January 2008 - Fractint - mailman.xmission.com

AOTD
by JackOfTradeZ＠comcast.net 14 Jan '08

14 Jan '08

. Animation of Jim Muth's FOTD -- January 02, 2008 (Rating 9.5) "Aurora Fractalis" is posted: http://www.fractal-animation.net/vid/aurorafractalis.zip WMV, 640x480, 52 sec, 8.5 Meg .

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FOTD 14-01-08 (New View of Seahorse [7])
by Jim Muth 14 Jan '08

14 Jan '08

FOTD -- January 14, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today we introduce a new formula, which draws the slices of the Julibrot that are missed by the other odd-slice and oblique- slice formulas. This formula draws only the oblique slices in which there is no annoying stretching or skewing that must be unstretched to be properly seen. I named the image "New View of Seahorse", and indeed, this is what it is. In the image we see the entire Julia set of Seahorse Valley as well as an enlarged view of a deep part of the valley itself in the same frame. And don't miss the peanut holes where the vertical valley meets the edges of the Julia parts of the image. The blank outer shape is immediately recognizable as one of the Julia sets of Seahorse Valley, while the colorful vertical inner stripe is a grossly enlarged but unstretched view of Seahorse Valley as it appears at a depth of y=0.004. The sides of the valley are parallel not because it is stretched, but because it is sliced at a depth where its sides actually are parallel. The inner part of the image is enlarged for the same reason that a 2-D slice of a circular cylinder can appear as anything from a circle to a stripe with straight and parallel edges. A cross- section of a similar 4-D cylinder is a sphere, and the cylinder can be sliced by a 2-D plane in a direction that stretches the projection equally in 2 dimensions. Such a two-dimensional stretching appears as a simple magnification. I rated the image at a nominal 7, a fair rating for an image with a rather slow calculation time of around 22 minutes. But why not forget about calculating by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the image there? Sunday turned out pleasant but a bit colder here at Fractal Central. The clouds that moved in during the afternoon held the temperature to 43F 6C and led to a cold rain mixed with snow after nightfall. The fractal cats and myself as well spent most of the day taking it easy in front of the TV. The next FOTD will appear in 24 hours. Until then, take care, and I wonder what happened to all the wonder I once felt as I read those early books about the wonders of science and the physical world. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= NewViewOf_Seahorse { ; time=0:21:58.54-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MoreSlices passes=t center-mag=0/0/0.86 params=-0.7500101/0.004/0.00014/0/0/0 float=y maxiter=40000 inside=0 outside=tdis logmap=yes symmetry=none periodicity=10 colors=000LQmKPjJNhIMeHKbGJ_FHX8FXCIWFLVJOU_LnaNld\ PjXdTVbVS`XQZZNX`LVbNWcOXcPXcQYcRZdSZdT_dU_dV`eWae\ XaeYbeZbeYcbXc`XcZWcXWcVVdTVdRUdPUdNTdLTdJSbNR`QQZ\ UPXXOV`NTcMRfLPjKNmJLqIJtIHwHJtHLrGNpGPmFRkFTiEVgE\ XdDZbD``DbZEZaEWcETeFPgFMiFJkGFmGCoG9qEDrDGrBKrANs\ 8Qs7Us5Xs4_t2ct1ft0itBblMWdXPYgIQrBJnAMj9Pf9Sb8VZ8\ YV7`R7cN6fJ5iF5lB4o74r33u03x5At9HpDOlHVhLadPgaNcVL\ _OJYHHSAFk4DmcHc`K8YNBVQESTHPWKMZNJaQGdTDgWAjY7nbB\ rgFzmJvfLvaMvXUvScvNmvJmuKmuLmuMmuMmuNmtOrtOvtPztQ\ ztQzsRzsSzsSzsTzsUzsUztSzuQzvOtwMrxKqyIpyHouKpqMqn\ OrjQrgSscUt`WtXYuT_vQavMcwJexFgxCiy8kz5mz7Zz9YzAXz\ BWzDVzEUzFTzGSzISzJRzKQzLPzNOzONzPMzQMzOOzNQzMRzKT\ zJUzIWzGXzFZzE_zCazBbzAdz9ezCbzF_zIYzLVzOTzRQzUOlX\ Lj_IhbGfeDdhBbk8`n6_oDYoJWpPUpVTq`RqfPrlNrrMkmKdiJ\ ZeISaHLXFFTE8PD2LC6JGAHJDGMHEQLCTOBWS9_W7bZ6eb4if2\ li1okBgmL_oVSqdKO_vNYsMXp } frm:MoreSlices {; Jim Muth ; P1 -- M-center of slice ; P2 -- angle of slice ; P3 -- J-center of slice z=pixel+(p3), c=p1+(pixel*p2): z=sqr(z)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 13-01-08 (Misfits [3])
by Jim Muth 13 Jan '08

13 Jan '08

FOTD -- January 13, 2008 (Rating 3) Fractal visionaries and enthusiasts: After a 10-rated fractal winner such as we had yesterday on January 12, all we could dredge up for today was a fractal loser, rating a measly 3, which is well below the FOTD average between 6 and 7. The image is a view of one of the Julia sets of the Quaternion Mandelbrot set, which, as far as I can see, is the 3-dimensional figure that the classic Mandelbrot set would trace out if it were rotated around its X-axis. The Julia set in today's image has obvious Seahorse Valley characteristics, but it comes in 3 sepatated parts, which is a sign that its associated Mandelbrot point lies outside the quaternion M-set itself. The name "Misfits" came about when I could think of nothing better. Luckily, today's calculation time is as brief as yester- day's was long. Today's image calculates in 4-1/2 seconds. As always, the finished image is available for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A perfectly average midwinter day prevailed here at Fractal Central on Saturday, with partly cloudy skies and a temperature of 39F 4C. The fractal cats, who enjoy smooth-running, routine things, took little notice of the weather. My day was occupied with clearing up odds and ends. The next FOTD will appear in 24 hours. Until then, take care, and take heed. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Misfits { ; time=0:00:04.29-SF5 on P4-2000 reset=2004 type=quatjul center-mag=0/0/1.1086 params=-0.75/0.1/0/0/0.2/0 float=y maxiter=5000 inside=0 periodicity=0 colors=000IIAIIAIIAIHAIHAIHAIHAHHAHHAHGAHGAHGAHFAH\ FAGFAGEAFEAEEADDACDABDAADAACAABAAAAAAAAAAAAAAAAAAA\ AAAKNlMOkQPjURiYTgaVfeWeh_bjb_lfXniUqmRspOutLwwJvx\ OuxStxWsx`rxdqxhpxmoxqnxunxykvwiuufssdrqapo_omYmkV\ liTjgQieOgcMfbPaXSYSVUNXQIcUGiYEpaCvdAqeDmeFieHeeJ\ `eLXeNTePPeROdUNdXMc_LcbLbeKbhJakIanH`qH`sH_rH_rG_\ rG_rG_rG_rG_rF_rFZrFZrFZrEZrEZrEZrEZrEZrDYrDYrDYrD\ YrCYrCYrCYrCXqBXqBXqBXqBXqBXqAXqAXqAWqAWq9Wq9Wq9Wq\ 9Wq9Wq8Wq8Vq8Vq8Vq7Vq7Vq7Vq7Vq7Vq8Up8Uo8Un8Tn8Tm8T\ l8Tl9Sk9Sj9Sj9Ri9Rh9Rh9RgAQfAQfAQeAPdAPdAPcAPbBOaB\ OaBO`BN_BN_BNZBNYCMYCMXCMWCLWCLVCLUCLUDKTDKSDKSDJR\ DJQDJQDJPEIOEINEINGDBEHMEHLEHLEHKFGJFGJFGIFFHFFHFF\ GFFFGEFGEEGEDGDDGDCGDBQ__PZZPZZPZYPYYPYYPYXPXXOXXO\ XWOWWOWWOWVOVVOVVNVUNUUNUUNUTNTTNTTNTSMSSMSSMSRMSR\ MRQMRQMRQLQPLQPLQPLPOLPOLPOLONLONKONKNMKNMKNMKMLKM\ LKMLJLKJLKJLKJKJJKJJKIJKI } END PARAMETER FILE=========================================

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FOTD 12-01-08 (Ultra-Extremism [10])
by Jim Muth 12 Jan '08

12 Jan '08

FOTD -- January 12, 2008 (Rating 10) Fractal visionaries and enthusiasts: Today's image rates a 10. This is no mistake. To find it, I went as deep as possible into Seahorse Valley to highlight one of the things there that I call peanut holes. I named the image "Ultra-Extremism" because it takes everything to the extreme. To start, the maxiter of 2,147,483,647 is the program's limit, and even with this maxiter there are open holes in the image. Next, the magnitude of 1.7*10^13 is at the limit of the conventional math routine, and finally, the calculation time of almost 7 hours is the limit of practicality. (Arbitrary precision math would finish the image in about 700 hours, or one month.) Since the image sets a new record in so many aspects and also is artistically pretty good, I decided to give it a rating of a 10, the highest possible rating, very rarely achieved. Perhaps the most interesting thing in the image is its lack of resemblance to anything that might be expected in a typical Seahorse Valley image. The net-like features, for one thing, are nowhere in evidence in the normally explored parts of the valley. I strongly advise against calculating the image yourself. The calculation time of almost 7 hours on my fastest machine will stretch into days on anything slower. The way to view the image is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where I have already sent the image for rapid posting. Friday started with heavy low clouds and rain here at Fractal Central, but at noon the rain ended and the sky cleared, leading to a most pleasant afternoon with a temperature of 48F 9C. The fractal cats celebrated by sleeping. My day was rather busy during the 7 hours the fractal cooked. But the wait was worth it. The next FOTD, probably not as good as today's but still worthwhile, will be posted in 24 hours. Until then, take care, and be thankful. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ultra-Extremism { ; time=6:57:45.09-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.75000000009776880/+0.000007999957639\ 72/1.702597e+013/1/15/0 params=0/0 float=y maxiter=2147483647 bailout=9 inside=255 periodicity=10 mathtolerance=0.05/1 colors=0000If0Gf0Ef0Cf0Af08f06h04h02h00h00h00h00f0\ 0d00a00Z00W00T00Q00O00N00N00N00P00R00T00W00Z00a00c\ 00d00d00d00d00d00d00d01d02d03d04d05d06d07d08d09d0A\ d0Bf0Cg0Dh0Ei0Fj0Gk0Hl0Im0Jn0Ko0Lp0Mq0Nr0Os0Pt0Qu0\ Rv0Sw0Tx0Uy0Vz0Wz0Xz0Yz0Zz0_z0`z0az0bz0cz0dz0ez0fz\ 0gz0hz0gz0ez0cz0az0_z0Yz0Wz0Uz0Sz0Qy0Ov0Ms0Ks0Is0G\ s0Eq0Cn0Ak08h06f04d02b00_00Y02Y04_06Y08W0AT0CR0EP0\ GN0IK0KI0MG0OG0QE0SC0UW0ZW0cT0hT0qT0yR0vR0vR0sR0sP\ 0qP0qP0qN0nN0nN0kK0kK0hK0hI0fI0fI0dG0dG0bG0bE0bE0_\ E0_C0YC0YC0WC0WA0TA0TA0R80R80P80P60P60N60N40K40K40\ I20I20G20G10E10E10N00I00E10A208404601800A00C00G00I\ 00K00N00P00R00T00Y00W00W00W10W40WA2WE8WKCWPIWTPW_W\ WdbWkhWqqWvvWzzWzzfzzszzzzzzzzzzzzzzzzzzzzzzzszzfz\ zWzzWzzWzzWzuWzpYzkYzfYzaYzaYzfYxkYwp_uu_sz_qz_oz_\ mz_kz_izbgzcezhczmazw_zzYzzWzzUzzSzvQzrOymMshKnfIk\ dGfdEddC_dAWd8Td6Qd0Nd0Kf } END PARAMETER FILE=========================================

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FOTD 11-01-08 (Gateway to Infinity [No rating])
by Jim Muth 10 Jan '08

10 Jan '08

FOTD -- January 11, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's trip to Seahorse Valley reveals an entirely new aspect of the valley. The slice is centered at C=-0.75+0.095i Z=0,0 and is sliced in an orientation double rotated 15 degrees from the Julia direction toward the Parabolic direction. Double rotation is another of the seemingly absurd things that are simple in four-dimensional space. It has no analog in 3-D space. The closeness to the Julia orientation is evident in the open top half of the image, which bears an unmistakable relation to the well-known Julia sets of Seahorse Valley. But the lower half of the image is a different story. Here we are apparently skimming through the buds of the valley, which have been stretched to infinity in the horizontal direction and appear as mere slits. Don't try to figure out which buds we are skimming through. I tried to deduce it and ended up totally mentally congested. It's just not possible for we beings of limited visualizing ability to mentally picture four-dimensional things. One of the more interesting aspects of the image is the ghostly transparent yellowish rings that are projected on the venitian- blind background of the bud slits. But strangely enough, when stretched in the proper direction, these ghostly rings prove to be quite ordinary Seahorse Valley elements. I named the image "Gateway to Infinity". The open background inspired the name. I gave the image no rating, since it is almost solely of mathematical interest. The calculation time however is very reasonable. The 24 seconds required to complete the calculation should try the patience of no one. The finished image is available as always on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With variable clouds and a temperature of 48F 9C, Thursday proved to be an ordinary day here at Fractal Central. The fractal cats must have agreed. They became so bored that they got into an overheated tussle and mouthed some disgraceful cat words at each other. My day was moderately busy, which means the day's work was up to schedule by 3pm. The next FOTD will be posted in 24 hours. Who knows what havoc we will wreak on Seahorse Valley at that time. Until then, take care, and I assume the objective world must be real because every time I open my eyes, I experience in my mind consistent visual, auditory and tactile mental images of an inde- pendently existing outer world. But what would I experience if I could directly know the thing or things that are causing those mental images to be generated? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= GatewayTo_Infinity { ; time=0:00:24.61-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=t center-mag=0/0/0.862069/1/0/6.08852815419518389 params=75/75/90/90/-0.75/0.095/0/0 float=y maxiter=6000 inside=0 logmap=yes periodicity=10 colors=000HCUIDUJEUKFULGULHUMIUOJUPKUQLUSMUSNUTOUV\ PUWQUYRUZSUYTUXUUWVUVWUUXUSWURWUQWUPWUOWUNWTMWSKWS\ JWRIWQHXPGXOFXNEXMDYMEYOEZQE_RF`TFaUFcWGdXGeZGf_Gg\ aHicHjdHkfIlgImiIojJplJqmJroJspJrqJqqJpqJpqJorJnrJ\ nrJmrJlrJlsJksJjsJisJisJhtJgtJgtJftJeuJeuJduJcuJbu\ JbvKavL`vM`vN_vOZwPZwQYwRXwSVxTXwUZvV`vWbuXduYftZh\ t_js`ksamrborcqqdsqeupfwpgyohzoiynjymkxllxkmxjnwiq\ whtwgwvfzvezvdzuczubzubztazt`zt_zsZzsYzsXzrWzrVzrU\ zqTzqSzqRzpQzpQzpPzoOzoNzoMznLznKznJzmIzmHzmGzlFzl\ EzmCzlEvkFrjHmjIhiKchLZhMUgOPfPLfRNeSOdTPcVRa_S_cU\ YhVWmWUrYSwZQz_OzaMzbKzdMzeOzfQzhSziWzjYzj_zkazkcz\ kezlgzlizmkzmmzmoznqznszotzouzpvzpwzpxzqyzqzzrzzrz\ zszzrzzqzzqzzpzzpzzozznzznzzmzzlzzmzzmzzmzzmzznzzn\ zznzznzzozzozzozzozzpzzpzzpzzpzzqzzqzzqzzqzzrzzrzz\ rzzrzzszzszzszzszzszzrzzrzzrzzrzzrzzrzzrzzrzzrzzrz\ zrzzrzzrzzrzzrzzqzzqzzqzz } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 09-01-08 (In a Hidden Valley [7])
by Jim Muth 10 Jan '08

10 Jan '08

FOTD -- January 09, 2008 (Rating 7) Fractal visionaries and enthusiasts: In keeping with the January theme, today's fractal takes us to a valley of the Mandelbrot set. It is not Seahorse Valley, but rather the inside of the east branch of the valley enclosing the large southern period-3 bud. This valley has a name, though at the moment I cannot remember the name. The image has a maxiter of 200,000, and a logmap value of minus 31,250, but thanks to the speeded-up type=mandel formula and the efficiency with which the P2000 unit handles the speeded-up for- mula, today's image calculates in just a few seconds more than a minute. Coloring today's image presented a bit of a problem. With the logmap turned off, the image was too chaotic to be useful, while with a positive logmap value, the iteration bands were squeezed too far toward the low end. The negative value works reasonably well however, though even in this case, the bands are squeezed a bit too far toward the high end. With nothing of exceptional interest in the image, I rated it at a 7. The name "In a Hidden Valley" is not only poetic but describes the location of the image. The calculation time of just over one minute on my fireball computer is quite reason- able, but could easily leap to an hour or more on an older machine. All problems may be avoided however by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Incredibly spring-like weather in midwinter continued here at Fractal Central on Tuesday as the temperature reached 70F 21C along with bright sun and gentle breezes. The fractal cats noticed the pleasant conditions, then rolled over and went back to sleep. My day was busier than expected, but nowhere near hectic. The next FOTD will be posted in 24 hours. Until then, take care, and science assumes that the physical world is real, and science works very well, so why then do philosophers keep discussing the nature of reality? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= In_a_Hidden_Valley { ; time=0:01:11.30-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.1197639246212\ 321/-0.6496272393531843/3.787523e+010/1/168.5/0 params=0/0 float=y maxiter=200000 inside=0 logmap=-31250 periodicity=10 colors=000_Yzj9MhANgAOfAPeAQdARcASbBSacz`cz_BVZBWY\ BXXBXZmz_IX`LXbOX000dUXfXXUWXhcXjfXk`XllXnoXorXpzX\ nrZmo`klbjjchgegdgebhd_jbXlaVm_SoZPqYNrXJiWFaVCTU8\ LT5Dl0yoAtrJouSkvPlvMmvJnwGowDowApx7qq4rt1rqChjT_c\ XRXZIzzUvwAmpAdlAZgBTaBTYBTVCURCUOCUKDUHDVDDVAEV6E\ V3EW4GX5HY6JZ7K_8M`9NaAPbBQcCSdKTeUVfUWgUYg_Zh_XiU\ WiUVjDUjCTkBSkARl9Pl8Om7Nr6Mv5Lz4Kz3Jz2Iv5Jr7Jm9Kh\ CKcEL_GLXJLULMSNMPQNMSNKUNPWJUXGYZDb_9ga6kb3la7l`A\ l_El_HlZKlYOlXRmXVmWYmV`mUdmUgmTkmSnmSq_`hMi_8qSFm\ TMiTSfUZcUecUkcVrcVxcVscYnc_icadcc_cfVchQcjLclGcnI\ coJcoKcpLhpNmqOrqPwrQxrRyrxzCtzDpzElzEizFezGazGZzH\ VzHRzIOzJKzJGzKDzKCzJCzIBzHBzGBzGPzaazvbzvazt`zs`z\ q_zpZznZzmWzlUzlRzlPzlMzlKzlHzdFzYDzRBzK9zDNzF_zHl\ zJyzLxzKxzKxzKxzKxzKxzKxzKwzKwzKwzKwzKwzKwzKwzKwzK\ pzHizEbzBWz8Pz5Iz2ezvcztazs`zrRzfHzW7zL8zR9zW9z`Az\ eAzjHzeNzaTzY_zTezPjzQjzO } END PARAMETER FILE=========================================

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FOTD 10-01-08 (Faster Than Light [No Rating])
by Jim Muth 10 Jan '08

10 Jan '08

FOTD -- January 10, 2008 (No Rating) Fractal visionaries and enthusiasts: Today we take a brief break from the Seahorse Valley theme of January to focus on the north bud of the M-set. The fractal is actually faster than light, calculating as it does in less than 3 seconds, in fact in less time than it takes the video to switch to 600x480x256. This is obviously why I named it "faster Than Light". The image is a scene near a larger minibrot in a spiral on the southwest shore of the large period-3 north bud of the Mandel- brot set. I found it in utmost haste, and for this reason I could not give it a rating. But it's kind of something new in the conventional math range of the type=mandel formula, and worth the couple seconds required to run the included parameter file. The image may be seen by running the parameter file or by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is or soon will be posted. High winds up to 60mph, 90kph raked the Fractal Central area Wednesday morning, but passed over with no damage. The wind kept the fractal cats a bit skittish until it died down in the afternoon. Otherwise it was a pleasantly sunny day with a temperature of 54F 12C. My day was busy. Thankfully, the fractal is the fastest in many days. The next FOTD fractal will appear here in 24 hours. Until then, take care, and of course the world is real . . . I think . . . Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Faster_Than_Light { ; time=0:00:02.93-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.2030651182443\ 4/+0.676851836106241/7.8e+010/1/-108.5/0 params=0/0 float=y maxiter=3000 bailout=9 inside=0 logmap=671 colors=000cUZcU_cU_cU_cUZcUZcUZcV_dW`fXahYZjZXl_Un\ _Sp`QraOtaLvbIxcFycDwaEu_FsYGrWGpUHnSIlQJkPJgNLdMM\ aLNZKOVIPSHQPGRMFSIDTFGUCJV9MWHPXPSXXVX_YTb`PddMgg\ IjdEl`BoX7rT3tQ0sN1rL2qJ2pH3oF3nD4mB4l95k75j76iK6i\ MKiMZgQaeSdcUgaWjZYhW_fTZdQYbNX_KYYH`WV`UX`OXbIacC\ de6gf0gh2ei4cj6ak7_m9YnBWoCUpESrGQsHOtJMuLKvMMwNOw\ NQwNSwOUwOWwOXwPZwP`wPbwQdwQfwQgwQhrOhmNhhMhcLh_Kh\ VIhQHhLGhGFhCEiFGiIIjLKjOMkRNkUPlWRlZTmaUmdWngYnj_\ nl`qhYseVubSwZPvUNuPKtKNsFPrASq5Up7So8Qm9OjAMgCLdD\ JaEHZFFWGKTIPQJSNKVKLYIM`NOcSQfUSi_UlcTraUq`SnYQkW\ NhTMdQM`NMXLLUIKQFJMCFIAAF9BM8JT8R_7Zf7am7nfz9AzO9\ za85o8DpCKqGSrKZsOftSmuWzzUnqSooQzzPpkNpiLqgKqeIrc\ GrbFmcGhhHcmI_rJdvAiz2IzYUzPdzGezNezUez`ezfXzXPzOH\ zE9z5Ez9JzDNzHSzLXzP`zTezXjz`nzctzfozdjzcfzaaz`YzZ\ TzYPzXKzYFzY6zSAzZizFdzI_zKVzNQzPLzSGzUBzXRzeLzcGz\ aBz_OzkJzgFzdAzauzvGzWEzY } END PARAMETER FILE=========================================

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FOTD 06-01-08 (This is not a Julia Set [No Rating])
by Jim Muth 08 Jan '08

08 Jan '08

FOTD -- January 06, 2008 (No Rating) Fractal visionaries and enthusiasts: The FOTD is late today because I was volunteered for a trip to view old junk at a remote antique mall on Saturday. Today's image is a scene in Seahorse Valley. But it is not a miniature Julia set. Nor is it a miniature Mandelbrot set, nor an Elliptic set, nor a Rectangular set, nor a Parabolic set. It does come within 1-tenth of a degree of being a miniature Oblate set however. (There are six independent kinds of sets in the Julibrot because in four-dimensional space there are six mutu- ally perpendicular planes through a single point.) Also, the Seahorse Valley in which today's image lies is not the main one of the M-set. It is the Seahorse Valley of the large minibrot at -1.75 on the negative X-axis of the M-set. An Oblate set is a slice through the four-dimensional Z^2+C Julibrot figure in the plane determined by the imag(c) and real(z) axes. The miniatures in Oblate sets can be shaped like anything but miniature Mandelbrot sets. They often take the form of Julia sets, but just as often do entirely their own thing, making figures that could never be found in a Julia set or the classic Mandelbrot set, (though I have seen Oblate-type miniatures in perturbed Mandelbrot sets). To visualize the location of today's image, start at the point at -1.768... of the M-set as being centered on the screen. This is the point where the two branches of Seahorse Valley meet. Then imagine the entire 4-D Julibrot in which the valley lies as being rotated so that the real(z) axis is perpendicular to the screen. The object in today's image then lies about 6 inches behind the point on the screen and is being viewed from the left. The object in question is not artistically very attractive, but it does show that Seahorse Valley, the FOTD theme for January, has more potential than can even be imagined. I gave the image no rating, though I did name it "This is not a Julia Set", a fact that is immediately apparent. The calculation time of 36 seconds is brief enough to inconven- ience no one. And as always, those who would rather download than render may do so at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed image is or soon will be posted. Milder temperatures arrived here at Fractal Central on Saturday, but so did clouds, and in the evening, rain. The fractal cats made the best of conditionss by sleeping most of the day, while FL and I spent most of the day down in Dillsburg. The next FOTD will appear in 8 hours. Until then, take care and stay with it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ThisIsNotAJuliaSet { ; time=0:00:36.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=-0.00210532115066575/+0.525784551738717\ 90/121.4231/2.0567/90/3.88578058618804789e-016 params=0.1/90/0/90/-1.76852957968/0/0/0 float=y maxiter=10000 inside=0 logmap=11 periodicity=10 colors=000JGCHDBGB9E98D77G89I9BKADNBFPCHRDJUELWFNY\ FO_IN`LNbONcRNeUNfXMh_MibMkeMlhMojKmkMlkOklQjlRilT\ hmVfmXenYdn_cnacobcodcpfcphcpicqkcrmcspctncsmcslcr\ kcqjcoicmhckgcifcgecedccccbccacc`bc_acZ`cY_cXYaWW`\ WX_WXZVXYUXXTXWSXVRXVQXUPWTOVSNURNTQMSPKROIQOGPNGP\ MFOLFNKFMJFLIFKLFKNFKPFMRFOSEPUDQWCRYASZ8T`6Ub4Vd2\ We0Xb3Y`5ZZ7_X9`UBaSDbQFcOHdLKeJMfHOgFQhCSiAUj8Wk6\ Yl1Tl4_m6em9lmBrmGpjLohQnfPhpSkjVmdYoZ`qTcsOdpRdnT\ dlVdiXdgZde`dcbd`cdZcdXcdUcdScdQcdOcdLcdJcdHcdFcfG\ cgHciIcjKclLbmN_oNWqPSsQNuSJwUFyVBzY5zW6yV7xU8wS8v\ Q9uNAtLBsJBrICqHDpGDoEEnDFmCGlBGkAHj8Ii7Jh6Jg5Kf4L\ e4Hd3Kc3Kb3Ka3K`3K_3KZ2KY2KX2KW2KV2KU0KT2KV4KX6KZ8\ K_AKaCKcEKeGKfIKhKKjMKlOKmQKoSKqUKrUKrUKrUKrUKrUKo\ TKmRKjOKhMJeKIcIE`GAZE7MPQ6Yi9_gB`fEaeGbdJdbLeaOf`\ Hb_Me_Qg_Ui_Zk_bm_fo_ltajq_hoZgmXejWchUbfT`dSZaQY_\ PWYNVWMTTLRRJQPIOMGMKFLIE } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 08-01-08 (The Center of it All [8])
by Jim Muth 07 Jan '08

07 Jan '08

FOTD -- January 08, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's agonizingly slow fractal is a dive down to the minibrot lurking invisibly at the center of yesterday's image. Today's image might or might not be worth the effort of calculating it, but it is certainly worth the effort of visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is posted already rendered for hedonistic instant gratification. The rating of an 8 might have been an 8-1/2 if I had given a little more attention to the colors instead of enjoying the good weather. The name "The Center of it All" needs no explanation. The slowness of the image is due to its extreme magnitude, which requires the much slower arbitrary precision math, and also the fact that the single-pass method must be used to avoid missing a good part of the fine details surrounding the circular central mass of color. ---------------------------------------------------------------- A record-setting temperature of 68F 20C accompanied by full sun made Monday a day to be remembered here at Fractal Central. The fractal cats must have agreed, for they forsook their heat sources and spent the day by the window, which was open for the first time in months to save fuel by letting the warm air inside. My day was notably lazy. The next FOTD is due in 24 hours, and with any luck at all it will appear on schedule. Until then, take care, and how long must we wait before the much-ballyhooed theory of (almost) everything is finally ready for consumption by the eager public? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheCenterOf_It_All { ; time=2:01:55.29-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=0.321914508767132354909185/-0.035213130\ 684051331828963/2.098351e+019/1/80/1.4033219031261\ 9787e-013 params=0/0 float=y maxiter=32767 inside=0 logmap=5693 periodicity=10 colors=000G6JISHB_ClwQkpWkiajbgjWmkXokXpkXrkYskYuk\ YvkYwfUubQtE6NIBRLFUOKYSO`VTdYXgSYdNZaHZ_C_X6`U1`S\ 9aNGbIScEafOkiXtkeynnzpwxmvtjvkgvgdvZbvY`pTZjTXdOV\ _OTUOROOPIONDPPEQRFRSFSUGTWHUXHVZIV_IUcPTfWSjbRmiQ\ poTlkWhgYdc``_bXX`RW_MWZHWXBVW6VV1VT9WSGXQNYPVZNa_\ Mh`LoaPmdSlgWkjZjlbhoegrifulewk`skWpjRljNiiIfiDbh8\ _h4Xe4Wb4VRTIGq6HnHIlSIjbJhmJfxLbqNZjOVdQRYRNSZkZ7\ _RWYfsWuS76LF4FM38T22_1KOBaCLr0Uj7YcEaXKePRhIXlBcp\ 4is9cjEYbJSVOMNSHFOMGLRHIWHF`ICeJ9jJ8iL7iM6iN6mOD`\ LKTIRKFYCCw4AfCIiJQlQXoXdrclujsir1dj6`bBWVGSNKJJlH\ GkGEjFCiE9hD7gC5fB3eJBcQIaZR_fZYogWztU_SU000oQz4A0\ 6IU8JZAOmCXzEezFkzEXWDSAxhl`XUEMCHTKJ_SMf_OmfUkY_i\ Pzgareejefjeceec_eFXeHUeJReKV2DAoBEfLHZVLRcOJmRBvU\ InXOf_U_b`SefKglD`kMVkUPjaJjiGzgEzfCzdAzc8zb9ze9zg\ AziAzkAzmBzoBzqBzsezr_zoUzlPzjJzgEze8zb3z`CzbKzcTz\ d`zfizgqzhozamzWkzQizKPzN } END PARAMETER FILE=========================================

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FOTD 06-01-08 (The Center of it All [8])
by Jim Muth 07 Jan '08

07 Jan '08

FOTD -- January 08, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's agonizingly slow fractal is a dive down to the minibrot lurking invisibly at the center of yesterday's image. Today's image might or might not be worth the effort of calculating it, but it is certainly worth the effort of visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is posted already rendered for hedonistic instant gratification. The rating of an 8 might have been an 8-1/2 if I had given a little more attention to the colors instead of enjoying the good weather. The name "The Center of it All" needs no explanation. The slowness of the image is due to its extreme magnitude, which requires the much slower arbitrary precision math, and also the fact that the single-pass method must be used to avoid missing a good part of the fine details surrounding the circular central mass of color. ---------------------------------------------------------------- A record-setting temperature of 68F 20C accompanied by full sun made Monday a day to be remembered here at Fractal Central. The fractal cats must have agreed, for they forsook their heat sources and spent the day by the window, which was open for the first time in months to save fuel by letting the warm air inside. My day was notably lazy. The next FOTD is due in 24 hours, and with any luck at all it will appear on schedule. Until then, take care, and how long must we wait before the much-ballyhooed theory of (almost) everything is finally ready for consumption by the eager public? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheCenterOf_It_All { ; time=2:01:55.29-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=0.321914508767132354909185/-0.035213130\ 684051331828963/2.098351e+019/1/80/1.4033219031261\ 9787e-013 params=0/0 float=y maxiter=32767 inside=0 logmap=5693 periodicity=10 colors=000G6JISHB_ClwQkpWkiajbgjWmkXokXpkXrkYskYuk\ YvkYwfUubQtE6NIBRLFUOKYSO`VTdYXgSYdNZaHZ_C_X6`U1`S\ 9aNGbIScEafOkiXtkeynnzpwxmvtjvkgvgdvZbvY`pTZjTXdOV\ _OTUOROOPIONDPPEQRFRSFSUGTWHUXHVZIV_IUcPTfWSjbRmiQ\ poTlkWhgYdc``_bXX`RW_MWZHWXBVW6VV1VT9WSGXQNYPVZNa_\ Mh`LoaPmdSlgWkjZjlbhoegrifulewk`skWpjRljNiiIfiDbh8\ _h4Xe4Wb4VRTIGq6HnHIlSIjbJhmJfxLbqNZjOVdQRYRNSZkZ7\ _RWYfsWuS76LF4FM38T22_1KOBaCLr0Uj7YcEaXKePRhIXlBcp\ 4is9cjEYbJSVOMNSHFOMGLRHIWHF`ICeJ9jJ8iL7iM6iN6mOD`\ LKTIRKFYCCw4AfCIiJQlQXoXdrclujsir1dj6`bBWVGSNKJJlH\ GkGEjFCiE9hD7gC5fB3eJBcQIaZR_fZYogWztU_SU000oQz4A0\ 6IU8JZAOmCXzEezFkzEXWDSAxhl`XUEMCHTKJ_SMf_OmfUkY_i\ Pzgareejefjeceec_eFXeHUeJReKV2DAoBEfLHZVLRcOJmRBvU\ InXOf_U_b`SefKglD`kMVkUPjaJjiGzgEzfCzdAzc8zb9ze9zg\ AziAzkAzmBzoBzqBzsezr_zoUzlPzjJzgEze8zb3z`CzbKzcTz\ d`zfizgqzhozamzWkzQizKPzN } END PARAMETER FILE=========================================

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