June 2008 - Fractint - mailman.xmission.com

FOTD 21-06-08 (In Alien Territory [5])
by Jim Muth 21 Jun '08

21 Jun '08

FOTD -- June 21, 2008 (Rating 5) Fractal visionaries and enthusiasts: Wow! What a fractal! Talk about over-qualified! This is one of the most bombastic fractal images I have ever seen. It has no idea where to stop. The super-abundance of detail is so overdone that it actually detracts from the rating, which I could set at no more than a 5. The image is a scene in the Mandelbrot aspect of the East Valley of the same parent Julibrot that has supplied the past two days' images. I named the image "In Alien Territory", though I'm not sure where this alien territory is found. I used no gimmicks to produce the overwhelming detail in the image, which was rendered with the inside set to the color zero and the outside set to display equal-iteration bands. All the excitement lies in the numbers of the image itself. The calculation time of just over 3 minutes should give no one a case of impatience. And for even more convenience, the finished image is or soon will be posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A routinely pleasant day prevailed here at Fractal Central on Friday, with partly cloudy skies and a temperature of 77F 25C. The fractal cats noticed the conditions, then continued eating their dinner. My day was once again busier than I would have preferred, but not so busy as to affect the attention I gave to the FOTD, which failed to fulfill my hopes on its own account. The next FOTD is due to be posted in 24 hours. Until then, take care, and look before you iterate. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= In_Alien_Territory { ; time=0:03:10.62-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotMiN passes=1 float=y center-mag=+0.257194485268014/-0.0087089105892888/\ 3.721816e+008/1/-22.5/0 params=2.01/0/0/0/0/0 maxiter=2700 inside=0 logmap=297 periodicity=10 colors=000Zz0cz0hz0mz0rz0vz0zz0zz0zt0zt0zt0Ht0Kp0P\ p0Yp0dp0ip0Pt0Ct03t30tC0tI0zI0zI0zI0zI0zI0zI0zI0tI\ 0pI0iI0dI0YI0UI0PI0RI0UI0YI0`I0dI0hI0bI0YI0TI0PI0L\ I0II0FI0CI00I00I00I00I00I00I00I00I00I00I00J00K00L0\ 0M00N00O00P00Q00R00S00T00U00V00W00X00Y30_90aH0cP0d\ U0dd0ii0ip0pz0pz9tzKtzYtzpzzzzzzzzzzzzzzztzzpzzizz\ dzzYzzPzzKpzHizCdz9Yz3Ut0Ut0Pp0Pp0Ki0Ki0Hd0HY0CY0C\ U09U09P05P05K03H03H00C00C00900300903C09H0HK0PU0YY0\ id0ti0zt0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0tz0pz0dz\ 0Yz0Ut0Pt0Kt0Ct39p35p53p50d00p55tCCzKKzUUzddzppzzY\ zzKdz9Kz05z00z00r00r00m00m00m00h00c00c00c00c00c00c\ 30c90cC0cK0dU0dd0Yp0Uz0Pz5Pz9KzCHzHCzKCzP9zP9zP9zP\ 9zP9zU9zU9zU9zU9zU9zY9tY9pY9iY9dY9dd9Yd9Ud9Pd9Kd9H\ YCKd9Pd5Pd3Ud0Ui0Yi0di0di0ip0ip0pp0tp0tp0zt0zt0zt0\ zt0zz0zz0zz0zz0zt0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zi0 } frm:MandelbrotMiN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=(-z)^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

1 0

FOTD 20-06-08 (Independence Day [6])
by Jim Muth 20 Jun '08

20 Jun '08

FOTD -- June 20, 2008 (Rating 6) Fractal visionaries and enthusiasts: We finally have an image worth more than a rating of 5. True, the rating is only a 6, but mighty oak trees from tiny acorns grow. Who knows where this small improvement might eventually lead to. The image is a blow-up of what was barely a speck in the blank area of yesterday's image. The name "Independence Day" refers not to an invasion from space, but to the resemblance, at least in my mind, to an exploding skyrocket like those we see so many of here in the U.S. on July 4, which is Independence day. Is today's image a great fractal? No. Is there any such thing as a great fractal? Some fractal artists seem to think so, but I have yet to be convinced that any fractal could be called great. (Of course, if the multiverse can be taken as a fractal, as I suspect, then maybe there is a great fractal after all.) In contrast to yesterday's boringly slow image, today's image calculates in a little over 4 minutes. And even this short wait may be eliminated by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and seeing the semi-glorious completed image there. The cool and cloudy weather continued Thursday here at Fractal Central. The high temperature of 68F 20C felt more like April than June, while the fractal cats remained in curl-up mode. My day was less hectic than the day before, but nowhere near the easy-going type of day I prefer. The next FOTD will be posted in 24 hours. Until then, take care, and fractals are the answer. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Independence_Day { ; time=0:04:06.34-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot5 passes=1 logmap=yes center-mag=+0.2148023/-0.3043594/202.832/1.26/-55/0 params=89.995/90/89.995/90/0.25567/0.00843/0/0/2.0\ 1/0 float=y maxiter=1000 inside=253 periodicity=10 colors=000kQIlOKmMLnKNoIOvKnmGkeCiY9fQ5dI2btbpp_nm\ XliUkfRicOh_MfXJeUGcQDbNA`K8_OD`RH`VM`YQ`aV`dZ`hb`\ kg`ok`rp`vt`yx`wsaunbsjcqedpadnXelSfjOghJhgFhcHc_I\ _WJWSKROMNKNJGOECPA8Q6AP7BP7CO7DO7EN7FN7GM7HM7JL7K\ L7LK7MK7NJ7OJ7PI7QI7TJAVKDXKGZLJ`LMbMPdNSgNViOYkO`\ mPcoQfqQisRluRnRbST_UUXVWUWXRXYOY_M_`J`aGacDbdAce8\ dcAabB_aDY`EW_FTZJRYLPXMNWNKVOIUPGTQESRBRS9QT7PU5S\ T7VS8YRA_QBbPDePEhOFjNHmMIpLKsKLuKMpLNkMOfNPaNPbQQ\ cTRdWSeYTf`UgcVheWihXjkYknZlp_mr`nsaitSbrAWoEMlHHi\ KMfOQcRV`U_YYcV`hSclPfhKWeFLaAAZ60V78R8GO9NK9VHAaD\ BiABp8S`7gL6w67s68p69m6Aj6Ag6Bd6Ca6DZ6EW6ET6DVEDXL\ DZSC`_CbfCdmCftHboM_kQWgVTb_PZcMVhIRmKMqUIvcEzmAwc\ 8mU6fP5`M3VQ2UP3UO4TN5TM5TL6SK7SK7RJ8RI9RH9QGAQFBQ\ FBPDDPCEPBFPAGP8IP7JP6KP5LSDSULYWSdZ_j`gqbnwcjvdgv\ edvf`vgYvhVviSvjOvkLvlIvmFvnBvo8vp5vq2vk4of6ha7aX9\ WRBPMCIHEBCF5LJX00KJczKcz } frm:SliceJulibrot5 {; draws slices of (-Z)^n Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

2 1

FOTD 19-06-08 (Straight and Narrow [5])
by Jim Muth 19 Jun '08

19 Jun '08

FOTD -- June 19, 2008 (Rating 5) Fractal visionaries and enthusiasts: Today's FOTD is late due to a work rush. The feathery scene is an almost-Julia set of the East Valley area of the (-Z)^(2.01)+C Mandeloid. I call the image an almost- Julia set because it is oriented within 0.005 degree of being a true Julia set. I named it "Straight and Narrow" after the blue stripes running diagonally through it. The rating of a 5 seems fair enough. The image is better viewed than described. One way of viewing the scene is to start the included parameter file and wait a while. A better way is to view it in finished form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But due to the unusual hour of the posting, it might be a while before the image is posted there. Cloudy, blustery and unusually chilly weather prevailed here at Fractal Central on Wednesday. The high temperature of 68F 20C was well below normal. The fractal cats adjusted by shifting from stretched-out mode to curled-up mode. In my department, the day was very busy. And it now looks like tomorrow may be the same. Despite all this, the next FOTD will likely be posted in 24 hours. Until then, take care, and ain't fractals fun? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= StraightAndNarrow { ; time=0:27:09.25-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot5 passes=1 logmap=yes center-mag=-0.000471978/0/1.138295/1/-90/0 params=89.995/90/89.995/90/0.25567/0.00843/0/0/2.0\ 1/0 float=y maxiter=32767 inside=0 periodicity=10 colors=000KKCLLDMMENNFOOGPPHQQIRRJSSKTTLUUMVVNWWOX\ XPYYQZXHWWMUWQRVUPVYNUaKUeITiFTmDSq9OxBSuCVsDZqFao\ GdmHhkIkiKngLreMucNxaPvZRtWTsTVqRXpOZnL_mJakGciDeg\ Agd8ia5kY2lV0kZ7jbDjgKieQhjXhkbgmifnohryfoudmrckna\ ik_ggZedXb`V`YUZUSXRQVNQQLPTKOVKNXJMZJM`ILbIKdHJgH\ IiGIkGHmFGoFFqEw`5FsEItDLtDNtCQtCTtBVtBYuA_uAbu9eu\ 9gu8ju8nz5lu8kqBimEhiHfeKeaNdYQbTTaPW_LZZHaXDdW9gS\ 0lV5jXAiZEhaJfcNeeSdgWccR__NWWITSEPO9MK5IF0DH1FJ2H\ L3JN4LP5MR6OT7QV7SX8UZ9V`AXbBZdC`fDbhDcjAnk8xhArfC\ lcEgaGaZIWXKRUMLSNGPRBTPFWOJZNNbMQeLUhKYlJ`oIdrHhu\ 9wuGkuN_uUOtb4u`CvZKwXSxV_yTgzRozPwyOvyNuyMtxLtxKs\ xJswItwHuwGvvFwvExvDyuCzuBzuAzu9zb_zK`zLazMbzMczNc\ zOczOczPZzQZzNZzQZzSZzUZzWZzYZz_ZzaZz_ZzYZzWZzVZzT\ ZzRZzPZzOZzMZzKZzKZzJZzIZzHZzGhzFhzEhzDhzBhzDhzEhz\ FhzGhzHhzIhzJhzLhzMhzNhzOhzPhzQhzThzRhzQhzPhzOhzNh\ zMhzLhzKhzJhzHhzIhzJhzKhz } frm:SliceJulibrot5 {; draws slices of (-Z)^n Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

1 0

FOTD for June 19 to be delayed
by Jim Muth 19 Jun '08

19 Jun '08

>Fractal visionaries and enthusiasts: Due to the expected unexpected rush, the FOTD for June 19 will actually be posted on June 19 instead of late on June 18. Jim Muth

1 0

FOTD 18-06-08 (Portal to Infinity [5])
by Jim Muth 18 Jun '08

18 Jun '08

FOTD -- June 18, 2008 (Rating 5) Fractal visionaries and enthusiasts: I seem to be in one of those occasional fractal ruts, where I just can't seem to come up with a fractal that meets even my lowly standards of fractal worth. Yesterday's image was probably the least impressive FOTD of the past 11 years, and that's talking about a lot of fractals. Today's image is a small bit of an improvement. It is a view of Seahorse Valley, a slit view that I can virtually guarantee has never before been seen. The view is almost in the Rectangular direction, oriented so close to it that it was necessary to stretch the scene about 75 times in the vertical direction before the remnant of Seahorse Valley became recognizable. (The rectangular orientation is determined by the imag(z) and imag(c) axes of the Julibrot.) Where is the rest of the Mandelbrot set? This is a question I cannot answer. It is probably off somewhere, a lost potentia in a space of five or more dimensions, making the quest absolutely futile. I have been trying unsuccessfully for 20 years or so to visualize something with only four spatial dimensions, so far without success. Apparently I need to have my consciousness expanded before higher-dimensional awarenedd becomes possible. Maybe the local mystic, Madam Zucchini, can be of help. I named today's image "Portal to Infinity" and rated it at a 5. The calculation time of under 2 minutes should cause no hardships. And to be doubly sure no hardships are incurred, the completed GIF image has been posted for instant viewing and enjoyment on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A very pleasant and refreshing day here at Fractal Central on Tuesday, with a temperature of 72F 22C, was made even fresher by a quick shower that passed over at 6pm, followed by a brilliant rainbow in the east. The fractal cats, not appreciating the small pleasures of nature, slept through it all. My day was busier than I would have preferred, but much better than yesterday, when I posted a hasty fractal that virtually duplicated and was a poor imitation of the not-all-that-great image of the day before. The current work rush has about ended however, so tomorrow's FOTD, which will appear in the usual 24 hours, will likely be a vast improvement over today's. Until then, take care, and walk with the fractal elite. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Portal_to_Infinity { ; time=0:01:51.10-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=0/0\ /33.52388/0.01407/90/0 params=89/88/0/90/-0.75/0/0\ /0 float=y maxiter=3600 inside=0 periodicity=10 colors=000JEYKGaLIfMJjNLoONsOOwRNtUNrLEDLDDLCCLBCf\ AQgCSgETgGUgIVgKWhMYhOZhQ_hS`hUaiWciYdi_eiaficgjfk\ iehhdegdbfc_ebXdbUcaRb`Oa`L`_I_ZF_Y9ZZCY_EX`GXaIWa\ KVbMVcOUdQTeSSeUSfWRgYQh`QibPidOjfNkhNljMmlLmnLnpK\ orJptKuyJpvIlsHhpGcnG_kFWhERfDNcDJ`CEZBAWA6TA2RD5U\ F7XH9_KCbMEeOGhXFjeElnDmkGjhIheKfbNd_PbXR`UUZRWXOY\ VL`TIbRGdPHeQIeQIeQJeQKeRKeRLeRMfRMfRNfSOfSOfSPfSQ\ fTQfTRgTSgTSgTTgUUgUUgWVg_VgcWigXkkYmoZosZnrZlqZjp\ ZgpZeoZcnZamZ_lZYkZVkZTjZRiZPhZNgZLg`KeaKdbJbcJadI\ _eIZfIXgHWhHUiGTkGRlFQmFOnFNoELpEKqDIrDHsCFtCEuCDu\ JGuQJuXMucPujSupUtnTslSrjRqhRpfQodPnbOnaOm_NlYMkWL\ jULiSKhQJhPJiNIjLHkJGoKAmJDkIFjHIhGKgGNeFPcESbDU`D\ X_CZYBaWAcVAfT9hS8kQ7mP7oR9nTAmUClWDlYEkZGj`HibIic\ KheLgfNfhOfjPekRdmScoTcpVbrWavT_tV`sXarYbq_cpadobe\ ndfmfglghkiijkjilkhnlgpmfqnesodupaywbwtcvqdtneskfq\ hfpegnbhm`ilYjjVjiSkgPlfM } 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=========================================

1 0

FOTD 17-06-08 (Oblate Figure [5])
by Jim Muth 17 Jun '08

17 Jun '08

FOTD -- June 17, 2008 (Rating 5) Fractal visionaries and enthusiasts: Today's FOTD is late. My excuse -- too much work rush to finish the FOTD on time. Mandelbrot midgets are instantly recognizable. Julia midgets are more varied, but are almost as easily recognized. But what of the midgets in the other four planes of the Julibrot? Do they have certain characteristics that can instantly be recognized? Well, all the odd midgets resemble Julia midgets to some degree, but I can recognize certain Oblate features. Today's image, which lies in the Julibrot part of the second valley beyond Scepter Valley, is an Oblate figure, which explains the name "Oblate Figure". I rated the image at a 5. I have probably posted similar images in years past. The calculation time of 10 minutes is deceiving. About 90 percent of the total time is spent calculating the single center line, which lies along the real Z axis, and is actually the tiny space between the two branches of the valley. But why worry with slow center lines? Go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the totally finished image there. A warm muggy day here at Fractal Central on Monday turned quite pleasant when a mild thunder-shower arrived in the afternoon, dropping the temperature from 86F 30C to 64F 18C. The fractal cats enjoyed the refreshing change. My day turned more pleasant in the evening when the work was finished. It's too bad the hurried fractal left much to be desired. The next fractal, however good or bad, will be posted in 24 hours. Until then, take care, and be at peace. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Oblate_Figure { ; time=0:10:33.29-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=Oblate passes=1 center-mag=+0.00449922\ 471287127/+0/113.4132/1.3729 params=-1.39404628522\ /0/-1.39404628522/0 float=y maxiter=350000 inside=0 outside=tdis logmap=17 symmetry=xaxis periodicity=10 colors=000JikImlHqlGnkGkjGhiFehFbgF_fFXfEUeERdEOcD\ LbDIaDF`DD`EC_FC_FB_GB_GAZHAZH9ZI9ZI8YJ8YK7YK7YL6X\ L6XM5XM5XN4WN4WO3WO3WP4VQ5VR6VS6UT7UU8UV8TW9TXATXA\ SYBSZCS_CR`DRaERbEQcFQdGQ`9AdGQjMflKemIdoGcpEbqCas\ A`t8_u6Zw4Yx2Xy0Wx6axCfwHkwNpwSutVqrYnp_jnbglddjg`\ giYelUcnRaqO_sKYvHWxEXxGYxHYxJZxK_xM_xN`xPaxQaxSbx\ TcxVcxWdxYexZex`fxagxcgxdhxfixgixhgviftidricpianj`\ ljZjjYhjWgjVekTckSakQ_kPYlNWlMUlKSlJRlWVUTXRQ_NObK\ LeGJhDGk9Dn2Em6ElAEkEFjIFiMFhQFgUGfYGeaGdeGciHbmHa\ qH`uH_xJ0tI3qI5oI7mI9jIBhIDfIFcHHaHJ_HLXHNVHQTHSQH\ UOGWMGYJG_HGaFGcCGeAGg8MV9Gi6Bz4Ax39w39u38t38r37q3\ 6p36n35m35k34j33i33g32f32d31c31b36eBBgJFiQKkYRrgOm\ dLibId_F`YCWV5PUASTEUTIWTNYTR_TVaT_cTceTggTehSdhRc\ iQaiP`jO_jNYkMXkLWlKUlJTlISmHQmGPnFOnEMoDLoCKpBIpA\ Hq9Gq8Fq7Gp9GoBGnDHmFHlHHkJIkLIjNIiPIhRJgTJfVJeXKe\ ZKd`KcbLbdLafL`hL`iKej000 } frm:Oblate {; Jim Muth real(z),imag(c) z=real(pixel)+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================

1 0

FOTD 16-06-08 (Royal Scepters [5])
by Jim Muth 16 Jun '08

16 Jun '08

FOTD -- June 16, 2008 (Rating 5) Fractal visionaries and enthusiasts: Yesterday's fractal showed a little-known scene in the Oblate view of Seahorse Valley. Today's fractal does the same with the next valley out the negative X-axis of the Mandelbrot set, the valley at -1.25, also known as Scepter Valley. I named the image "Royal Scepters" because it is filled with the scepter-like elements that give the valley its name. When the time came to rate the image, I could grant it a rating no higher than a humdrum 5. Just as was the case with yesterday's image, I suspect I have already posted at least one FOTD image nearly identical to today's. In addition to the less-than-outstanding rating of today's image, its calculation time is a snail's pace near-19 minutes. No wonder I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> And BTW, the 'Oblate' sets are the set of planes determined by the real(Z) and imag(C) axes of the Julibrot. They are kind of hybrids, half Mandelbrot, half Julia, though in today's image at least, the Julia characteristics appear to dominate. Near perfect weather prevailed here at Fractal Central on Sunday, with blue skies, puffy white clouds, and a temperature of 86F 30C. The fractal cats must have taken the good weather for granted, as they slept through most of the afternoon. I tried to enjoy things as much as possible, though yard work always seems to prevent a day from being as pleasant as it otherwise could be. The next fractal will be posted in 24 hours, more or less. Until then, take care, and they say that God knows everything. Why then, does He bother to create souls that He already knows are destined to be lost? Another question: what could a person do to save himself if he discovers that God knows he is destined to be lost? (Or is this just another version of the grandfather paradox?) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Royal_Scepters { ; time=0:18:51.52-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=Oblate passes=1 center-mag=-1.70684/0/\ 48.56702/2.774 params=0/0/-1.25/0 float=y maxiter=1750000 inside=255 outside=tdis logmap=4 symmetry=xaxis periodicity=10 colors=000BEf8Ff5Gf3GfEOiPVl_aojhrd`m_UiUNePF`J8XE\ 1TK7OQDKWJGi6Kn2NpBSrJWtR_vZcxfgynkvomtpnrqopqpnrq\ lsrjtshttfupevmdwjqxlqylqzkpzkpzkpzkozkozjozjnzjnz\ jnzjozkpzlqzltzmuzlvzlwzmxznyznzzozzpzzWzzWzzXzzXz\ zXzzYzzYzzYzzZzzZzzZzz_zz_zz_zz`zz`zz`zzazzazzbWRt\ WPsXNsXLrYJrYHqYFq_GnaHkcIheJfgKciL`kLZiM`hMagMbfM\ ceMddNfcNgbNhaNi`Nj_Nk`PiaRgbTfcVddWbeYae__faYgcXh\ dVifUjhSjjQklPlmNmoLnqKosIotHmrGlqGjoGinGglGfkFeiF\ chFbfF`eF_dFZbEXaEW_EUZETXESWDQUDPTDNRDMQDLPDPNFTM\ HWLJ_KLcJNfIOjHQnGSqFUuEWxDXoKUfQSYXQQbOHiM8oK0uI1\ vG1wE1wC2xA2x82y62y52q62j72b82W92OA2HB2AC6CFADHEEJ\ IFLMGNQHPUIRYJTaKVeLXhMZeLabKc`JeYIgWHiTGkQFmOEoLD\ qJCsGBuEBwDDsCFpBHlAJi9Le9Nb8PZ7RW6TS5VP4XL4ZI5`K5\ aL6cN6dO6eQ7gR7hS7iU8kV8lX9nY9o_9p`AraAscAtdBvfBwg\ BxhAvaAtVArO9pH9nA9l4Cm8EmBHnFJnIMnLOoPRoSTpWWpZYp\ a`qebqhdqkbjl`dl_YlYSlWMl } frm:Oblate {; Jim Muth real(z),imag(c) z=real(pixel)+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================

1 0

FOTD 15-06-08 (A Pale Seahorse [5])
by Jim Muth 15 Jun '08

15 Jun '08

FOTD -- June 15, 2008 (Rating 5) Fractal visionaries and enthusiasts: I named today's image "A Pale Seahorse" and rated it at a 5. The unimpressive rating is due to the fact that I might have posted a couple very similar images during the long history of the FOTD. The name refers to the rather pale interior of the image, as well as the fact that it is an unfamiliar view (part of the Oblate view) of Seahorse Valley. Due to the extreme maxiter, the only way to color the image effectively was to use both the logmap and 'tdis' options. To give optimal proportions, it was necessary to compress the scene slightly in the vertical direction. The calculation time of 2-3/4 minutes is fair enough for most fractalists. And if the included parameter file fights back on an over-qualified machine, the finished image is easily viewed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Lots of haze, clouds and high humidity made Saturday less than ideal here at Fractal Central. The high temperature of 88F 31C made things even worse. The rain threatened but never arrived. The fractal cats mostly ignored the outside conditions, but they did watch carefully as a chipmunk scurried about in the grass, stuffing his face with who knows what. My day was un-notable and I expect tomorrow to be the same. The next FOTD will be posted in 24 hours. Until then, take care, and use it, whatever it is, to the utmost. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Pale_Seahorse { ; time=0:02:42.22-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=-1.4048/0/7.48356/1.7871 params=0/0/90/0/-0.75/0/0/0 float=y maxiter=300000 inside=255 outside=tdis logmap=4 symmetry=xaxis periodicity=10 colors=000GX7GV7GS7IP7IN7IL7JI7JG7JE5LA5L95L75N35N\ 15N05N05S3AZ9GbCLhIPmLVqR`xVdz`jzdozjtzmzztzzxzztz\ zoqzlhzh`zdRx`JqXAmS3hP0dL0`J0XN0VR0SS0PX5N`ALbGIf\ NGjSElZAof9tl7vq3zz1zz0zz5zz9zzCzzIxzLvzPtzVqzZozb\ mxhlvljtohtvfqzdozbozZtvVvqRxoNzlJzhGzdCzb9zZ5zV1z\ R0zP0zS0zX1zZ3zb5zd7zh9zi9zjAzkBznDzqFzrHzuLzwPzyT\ zzXzz`zzdzxgzxhxxgtxgoxelxchzbbzaZzaSzbPzdLzfGzhCz\ j7zl3zl0zj7zhEzfLqdSjb```hRZoIXxAXzL`vVdodhjmjdzmX\ zqRzvLzxGzzJzzNzzRzzSzzXvz`qzblzffzj`zmXzoRztLzxIz\ zNzzRzzXmz``zfPzjCzo1zt0zx0zo5zhVz`xzVzxPzmLzfGzXC\ zPL00E0090310700C00G00J00L01N7CPENRN`SVlVdxXlzZtzZ\ zzdzzjtzoSzt3zx0zzSLzXJz`JzdJzhIzlIzoIzqIzV7z90z00\ zXEfVIjVLmSNqSRvRVzRXzR`zPdzPfzNjzNmzNoz9xx0z`0zE0\ zI0zJ0zL0zP0zR0xS0tX0qZ0o`0md0lf0jh0hj0db0`V5XNASG\ IP9NL1SI0ZE0dC0hG0jI0lJ0mL3qN9tPEvRIxSNzVSzXZzZdz`\ jzbmPNdJIREEEAA1CJ5ES7E`9 } 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=========================================

1 0

FOTD 14-06-08 (The Bug-Eyed Tree [6])
by Jim Muth 14 Jun '08

14 Jun '08

FOTD -- June 14, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's strange image shows a kilroy-like alien head peering over the bottom of the frame. The top part of the image shows fractal stuff on the way to becoming a fractal tree. Combining both, I named the image "The Bug-Eyed Tree". The image is actually a near-Julia set of the (-Z)^sqrt(2)+C Julibrot. Actually, the slice is oriented 0.02 degree from the Julia direction toward the Oblate direction. This tiny rotation is quite important. To see how important, change the real (p1) parameter to 90 and do a thumbnail fractal. I rated the image at a 6. I have seen a few too many of this type of image to rate it any higher. The calculation time of under 3-1/2 minutes is rational, for all this is worth. The finished GIF image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heat, haze and humidity moved back into the Fractal Central area on Friday. As the temperature reached 88F 31C, the fractal cats sought the cool air vent. My day was acceptable; the fractal, a bit goofy. The next fractal, goofy or not, will be posted in 24 hours. Until then, take care, and why must all space aliens have bug-eyes? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Bug-Eyed_Tree { ; time=0:03:28.90-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot5 passes=t float=y center-mag=0.190223/0/15.24794/0.8869/90/0 params=89.98/90/90/90/-1.124575/0/0/0/1.4142/0 maxiter=3600 inside=0 logmap=20 periodicity=10 colors=000KKVKKUKKTJKSIKRHKQGKPFKOEKNDKMCKLBKKAKI9\ KG8KE5KA2K73K93KB3KC3KE4KG4KH4KJ2KG4KK6KO7LS9LVBLZ\ CLbELfEHlFJjFLiFNhFPgFRfFTeFVcFVbFVaFT`FR_FQbFO`FM\ ZAKY6KW2IV4JT6KS8LRAMQCNPEOOGPNIQMKRLMSKOTGNSJNRMN\ QONPRNOTNNWNMYML`MKcMJeMIhMHjMGmGEkJFmMGoPHpSIrVJs\ SLqQMpNNnLOmIPkGQjERiBSg9Tf6Ud4Vc2Wb5Uc7ScARdCPdFN\ eHMeKKeMIfPHfRFgUDgWCgWBfWBfWBeWBeWBdWAdWAcWAcWAbW\ AbW9aW9aW9`W9`W9`NRbEgd6xfAq8Do9GmAJkBLjCOhDRfETeF\ WcGZaH``IcZJfXKhWLkUMnSNoLOpROpXOqaOqgOeOmtkMqlOol\ QmlSklUimWgmYem_bma`mcZneXngVniTnkPuvQqqRnlSjhSgcT\ c_UcVVcRVcMWcIXcDZc9`c6bb6dc6fd6gf6gg6gh6hj6hk6hl6\ in6io6ip6ns7io6di6`a5WU5PC1RI3SL5TP7VU8WYAXbCZhD_n\ F`uH_wWazKenPldUhcZdbc`ahcamf`ri_wlVzmXzn_znazoczp\ fzpizqkzrnzrpzuuzvwzzzztvzsszqovokrnhmmehmcdlbblb`\ kb_kaYjaWjaVj`Ti`Ri`Qh_Oh_MlYHjZJh_Lf`NdaPbbR`cSZd\ UXeWVfYTg_RhazYxgcmPhb3pR } frm:SliceJulibrot5 {; draws slices of (-Z)^n Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

1 0

FOTD 13-06-08 (Bat-Fractal [No Rating])
by Jim Muth 13 Jun '08

13 Jun '08

FOTD -- June 13, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's ultra-quick image is simply a new view of East Valley of the Mandelbrot set. More accurately, it's an oblique view of the East Valley complex of the Z^2+C Julibrot. I named it "Bat- Fractal" after one of my favorite comic book heroes from long ago -- Batman. The large dark bat-shaped feature dominating the image inspired the name. I particularly enjoyed the Batman stories because Batman was, and still is, a mere mortal human with finely-honed but still normal human abilities as well as vulnerabilities. I could dream that one day I might be like the Batman, while heroes like Superman and Captain Marvel were total fantasies, far beyond human attainment. I also enjoyed the Green Lantern stories, about a hero who used psychokinesis, the power of his mind, to overcome his enemies. Too bad none of these old comic heroes ever heard of fractals. Well, there's not much to be said about the appearance of today's image, except that this is how one of the four- dimensional 'bridges' of East Valley appears when stretched about 100 times in the vertical direction. Some hints of the East Valley elephants are also scattered throughout the scene, though I could find no fully formed ones. Unfortunately, the image does not earn a rating, but it still has a bit of curiosity value. And the calculation time of only 3-3/4 minutes is not at all bad. The most convenient way of enjoying the image, as always, is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it in finished form there. Near perfect conditions prevailed again on Thursday here at glorious Fractal Central. The clear skies and temperature of 84F 29C made everyone including the fractal cats happy. My day would have been a bit more pleasant if the work had been a bit lighter, but I'm not complaining. The next FOTD will appear in 24 hours. Until then, take care, and do what's right. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Bat-Fractal { ; time=0:03:37.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=+0.002707327725631/0/124.5/0.01064/-90/0 params=45/90/0/45/0.265/0/0/0 float=y maxiter=6400 inside=253 logmap=23 periodicity=10 colors=000mJKDNRH4DBCK6KRaW9otfblcQeaDYZYh7PcEH_K9\ VRDZOAXR7VT4TVRzoInh9bbvm4wQehRbUR`FRZcjRRloKfjEae\ 7W`w0t6l14f93aH2WPFkMAdQ5YU2Bt1Hl1MdmyIPgQl84`DCPI\ JDNQfsdTiaF_ZPbkHZf9VaIRMDRP9RS5RVP15DEJQvGJnLDfP7\ ZT8py5go3Ze1o11h91bH1XPpVfcUcRTaESZbaLKKuEjx9cn5Xe\ K`d2uF1jL1`RLhWbCPKcnpWLcUORTRESUh9CNINK53DDD7KNOd\ vZ7rIHgzdmj`hWYdGU`fWyWUqMTjBSc4i`3d_2_Z1VYrntdhnS\ bhEXbfSMWRPMRSBRVE9P7ITlQ3_T6ISK3T3VffGZab17KEKN9g\ CIa3Z42XC2VJ1TQp77RHKL73GCBBHI6MQpRJZROIRTA1T7AV4J\ WTCq7kQ5dT3YVDloHryBho6_e8jk4`cY1uNAlCJdJyHEpLAgP5\ ZT`F2JLIB2G7BM4JSPELHJP9NTOTjTmZJeYAYXHGIBKN6OS_RS\ ORUCRW1eBHzz9zzOzzvzzUzz2zzNzz`zzSzzJzzAzzDzzAzz7z\ z4zzFzz8zzozzyzzqzzUzzMzzFzz8zzQzzJzIDzN7zSZzqNzjC\ zcuzVLzYBzXUzvKzmAzd1zV1zWwzzUzzBz87zH4zPhzqYzkNzf\ zzwWzwXzw`zrcznfzjizfhzRhzzbzzYzzMzzBzzDzzFzzHzzIz\ zPzzVzz`zzfzzhzzM0`ozzbzz } 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=========================================

1 0