGU_GU_GVaEY_GV`FW`FW`FW`FXaEXaEYaEYzzzzzzzzzzzzzz\ zzyzwtytrwqpuomsmkqlhojflicig`ffZcdX`cUZaTYZQYXNXX\ KXVIWVGUTESSDQQBOP8OQ6RTCTW9W_9YbE_cJfbIgbHlaGsB08\ C09D0AD0AE0BE0BF0CG0DG0DH0EH0EI0FJ0FJ0GK0HK0HL0IM0\ IM0JN0JN0KO0LP0LP0MQ0MQ0NR0OS0OS0PT0PTEQUGQVLRVQSW\ VXW_aXdfYikYnoZsszxWzzWzzXzzXzzYzzYzzszzszzszzszzs\ zzszzszzszzszzszzszzszzszzszzszzszzdzzdzzczzczzbzz\ bzzazzazz`zz`zz_zz_zzZzzZzzYzzYzzGzzGzzHzzHzzHzzIz\ zIzzJzzJzzJzzKzzKzzLzzLzzLzzMyzMxzNwzNvzNuzOszOqzP\ ozPmzPkzQizQgzRezRczRazS_zSYzTWzT`z7Yz9UzBRzDOzFLz\ HHzJEzLBzN8zP5zR6zT7zU8zV } frm:DivideBrot2 { ; Jim Muth z=0, c=pixel, aa=real(p1), bb=imag(p1), dd=real(p2), ff=imag(p2)+100: z=z^aa/(z^bb+dd)+c |z| < ff } END PARAMETER FILE=========================================

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FOTD 25-06-08 (The Cubic Squared [8])
by Jim Muth 25 Jun '08

25 Jun '08

FOTD -- June 25, 2008 (Rating 8) Fractal visionaries and enthusiasts: My new formula, the DivideBrot2, appears to be another winner, which I will use often in future FOTD's. Today's image barely scratches the surface of the things it can do with the higher- order minibrots, all of which until now have looked pretty much the same. Today's image is one of the best cubic minibrots that I have yet stumbled upon. The parent fractal closely resembles the figure drawn by the marksmandel formula of Fractint when the exponent is set to 2. But the buds of today's parent, instead of being quadratic, are cubic. Today's image lies in the northern suburbs of this parent. I named the image "The Cubic Squared" because I felt like it. I rated it at an 8 because that's what I think it's worth. When I rendered the image, I used nothing more than the tradi- tional equal-iteration bands on the outside with a flat black on the inside. All the excitement is in the fractal itself. The calculation time of a mere 42 seconds can hardly be beat. But if running parameter files is not your cup of tea, forget the colloquialisms and beat it to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completely rendered image is posted for viewing. The perfect weather at Fractal Central on Tuesday was appreci- ated to the fullest by the fractal cats, who enjoy plenty sun, low humidity and a temperature of 79F 26C. I would have enjoyed a day a little more peaceful, but the day I had was not too bad. The next FOTD, another good one, will appear in 24 hours. Until then, take care, and be fractally correct. Never mention undesirable things about fractals that everyone wants to continue denying are true. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Cubic_Squared { ; time=0:00:42.23-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot2 passes=1 center-mag=+0.014489004226624/+0.777624726013028/\ 2.005397e+007/1/-86/0 params=1/-2/1/0 maxiter=1800 float=y inside=0 logmap=53 periodicity=10 colors=000NOPOONDKU8If6JY5JQ4JH3JD2J81J30J05QRAXaF\ cnKjsPqwUwzYzzawxdrsgmrjgonaoqXotRowMoKDGUIKcKOhQS\ mSWrU_vWbk_ZacVSgSHkO7oK0sH4rIBrJIrKOrLVrMarNgrNZm\ ORhPJdQB_R3WR1WR2`Y3dc4hi4lo8fgCa_GXSKRLOMDSH5VC0_\ BIcA`g9sfBqeDodEmcGkbHiaJg`Ke_McZNaYP_YQZ_O`aNacMc\ eLdgJeiIgkHhlGicEhVChNAhJCiFDiCEi8Fj4Gj1HjLRnIWhG_\ cEcZBgT9kO7oJ4sD2w80z35y59w7Du9HtAMrCQpEUnGYmHWgHU\ aHfjIbfHZcHV_H7B`EJULQNfHkaN`XSR0z08r5IgB4SpwzelpX\ afPT_RSZOSYMSXJIU0MV5PWBi9QTOUSRPSULTosShfSbU3IECN\ FKSGMuWqP7hSB_VEpdvc`a0xVDjOsvLloKeiJZbICRgjkEcfFY\ aGLDpPNZ0K9ERDpzidhh_dZW`QOtrPnhQh_RzQNzcPzYQzSRzM\ kzYfzTwzPwzLwz0wz7wz9wzCwzFwzLwzJwz_wzQwzXwzTwzPwz\ Lwzdwz0wzpwzMwzvwzMwzCwz2wzRwzoFzqLzsRzuWzvczikzXs\ zKNzTlzJezIZzHezdazZZzTVzNUzuHzgOz0Qz9CzHKzHvzfCzQ\ nzqhzgbzZXzQjzK`zIQzaRzRBzcHzWNzOYzbVzSjz3ez7`zAWz\ E6zoHzY0zvwz0oz3gz8_zDCz0 } frm:DivideBrot2 { ; Jim Muth z=0, c=pixel, aa=real(p1), bb=imag(p1), dd=real(p2), ff=imag(p2)+100: z=z^aa/(z^bb+dd)+c |z| < ff } END PARAMETER FILE=========================================

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FOTD 24-06-08 (Strangeness [Rating--Not Yet])
by Jim Muth 24 Jun '08

24 Jun '08

FOTD -- June 24, 2008 (Rating Not Yet) Fractal visionaries and enthusiasts: At first glance, today's image appears hopelessly dull. It's another rendering of the Mandelbrot set, no big deal. But this Mandelbrot set is strange indeed, for it is the Mandelbrot set only on the surface. The deeper one delves into it, the more its elements change from the quadratic kind to the cubic kind. For a striking example of this strangeness, check one of the very small minibrots on the main stem, the smaller the better. You will find not a Z^2+C minibrot but a Z^3+C minibrot. The same is true throughout the entire parent fractal. And the most incredible thing about the formula is that by changing the imag(p2) parameter, the quadratic M-set can be made to have in its depths characteristics of any order whatever. The formula that does all this is pure serendipity. When I wrote it, I had nothing particular in mind. I simply wanted to see what the expression would do. And was I surprised! Today's image is not the last we will see of this formula. I have already found two outstanding cubic midgets, which will appear as the FOTD's for June 25 and 26. The name "Strangeness" is self-explanatory. The calculation time of 23 seconds makes running the included parameter file a breeze. And those who do not enjoy windy conditions may escape the breeze by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Fine weather prevailed here at Fractal central on Monday until nightfall, when a heavy thunder-shower moved in, leading to a pleasantly cool night. The temperature of 84F 29C and the plentiful sunshine during the day suited the fractal cats just fine. My day was made more interesting by the discovery of today's image, which promises an abundance of goodies. The next in the endless line of FOTD images bearing goodies will appear in 24 hours. Until then, take care, and the best is yet to come from this formula. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Strangeness { ; time=0:00:23.22-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot2 passes=1 center-mag=-2.879\ /0/0.17468 params=2/-1/5/1000 float=y maxiter=1000 inside=0 logmap=yes symmetry=xaxis periodicity=10 colors=000KB1JF8JJEIMKIQQHUXHXbG`hGcnSZpcVqoRrzNsp\ PrgQrZRrQTrHUr8VrEYpK`nPclVfj`ihekgXmhPnhHph9qh1rh\ 5sd9s`CsYGtUJtRNtNQtKMuOIvSEvWBwZ7wb3xf0xi2yg3ye5y\ c6ya8y_9yYAyXBuYCrYDoZElZEiZRjbbkenlizllfkfOkaSdZV\ ZWZTTaNQYQTUTVQWXNZZJaaFdcBge8igIdfS_f`WfjRfsNfrPg\ qQgqSgpTgpUgnXbl_ZjbUieQghMekHcnDbp9YoETnIOmNJlREk\ VFlQGmLHmGInBJo6Jo2KhKLaaMWrJVqGVpDVoAVn7VnFalMgjU\ mh`sfethjujnvkswmwxntveruYptQmrIkqAip2hn3gz3fz4fz4\ ez4dz5cz5cz5WzIPzVIzgHzcHz`HzYHzVHzRHzOHzLHzIMzKRz\ MWzO`zQezSjzUozWszYozakzegzhhz`hzTizMizEiz7ozFuzMz\ zTrzUkzUczUXzVPzVIzVGzdEzm1zzAzhJzRJzF`zErzDjzEczE\ WzFPzFPzLPzRPzXPzbPzgSzfVzeYzd`zcbzbXzkRztRzrSzoSz\ lTzjTzgUzeVzbVz_WzYWzVXzSXzQYzNYzLczNlzLhzPJzoKzqM\ zrNztPzuNzzQzvTzrWznZzkazgdzcgz`dzWazRZzMWzHTzCRz8\ QzEQzJPzPPzUOz_OzdQzbSz`Uz_WzYYzW_zVazTbzS`zYZzbXz\ gVzmTzrRzwPzuNztLzsKzrIzq } frm:DivideBrot2 { ; Jim Muth z=0, c=pixel, aa=real(p1), bb=imag(p1), dd=real(p2), ff=imag(p2)+64: z=z^aa/(z^bb+dd)+c |z| <= ff } END PARAMETER FILE=========================================

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FOTD 23-06-08 (Quartic Minibrot [?])
by Jim Muth 23 Jun '08

23 Jun '08

FOTD -- June 23, 2008 (Rating ?) Fractal visionaries and enthusiasts: Today's image springs from a new formula, one that I wrote on Sunday and named 'DivideBrot2'. The formula is so new that I have little idea what it does or how it works. Today's particular parameters create a parent fractal that resembles a Mandelbrot set with two main bays. But even though the parent resembles the M-set, the minibrots in it are quartic. And though today's image is located in what appears to be Seahorse Valley of the parent fractal, the elements in the image more closely resemble those of an East Valley. Since I have very little idea of what the formula can do, I had no idea how to rate the image. The name I gave it -- "Quartic Minibrot" -- is nothing more than a description. This formula appears to get more out of a quartic fractal than the simple formula Z^4+C. Hopefully it will do the same for some of the higher order fractals. I'll work with the new formula for a day or so before deciding whether to consign it to the storage bin. If anything of unusual interest turns up, I'll post it as a FOTD. Today's image is rather slow, taking almost 9 minutes to finish on the fastest machine. Any budding impatience may be nipped by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the completed image there. The weather was good enough here at Fractal Central on Sunday, with sunny skies and a temperature of 84F 29C. The clouds that moved in at 5pm and the light thunder-shower than followed arrived too late to spoil the day. The fractal cats spent most of the day watching for squirrels and passing tomcats. My day was appropriately lazy, and if I have my way, tomorrow will be the same. The next FOTD will appear in 24 hours. Until then, take care, and if it doesn't make good sense, question it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Quartic_Minibrot { ; time=0:08:58.05-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot2 passes=1 inside=0 center-mag=-1.045188369333446/+0.03206533434293096\ /1.098195e+012/1/82/0 params=2/-2/1/0 float=y maxiter=15000 periodicity=10 mathtolerance=0.05/1 colors=000YmXXhUWdRV_OUWLSRIRNFQICPE9O96N53M10O32P\ 44Q56R68T8AU9CVAEWBGYDIZEK_FM`GNZFOYEPXDPWCQUBRTAR\ S9SR8TQ7TO6UN5VM4VL3WK3WQDUVMT`WSedQknPpwOltTirYfp\ bbmg_klXipVfmTdjRagP_dNXbLV_JSXHQUFNRDLPBIM9GJ7DG5\ BD39B88GD7LH6PM6UR5YV4b_3fd3kh2om1tq1xq2Zq39o5Dn6G\ m8Kk9NjBRiCUgDXfF`eGccIgbJjaKm`Mk_OjZQiYShXUgWWfVY\ eU_dTacSbbOcaKc`Gc_CdZ8dY5dX6IRBNSGRTLVTP_UUcUZgVb\ lWgpWltXpxXjpUeiS_aPVVNPNKKGIE8F91DB6JDBOFGTHLYJQc\ LVhN_mPdrRhwTdqU`kVXeWT`YPVZLP_HJ`DEeGMjIUoKatMiyO\ qSvqOmgLeYIYOFQECI4FH8HHCJHFLGJNGMPGQSFTUFXWF_YEc_\ EfaEjcEm`FlZFkXGjVGjTHiRHhPIgNIgKJfIJeGKdEKdCLcALb\ 8Ma6MaTVgSThSRhSQhSOhSNhSLhSKhRIhRGhRFhRDhRChRAhR9\ hU8gW7gZ6f`6fc5ee4eh4dj3dm2co2cdWaVx_YwX_vVauSctQf\ tNhsLjrIlqGnpDqpBso8un6wm3ym1xj4xg6wd8waAvZCvXFuUH\ uRJuOLtLNtJQsGSsDUrAWr7Yr5_s4Ys4Ws3Us3Ts3Rs2Ps2Os1\ Ms1Ks1Jq2ICqb9sdNuc`vcZq_ } frm:DivideBrot2 { ; Jim Muth z=0, c=pixel, aa=real(p1), bb=imag(p1), dd=real(p2), ff=imag(p2)+64: z=z^aa/(z^bb+dd)+c |z| <= ff } END PARAMETER FILE=========================================

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FOTD 22-06-08 (Zitty Minibrot [7])
by Jim Muth 22 Jun '08

22 Jun '08

FOTD -- June 22, 2008 (Rating 7) Fractal visionaries and enthusiasts: Instead of writing a FOTD discussion on Saturday, I noticed the perfect weather and decided to go out with FL and enjoy the day, which we did quite well. (There is a little more [but not too much more] to life than fractals.) Today's minibrot is so unus- ual however that I must let it go without the usual description. The parameter file runs in 1-2/3 minutes. Run it and enjoy the result, or give Paul a chance to post the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Zitty_Minibrot { ; time=0:01:40.48-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot5 passes=1 center-mag=-1.749153775791796/+0.00000097001782827\ /9.389332e+012/1/180 params=0/0/0/0/0/0/0/0/\ 2.000001/0 float=y maxiter=1500 inside=0 logmap=242 periodicity=10 mathtolerance=0.05/1 colors=000D69D8BCADBCEAEG9GI7IK6KL5MN4OP2QR2SS6VWB\ XZEZbJaeMciQelUhpXjs`lwcnz`ozZpzXqzUrzSszQtzOuzLvz\ JwzHxzFyzCzzAzz8zz6zzYzz`zzbzzdzzfzzHzzJvzLrvOmrRh\ mUchYZc`UZcQUgSPjUKmWHpYHt_IwaIzcIwaLt_NqYPmWSjUUf\ SWcQZ_P`XPbUOeRNgOMiNMkKK9KKAKKAKKBKKBKKCIKCGKC_K7\ rX2qY7qYBpZFpZJo_No_Ro`Vn`_nacmagmbklbolcslcwmdund\ toesperqfprfosfntgmuglvhjwhixihyigyif1GR0Lk1Ml1Nl2\ Om2Pm3Qm3Sn4Vn4Yo5`o5co6fp6hp7jq7mq7pqBunczlcziczg\ cziczkczlcyncxoHzqGzrFytEwuDvwCuxErtFtqGtnHsjIugJw\ dKxaNpeQiiTbmWWqZPuaIy`Hr`Gl`Gf`F`_EV_EP_DJ_DDhMPp\ U`xakfiXPqI8x3IuHRsV_phhnucnoZnjUnePn`KnWLkSMhNOeJ\ PbEQ_AOXBNUCMSDLPEKNFOJQSG`WDkGD`NHWTKSZNOdRKjUGpX\ Cv_8wZAxZByZCzZDzZEzYGz_HzaIzcJzeKzgLziMzkNzmNzoOz\ qPzsPzuQzwRzxRzySzzTzzTzzUzzVzzVzzUzzTzzSzzRzzQzzP\ zzOzzRzzTzzVzzXzzZzz`zzbzzdzzfzzhzzjzzkzz2zz2C03C0\ 3D04E04F05G05G06H06H07I27 } frm:SliceJulibrot5 {; draws slices of (-Z)^n Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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