March 2005 - Fractint - mailman.xmission.com

FOTD 13-03-05 (Distant Horizons [6])
by Jim Muth 13 Mar '05

13 Mar '05

FOTD -- March 13, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's FOTD came about as I was experimenting with color schemes. There was a period several years ago when I did quite a few images like today's, with its banded low-iteration stuff in the foreground and its more distant high-iteration stuff partly obscured in the background. With the proper coloring, such images can be given a strikingly convincing three-dimensional effect. The coloring of today's image is not the best of all time, but it does capture some of the three-dimensional effect of such scenes. I named the image "Distant Horizons". The impression it gives is one of standing behind a mass of twisting fractal material in the foreground, looking out into the infinite distances of the world of fractals. The location of the Parabolic scene is related to the north bud of the Mandelbrot set, or more correctly, if extended, one of its dimensions would intersect the north bud. The other dimen- sion has a similar relation to the Julia set of the north bud. The rating of a 6 is based almost entirely on the coloring. The render time of under 2 minutes is quite reasonable. A download of the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is equally reasonable. Partly cloudy skies and a temperature of 46F 8C made conditions acceptable for the fractal cats on Saturday. They spent about 2 hours lurking well concealed in the holly thicket, waiting for something to happen. Nothing did, and the duo came inside satisfied that they had done their job. Today is starting mostly cloudy and chilly. I expect a repeat. As for me, I will likely do as little as possible for the rest of the day, except for fractals, that is. The next FOTD will be ready in 24 hours. Until then, take considerable care, and keep fractaling. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Distant_Horizons { ; time=0:01:46.06--SF5 on a P200 reset=2004 type=formula formulafile=slices.frm formulaname=Parabolic passes=1 center-mag=-0.04878\ 05/-1.06478/21.01469/2.7296/-90/-12.042575142884886 params=0/0.7071/0/0.7071 float=y maxiter=38000 inside=255 logmap=10 symmetry=none periodicity=10 colors=000E7HKJKG9IMKKIBJOMKKDKQOIMFJSQKOHLUSMQJNW\ UOSLPYWQVMRZXSVNT`XUXNVaYWYOXcZXZPYd_Z`Q_e``aRagab\ bSchaddTejbfeUgkchgVildjhWjnekiXlofmkXnqgolYprhqnZ\ rriso_ttjup`vtkwraxwmyraxrjwo_vohukYtkfshVrhcqeTpc\ `obSn`Zm_Qm`ZlaSka_jbTic_hcVgdafdWeebdfXcfcbgZahc`\ h`_idZiaYjfXkbWkgVlcUmgTmfSnhRngQoiPphOpkNqiMrkLrk\ KslJtmHslIrlJqlJplKokLnkLnkMmkMljNkjOjjOijPiiQhiQg\ iRfiRehSdhTdhTchUbgVagV`gW_gW_fXZfYYfYXfZWe_Ve_Vea\ UecTdeSdgRdiQdkQdmQeoPeqPfsPfuPgwPhxPhyOizOizOjzOj\ zOkzOkzNlzNlzNmzNnzNnzNozNozMpzMpzMqzMqzMrzMrzLszL\ tzLtzLuzLuzLvzKvzKwzKwzKxzKxzKyzKyzKzzLzzMzzNzzOzz\ PzzQzzRzzSzzTzzUzzVzzWzzXzzYzzZzz_zz`zzazzbzzczzdz\ zezzfzzgzzhzzizzjzzkzzlzzmzznzzozzpzzqzzrzzszztzzu\ zzvzzwzzxzzyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzz0HP } frm:Parabolic {; Jim Muth real(z),real(c) z=imag(pixel)+p1, c=real(pixel)+p2: z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 12-03-05 (Warp-10 [6])
by Jim Muth 12 Mar '05

12 Mar '05

FOTD -- March 12, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's image is titled "Warp-10". In the world of Star Trek, warp-10 equals infinite velocity, the velocity of a hypothetical tachyon that has totally exhausted its energy. But in the equally fantastic world of fractals, warp-10 describes an image of a Mandelbrot midget that looks as though it is moving at a very high velocity. The velocity is not infinite, but the mid- get is moving faster than the velocity of light in the medium, presumably a gas, through which it is moving, and is emitting Cherenkov radiation as it plows along. The scene, which is sliced in the Parabolic direction, shows a sub-midget located deep in East Valley of the large midget on the negative X-axis of the Mandelbrot set. Its appearance shows why I named this particular orientation the Parabolic. The rating of a 6 might be a bit conservative. Having been here often before, I found the scene almost automatically, and had no surprise when I saw the final result. A good part of the rating of the FOTD images comes from the satisfaction I get from seeing something new. If I had never before seen an image like today's, I would have rated it around a 7. But as it is, the rating of 6 will have to do. The render time of 46 seconds is less than it will take to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and download the completed GIF image from there. But for those with handicapped computers unable to run Fractint parameter files, it might be the only way of viewing the image. With some sun and a high temperature of 52F 11C, Friday was pleasant enough to merit the approval of the dynamic duo. In the evening a light thunder-shower moved over, but by then the duo had finished their outdoor exploration and were enjoying their tuna. Today is starting sunny and only slightly colder. The duo should grant their approval. For me it looks like an average day coming up. The next FOTD will appear in 24 hours. Until then, take care, and be of fractal heart. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Warp-10 { ; time=0:00:46.90--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=flip/ident center-mag=+0.0003416292/0/1144.691/63839 params=9\ 0/0/2/0/0/0.00025/-1.75/0 inside=0 maxiter=2500 logmap=220 periodicity=10 symmetry=xaxis float=y colors=000D0FD0DE0AF58G66G94HC5HF6II7IM8JQ9JVAKZBK\ cCPhDUmEZqFcwGhzGmzJrzMvzPzzSzzVzzYzv`zrczmfzhimcl\ cZodUrePufMxbKuZOrVSpRXmN`kJdhFieBmc7q`3uZ7s_Aq_Dp\ `Gn`JlaMkaPibSgbVfcYdc`bdccdZgXUmPPrIKxAGz3Iz5Jz6K\ x7Mw9NvAOsBQrDRpESnFUmHVkIWiJYgLZfM_eN_dN_bN_aN_`N\ Z_OYYPXXQWWRVVSUUTTTUSSVRRWQQXPPYOOZNN_MM`LLaKKcJJ\ eIIgHHiGGkIHmQIoVQq_WpeanjglpmjushzyfxxcwxavxZuxXs\ wUrwSqwPpwNnqSllXjg`ibegYjeUncUsbUwU`dMcNPOMSRLUSL\ XUKZWJaYJd_IfaHicHkeGngFphFphDpgCpeBpdApb8p`7pY6pW\ 5pT3pQ2pN1pM0hSIaYZVcoTdkRdhPeeNebLf_JfXHgUFgREgOJ\ hRNhUSiWWiZ`j`djcikfmkhrlkvlmrmhomdkm_hnWenSanNZnJ\ WoFSoAPo6Mo2esPywkwufvtbusZsrVrqRqoNpnJnmFmlBlk7kj\ 3ih4hf5fd5eb6d`7b_7aa8`c9Ze9YgAXiARkFLmKFoO9qT4sX8\ uVCwTGxRKyPOzNSzLWzJ_zHczFgzDkzBhzFezIbzL_zOXzRUzU\ RzXOz_LzbIzeFzhCzk9zn6zq3zt0zwBzpLzjVzddzZnzTxzNjz\ XXzfJzp6zyBzwAzOAzMBzKCzH } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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FOTD 11-03-05 (Peaches and Cream [6])
by Jim Muth 11 Mar '05

11 Mar '05

FOTD -- March 11, 2005 (Rating 6) Fractal visionaries and enthusiasts: For some reason, I keep winning contests that I have never entered. Yesterday is a typical example. While waiting for a tardy customer to call in the final corrections for his job, I heard the phone ring. When I answered the phone, I heard a very excited voice congratulate me, telling me that I had just been selected to win a brand new Lexus. Suspecting with good reason that something was not as it seemed, I asked the caller if I had actually already won the Lexus or if the dealer was merely having a sales promotion. When the caller started talking about the great deals they were offering, I was disappointed but not surprised. Today's image is not quite up to yesterday's, and it is certainly not up to a new Lexus, but it is not disappointing and it is actually a bit surprising. It takes us to the north valley of the Mandelbrot set (I forget the valley's name) and looks at it from the Parabolic direction. Once again, the image resembles one of the miniature Julia sets found in the parent Julia sets of the area. The slices of the Julibrot in the Parabolic orientation are filled with features that resemble Julia sets. But unlike true Julia sets, where all miniatures in the same set are the same shape, the Julia-like miniatures in Parabolic sets can be of any shape, even in the same parent fractal. There is an orderly arrangement of the shapes of the miniatures in Parabolic sets, though I have not yet completely figured it out. Today's image needed far less un-distorting than yesterday's. It still has been stretched in the vertical direction however, by a magnitude of 2, and skewed by a factor of 9. Like yesterday's image, today's image turned out to be a perfect Julia-like miniature once the corrections were applied. The coloring of today's fractal is not quite up to that of yesterday's image, but it is still unusually smooth for a GIF fractal. And the incredibly fast render time of 1-1/2 minutes makes the task of rendering the image from the included parameter file a minor event. I named today's image "Peaches and Cream". The peach tint around the edges inspired the name. Actually, it would be more correct to say that the tint was the cause of the name. Little inspiration is involved when choose the FOTD names. As always, the final product is available for download on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Limited sun, chilly winds, and a temperature of 37F 3C made life unpleasant for the fractal duo on Thursday. The 20 minutes they spent in the yard were far too little to satisfy their adventur- ous spirits. But a generous serving of tuna and New York white cheddar cheese made their evening acceptable. Today is starting cloudy, with light snow forecast but not yet in sight. The cats already look unhappy. I expect my day to be uneventful, that is except for the next fractal. Until 24 hours have passed, and that next fractal appears, take care, and what are dreams made of? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Peaches_and_Cream { ; time=0:01:16.78--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00033419957414436/+0.000010038281058\ 69/2.31979e+008/0.5987/13.7810528843527536/9.49271\ 279099203547 params=0/0/2/0/0.0089773333/0.6656844\ 316/0.0089773333/0.6656844316 float=y maxiter=3800 inside=255 logmap=89 periodicity=10 colors=000wlcvlculctlcslcrlcqlcpkcojcnicmiclhckhcj\ gahg_efYafWZeUVdSQcQNbOJaLG`JDZI8YG4XE1YD0XB0Y90ZG\ 0_L2aQ4eV8i_9mdDqiEvpIztJzzNzzOzzRzzTzzTwzT_zTDwT0\ pX0n_0lb0lf2kg6kk8inBiqDgsGgwJfzLfzOdzQdtLalI_dEXX\ BVO8TTBRXDR_GQbIQfJOiNOlPNpSNsWLwZLzaLxYJwWItVGsTE\ qQDpNDpMBnJ9lG8kD6iC6g94f52f21d10b00a00_00Y00X00X0\ 0T00Q00N00J20G61E91BD28G44J61N80Q90R90QB0QB0QD0QD0\ QD0QE0QE0QE0QG0QG0QG0JT0Ed28q82z41z21z11z01z01z01z\ 01z04z08z1Bx2Et4Gp6Jl8Ni9RdBSaETXGUTIVOJWLLXINYDOZ\ 9Q_4R`1Ta0Vb0Vc1Xd2Xe4Xf4Yg6Yh8_i9_jB_kBalDamEbnGb\ oGbpIdqJdrLfsNftNguOhvQiwRjxRkyNlzImzDnz8oz2pz0qz1\ rz4sz8uxBwtDtqGsnJqkNpgOndRlaViYYgVafRbdOfbLiaIl_E\ nYBqX8tV4xT1zf2ng4di6Tl8JpLbQYt0kz8dzI_wRTnaOgkI_t\ DRz8Lz9Nz9QzBTzBXzB_zDbzDfzEizElzEpzGszGwzIzzIzzIz\ zJzzJzzLzzLzzLzzDzz6zz0zz0zz0zz0zz0zz0zz0zz2zz6zz9\ zzDzzXzzazzbzzdzzfzzgzziz } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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FOTD 10-03-05 (The Phantom Gift [7])
by Jim Muth 11 Mar '05

11 Mar '05

FOTD -- March 10, 2005 (Rating 7) Fractal visionaries and enthusiasts: Today, for a change, I did not goof. The pleasant scene is sliced through the Z^2+C Julibrot in the Parabolic direction. The slice is located near the Seahorse Valley of one of the Mandelbrot midgets in Elephant Valley. As a result, we have a Seahorse-looking Julia midget surrounded by Elephant-looking features. The name "The Phantom Gift", which I gave to the image, has no relation to the image's appearance. I chose it on a total whim because it sounds artistic. The rating of a 7, however, is well earned. The coloring, at least on my monitor, comes as close as possible, without checkerboarding, to the smooth appearance of true-color. The bands are there, but to see them, one must look carefully. Images of midgets sliced in the odd directions often have a rather unpleasant stretched appearance, but sometimes, as in today's FOTD, they appear totally undistorted. There is a catch however. To achieve today's undistorted image, it was necessary to stretch the image in the vertical direction by a factor of 380, and skew it by a factor of almost 90. This manipulation is part of the fun of the odd planes, getting something from nothing as it were, and if it were not done, today's image would consist of nothing more than a screen filled with multi-colored horizontal stripes. The render time of 4 minutes may be avoided by downloading the completed GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I have just received a copy of the book "Schrodingers Rabbits", which discusses the many-worlds interpretation of quantum theory. I can already see that it contains things that will need to be worked into the next installment of my philosophy. This means a further delay, but anything worth having is worth waiting for. Partly cloudy skies, biting winds, and a high temperature of only freezing kept the fractal cat duo safely indoors all day Wednesday. In mid-afternoon, the intruder from up the hill showed up and left his mark in the yard. The duo somehow knew the other cat was in the yard, and kept careful watch until he casually walked away. Today is starting with hazy sun and continued cold temperatures. The forecast calls for possible snow later this evening, but by then the duo will have finished whatever they have planned for the day. The next FOTD will appear at this same spot 24 hours from now. Until then, take care, and don't get lost in Fractal land. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Phantom_Gift { ; time=0:03:54.70--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00000312419553334/-0.000000002198513\ 13/4.551921e+010/0.002633/0.627306089407922651/89.\ 4765892407080514 params=0/0/2/0/0.265019899971/0.0\ 03084106765/0.265019899971/0.003084106765 float=y maxiter=5000 inside=0 logmap=383 periodicity=10 colors=000aaqb`qc_qdZqeYqfXqgWqhVqiUqjTqkSqlRqmQqn\ PqoOqoNqpMqqKqqJqrHqrGqqFopEmoEjmEhkEdiEagEXeEUcEQ\ aEN_EKYEGWEDUF6SE8QEAOEBMEDKEEKDGLDHMDJNDLODMPDOQC\ PRCRSCSTCUUCWVCXWBZXB_YBaZBb_Bd_Be`Cc`DbaEaaF_bGZb\ GYcHWcIVdJUdKSeLReLQfMOfNNfOMgPKgQJhQIhRGiSFiTEjUC\ jVBkWAlX8nY7oZ6qZ4rZ3qZ2oZ6nYAmXDlWHlVLlUOlTSlSWlR\ ZlQblQclQenRhqSktSnvTmvTmuUluUltVltVksVksWkrWjqXjp\ XjoYhnYfmYdlYbkT`jOZiJXiEVi8TiARiBPiCNiELiFJiGHhIF\ hJDhKBhMAhNBhOCgQDgREgSFgUFgVGgWHfYIfZJf_KfaLfbMfc\ NeeOefPegQeiRejSekTelTdkSckSbjSajRajR`iR_iQZhQZhQY\ hQXgPWgPWfPVfOUfOTeOSeNSdNRdNQdNPcMPcMObMNbLMbLMaL\ LaKK`KJ`KJ`KIaLIaMIbMIbNIbNIcOIcOIcPHdPHdQHdQHeRHe\ RHeSHfSHfTGfVGgXGgZGg`GhbGhdGhfGihFjiFkjFlkFmlFnmF\ onFpoGqpFrqFsrEtsEutDuuDuvCuwCuwBuwBuwAuwAuw9uw9uw\ 9uw8uw8uw7uw7uw6uw6uw5uw5uw4uw4uw3uw3uw3uw5uw7uw8u\ wAuwBuwDuwEuwGuwHuwJuwIuw } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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Re: FOTD 08-03-05 (Parabolic Horse [6])
by Jim Muth 10 Mar '05

10 Mar '05

At 11:47 AM 3/8/05 -1000, david wrote: >Shoots, image not up on the web site yet ... >I was gonna say that no matter how I tried, I >couldn't see a pair of bolic horses, only one ... >but maybe I should wait until I can actually see >the picture ... Your inability to see horses is not surprising. There are no horses at all in the image. Both it and the discussion contain glaring errors. The goof-ups will be corrected in tomorrow's FOTD, which will appear on schedule in 12 or so hours. Jim M.

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FOTD 09-03-05 (I Goofed [No rating])
by Jim Muth 09 Mar '05

09 Mar '05

FOTD -- March 09, 2005 (No Rating) Fractal visionaries and enthusiasts: The fractalist has failed. I should have seen it sooner. How could I have missed such an obvious error? Yesterday's image is centered at -1.3 on its Y-axis, which is -1.3 on the X-axis of the Mandelbrot set. This point on the Mandelbrot X-axis is not just beyond Seahorse Valley, it is just beyond Scepter Valley, which is the next valley beyond Seahorse Valley. The bright horizontal stripe that appeared in yesterday's FOTD image is not a view of Seahorse Valley from above, as I claimed in the discussion. It is a view of Scepter Valley from above. Since I cannot permit such blantant errors to go unchallenged, I have corrected the situation in today's image, which is an expansion of yesterday's image to include the true Seahorse Valley. In today's image, Seahorse Valley appears as the thin, bright horizontal line near the top of the frame. The open area above it, at the top edge of the frame, is part of the main bay of the M-set. The broader horizontal stripe near the bottom of the frame is Scepter Valley, with the main period-2 bud appearing as the open area between the two stripes. Since today's image is basically a repeat of yesterday's, I have not given it a rating. But it is a marginal improvement and renders in only 1-1/2 minutes. Only little time is needed to bring it to life. The image also is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The rain changed quickly to snow in the late morning here at Fractal Central on Tuesday. About 1/2 inch 1cm fell before it ended. The temperature fell steadily all day to around 25F -4C by late afternoon. At the same time the wind blew in gusts to 45mph 70kph, making conditions far too harsh for the sensitive whiskers of the fractal duo. Today is starting sunny, but it is still quite windy and very cold, with a temperature of 18F -8C. The cats will be unhappy today. My happiness will increase if I can avoid errors in my next FOTD, which will appear in 24 hours. Until then, take care, and almost everything can be described by the proper numbers. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= I_Goofed { ; time=0:01:36.29--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=0/-1.06505/2.823547/0.3312 params=0/0/2/0/0/0/0/0.051 float=y maxiter=40000 inside=255 logmap=11 symmetry=yaxis periodicity=10 colors=000MY0S_0U_0Yb0ee0rd0zg0zj0xe0m_0eU0YP0SH4M\ CCK6HE4PC6UH9SMCPPHPUMMYSMbSKeSKjSHmSHrSErSCuSEuSH\ uSHuSKuSKuSMuSMuSPuSSuSSuSUuSUuSYuSYxU_xYbx_bxeexg\ exjgxmgxrjxumxxmxzpxzpxzrzzxxzrrzpmzmgzjbzg_zbUz_P\ zYKzUEzS9zP6zK1zH0zE0zC0z90z60z40x44r49j4Ee4M_4SU4\ _M4eH4jC1r41x01z01z01z01z01z01z01z09z0Ez0Kz0Su0Ym0\ be0j_0pS0uK1zC4z46z0Cz0Ez0Hz0Kz0Mz0Pz0Sz0Uz0Yz0_z0\ bz0ez0gz0jz0mz1pz4rx6uu9xp9zmCzjEzgHzeKzbMzYKz_Hz_\ Ez_Cz_Cz_9z_6z_4zb1zb1zb0zb0zb0zb0zb0ze0ze0ze0ze0z\ e0ze0zg0zj0zm0zp0zr0zu0zx0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz4zz6zzCzzEzzKzzMzzSzzUzz_zzbzzgzzjzzpzzrzz\ xzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzxzzuzzrzzmzzjzzez\ zbzz_zzUzzSzzPzzKzzHzzCzz9zz6zz1zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz4zz6zz9zzEzzHzzMzzPzzSzzYzz_zzezzgzzjzzpzzrz\ zxzzzzzzzzzzzzzzzzzzzzKPZ } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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Re: FOTD 08-03-05 (Parabolic Horse [6])
by gnome＠hawaii.rr.com 08 Mar '05

08 Mar '05

Shoots, image not up on the web site yet ... I was gonna say that no matter how I tried, I couldn't see a pair of bolic horses, only one ... but maybe I should wait until I can actually see the picture ... David gnome(a)hawaii.rr.com ----- Original Message ----- From: Jim Muth <jamth(a)mindspring.com> Date: Tuesday, March 8, 2005 4:56 am Subject: [Fractint] FOTD 08-03-05 (Parabolic Horse [6]) > > FOTD -- March 08, 2005 (Rating 6) > > I named today's image "Parabolic Horse". No, I have never seen > such an oddly shaped land-horse, but a valley named after the > sea-horse does appear in the image, and the image most certainly > is filled with parabolas, so I suppose the name is justified.

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FOTD 08-03-05 (Parabolic Horse [6])
by Jim Muth 08 Mar '05

08 Mar '05

FOTD -- March 08, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today, we shift our attention to what I call the Parabolic slices of the Julibrot, which are determined by the real(c) and real(z) axes. To visualize the orientation of these slices, we must imagine the three-dimensional section of the Julibrot that exists in our space when the Mandelbrot set is on the screen and the real(z) axis is perpendicular to the screen. The Oblate slices that we have been examining for the past seven days are what we would see if we were to view this three-dimensional object from the left of the screen. The Parabolic slices that we will be examining for the next seven days are what we would see from above the screen. In the image, the vertical direction is the east-west direction of the Mandelbrot set, with east on top and west on bottom, while the horizontal direction is the in-out direction when the M-set is on the screen and the Julibrot is oriented so that the real(z) axis is perpendicular to the screen. The left half of today's image is the part of the Julibrot section behind the screen, the right half is in front of the screen. In today's image I have sliced the Julibrot through the upper branch of Seahorse Valley. Yet no valley is visible on the screen. Nor is anything visible resembling the Julia sets of the valley. The Valley has been transformed into the bright horizontal ribbon that appears near the top of today's image. Actually, the Seahorse ribbon is actually much narrower than it appears in today's image, which has been stretched in the vertical direction to 15 times its normal width. The narrow bright horizontal line lower in the image is one of the small valleys on the western shore of the large period-2 bud of the M-set. The broad area below that is the start of the Mandelbrot mainland in the vicinity of Scepter Valley. I named this orientation the Parabolic direction because it is filled with parabolas. In fact, the Parabolic slice through the origin of the Julibrot starts as one great parabola, which is actually the graph of the function X^2. Checking the Parabolic slice through the origin of a fractal is one way of finding the critical points of that fractal's formula, and is one of the methods I sometimes use. I named today's image "Parabolic Horse". No, I have never seen such an oddly shaped land-horse, but a valley named after the sea-horse does appear in the image, and the image most certainly is filled with parabolas, so I suppose the name is justified. I rated the image at a 6. Most of the rating is due to the colors, which I spent a little extra time on, and are rather intense. The render time of 2-1/2 minutes is quite reasonable for such an image, but so is the minimal effort required to download the completed image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The time for the completion of the philosophy, which I abruptly discontinued, is drawing near. It should appear within a week. I will say little about my views at this time other than to state that I consider myself bound by neither scientific nor rational correctness. Warm sun and a high temperature of 70F 21C gave the fractal duo of cats nearly an entire day in the yard on Monday. They passed most of the time lurking in the holly bushes, but when the obnoxious gray-and-white cat from up the hill intruded in the yard, Thomas sprang into action, and with a mighty yell, sent the intruder scurying back where he belongs. Tippy watched the action with interest. When the day ended, I rewarded both of them with a generous serving of tuna. Today is starting rainy and windy, with rapidly falling tempera- tures and talk of snow on the way. It looks like the cats' good day will not be repeated. For me the day looks like it will be on the slow side, which means lots of time for the next fractal. Until that next fractal appears in 24 hours, take care, and why does 0! equal 1 instead of 0? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Parabolic_Horse { ; time=0:02:25.50--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-xz-yw-new passes=1 center-mag=0/-1.30045/13.90355/0.06894 params=0/0/2/0/0/0/0/0.051 float=y maxiter=40000 inside=255 logmap=11 symmetry=yaxis periodicity=10 colors=000MY0S_0U_0Yb0ee0ug0zg0zj0xe0m_0eU0YP0SH4M\ CCK6HE4PC6UH9SMCPPHPUMMYSMbSKeSKjSHmSHrSErSCuSEuSH\ uSHuSKuSKuSMuSMuSPuSSuSSuSUuSUuSYuSYxU_xYbx_bxeexg\ exjgxmgxrjxumxxmxzpxzpxzrzzxxzrrzpmzmgzjbzg_zbUz_P\ zYKzUEzS9zP6zK1zH0zE0zC0z90z60z40x44r49j4Ee4M_4SU4\ _M4eH4jC1r41x01z01z01z01z01z01z01z09z0Ez0Kz0Su0Ym0\ be0j_0pS0uK1zC4z46z0Cz0Ez0Hz0Kz0Mz0Pz0Sz0Uz0Yz0_z0\ bz0ez0gz0jz0mz1pz4rx6uu9xp9zmCzjEzgHzeKzbMzYKz_Hz_\ Ez_Cz_Cz_9z_6z_4zb1zb1zb0zb0zb0zb0zb0ze0ze0ze0ze0z\ e0ze0zg0zj0zm0zp0zr0zu0zx0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz4zz6zzCzzEzzKzzMzzSzzUzz_zzbzzgzzjzzpzzrzz\ xzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzxzzuzzrzzmzzjzzez\ zbzz_zzUzzSzzPzzKzzHzzCzz9zz6zz1zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz4zz6zz9zzEzzHzzMzzPzzSzzYzz_zzezzgzzjzzpzzrz\ zxzzzzzzzzzzzzzzzzzzzzKPZ } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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FOTD 07-03-05 (Seahorse Oblate [6])
by Jim Muth 07 Mar '05

07 Mar '05

FOTD -- March 07, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's image is the last in the current series of seven Oblate pictures. (Well, all right, yesterday's image had more of a Rectangular orientation.) Today's image shows an Oblate view of a mini-Mandelbrot set lying in Seahorse Valley. The Mandelbrot version of the picture may be seen by changing the (p1) parameter from 0,90 to 45,45 and resetting the x-magnification factor to 1. When this is done, a perfectly-formed, though somewhat under-iterated, Mandelbrot midget typical of those in Seahorse Valley will appear. The pattern surrounding the Oblate midget closely resembles that of both the Mandelbrot and Julia versions of the scene. The main difference is that the pattern is distorted into a triangular shape. This triangular distortion is typical of most midgets in the Oblate orientation. The mathematical reason for this is probably known, though I have no idea of what that reason might be. The name "Seahorse Oblate" is a description, and hardly more than a catalog number. The rating of a 6 reflects the small amount of extra effort I put into the coloring. The render time of 3 minutes is about the same as the time required to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and download the finished image from there. Starting with tomorrow's image, we will spend 7 days investiga- ting what I call the Parabolic, real(c)real(z), orientation of the Julibrot. A sunny mild day on Sunday, with a temperature of 54F 12C, kept the fractal duo quite happy in the yard most of the afternoon. When evening came, they were so exhausted that they almost forgot their tuna. Today promises to be even warmer. This is good news for the dynamic cats. For me, there is a modicum of work to finish before I get to the fractals, the next of which will appear in 24 hours. Until then, take care, and sometimes I wonder whether there are an infinity of fractals or only one fractal with infinite aspects. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Oblate { ; time=0:03:06.09--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=-0.00000000000200438/+0.000000\ 00000203913/1.205523e+010/0.3459/32.5/3.8857805861\ 8804789e-016 params=0/90/2/0/-0.7291299973892553/\ 0.2357647081925723/-0.7291299973892533/0.235764708\ 1925723 float=y maxiter=1800 inside=0 logmap=320 periodicity=10 colors=000jNvjNujNtiNsiNrhNqhNpgNogNnfNmfNleNkeOid\ PgdQecPcbOaaM_`LY_KWZJVZIT_KU`MUaOUbQWcSXcUZdW`eYb\ f_cgaehcfiehigijijkkllmmlnnmppnrqotspvtrxutzwvzxwz\ yzzzzzzzzzzzzPkWUkcYlaSm_NnYHoWCpU6qS1rQ8ZYEGeDFdC\ FcCEcBEbBDbADa9C`9C`8B_8B_7AZ7AZ6B`5Bb5Bd4Ce4Cg3Ci\ 3Dj2Dl2Dn1Eo1Eq0Es0Et4Gs8IsBKsFLsINsMPsQQsTSsXUs_V\ sfbklicsqWyxOxuNxrNxoNwlMwjMwgMvdLvaLv_LuXKuUKuRPu\ OUzLZzNczRhzUlwYktalqdlnhlmlllolkjZjeMi`9dXE`UJXRO\ TNTOKYKHbGDgCAl87q9CrAGrBKrCPsDTsEXsF`sGetHitImtJq\ tKmpKjmKgjLdfLacLY`MVXMSUMPRMMOR`TWoY_zb`z``wZ`tYa\ qWanUakTahRbePbbOb_MbYLeWIhVGkUEmTCpSAsR8uQ6qO9nNB\ kLDhKFeJHbHJ_GLWFNTDPQCRNBTK9VH8XE7ZI6`L6aO6bS5cV5\ dY5f`5gd4hg4ij4jm4lq3mt3nw3oz3pr9rkEsdJtXPuQUvJZwK\ _rL`nMajNbfOcbPdZPdVSdUVdTYdT_bSa`ScZSdXSfVS8Hz8Jz\ 9Lz9Nz9PzARzATzAVzOXz6Zz7`z7bz7cz8dz8ez8fz9fz9fz9f\ zAfzAfzAfzCfzEfzFfzHfzIfz } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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FOTD 05-03-05 (Oblate Miniature [6])
by Vortex Swirling 07 Mar '05

07 Mar '05

This took me a little over 23 hours to produce, and I'm running a 2.53 mhz pentium 4. I think it is because I've started to run Seti@Home and some other cpu sharing screensavers. After creating a 1280x1024 image of this one, I'm am quite impressed. The coloring gave it a sort of 3D look where the central mass seems to be floating on the blue. You can see it a little bit on the FTOD page but at the larger scale it is much more impressive. -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.6.2 - Release Date: 3/4/2005 -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.6.2 - Release Date: 3/4/2005

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