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FOTD 28-01-11 (FMOD on the X-axis [7])
by Jim Muth 27 Jan '11

27 Jan '11

FOTD -- January 28, 2011 (Rating 7) Fractal visionaries and enthusiasts: Things were very hectic here at FC again on Thursday. (And I thought we were in a recession.) But at least FL is on the mend, and will likely be back in action by Friday, which will relieve the pressure on me and allow more time for a proper fractal search. But most likely, we will remain in the M-set. Today's image is another very deep scene at the end of the nega- tive X-axis of the Mandelbrot set. But today, the image has a difference. The bailout radius of the M-set has been set to 3, which causes the X-axis to be cut off at a point around sqrt(3). The tiny minibrot at the center of the image is located very near the end of this shortened main spike. The basic equal-iteration rendering of the scene was very dull, so I livened things up by rendering the scene with the outside set to 'fmod'. The result earns a rating of an honest 7. The name "FMOD on the X-axis" simply tells it like it is. Though the magnitude of the image is well within the range of arbitrary precision math, the actual magnitude of around 10^21 is much less than the magnitude of the images of the past few days, cutting the calculation time to a much more reasonable 9-1/4 minutes. But a calculation time of over 9 minutes is still a lot of time to devote to an FOTD image. The remedy is to surf down to the active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image is or soon will be posted. The original FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> A mix of clouds and sun, occasional flurries of snow, and a temp- erature just around freezing made Thursday a typical midwinter day here at Fractal Central. Two inches of fresh snow piled up overnight Wednesday, but on top of the foot (30cm) or so of old snow, made little difference. The fractal cat duo tried their window shelf, but soon decided the sun was too irregular, and took to the shelf over the heat. With FL feeling better but still out of action, my day was another hectic one, doing double duty. Luckily, the Mandelbrot set once again came to the fractal rescue with a quick image. The next FOTD will be posted in 24 hours. Most likely it will be another scene in the infinitely complex and extremely fast Mandelbrot set. Until then, take care, and what is wrong with the current world? (Maybe it's that I'm nearing codgerhood.) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= FMOD_on_the_X-Axis { ; time=0:09:15.35-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.7320\ 4993548250847092178/0/9.545e+020 params=0/0 float=y maxiter=5000 bailout=3 inside=0 proximity=0.0003 outside=fmod symmetry=xaxis periodicity=6 colors=000zZKyYIwWGuSErPCoMBlGAfC9`88U37KA0G70C508\ 92830410EzzMzzWzwVyuVxsUwqUvqUvqTupTupTtoStoSsoRsn\ RrnRqnQqmQpmQplPolPolPnkOnkOmjNmjNljNliMkiMjiMjhLi\ hLigKhgKhgKgfJgfJffJfeIeeIedIddHcdHccGbcGbbGabFabF\ `aF`aE_aE_`DZ`DZ_DY_CX_CXZCWZBWZBVYBVYAUXAUX9TX9TW\ 9SW8SV8RV8QV7QU7PU6PU6OT6OT5NS5NS5MS4MR4LR5JO4KP4L\ Q4LR4MS4NT4NT4OU4OV4PW4QX4QY4RY4RZ4S_4T`4Ta4Ua4Vb4\ Vc4Wd4We4Xf4Yf4Yg4Zh4Zi4_j4`j4`k4al4bm4bn4co4co4dp\ 4eq4er4fs0ev1fu2ft3ft4fs5fs5gr6gq7gq8gp9gpAgoAhnBh\ nChmDhmEhlFhlFikGijHijIiiJiiKihKjgLjgMjfNjfOjePjeP\ kdQkcRkcSkbTkbUkaUl`Vl`Wl_Xl_YlZWjWXkXYkYYlZZl_Zm`\ _ma_nb`nc`odaoeapfbpgbph`ng_lfYkeXidVhdUfcSdbRcaPa\ aO``MZ_LXZJWZIUYGTXFRWDOXEPWEQWEQWFRVFSVFSVGTUGTUG\ UUGVTHVTHWTHWSIXSIYSIYRIZRJZRJ_RJ`QK`QKaQKaPKbPLcP\ LcOLdOMdOMeNMfNMfNNgMNgMNhMOiLOiLNonNonNonNonNonMo\ nMonMonMonMonMonMonMon6ag } END PARAMETER FILE=========================================

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Re: [Fractint] Am I correct in thinking that the radialspokes...
by Jim Muth 26 Jan '11

26 Jan '11

At 01:44 PM 1/26/2011 -0500, Hal wrote: >Am I correct in thinking that the radial spokes in the >FOTD 25-01-11 (A Googol is Deep [No Rating]) >(it's actually January 26th's fractal) >are structures associated with period doubling? Yes, the radial spokes are associated with period doubling. The period continues doubling as a minibrot is approached, until I assume it reaches infinity at the edge of the minibrot. In minibrots of limited magnitude, the high-order elements lie so close to the minibrot that they cannot be resolved, but as the magnitude increases, the basins around the minibrots grow larger, and the farther from the minibrots the higher-order elements lie. The image of Jan 26 is of such a high magnitude that the period-1024 elements lie far enough from the minibrot to be rather easily resolved. The situation becomes complicated with minibrots that lie in the basin of a larger minibrot, as does the minibrot in the Jan 26 image. In this case the doubling sequence reaches infinity well away from the minibrot then resets itself to a lower value and starts doubling all over again. This is quite clear in the image for Jan 25, where we see 128 greenish then 256 amberish stripes around the edge, yet find only 16 amber-blue spokes at the center. >On a slightly different aspect of this image -- the fact >that it uses about 100 digits of arbitrary precision math -- >makes me wonder how many sheets of paper it would take >if all the numerical values of all the iterations calculated >for all the 1,080,000 pixels I calculated were printed out >on 8 1/2 x 11 inch paper... I imagine it would take a googol sheets of paper. ;-) Seriously, as a wild guess, the number would probably be well into the billions. Jim

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FOTD 27-01-11 (Backing Out [No Rating])
by Jim Muth 26 Jan '11

26 Jan '11

FOTD -- January 27, 2011 (No Rating) Fractal visionaries and enthusiasts: With FL out of action, it was another hectic day for me here at FC. The double work load left no time to search through a new parent fractal, so I returned to the immense minibrot basin of the two most recent images, where I found today's image. Today's image, with its magnitude of 2(10^87) is a back-out from yesterday's googol-deep minibrot. It actually lies about twice as far from the central minibrot as the image of two days ago, Jan 25, which lies in the same basin. I named the image "Back- ing Out", for obvious reasons. Since the image is the third consecutive one in the same mini- brot basin, I could not honestly rate it. Actually however, it's a rather pleasant image of slightly questionable character, and well worth a look. Since the scene is of a notably lesser magnitude, the calcula- tion time has been cut to a more reasonable 22 minutes, though this is still quite slow by FOTD standards. To speed up the satisfaction, I suggest viewing the finished image on the active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> But give Hal a bit of time to calculate and post it. The old original FOTD web site may be found at: <http://www.Nahee.com/FOTD/> The last time I checked, it was not up to date, but that was almost 2 weeks ago, and something might have happened since then. Heavy clouds hung over Fractal Central all day Wednesday, with snow flurries in the morning and steadier snow in the afternoon. The temperature of exactly freezing kept the fractal cats con- fined to their warm shelf. My day was quite busy. With FL down with the bug, it was up to me to do the work of the two of us and keep the hot chicken soup handy. Luckily, I knew the fractal was there before I ever saw it. The next FOTD will be posted in 24 hours. Until then, take care, and be thankful that fractals exist. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Backing_Out { ; time=0:22:25.89-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.9999\ 99999999995570588474637616346760358903286522128797\ 5190794248519602192032643927978653766/0.0/\ 2.388852e+087 params=0/0 float=y maxiter=12000 inside=0 symmetry=xaxis periodicity=6 colors=000SegQciPbjOakN`lM_nLZoKXpJWqIVsHUtGTuFSvE\ BIHDLKEONFROGSPHTQIU00URKWS0XTKYT0ZUO_VP`VQaYUYaYU\ wdppcgjbZdaQZ`HDT4LX7T`9`dBhhEplGxoIczERfK6`jFLPzz\ ce_CazfN63SBAWGH_DF_LN_SV__b`ij_fi_di_bhZ`hZZgZXgb\ Qm`TjZVgYYdW_aUbZTdWRgTXZGMhOLkLJnIIqFGtCFw9Ez6Mp7\ Tf7_X8fN8mD9t49r5Cq5Fp6Ho6Kn6Nm7Pl7Sk7Vj8Xi8_h8bg9\ df9ge9iUaOIz2Ty9czGnqNxmTnePdYLVQILIEBABR_GSaKSbOT\ cSTdVUeZUfbVgfVhi_ghdfhiehnehhajcZlZVnTSpOOrJLtEIu\ JOpOUlTWhYYdbk`gqXlzTmtWnrYnp_onapldpjfqhhqfjndkkb\ liamf_ndZoaXp_WqXUrUSsSRtPPuNOvKMwKMwFJUDIUFMUHPUJ\ TULWUN_SPbLQiDNeDLaEJUEGPFEMGCKGAIH7HI5GI3FJ1EJ30F\ 50B708A07C07EA6GF6JG6LI5NJ5PL4SM4UN4WP3YQ3_R3`NJaJ\ YaGlcHjdIheIffJdhJbiK`jK_kLYmMWpMUrNStNQvOOxONzY`m\ hmsghd_bX40O40G40840ZJEXHDSFDZDCeBBlKBsUAzcAuUEoKI\ jAMdCQ_ETVFbRHrMJzIKzKMzMOzOQzQSzSUzUVzWXzYZz_`Uab\ ObcMmWLzOLzGKz9KzdWze_zec } END PARAMETER FILE=========================================

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<Jim Muth> Am I correct in thinking that the radial spokes...
by Hal Lane 26 Jan '11

26 Jan '11

Am I correct in thinking that the radial spokes in the FOTD 25-01-11 (A Googol is Deep [No Rating]) (it's actually January 26th's fractal) are structures associated with period doubling? I'm used to seeing (for example) a pattern repeated eight times around a minibrot, surrounding a similar one repeated 16 times, surrounding a pattern repeating 32 times, etc. The largest number of these repeated structures that I've ever been able to see in the past was 256. In your FOTD there appear to be 128 of the largest spokes surrounding a smaller ring of (apparently) twice as many yellow and purple spokes, surrounding a smaller ring of (apparently) four times as many yellow and purple spokes -- still clearly visible. This would make 512 easily-visible period-doubled spokes, and is double my previous record. ;-) For a minute I had thought I had figured out that I was seeing 1024 spokes, but I had gotten it wrong. Perhaps one could see 1024 if the image were calculated at a substantially higher resolution. I'm not going to do that today, because the one I put on your FOTD web page at 1200 x 900 took about 6 1/2 hours on my 2.2 GHz machine. It's fortunate that "symmetry=xaxis" is in your parameter file and halves the calculation time... On a slightly different aspect of this image -- the fact that it uses about 100 digits of arbitrary precision math -- makes me wonder how many sheets of paper it would take if all the numerical values of all the iterations calculated for all the 1,080,000 pixels I calculated were printed out on 8 1/2 x 11 inch paper... Again, am I correct in thinking that the radial spokes in the "A Googol is Deep" image are associated with the usual period doubling seen in many fractals? - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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Re: [Fractint] Some Lyapunov Variations
by Tony (Anthony) Hanmer 26 Jan '11

26 Jan '11

Here are some pars (attached) from a variation of the Lyapunov fractal type, which has long been a favourite of mine - I asked for the variation so as to have more control over its parameters, and sometimes you get exactly what you wish for. These have quite a strong space/SF theme, and look great rendered as large as possible. Is there any *full-colour* freeware fractal programme which can handle such "homemade" as formula files as opposed to Fractint's "hard-wired" ones, and Fractint-type .par files as well? I'd really like to see these without the banding that the 256-colour map gives. Tony Hanmer Mestia, Republic of Georgia Ps NB This attached text and the next one want to be cut and pasted into Notebook or your equivalent text editor, then saved as TLYA2010.PAR ; then it can all be run in Fractint. Also, save the two formulae, Lyapunov02 and 07 (everything after frm:) deleting the "frm:" in each case, into a separate .frm file, called LyaVars.frm or whatever.

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FOTD 25-01-11 (A Googol is Deep [No Rating])
by Jim Muth 25 Jan '11

25 Jan '11

FOTD -- January 26, 2011 (No Rating) Fractal visionaries and enthusiasts: Yesterday's image showed the outer parts of the basin surround- ing a minibrot lying at a depth of one-googol on the main stem of the Mandelbrot set. In yesterday's image, the minibrot was invisible; today's image takes us down to the minibrot itself. At this extreme depth the minibrots have a tendency to all look the same, with little more than rings of concentric circles surrounding the minibrots and extending out to the point where the minibrot itself becomes invisible. Another problem is visible in today's image, where the finer details merge into a chaos of Moire interference patterns. Some- times these patterns can become quite interesting, though this is not the case in today's image, where they simply spoil the effect. Calculating the image at a higher resolution will reduce these interference patterns, but this will also increase the calculation time, which even at 640x480 is over one hour. I could give the image no rating. After all, it is a virtual repeat of yesterday's image. The name "A Googol is Deep" refers to the depth of today's scene. A googol is also a very large number, yet still merely an infinitesimal part of infinity. The calculation time runs just over one hour. To make the image worth the effort, I recommend viewing the finished image on the active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> remembering, of course, to give Hal a chance to render and post the finished image. And don't forget the original FOTD web site at: <http://www.Nahee.com/FOTD/> I see that some fractal fans on the list are still wondering what ever happened to the FOTD CD I was talking about a number of years ago. What happened was that I realized that the estimated profit from creating such a disk would fall far short of justifying the effort needed for its creation. Among other things, I would need to calculate high-resolution versions of all the past FOTD images. But the idea is still simmering on the back burner, and if I saw a reasonable demand from people who were willing to pay a fair price for the disk, I could produce it in about a month. As things stand now however, I feel such a demand is unlikely to happen. Meanwhile, the FOTD web site is on the way. Perhaps I was too optimistic in estimating the amount of time needed to create a satisfactory design and the amount of work required to achieve that design. To avoid further disappointment, I'll stop comment- ing on the web site's progress until it is up and running. Nondescript conditions prevailed here at Fractal Central on Tuesday. The cloudy skies and temperature of 34F +1C were a welcome relief from the bitter cold of the past several days. But the forecast is for more snow on Wednesday. The fractal cats spent their day keeping warm. I spent my day doing double duty, while FL spent her day trying to fight off a cold or the flu. She got rather annoyed when I jokingly said the flu shot she got in November must be finally starting to work. The next FOTD will be posted in 24 hours. Until then, take care, and if I am a Boltzmann brain, then Boltzmann brains are all in my mind. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= A_Googol_is_Deep { ; time=1:08:21.65-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.9999999999999\ 95570588474637616346760358903286522128797519079424\ 85196021920326439279786537664314359319502/0.0\ /1e+100 params=0/0 float=y maxiter=18000 inside=0 passes=1 symmetry=xaxis colors=000SegQciPbjOakN`lM_nLZoKXpJWqIVsHUtGTuFSvE\ BIHDLKEONFROGSPHTQIU00URKWS0XTKYT0ZUO_VP`VQaYUYaYU\ wdppcgjbZdaQZ`HDT4LX7T`9`dBhhEplGxoIczERfK6`jFLPzz\ ce_CazfN63SBAWGH_DF_LN_SV__b`ij_fi_di_bhZ`hZZgZXgb\ Qm`TjZVgYYdW_aUbZTdWRgTXZGMhOLkLJnIIqFGtCFw9Ez6Mp7\ Tf7_X8fN8mD9t49r5Cq5Fp6Ho6Kn6Nm7Pl7Sk7Vj8Xi8_h8bg9\ df9ge9iUaOIz2Ty9czGnqNxmTnePdYLVQILIEBABR_GSaKSbOT\ cSTdVUeZUfbVgfVhi_ghdfhiehnehhajcZlZVnTSpOOrJLtEIu\ JOpOUlTWhYYdbk`gqXlzTmtWnrYnp_onapldpjfqhhqfjndkkb\ liamf_ndZoaXp_WqXUrUSsSRtPPuNOvKMwKMwFJUDIUFMUHPUJ\ TULWUN_SPbLQiDNeDLaEJUEGPFEMGCKGAIH7HI5GI3FJ1EJ30F\ 50B708A07C07EA6GF6JG6LI5NJ5PL4SM4UN4WP3YQ3_R3`NJaJ\ YaGlcHjdIheIffJdhJbiK`jK_kLYmMWpMUrNStNQvOOxONzY`m\ hmsghd_bX40O40G40840ZJEXHDSFDZDCeBBlKBsUAzcAuUEoKI\ jAMdCQ_ETVFbRHrMJzIKzKMzMOzOQzQSzSUzUVzWXzYZz_`Uab\ ObcMmWLzOLzGKz9KzdWze_zec } END PARAMETER FILE=========================================

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RSS Feed
by Roger Kaufman 24 Jan '11

24 Jan '11

I tried the RSS feed on the Droid phone today using the RSS reader RssDemon. First I must say thanks for the great effort to organize the FOTD archive in this manor. One problem it has in the RSS feeder I am using is how the entries are ordered. There are several ways to sort the list and I am trying sort by ascending date. But when I try that, the top entry is "Filler Thriller" from April 21, 2009. This may be the last one generated? There is an option to sort by title. The date could be part of the title but that would cause the sort have the oldest at the top. There may be no way around this. For now I have marked them all unread and then any new ones will come in at the top of the list. But this sorts all the marked read ones by title and so again the oldest are at the top. The only thing I could suggest is that once the whole archive is generated that the RSS feed be regenerated from oldest to newest. But this world be a lot of work. Then there is the issue of how many entries one wants to download. It could be limited locally but I might be the only person thinking I'd want all of them on a hand held device! This may not be wise and instead maybe only the last months worth should be available? For now, if I click on the year/month in the title, it takes me to the xmission pages such that I could find the latest there. But this is a little less convenient. Roger

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FOTD 24-01-11 (Deep Underground [7])
by Jim Muth 23 Jan '11

23 Jan '11

FOTD -- January 24, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's scene lies in a side filament of the period-7 bud on the northwest shore line of the large minibrot on the main spike of the Mandelbrot set. It lies so deep that arbitrary precision math is required to calculate it, which means the calculation time is an inconveniently long 36 minutes. The rating of a 7 is more a matter of taking credit for some- thing I did no work on than a reward for my brilliant effort. I spent most of the day lost in thought. The fractint program did 90-percent of the work. The name "Deep Underground" refers mostly to the extreme depth of the scene, and partly to the depth of my ponderings on Sunday. The image may be seen by running the included parameter file and waiting a half hour or so, or by surfing down to the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image is posted. But it may take a short time for Hal to calculate and post it. The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> My own FOTD web site will soon be available on-line. Keep waiting for the announcement with bated but not abated breath. Ample sun but a chilly temperature of 23F -5C kept the fractal cats close to the heat here at Fractal Central on Sunday. My day was one of the slowest in quite a while. It was so slow in fact that laziness got the better of me, and FL had to ask if I felt all right. Luckily, when fractal time arrived, the M-set once again came to the rescue with one of its infinite mini- brots. But Monday will likely bring more work, so the peace will not last. The next FOTD will be posted in 24 hours. Until then, take care, and find the calmness that lies within. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Deep_Underground { ; time=00:36:14.79-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.76641\ 5736936545845601733295/0.00709681589493994603636566\ 88/1.526688e+023/1/21/0 params=0/0 float=y maxiter=12000 bailout=6 inside=0 colors=000qdZqeYpfXpfWqeTreQseNteKueHvdEwdBxd8yd5z\ d2zd0iZ9TTHDNPORMMTKLVJKXIIZHH`GGbFFcEDeDCgCBiB9kA\ 8m97o86p77q67q68q58r58r59r49s4As3As3At3Bt2Bt2Bt2Dn\ 5Fh8GcAIYDKTFLNINIKPCNQ7PO6NN6LL6JK6HI6FH6DF6BE69C\ 67B65963862D85IA7MCARDCWFF_HHdJKhKMePNcTNaYN_aNYfN\ _jNaoNcsNewNgzMizMkzMmzLozLqzLszKuzKwvKxrKymMshNmc\ Oh`PcYQZ`SUbTPeUPgVRiWkHvlHvlHwmHwmHxnHxnHxjFwfEvc\ Cv_BuW9tT8tSAsSCsSEsSGsSIsSJsSLsRNsRPsRRsRSsRUsRWs\ RYsQ_sQasQbsQdsQfsQhsQjsQksTrpW`rZJta2ub3qb3nb4kb4\ gb5db5ab6Yb6Vc6Sc7Oc7Lc8Ic8Ec9Bc98c95bD4aG4`J4`N4_\ Q4ZT4YW4Y_4Xb4We4Wh4ae8fbBk`FpYIuVMzTPYopShiMabGWW\ LSTQORVKP_HNdDLi9Jn5Hs2FpkJmzNjzQmwzmwzmwzmwzmwzmw\ wmwumwqmwmmwimyemxamwYmvUmuQmtMksIhqEeoAbmC_kDYiFV\ gGSdIQaJNZLKVNISOFPQCMMAIJ7FF4CC29DAGOHNUOUcV`iafs\ `dq_czZazY`zXZzWYzVWzUVzTTzSSzRQzQPzPNzOMzNLzWOzcR\ z`UzZWzWZzU`zRbzsazsbzrcz } END PARAMETER FILE=========================================

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FOTD 23-01-11 (The Edge of Forever [7])
by Jim Muth 22 Jan '11

22 Jan '11

FOTD -- January 23, 2011 (Rating 7) Fractal visionaries and enthusiasts: An unexpected antiquing trip arose Saturday morning here at FC, and by the time we returned, the sun had nearly set. To make things worse, extra work had come in by e-mail while we were away, forcing me to turn to the hyper-fast Mandelbrot set for a fractal in a hurry. Today's image is a scene in a small side spiral on the northwest shore line of the Mandelbrot set. It's something that has often been seen before, but I did put extra coloring effort into it, which allows a rating of a not-too-bad 7. The name "The Edge of Forever" refers to the limitless infini- ties that lie in the M-set, beyond today's scene. The calculation time of under 3 seconds shows how fast the type=mandel formula runs. The pre-calculated image is available on the FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The traditional FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> My own web site is coming along, but far too slowly. The temperature here at Fractal Central rose from a morning low of +7F -14C to an afternoon high of 19F -7C. But despite the cold, the sun was very strong, and the fractal cats took full advantage of the afternoon sun on their window shelf. When we returned from the antiquing expedition, they leaped from the shelf and ran to the door to greet us and complain about our absence. Unfortunately, when we checked the work, we found an unexpected job waiting. The rest of the day was busy. The next FOTD will be posted in 24 hours. Until then, take care, and bring it to completion. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= TheEdge_of_Forever { ; time=0:00:02.85-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.5252836856416\ /+0.5225261871496/5.846441e+008/1/175/0 params=0/0 float=y maxiter=5000 bailout=6 inside=0 logmap=-814 colors=000AFbAGaAH`AI_AJZBKYCLXEMYFN`GPcKRcOVgSZkW\ aoZdo_hqajsclwenzdpsdnuckzahz_dzZbzX`vVYrTWmRUhPSc\ NPZLNUJLSHIPFGNDELBCJADMADOAERAETAFWAFYAG`BGbDGdGH\ gJHiMJlPKnSMqVNsYPv`QxcRzcQyZPxUNwPMuKKsFJqAHo6Gm6\ Fj5Fh5E_5ES4EQ4DO3DM3CJ2CG2BD2BA1AA1AA09A09A09A6BN\ 6DL7FL7HK8IU8Kc9Mm9OmAQcARUAQKAPJBPHBOFBODBNB2L84N\ 95O96PA8RA9SBATBCVCDWCEXDGYDH_EI`EKaELcFMdFOeGPfGQ\ hHSiHTjIUlIWmJXmJYmJYmJZmEcm9cm7cm5cmFcmPcmYcmgccu\ cUpJMlNMhRLcVK_YKWaJSeINiIJmHFpHBmJDkKEiPFfSGdUHbW\ I_YJY_KWaLTcMReNPfOMgPKhQIiRFjSDkTBlUDmRFmPGmNImLK\ mJLmHNmFPmDRmAQmBQmBQmBPmBPmBPmBPmBOmBOmBOmBOmBNmB\ NmBNmBMmBMmBMmBMmBLmBLmBLmBAmBLmBWmLap`gsfmvfryfsz\ gtzhuziuzjvzlwzmxznyzoyzptzmozkjziezfazdXzbSz_NzYK\ zTJzWJzZIzaIzdHzfHziGzlGzoGzqSzUcz6fzCizIlzOozUrz_\ uzexzkzzpxznvzltzjrzhpzfnzelzcjzahz_fzYdzWbzV`zTZz\ RXzPVzNTzLRzKPzINzGnzLnzN } END PARAMETER FILE=========================================

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FOTD 22-01-11 (Five-Eighths There [7])
by Jim Muth 21 Jan '11

21 Jan '11

FOTD -- January 22, 2001 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us back once again to the parent almost- Mandelbrot set fractal of the Jan. 8 FOTD image. This time I checked the trunk of the period-46 elephant on the southern side of the valley. Only a slight distance into the trunk I found a quadratic minibrot caught morphing into a quintic minibrot. Today's scene lies in a chunk of left-over quadratic stuff inside the main bay of this minibrot. The much smaller minibrot at the center of today's image lies just beyond the limit of resolution, but it is a purely quintic one. The outer elements surrounding the minibrot are quadratic stuff however, which leads to a diamond-shaped area of confusion where one type of stuff changes to another. The rating of a 7 indicates that the image is a cut above aver- age. The name "Five-Eighths There" came about when I noticed the normal 2,4,8,16... quadratic series going through the area of confusion before changing into the unlikely quintic series of 5,25,125,625... The name doesn't make much sense, but a name is a name, and this will be the name of today's image. The calculation time of 5 minutes is a bit of a burden. The burden may be lifted however by surfing down to the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site at: <http://www.Nahee.com/FOTD/> is still worth a look. Due to the rush here at FC on Friday, my own FOTD web site made no progress. There is no time limit however, and before long the site will be up and running. About 3-1/2 inches (9cm) of snow fell overnight Thursday here at Fractal Central, which meant a Friday morning of sidewalk clearing. The fractal cats gave moral support by watching from the window, while FL kept the coffee hot and the work moving. Friday afternoon was partly cloudy, with snow flurries, brisk winds and steadily falling temperatures, which reached 19F -7C by sunset, with a forecast low of +7F -14C. The rest of the humans' day was again quite busy, which seems to be more the rule than the exception these days. Maybe it's a sign of the improving economy. The next FOTD will be posted in 24 hours. Until then, take the usual care, and when someone wonders about the meaning of life, tell them the question is meaningless and see if they consider the answer satisfactory. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Five-Eighths_There { ; time=0:04:31.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip float=y center-mag=+0.254554234183668/-0.00046753213376652\ /8e+012/1/-75/0 params=5/500000000.0/0/0 logmap=724 passes=1 maxiter=5000 inside=0 mathtolerance=0.05/1 colors=000BG_BG_CG_CG_DGZDGYEGXEGWFGVFGUGGTGGSEGRD\ GQCGPBGOBGNBGMBGLBGKBGJBGIAGHAGGAGGAGGAGGAGGAGGDGG\ FGGmGGmGGmGGmGGmGGzGGzGGzGGzGGzGGzGGzIGzKGzNGzRFzV\ DzZBzaAzd8zg6zi5zk5xm5zn5zn5zm5zk5zi7zf9zcAz`CzZEz\ XFzUHzQJzOKzMIzJHvGGrBFm7Eh4Dc6A_B8_H6_M5`R5`X5`a5\ `f5bc5c`5dY5eV7fSAgPDhMGiJIjGLkDOlBQiCRfCRcCS`CSZC\ TWCTTCUQCUNCVLCVICWFCWCCXACXCFWEHWGKVIMVJOVLRUNTUP\ WTRYTS_TQWVPTWNQXMNZKJ_JG`IDbGAcF6dD3fC0gB0h86j6Fl\ 4On2Xo7VlCTiHRfMPcRN`VLZ_JWdHTiFQnDNrBLpHNnNPlSRdN\ NYIKRDHWMU`VfaWdbXccXadY`eZZfZYg_Wh`Vi`TjXSoSReSQ`\ ePWnO`mieliilqilvilgileildilbil`il_ikYikWikVikTP45\ Q56S56S67U77V88W98Y99ZA9_BA`CAaDBbDBcECdFCeGDfHDmH\ DzIEzJ_zKFzL_zLGzM_zNHzO_zPIzP_z_JzRiz_KzTiz_LzUiz\ VMzWiz_Nz_vz_Nz_vz_Nz_vz_Nz_vz_Nz_vz_Nz_vz_Nz_vz_N\ z_vz_Nz_vz_Nz_vz_Nz_vz_Nz_vu_Nu_Nu_Nu_Nu_Nu_Nu_Nu_\ Nu_Nt_Nt_Nt_Nt_Nt_Nt_Nt_N } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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