July 2008 - Fractint - mailman.xmission.com

FOTD 31-07-08 (Chaplet of Fractals [6.5])
by Jim Muth 31 Jul '08

31 Jul '08

FOTD -- July 31, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Yes, I know I said there would be no FOTD for July 31, but the repair work at Old Fractal Central went astonishingly fast this morning, and by 11am I was on my way back to New Fractal Cen- tral. The only downer was Thomas, the one remaining old fractal cat. My sister said he has been very depressed since his brother Tippy passed on to cat heaven about 5 months ago. I tried to cheer him, and he did raise his head and murmur a few small purrs when he saw me, but then he rolled over, curled up and returned to sleep, where he likely is still with Tippy. Today's image shows an order-7 minibrot lurking in an almost- Mandelbrot set. The scene is located on the northwest shoreline of the bud immediately west of the large period-2? bud of its parent fractal. I never realized these higher-order minibrots could be so interesting. I rated the image, perhaps a bit liberally, at a 6.5. I named it "Chaplet of Fractals" when I noticed the ring of blossom-like elements surrounding the central minibrot, each blossom with a still smaller minibrot at its center. The calculation time of 2-4/5 minutes is worth the wait. And equally worthwhile is a trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished product there. Hot muggy conditions prevailed Wednesday morning at Old Fractal Central, while the conditions at New Fractal Central in the aft- ernoon were noticeably better. The temperature ranged from 95F 35C at O.F.C. to 88F 31C at N.F.C. The fractal cats greeted me reservedly when I arrived back at New Fractal Central unexpected- ly early, with enough time remaining in the day to crank out an unexpected FOTD. The next FOTD will be posted in 24 hours. Until then, take much care, and search for good fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ChapletOf_Fractals { ; time=0:02:49.91-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=-27.07629943909\ 749/+0.8305626339739348/7.520937e+011/1/-75/0 params=7/20 float=y maxiter=8500 inside=0 logmap=346 periodicity=10 mathtolerance=0.5/1 colors=000RBZSBZTCZUDZVDZWEZXC_YEZZFZ_GZ`HZaJYbKYc\ LYdMYeNXfPXgQXhRXiSWjUWkVWlWWkXWkYWk_Xk`XjaXjbXjdY\ jeYifYigYihYijYhk_hlahmckoeiqghrigskfsmermdrmbrmar\ m`qm_qmZpmWrmXpmYomZnm_mm_lm`kmaimbimbhmchmdgmegmf\ fmfekgeihdgideiccjbakb_laYmaWm`Un`So_QpZOzZMzVMzdM\ z`NzTJzXNs`QsdTsgWskZsoazrdtoetlftjfzgguegubhv_hvY\ ivViwTjwQjwNkxLkxIlxGlvImuKmtMmsNnrPnqRnpTooUonWom\ Ypl_pk`pjboicnhemgflggkfijejidkhcmgcnfboeaqd`rcerg\ `scWs_RsXMtTHtQCtM7tJ6rI6pHzzzzzz6jF5hF5gE5eDzsD5a\ C4_C4YB4WAhimcTz4R83P83N73L73J63I52G52E42C32A32822\ 723943A63B83CA4DB4ED4FF4GH5HI5IK5JM5KO5LP6MR6NT6OV\ 6PX7QY7R_7Sa7Tc8Ud8Ve8Wf8Xg0_h8YiFYjM_kTal_cmfenmg\ oyipvkqtmrrospqtnsuluvjwwhxxiyyjzzjzzkzzlzzlzzmzzn\ zznzzozzozzpzzqzzqzzrzzszzszztzzuzzuzzvzzyzzwzzvzz\ uzzszzrzzszzrzzqzzpzzozznzzmzzqzzmzzjzzgzzdzzazzZz\ zWzzSzzPzzozzozzozzozzozz } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 30-07-08 (Seven Squared [5])
by Jim Muth 29 Jul '08

29 Jul '08

FOTD -- July 30, 2008 (Rating 5) Fractal visionaries and enthusiasts: Due to a lack of time, today's discussion will be short. But many words are not necessary, since today's image speaks for itself. Today's image is a scene in East Valley of an almost-Mandelbrot set. The minibrot at the center is clearly of order-7, while the surrounding pattern holds quadratic features. All in all it makes an interesting, though not exceptional picture. I named the image "Seven Squared" because it contains elements of both Z^7 and Z^2 Mandeloids. I rated it at an average 5 because I can find nothing out of the ordinary in it that could make it worth more. The calculation time of 2-1/3 minutes is fast enough to make calculation, if not exactly a pleasure, then not too long an effort. And the finished image is available as always on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another typical midsummer day passed uneventfully here at Fractal Central on Tuesday. The temperature of 86F 30C and hot sun was perfect for any outdoor activity. It was perfect even for indoor activity, as the fractal cats were unusually active most all day, thundering back and forth up and down the hallway, ducking in and out from behind the books on the shelves, chasing each other around for the fun of it. My day was rather busy, both with work and with preparations for the trip back to Old Fractal Central on Wednesday. Because of that trip, there will be no FOTD for July 31, but if all goes well, (as I hope will be the case), the FOTD for August 1 will appear on schedule in 2 days. Until then, take care, and you may already be a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seven_Squared { ; time=0:02:22.53-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 passes=1 center-mag=+5.278336322581068/-0.0532935461935686/\ 1.004852e+009/1/-52.5/0 params=7/20 float=y maxiter=1800 inside=0 logmap=186 periodicity=10 colors=000XeTagSfjQlmPqmOvnWpo`knefljakoXitShyRirR\ jkRkdRlYRmRRnKRoDRo7WmE_kLdjShhYlfdqekucru`vq_pnXj\ hWbcUWYSNTPEPLDLJDIHDEFDADD7CDIZ8Tu3SoCRjKRdSQ__PU\ gPPoUMrZJucGxgDzdIvbNs`SpYXmWajUegen7giFieNjaVlYbn\ UjoQqY_XHiCGjFGkHFlKFlMZDVdG_iJcnMgsOk`TWJYG1b0A`4\ JZ7SXA`VEiTHrRKzPNwQPuQRsRTpRUnSWlSYjSZ8UvOSgcRTrQ\ FiLC`GASB7J65A23tmlrjdqhXoePncIhgGckFoFhjQff`dakbY\ u``kXbaTeTPgJLj9Hl0EoAKqJPsSUva_xjdzsiprdfr_YrVjWN\ w9FmDIcGKUJNLMPKSTKXWKb_KgbKmfKriN`J2xj5mi7chAUgCK\ gGIdJGbNE_QDYUBVX9T_8R`9Ua9Xa9ZbAacAdcAf`BeZCeXCeV\ DeTDeQEeOEeMFeKFeIGeGGeIIaJJZLKVMLSOMOPNLROHSPEPRD\ MUBJX9GZ8IY9JYAKYBMYCNXDOXEQXFRXGSWHUYIV_JWaKXcKWe\ NBgL1iICkKNmMYoOhqQgsVgu_fwdfxieynezr_zfUzWPzPzzJz\ zCzz6zz0zz3zz5zz7zzAzzCzzEzzGzzSzzczzfzzizzIzzKzzM\ zzO`zQfzSlzUhzYdz``zcYzfUziQzlNzoPz`QzMRz8nzMozPpz\ RkzSgzTbzUZzUUzVQzWMzWSzU } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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Fractal cats and weather
by Jim Muth 29 Jul '08

29 Jul '08

Fractal fans: I kind of miss reporting the local weather as well as writing about the antics of the fractal cats. After all, cats are fractal by nature. Their latest excitement came around 4am Saturday morning when two roaming tomcats got into a noisy fight in the back yard. The fractal duo dashed to the window and kept watch, protecting Fractal Central until we humans were up for the day. So I'll resume the brief weather and cat reports in the FOTD for July 29. But I will not post the FOTD to the philofractal list unless I have some genuine philosophy to go along with it. Jim Muth

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FOTD 29-07-08 (Frankenberries [7])
by Jim Muth 28 Jul '08

28 Jul '08

FOTD -- July 29, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today we return to the DivideBrot5 formula to check a fractal that is quadratic on the surface, but of order-7 in its depths. This oversized fractal at first appears to be a Mandelbrot set blown up like a balloon, but it is totally different once one wanders beneath its deceiving surface. At first the quadratic minibrots appear merely distorted, as though they were not critical, but they soon evolve into perfect order-7 minibrots, with far more interesting detail surrounding them than could ever be found in the simple Z^7+C Mandeloid. Today's surprisingly rich minibrot is located near a minor bud on the northwest shore line of the main bay of the parent near- Mandelbrot set. I especially enjoy the awkward way the 7 arms radiating from the minibrot merge into the quadratic pattern a little farther out. An outzoom will reveal more detail of this merge area. I named the image "Frankenberries". I think I did it because the wine-colored basins remind me of the color of rasperry ice-cream, which strangely enough I have a sudden urge for. The rating of a 7 is about FOTD average. The calculation time of 2-1/3 minutes can be eliminated by surfing to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoying the already-completed GIF image there. The weather report, back by popular demand, for Monday at Fractal Central in central Pennsylvania is one of typical midsummer conditions -- partly cloudy skies, a temperature of 86F 30C and contented fractal cats. The cats are contented because the wandering tomcats that had a noisy catfight in the yard a few nights ago have apparently moved on to other territory. My Monday was just a little busier than average. Tuesday will probably be the same. Early Wednesday the 30th I must take a 140-mile-each-way trip back to Old Fractal Central to arrange to have some repair work done on the old place, but I'll be back to New Fractal Central by Wednesday evening. As a result, there will most likely be no FOTD for July 31. The next FOTD, the one for July 30, will be posted in 24 hours or less. Until then, take care, and maybe what really is, really isn't. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Frankenberries { ; time=0:02:20.40-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=-9.17759645799/\ +7.267304008055/2860593/1/7.5/0 params=7/16 float=y maxiter=13000 inside=0 logmap=118 periodicity=10 colors=000UI0VJ0WK0XL0YM0ZN0_O0`P1aQ1bR1cS1dT2eU2f\ V2gW2iY3jZ3l`3na3oc4qd4sf4wi3tg4re5oc5mb6j`6hZ7eY7\ cW8aU9ZT9XRAUPASOBPMBNKCGHALJCQLDVMF_OGdQIgTHiRJjQ\ KkPMlONmNPoLQpKSqJTrIVx5ZsHWoTTkdQieRhfRgfRegRdhRc\ hSbiS`jS_jSZkSYlTWlTVmTUnTUqRTnTSkVRhXQeYPb_O_aNXb\ MUdLRfNGfKPgIYgGfhFmjEnhEofEodEpbEp`EqZEqXErVEsTEs\ REtPEtNEuLEuJEvH4y9EvFNsLWpRdmWUmvTmtTisSerSapRYoR\ UnQPlQLkPHjPDhO9gO5fK7gH9hDBiACiMA`X8Si2Ig7KeBLdFM\ bJOaNP_RQZVSXZTWbUUfWTjXRnYQrZToYVmXYjW_hVbfUdcTga\ SiZRlXQnVPqSOsQNtPNuONrMMoKLlILiHKgFJdDJaCIZAIX8HU\ 7GR5GO3FN1EN2FO2GP2HQ3HR3IS3JT4JU4KV4LW4MX5MY5NZ5O\ _6O`6Pa6Qb6Rc7Rd7Se7Tf8Tg8Uh8Vi9Wj8Vk8Vl8Vm8Vn8Vo8\ Vp8Vq7Vr7Vs7Vt7Uu7Uv7Uw7Ux6Uy6Uz6Uz6Uz6Uz6Uz6Uz9Vz\ BWzCXzDYzEZzF_zG`zHazIbzJczKdzLezMfzNgzOhzPgzQfzRe\ zSezTdzUczVbzWbzXazY`zZ_z__z`ZzaYzbXzcXzdpzepzfpzg\ qzhqziqzjqzkYzlXzmXznWzoW } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 28-07-08 (Pyramidal Ribbons [7])
by Jim Muth 28 Jul '08

28 Jul '08

FOTD -- July 28, 2008 (Rating 7) Fractal visionaries and enthusiasts: Before giving up on the almost-linear Mandeloids, I ran the Z^(1.009)+C Mandeloid through the Fractint evolver feature and found a fractal with enough variety to actually be interesting. The real(p2) parameter reveals that I let the program find the parameters. I would never enter such a value on my own. This parent fractal is shaped like most Mandeloids in this range -- somewhat like a roughly parabolic, stone-age arrowhead. It has a bit of chaos on its southeastern shoreline. Today's scene is located in this chaos. I surprised even myself when I found today's image, which resembles festive colored ribbons twisting around the apex of a dark brooding, sickly green pyramid. I thought of the name "Pyramidal Ribbons" almost at once. The magenta-ish background pattern is truly fractal, with the herringbone pattern continuing unchanged at ever smaller scales, apparently without limit. Whether the image truly deserves its rating of 7 is up to the individual viewer to decide. In my opinion, the image is well worth the rating. The calculation time of just over 4 minutes could be a bit faster, but it is not beyond the range of reason. Another reasonable way to see the image is to surf over to the FOTD web page at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the image already calculated and posted there. The next FOTD will appear in 24 hours. At this time I have no plans as to the theme, so check in then for a possible surprise. Until that glorious moment, take care, and keep your fractals simple. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pyramidal_Ribbons { ; time=0:04:04.65-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident float=y center-mag=-6.9182776751/-18.4032734921/11051.95/\ 1/-33/0 params=1.009/0/922.5954466383862/3500 maxiter=2500 inside=0 logmap=410 periodicity=10 colors=000KJAKJAKJAKJAKJAKJAO9AQ8CS8EV7FX6E_5Da4Cb\ 29c4Cd5Fe7Hf8Kg9MgBPhCRiDUjFXkGZkIalJcmKfnMhoNkoOm\ nNlmNllNlkMljMliMkhLkgLkfLkeLkdKjcKjbKjaJj`Jj_JiZI\ iYIiXIiYGhXIiXJjXLkXMlXNlXPmXQnXSoXTpXUpXWqXXrXZsX\ _tXYxX`tXbpXnmXfiXhf`qbXmZXoWctSXsPcuLhvHswIkvIptI\ msJcqJoqJVoJUmKkmKTjKTiKghLSfLSdLbdMRbMQ`MX`MPYNPX\ NWXNOUNOUSWUONQOOSSUSMNPOMUTUUSJVUJXXHYYG__EaaDccC\ deBfg9hi8jk7jm7lq6mo6mm6mk6mi6mg6mf6md6mb6m`6nZ6oX\ 6pW6qU6rS6sQ6tO6uN6vL6wJ6wH6wF6wD6wC6wA6z86z66z46z\ 37z67z88zA8zCBzQ9zP4zQ7zPAziCziEyiGxjHwzJuzLszNqzP\ ozRmzTmzUmzWmzYmz_mzamzcmzemzemzfmzglzgkzhizigziez\ jczjazkZzlUzlSzmQzmPznPzoOzoOzpNzlNzlMzmMzmLznKzoK\ zoJzpJzmIzmIzmHzmHzmGzmGzmHzmHztIzsIzrJzqJzoKznKzm\ KzlLzkLzjMzhMzgNzfNzeOzdOzcOzjazrczqczpczocznczmcz\ lczkczjcziczhczgczfczeczdczcczbczacz`cz_czZczYczQc\ zQczPczPczOczOczNczNczMcz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 24-07-08 (Ratcheting Onward [6])
by Jim Muth 27 Jul '08

27 Jul '08

FOTD -- July 24, 2008 (Rating 6) Fractal visionaries and enthusiasts: I have made a decision to stay more on topic. Starting today I will no longer post a copy of the FOTD to the philofractal list. Except for the FOTD, the philofractal list has been dead for years. The topic of the Fractint list is fractals, not my ideas about God, science, or the paranormal. There are quite a few forums where these things are eagerly and properly discussed. And I'm not too sure of the importance of the daily weather report from central Pennsylvania, which can always be found on the internet. If the goofy fractal cats do anything exceptionally goofy, I'll tell about it however. (Yes, FL did have something to do with my decision to stick more to the topic.) Today's image shows some of the unexpected stuff that goes on in the fractals created by the formula Z^(1.075)+C. The most surprising thing about these almost-linear fractals is that they actually contain fiercely detailed Minibrots, which can be easily found with my 'secret' method of finding minibrots. One of these unlikely minibrots lies at the center of today's image, at the very limit of resolution. I have not gone deep enough to make the minibrot visible in today's image because at that depth, the surrounding pattern breaks down into near total chaos. At the modest magnitude of today's image, the pattern is far more interesting, rather resembling a ratchet wheel surrounded by a lacy network of lightning. I named the image "Ratcheting Onward" because of the ratchet pattern. This heavily fractured, circular effect is typical of the minibrots in fractals of such a low order. The rating of a 6 is what I think the image deserves. The calculation time of 1-2/3 minutes is a real bargain. An equal bargain may be found at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished GIF image is posted. Until next time, take care, and keep a stiff upper fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ratcheting_Onward { ; time=0:01:41.60-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-14.94607802098338/-2.324758141946301/\ 8252035/1/-162.5/0 params=1.075/0/18/1500 float=y maxiter=1800 inside=0 logmap=131 periodicity=10 colors=0009G06H0AI6DJFHDKKKZOPdRVmUfuZitzksonrwnqz\ uphVsZ9uX8pV7lU7hS6dR6`P5XU5Tc6Nm6Zr6Zz6Zz6ZIlq3Wp\ BafIguPmuWruVzuUzuTluShuRhuQfuPduOcuPiuQnuRsuOmuMg\ uKUuLUuMUuNUuPUuQUuRUuSUuTUuVUuWUuXUuYUu_Uu`UuaUub\ ZucZueYufXugWuhVuiUukTulcUmcVncVpcWqcXrcXscYtcYvcZ\ wc_xc_yc`zc`ycaycaycbycbyccxccxccxcdxcdxcewcewcfwc\ fwcfwcgwcgvchvchvchvcivciucjucjuckuckuckucltIltImt\ ImtIntInsInsIosIosIpsIptHqsIpsIpsIprIprIprIorIoqJo\ qJoqJoqJopJnpJnpJnpKnoKnoKnoKmoKmnKmnKmnLmmLlmLlmL\ lmLllLllLllMklMkkMkkMkkMkkMkjMjjNjjNjjNjiNjiNiiNih\ NihOihOihOigOhgOhgOhgOhfPhfPhfPgfPgePgePgePgfIkePg\ eVcda_dgWcnSctOczKbZ8a60b70c80d91dA3eB5fB7fC9gDBhE\ DhFFiFHjGJjHLkINlJPlKRmKTnLVnMXoNZpO`pOamPbjQbhRbe\ SccSc`TcYUdWVdTWdRWeOXeMYeJZfG_fE_fB`g9ag6bg1bf3bg\ 4bg6bg7bg8bgAbgBbgCbgEbgFbgHbgIbgJbhLbhMbhNbhPbhQb\ hRbhTbhUbhWbhXbhYbh_bh`bi } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 27-07-08 (The Limbo Factor [6])
by Jim Muth 27 Jul '08

27 Jul '08

FOTD -- July 27, 2008 (Rating 6) Fractal visionaries and enthusiasts: In today's image I tried to go down to an exponential level only half as far from unity as yesterday's exponent of 1.0125. But I could find nothing of interest in the fractals with an exponent of 1.00625, so I tried an exponent of 1.009375, which is 3/4 as far from unity as yesterday's 'forest floor' image. The searching down there was difficult, minibrots were nowhere to be found, but I finally found an interesting patch of chaos in the Z^(1.009375)+C Mandeloid fractal right at ground level of the complex hyper-ladder. Today's image shows a small sample of that interesting chaos. To me, the most amazing thing with the image is that the graph of its generating expression is virtually a straight line. But even such a tiny departure from straightness can do unexpectedly intricate things when iterated a sufficient number of times. In today's image we have areas of near total chaos, areas that are totally featureless, as well as areas of fractal patterns that repeat at ever smaller scales. There are also several dis- tinct fractal themes in the image. Despite the ridiculous expo- nent, today's fractal image is as fractal as any fractal could be. I named today's image "The Limbo Factor". After all, the point of the Limbo is to go as low as possible. Then I rated it at a 6. My inability to find a minibrot in the parent fractal cost the image at least one whole rating point. The calculation time of under 4 minutes on a computer running at 2000mhz is reasonably brief. And the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image there can be equally brief, if not briefer. The next FOTD will be posted in 24 hours. Until then, take care, and view the world through fractal-colored glasses. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Limbo_Factor { ; time=0:04:54.34-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-10.29306825/+0.0410706/163.76/1/142.5/0 params=1.009375/0/0/3500 float=y maxiter=16000 inside=0 logmap=456 periodicity=10 colors=000KBULBUM9UN9UO8UP8UQ8TR6SS6TT4RU4RU4RU2PU\ 2NU1NU1MU1MU0KU0IU0IU0HU0FU0FU0DU0BU0DU0DU0FU1FU4F\ U6HU9HUBIVDIVHIXIKXMKXNMYRMYSMYUN_XN_YP_aPabPafRbg\ RbiSblSdmSdpUdrUfuVfvVbvSdxUfxVgxXgyXiyYjy_jy_lzam\ zbozdozdpzfrzgrzgpslojomarmSulIxj8zg0zi0zj0zj2zl4z\ l8ymBxoFvoHupKspNrrRpsSosVmuYluajvbixfgxifyldymbzp\ azs_zvYzxXzzVzzUzzSzzRzzPzzNzzMzzKzzMzzNzzPzzRzzSz\ zUyzVxzXvzYuz_sz_rzapyboxdmvflugjsiirjgplfomdmmblo\ ajp_irYgsXfuVdvUbxSayR_zKVzNXzPYzS_zVYzU_zS_zRazPa\ zNazMbzKbzIbzHdzFdzDdzBfz9fx8fv6gs4gp2ip1ip0ip0jp0\ jp0jp0lp0lp0lp0mp0mp0mp0lr0lr0jr0js0is0is1gs4gu6fu\ 8fuBdvDdvFbvHbvKaxMaxN_xR_ySYyUYyVXyYXz_VzaVzdUzbV\ zbVzbVxbVubVrbVpbVmaXjaXgaXdaXbaX_aXXaXU_YR_YP_YM_\ YI_YF_YBgV1bX6_Y9XYDU_HR_KNaNKaRHbUDbX9d_6db2ff0gg\ 0fi0fi0fi1fj1fj1dj1dj2dl2dl0Kl0Km0Mo0Km0Kl0Il0Ij0I\ i0Hi1Hg1Ff2Ff2Fd4Dd4Db6Ba } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 26-07-08 (The Forest Floor [8])
by Jim Muth 26 Jul '08

26 Jul '08

FOTD -- July 26, 2008 (Rating 8) Fractal visionaries and enthusiasts: Our asymptotic approach to unity continues today as we investi- gate the fractal that results when the formula Z^(1.025)+C is calculated 43 levels up the complex logarithmic hyperspiral with no function applied. Actually, I am not certain which, if any, function is the 'correct' one to use with the MandelbrotBC3 formula, or even if there actually is a correct way to deal with the infinity of 'correct' solutions to the multi-valued complex- logarithm. Today's parent fractal is an oversized parabolic-shaped thing with the focus of the parabola on the east-southeast side. This parent requires a bailout radius of 3600 to give it room to spread to its full extent. An area of chaos appears at its northwest extremity, with today's scene located in this chaos. There is a minibrot at the center of the image, but don't waste time trying to reach it. It lies far beyond the limit of resolu- tion. At the magnitude of the actual image, the picture reminds me of a scene in a forest, looking upward from the forest floor toward a mighty fir tree. I named the image "The Forest Floor". If I had more time, I might have made the fir tree likeness more convincing. As it is, even with its flaws, the image rates an 8, which is pretty good as fractals go. The calculation time of just under 6 minutes can be eliminated by viewing the already-calculated image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tomorrow's FOTD will be posted in 24 hours. Just for the fun of it, I'll reduce the exponent to 1.00625 to see if I can find anything. But with an expression whose graph is virtually a straight line, I can guarantee no success. Regardless, until then, take care, and stay on the straight and narrow fractal path. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Forest_Floor { ; time=0:05:55.52-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident float=y center-mag=-26.71933195088172/+9.587738968748848/\ 2.907681e+010/1.0234/-22.5/0 params=1.025/0/43/3500 maxiter=2800 inside=255 logmap=455 periodicity=10 colors=000KbzKczKdzKezKfzKgzKhzKizKjzKkzKlzKmzKnzK\ ozKpzKqzKrzKszKszKrzKqzKpzKozKnzKmzKlzKkzKjzKizKhz\ KgzKkzKizKgzKezKczKazKazKYzHgzCUz2_z8QzEOzKOzPRpPQ\ nOPzNUzMOzLWzKNzJMzILzHLzGKzFVzEJzDIzCHzCCzFHzHMzK\ MzMRzOWzR`zTez_jzgozntzwyzzxzzwzzxzzyzvzzrzzmzzhzz\ czzZzzUzzPzzJzzHzzGzzEzzCzzBzz9zz8zzAvzBrzCmzDhzEc\ zDZzCUzRUTRUTRUSQUSQUSQURQURPURPUQPUQPUQOUPOUPOUPN\ UONUONUOzcOzcNzcNzcNzcMzcMzzMzzLzzLzzLzzKKKKJKKJKK\ JKJJKJIKJIKIIKIHKIHKHHKHHKHGKGGKGGKGFKFGKGGKGGKGHK\ HHKHHKHIKIIKIIKIJKJJKJJKJKKKKKKKKKLKLLXLLYLMYMMZMM\ _MNaNM`MM`MM_MM_MLZLLZLLYLLYLLYLKXKKXKKWKKWKJVKJVJ\ JVJJUJJUJITJITIISIISIHRIHRIHRHHQHHQHGPHGPHGOGGOGGO\ GFNGFNFFMFFMFELFELFEKEEKEEKEDJEDJEDIDDIDCHDCHDCHDC\ GCCGCBFCBFCBECBEBADBADBADBACBACA9BA9BA9AA9A99A9899\ 89988988877877876876876765765764764753653653652652\ 6415415405405405516516527 } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 25-07-08 (Into the Depths [7.5])
by Jim Muth 25 Jul '08

25 Jul '08

FOTD -- July 25, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: With today's image we continue the explorations of minibrots in the Mandeloids of very low order, going down from yesterday's 1.075 to 1.05. The parent fractal is a grossly oversized thing, shaped rather like a comet, with debris fields on both sides of its squared-off outer extremity. It was produced by calculating the formula Z^(1.05)+C at a level 13 turns up the logarithmic hyperspiral. Today's image is located at the edge of the southern debris field at the outer extremity of the parent. The exact spot is impossible to recognize on the surface, and I needed to use my not-so-secret method of identifying minibrots to ferret out the elusive little midget. In fact, I never did reach the minibrot itself. The resolution breaks down well before the minibrot becomes visible. But the pattern around it is quite interesting -- perhaps the best de- fined pattern I have yet found around a minibrot in a fractal of such a low order. Or maybe it's just that I put a bit of effort into the coloring. I named the image "Into the Depths", which is a fair description of the impression I get while studying it. I rated it at a 7.5, mostly because it is surprisingly rich for a scene in a fractal of such a low order, but also to give myself a pat on the back for the coloring. The calculation time of just under 2-1/2 minutes on a fireball 2000mhz machine should bring tears to no one's eyes. But compu- ters are notoriously prone to stubbornness, so to guarantee dry eyes, I recommend visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. The next FOTD will appear in 24 hours, most likely continuing the same theme with an exponent even closer to unity. Until then, take care, and take no fractal for granted. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Into_the_Depths { ; time=0:02:24.45-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-14.84534363332544/-23.4626947348403/\ 4.554307e+010/1/-21.75/0 params=1.05/0/13/1500 float=y maxiter=1500 inside=0 logmap=228 periodicity=10 mathtolerance=0.05/1 colors=0000FTWQh00fKDZWLa00ZGIZOHYWFSE4JUCZRAbW9JT\ QJUFdzuJwcLUL`UJeQUQRNSUGjT9dT3WU9bVFqzLnzMoVMoVNz\ zTzUOZUOzTPrT0qTQsSQzSGtSRtRSuRSzRTvRTvPUwNUwLVwJV\ wHWwFWwDXxBXx9Yx7Yx5Zx4Zx5`t5ap5cm5di5fe6gb6cZ6jV6\ lS6mO6nLDsFJc9NcGRyMVcSYyYacceziizolzuhxtdvt`ttXrs\ TpsPnsLlrHjrEirvN0qR7mVDiYJeaP`eVXh`TlfPplLsrCfS4U\ 18XAC_JGaRKd_OfgQccRa`S_XUYUVWQWUNXSKVXIT`HReFPiEN\ nCLrBMrDNrEOrGPrHQrIRrKSrLTrNUrOUrPUnMUjKUgzUczU`z\ UXzUUzUQzUNzROzOPzLPzIQzFQzCRzARzEUzHWzKZON`UQc`Te\ fWhlZjralxXgwTbwPYvLTvHOvDJu9Eu5AuCEzJIzKHzLGzMFzN\ EzOFzOGzPHzPIzQJzQKzRLzRLzRMzSNzSOzTPzTQzURzUSzUSz\ TRzSRzRRzRRzQQzPQzPQzOQzNPzNPzMPzLPXLPZKN`JLaJJbII\ cHGdHEeGCfGBgDAjA9m78pCDqHIrMMsRRtWVu`_vecw_YtVSqQ\ NnbrA`q9Zp9Yo9Wo9Vn9Tm8Sl8Ql8Pk8Nj8Mj8QkDUlHXmM`nQ\ cnUbmXblZbkaajcajeaihahj`gl`fo`fq_es_dv_cx_czX`wVZ\ tTXqRVnOTkMRhuAPXXrWVoWTm } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 23-07-08 (Theological Puzzle [5])
by Jim Muth 23 Jul '08

23 Jul '08

FOTD -- July 23, 2008 (Rating 6) Fractal visionaries and enthusiasts: For today's image we return to the formula that has supplied more FOTD fractals than any other -- the MandAutoCritInZ formula. We check the fractal that results when 1.5 negative parts of Z^(-5.5) are combined with 1.3 negative parts of Z^(-1.3) and (1/C) is added. The parent fractal reminds me of a large ant complete with head, thorax and abdomen, crawling southward across the screen. Today's image is located in the east branch of the valley where the thorax meets the abdomen. When I named the image, I was pondering one of the unanswerable theological questions that I once pestered my religion teachers with -- why does an all-good, all-knowing and all-powerful god permit bad things to happen to good people. This explains the name I gave the image --"Theological Puzzle". I really should curb my theological pondering. It constantly gets me into trouble. God, whatever truth lies behind that idea, must lack at least one, and possibly all of these attri- butes. Perhaps God is not all-good. After all, goodness is a human concept, and why should God's idea of ultimate good be the same as ours? Or perhaps God is not all-knowing. Could even a god know absolutely everything, which by definition must include what every sub-atomic particle in the universe has ever done, is now doing, and ever will do -- things that by their nature are unknowable? Or perhaps God is not all-powerful. Could even an all-powerful god do something that is impossible, such as making 2 plus 2 equal 7? Of course, theology is not the only discipline with unanswerable questions. Check one of the popularized science books about cos- mology or quantum theory, or grab one of those currently trendy books about new-age mysticism. As I often say, 'we don't know what we don't know'. And to make matters worse, I don't even have the option of avoid- ing the theological question by trying to convince myself that God does not exist and then claiming to be an Atheist. Now that I have indulged myself in this theological diversion, it's time to get back to the fractal business at hand. I rated today's image at a 6, which is all I think it is worth. The cal- culation time of under 3 minutes will not be much of a problem. The finished image is also posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A light midday shower did not spoil the otherwise near-perfect midsummer weather on Tuesday here at Fractal Central. The high temperature of 86F 30C and lower humidity were great for everything but snowmen. The fractal cats imagined themselves tigers as they watched a chipmunk in the back yard grass. My day was average, which means nothing happened. The next FOTD will be posted in 24 hours. Until then, take care, and ponder the hard questions. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Theological_Puzzle { ; time=0:02:53.84-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.934500853218/+1.854567358803/14309/\ 1/-120/0 params=-1.5/-5.5/-5/-1.3/0/0/0/0 float=y maxiter=1800 inside=0 logmap=120 periodicity=10 colors=000lcmkamj_miYmfWmcUm`SnYOoVKpRGpOCqL7vL8qL\ 8mL8hL9dL9_R1bL9WGGPBNJGQKLTKQVLuYLZ`MzbMheNzgNud2\ vcBwbKwaTx`ax_jwKow4tu9utDurHuqLvoPvnTvr_svhpoinhk\ lanjVphLvkOrfRnaTjXWfSZbN`ZIcVDhS4eR8bRB`RFYRIVRLT\ RPQRSEXWORVXMUmHTwEWzB_m8bi5egFVfOLeXAde0ad8ZdGWcN\ TcVLVkQca_hdVkTQnImq7KmAIiDGeGEbIKWPPPWa5nUJaMWPFh\ DGeCHbCI_CJYCKVBLSBMPBMNBzzAFv9mrFQoLVlR_iWeezjbzo\ _ztXzoJzk6ziFzhOzgRzgTzfVzfXzj_zfZzcYz`XzYXzUWzRVz\ OUzHRzLUzOWzRZzU`zXcY_eTbgPXdORbNUa5M`M5j`FfbPcdZ_\ fiVigXgeYfcZda_c_`aYa`Xb_YaYYaWZ`UZ_S__Q_ZO`YM`YKa\ XIaXHjFubNsVUrOapGho9on7Rh52bBA`HIZNPXTXWZdUdkUjsZ\ pzclwhitmfrrcov`lzYjzVgzSdzPbzM_zJ_yGawDcuAesDgq7i\ o8km8mk8oi8qg8se9uc9wg9xl9yq9zuKzuUzuaztczudzuezvf\ zvgzvhzwjzwkzxlzxmzxnzyozypzypzupzqpznpzjpzgpzcvz`\ rzYozVkzThzQdzNazL`zO`zR_zU_zX`za_z_ZzZZzYYzXXzVXz\ UWzTezEWzSMzdDzqMzmVzjtzh } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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