October 2011 - Fractint - mailman.xmission.com

FOTD 02-10-11 (Rectangular Reason [No Rating])
by Jim Muth 25 Oct '11

25 Oct '11

FOTD -- October 02, 2011 (No Rating) Fractal visionaries and enthusiasts: The math expression that was iterated to create today's image is Z^2+C, the same expression that gives us the well-known classic Mandelbrot set with all its perturbed sets, as well as all the Julia sets. Yet the image is clearly nothing at all like a Mandelbrot set, pure or perturbed, nor does it resemble any Julia set. This is because it is a slice through the Z^2+C Julibrot in what I call the Rectangular direction, which is defined by imag-C,imag-Z. The rectangular shape of the slice shows why I call this particular orientation the Rectangular direction, and also explains the name I gave to the image -- "Rectangular Reason". The large open area that fills a good part of the frame is a different view of the main bay of the M-set. The narrow bluish stripes running horizontally at the top and bottom of the open area are what I call 'bridges'. In this case they are sideways views of the west branches of the valleys leading to the large north and south period-3 buds of the M-set. The horizontal open areas above and below these 'bridges' are sideways views of the buds themselves. I gave no rating to the image, since almost all its interest is in its mathematics. But don't downplay the math interest. To make things much clearer than I can explain in words, gradually decrease the value of the real(p1) parameter from 90 to zero in increments. (Keep the imag(p2) parameter unchanged.) The images are very fast and the process will take little time. By the time the value is reduced to 50 the destination will be apparent. Doing a 360-degree rotation would make an interesting animation, but I doubt that I'll get the chance. (Decreasing the imag(p2) parameter of today's image to zero while leaving the real(p1) parameter unchanged brings us to the Elliptic orientation, but that's another story.) To create today's image, I oriented the 4-D Julibrot figure so that the imaginary Z-axis is perpendicular to the Mandelbrot set on the screen and ignored the parts of the Julibrot that did not fit into our 3-space, leaving an imaginary invisible 3-D slice of the Julibrot intersecting the screen. Then I rotated the screen image around the line perpendicular to the X-axis at the point -0.2. The resulting image is what would be seen by a viewer located in the plane of the screen just to the left or right of the screen when the invisible 3-D slice was sliced at the point of -0.2 on the real-C axis. All this talk does not mean the image is a slow one. In fact, it finishes in a lightning fast 5 seconds. The finished image is available on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version is available at. <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic original web site may be accessed at: <http://www.Nahee.com/FOTD/> Heavy clouds and a temperature of 50F 10C made today a day to be forgotten here at Fractal Central. The occasional showers helped none at all. And the experts assure us that more rain is on the way tomorrow. The fractal cats always live in the present, so they usually forget a day's events at the first stroke of midnight. Many humans are not so forgetful. They hold long term grudges and resentments that fester until war breaks out. FL and I fall between the cats and the long-term resenters. The next FOTD, a continuing adventure in 4-D hyperspace, will be posted in 24 hours. Until then, take care, and I just read that there is some evidence that the sub-atomic particles known as neutrinos might travel faster than the speed of light. The claim is not yet confirmed, (In fact, I doubt it), but if this proves to be true, then neutrinos can move backward in time. This would surely play havoc with our scientifically accepted ideas of an effect following its cause, but after a century of relativity and quantum mechanics, we should not be so surprised when we find one more thing that violates our common-sense view of reality. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Rectangular_Reason { ; time=0:00:05.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/0.73/1/\ 90/0 params=90/0/0/90/-0.2/0/0/0/2/0 float=y maxiter=5000 inside=0 periodicity=6 colors=000D08F09H0AK0BQ0CW0E_0Gb0Ih0Kn0Mp0Ot0Qm5Pc\ 7OU9NEJMJSMN`MSiLXrL`zPZuUYpZWkcVghTbmSYrQTvPPzOOz\ OOzNNzNNzG_zHVzIRzJMz`ezW_zSUzOOzQLzPKzOKzNJzNJzMJ\ zmIzmIzmTzmRzmPzmNzmLzmJzmdzmTzmgzmZzmQzm8zmAzmCzr\ EzrGzrxzrHzrIzrIzrIzrIzrGzrHzrHzrIzrXzrUzrSzrQzrOz\ rMzrKzrRzrPzrOzrNzrLzrKzrJzrzzrszrkzrdzrXzrPzrJzru\ zrazrGzrHzrHzrHzrHzrIzrIzrIzrWzrUzrSzrQzrOzrMzrKzr\ dzr`zrYzrVzrRzrOzrLzrizrdzrXzrPzrTzrQzrNzppgppgppg\ ppgppgppgpogpogpogpohpohpohpohpohpnhpnhqnhqnhqniqn\ iqniqniqmiqmiqmiqmiqmiqmjqmjqmjqljqljqljqljqljrljr\ lkrlkrkkrkkrkkrkkrkkrkkrkkrklrjlrjlrjlrjlrjlrjlrjl\ rjlrjlsiksijsiisihsigsifsifsheshdshcshbshashash`sg\ _sgZsgYsgXsgWsgWsgVsgUsfTsfSsfRsfRsfQsfPsfOseNseMs\ eLseLseKseJseIseHsdGsdGsdFsdEsdDsdCsdBscAscAsc9sc8\ sc7sc6sc5tb6sc5sc5sc5sc5sc5sc5sc5sc5sc5sc5sc5sc5sc\ 5sc5sc5sd5sd5sd5sd5sd5sd5 } frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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For Deep Sake
by Mike Frazier 25 Oct '11

25 Oct '11

I am improving deep zooming in Fracton. Until now, there was a maximum magnification limit of about 1e300. Now that has been increased to 1e5000. While testing the new capability, I tried a deep zoom into a fractal on the FractInt Deep Zoom web page. The fractal was called 233 because it had a magnification of 1e233. I zoomed into a "two way symmetry" until I found the two armed oval this added to the fractal. That wasn't quite deep enough to test the new capability so I kept zooming until I got to this 4 armed oval at a magnification of 4e355. Here is a link to an image: http://dl.dropbox.com/u/33642054/image/for_deep_sake_800_5.jpg The parameter file used to make the image: For_Deep_Sake { ; Exported from Fracton. ; Very deep zoom into 233 by Henry Birdseye ; time = 25 min 52 sec at 640 x 480 with no aa ; on a Mac Pro 2 x 2.8 Ghz Quad-Core Xeon ; by Mike Frazier, public domain reset=2004 type=mandel passes=1 float=y center-mag=-0.732029929828136198455293015271057305\ 56951672230492293928276495641157718102978454448408\ 12404043441296278932140339697145134072822677086003\ 31825208146977091604215917875596703200044518808133\ 12801254326908977150030223083472061881359083259002\ 83828081904425741653511148955679003264312972988485\ 99604251927584934955556100991250337284373373831428\ 61012978245857780794715230007269210452612877056774\ 14739098258016795/0.362254943051205664189634244517\ 66242823791702343502563424963735040314093089208022\ 27682889214854224732520160831281692440946744540034\ 20702120965466655270667981376175896195517699326525\ 26234883861539394603456149411457895604893495093606\ 28103863820000164681452390320212490757742403863463\ 36423030849760452187370470065159297457100639142719\ 24057038297466507954806920894911320212951920345452\ 97489894023152920291521/0.43185401e356/0.1e1/-58/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=10000 inside=1 colors=pH6rH5vH3zH0vH2rG3mE2hD2cB2ZA2U81P71K51F41A\ 30510000330760BA1ED1IG1LJ1PN2SQ2WT2_W2b_3fb3ie3mh3\ ql4tq3wu1zz0ww1tt2pp3mm5jj6gg7cc8``9YYAXVBURBROBOK\ BLHBJDBGABD6CA3C80CC4CHH8MJ9RLBWNC`PEeSFkWInZHqaHt\ cGwfGziFwfFtdFqaEnZEkWEhUEeREaODZMDWJDTGDQDCNBCK8C\ 413000443775BB8EFAIIDLMFPQISUKWXNZ`PbdSegUikXloZpr\ asvcsvcsvcsvcqsaoq`mnZlkXjiWhfUfdTdaRbZP`XO_UMYRKW\ PJUMHVKGWJGXHFYGFZEF_DEaBEbAEd9Dg9Cj8Bl8Ao89r78u77\ r67p67n68l68i59g59e59c5A`5BZ6CW7EU8FR8GP9IMAJKBLMC\ IOFKQHNSKPUNSWQUYSX_VZ`Y`b`cdcfffihiljlolornrulprk\ mnikkgihffdddabbZa`W_YSYWPWUMVRITPFRNCQK8OI5RK7TN9\ WPBYRD`TFbWHeYJg_LiaNkcPneRpgTsiVulYxn_zpawn`tk_pi\ YmfXjdWgaVcZT`WSYURVRQROPOLOKJNHGMDDLAAKADMAGNAIPA\ LQAOSARUBUWBXYB__CbaCecChfCkhDnjDqlDtnCqlBmjBjiAfg\ 9cf8_d8Xc6SY5NS4IM3EH29B145000311632943D54G75J87MA\ 8QB9TCAWEBZFCbHEfHBjH9nH7 } -- Mike Frazier www.fracton.org

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FOTD 03-09-11 (Outcome Infinite [7])
by Jim Muth 25 Oct '11

25 Oct '11

FOTD -- September 03, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows a minibrot in the center of the nuclear blast that made yesterday's FOTD image a blast. Apparently, conditions at the center of nuclear explosions are so extreme that not even the laws of mathematics can survive undamaged. Check today's minibrot for a sample of mathematical damage. The minibrot in today's image is of order 2.000001, which means it should be barely distinguishable from an everyday quadratic minibrot, but today's minibrot looks nothing at all like a normal minibrot. It appears to be eroded and moth-eaten, most likely from the intense heat of nuclear fission. The same scrambled confusion exists in the surroundings, which appear to be trying to reach the usual 4,8,16... series, but are falling apart before getting there. It's a good thing the minibrot is about at the limit of resolution. Who knows what might lie deeper in its basin of attraction. The rating of a 7 is about average for FOTD images. The name "Outcome Infinite" means not quite as much as it implies. The calculation time of just under 7 minutes is slow by conventional math standards. Thank goodness for the web sites. The image may be viewed already calculated on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> The muggy conditions today here at Fractal Central made the temperature of 86F 30C feel warmer than it otherwise would have. The fractal cats had a thrill when Nicholas sensed a stray cat passing by, and both he and Cassie dashed to the window to make sure the cat continued on its way. The humans did what humans usually do on days that resemble thousands of other days. (No, I am not bored with life.) Unless armageddon arrives first, the next FOTD will be posted in 24 hours. Until then, take care, and if armageddon does arrive, I'M A GEDDON the heck outta here. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Outcome_Infinite { ; time=0:06:54.86-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotN passes=1 center-mag=-1.860582988052293/+0.00000500759982719\ /3.449945e+011/1/102.5/0 params=2.000001/0/0/0/0/0 float=y maxiter=32767 inside=0 periodicity=6 colors=000c8iZ9fTBcND`IEYOCUUAQ_8Ne6Jk4Fq2CmEYjPr`\ JpREoH9m74lGBjPIhYOg`QecRdeSbhTajU`iQ_iMZiIYiFXiBW\ i7Vi4Vc5QY6LS6HM7CG57B438426514611800B00E00H07J3EL\ 7HMBJOFQNISPBRR4QT0PV0QX1WZ2TK9_SGf_N_RLUJJOAII2GC\ 2F6VFzzzzzzzzzzzzzzzzzzzzzzzzzzzHSMbKW_FXYBXV7XT3X\ Q2YO2YL2YJ2YM2VO2SQ2PS2MU6JWAGYED_HBZB9Z57Z25Z23Z2\ 2`23b23c24e24g24h25j25k25f29b4CZ7GVAJOMLHYMAiNBaRC\ UUDNXEF`F7cF2fC2hA2i72k52l32n02o02q02rA3`O8JaD2bJ2\ bP2cV2c`2cf2VWGNMTFCe72rbHFfKEdIDcGDbECaCC`AC_8BZ6\ BX4AW2AV2AU29T29S28R28Q28X3AbEBiPDo_EjaDebC`cBWdAR\ f9Mg8Hh7Ci67j6Ce7Ha7LY7QT8UP8ZL8bH8dJ7eL7fM7gO7hQ6\ iR6jT6kU6hT7fS7dS7bR7`R7YQ8WP8UP8SO8QO8NN9LM9JM9HL\ 9FL9IKBLKCNKEQJFTJHVJIYJJ`ILbIMeIOhHPjHRmHSoHTcMYS\ RaGWf4`jAalGamManSaoYapbaqa`o``n__mZ_lYZkYZjXYiWYh\ VXgUXfUXeWWdYVd_UcaUccTbeSbgSaiRakQ`lQ`hMaeJaaGaZD\ aV9aS6aO3aL2aI2aK2`o4oi6l } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 24-10-11 (Blobs in the Night [7])
by Jim Muth 24 Oct '11

24 Oct '11

FOTD -- October 24, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that results when Z^(1.1) is subtracted from Z^(-5.5) and straight C is added. This parent consists of a Mandeloid rotated so that its normally west end points southeast. Its main period-2 bud is quite large, while its East Valley is shrunken. A large blob surrounded by fields of smaller blobs lies just beyond the east valley. The image for today lies in one of these debris fields. I named the image "Blobs in the Night", mostly because of the rather somber color scheme, which despite its brilliant highlights, still creates an impression of night. I almost named it something like 'Bursting Bubbles', but decided not to when I found no bubbles that are actually bursting. The rating of a 7 is adequate, but if I had put more effort into the colors, I might have raised it to an 8. The 45-second calculation time will cause no distress. This time is an estimate of the time the image would take to finish on the 2000mhz machine. It took 2-1/2 minutes on the 200mhz unit. The official FOTD web site, still under construction, may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The FOTD images are posted in high definition and sometimes anti-aliased at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site, now classic, may be found at: <http://www.Nahee.com/FOTD/> A few too many clouds and a few drops of rain spoiled the day here at Fractal Central. The temperature of 59F 15C was a bit chilly for total comfort, but near average for the season. The fractal cats spent the day on watch for an orange lop-eared tomcat that has recently appeared in the area and is showing signs of hanging around a while. The humans spent the day doing what needed to be done, which kept us busy but would be very boring to report in detail. The next FOTD will be posted in 24 hours. Until then, take care, and if the hardships of life are a learning experience as the local armchair philosopher says, when will we make use of the material world skills that we have struggled so hard to learn? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Blobs_in_the_Night { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=-0.056705950601755/-0.340265933261999/\ 5.804852e+007/1/155/0 params=1/-5.5/-1/1.1/0/0/0/0 maxiter=700 inside=0 logmap=72 periodicity=6 colors=00000AALKK`UWjfcqzmzzhthbq`XnUVjXUg_TdaSbdP\ bdLbeHceHccHbaH`_HYXGSUFLREEND7IC1HD9GDHFDOEDWVDba\ DjgDqzAiq8aM5UR3MV4LU4LU5LU5KU6KU6KU7KU7JU8JU8JU8J\ U8`1Ca6FaAJbEMbIPcMTcQWdUZdYRZRJTLBNF3I94ID4II5IM5\ IQ7GN9EKACICAFD8DT8ah8yeBobDf`FYYIPVKGTM7WSEYXL`aS\ bfZekegplagiX_gRSdMJbGB_B3Y97X8AW7EW5HV4LV3OU2RU5d\ e8qqKr_WsIfs1jn2mj2pe2sa2gf7XkBLpFAtJIkGPcDXWAcO7k\ G4r82dJASTHFbO2lV3dN3XG3P83H1GLHSOWdRkpUzkYsgalcdf\ _h_VlTRoNNsGJvARq9Ym8di7ke6faDbZKZVRVSXQPcMLjIIqEF\ wJDpOCiTAcY9Xb8Qg6Kl5Dp47oHAoUDnfGnsJorJorJpqJpqJq\ pJqpJhiG_bDchEgnFktGnyG`qbNjxJayFUymMzmEzm6zmHnmSc\ maTmlIzv7zkGzaOzSXzIdz8lzEnzKozQqzWrzaszguzmvzswzl\ qzfkz`ezV_zPUzJOzDJzGNzIRzLVzNZzQbzSfzUgzWhzYizZjz\ `kzblzdmzemzcezbZzaRz`Kz_DzRKzJQzBWzFXzIXzLYzOYzRY\ zUZzXZz_ZzUTzPNzKHzFBzA5z50zCIzJ_zPpzYtzfwzWvzLuzB\ uzGrzLozQmzVjz_gzdeVibzn` } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

1 0

FOTD 23-10-11 (A Sheep in the Deep [7])
by Jim Muth 24 Oct '11

24 Oct '11

FOTD -- October 23, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a scene in the East Valley of the large minibrot on the main stem of the Mandelbrot set. The parent fractal is in fact a Mandelbrot set that takes on order-9 characteristics in its depths. The minibrot at the center lies near a larger minibrot, which in turn lies near an even larger minibrot . . . At this point I lose count of the minibrots, but I think there are about four of them in the ladder-chain up to the surface. The name "A Sheep in the Deep" has no connection at all with the image. It simply popped into my head when I made my mind a blank, a task I find quite easy to accomplish. The rating of a 7 includes a full point for the coloring, which took over twice as long as calculating the image. The calculation time of 3 minutes entered into the parameter file is an educated guess of the time the calculation would have taken on the faster but now dead machine. (The image actually took 12-1/2 minutes to finish on the slow unit.) The finished image may be viewed on the official web site at: <http://www.crosscanpuzzles.com/Archives.html> without the need to calculate it. The high-definition version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic web site may be accessed at: <http://www.Nahee.com/FOTD/> The morning fog cleared off by 11am here at Fractal Central today, leading to a sunny afternoon with a temperature of 59F 15C. The fractal cats, still on watch for a possible return of the fighting tomcats, spent the first part of the day in the window facing the back yard. But the fighters have apparently moved on, and by the afternoon the fractal cats shifted their watch to the sunny shelf in the southwest window, which faces the front sidewalk. The humans spent the day doing nothing, which is quite enjoyable when it is done in moderation. The next FOTD will be posted in 24 hours. Until then, take care, and would this country's real savior please put in an appearance. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= A_Sheep_in_theDeep { ; time=0:03:00.00-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.749083935595091/+0.00000124195835773\ /1.4056e+013/1/-42.5/0 params=9/500000000000000.0/\ 0/0 float=y maxiter=2600 inside=0 logmap=333 periodicity=6 mathtolerance=0.05/1 colors=00000200300401502603613724835846956A67A78B8\ 8C99CAADBBEBBEBCFBDG9HzAGvAGrAFmAFhBEcBEZBDUBDRQzz\ PxxOvvOttNqqNnnMkkLhhLefKcdKacJ`aJZ`IYZHWYHUWGTVGR\ TFPSFOREMQDLPDJOCINCHMBHLBHKBGGAFEAECADAAC8AB6AA4A\ A5AA6AB7AB8BB9BCABCBBCCBDDBDEBDECEECEFCEGDFGDFHDFH\ CGICGICGJBHKBHKBHLAILAIMAIN9JN9JO9JP8KP8KQ8KQ7LR7L\ S7LS6MT6MT6MU5NV5NV5NW5NW7PW9RWBTWDVWFXWHZWJ`WKaWM\ cWOeWQgWSiWUkWWlWXlWWlXVkXVjYUhYTgYTfZSdZSc_Rb_Q`_\ Q_`PZ`PXaOWaNVaNTbMSbLRbLPcKOcKNdJLdIKdIJeHHeHGfGF\ fFDfFCgEBgEAgICeLEdOGcPHbQHcRHaSHYSHXSHUMHUHIUBIU6\ IU1IUBGUKFWUEOTDG`C9jAFp9Kz7Pi6Vh4_h3dd2Ya1RZ1LV0E\ N08U1Og2bk2qh8jbEd`KZZQTXWMVaGTgARm4LDpQJnVPl_Vkd`\ ihfhlZboRYrKT_CNbFLdHJgKHiMFkODjLFihHhmJgmcfmcemcd\ mccmcUmcLmmZmmlmmymmsmmnmmhpmczzZzzVzzRzzUzzXzz_zz\ bzzezzhzzkzznzzdzzVzzLzzBzz1zzxzzpzzizzbzzWzzTzzQz\ zOzzKzzGzzDzz9zzbzzbzzXzz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

2 1

FOTD 21-10-11 (Evaporation [8])
by Jim Muth 23 Oct '11

23 Oct '11

FOTD -- October 21, 2011 (Rating 8) Fractal visionaries and enthusiasts: In these FOTD discussions I often mention the parent fractal of an image. In most cases, this parent fractal is the image that appears on the screen when the formula parameters are entered and nothing is changed. My default settings are: a magnitude of 0.66..., the default color palette, a maxiter of 1500, a periodicity of 6 and a logmap of zero. Sometimes an outzoom is needed to fit an entire oversized parent onto the screen, or an inzoom is needed to enlarge an undersized parent to fill the screen. In other cases, there is no limited fractal that could be called a parent fractal. The entire parent fractal appears to be of unlimited size. Today's image is one of these misfits. Today's image lies in the apparently infinite fractal that is created by the MandNewt06 formula. This can be demonstrated by repeatedly outzooming from the image until the limit of Fractint is reached. Even way out here, there is no sign of the fractal coming to an end. As for the image itself, it reminds me of blue clouds caught evaporating away to reveal a universe of brownish spheres loosely arranged into nets and spirals. I rated the image at an 8, a full point of which is a bonus for the coloring effort needed to get reasonable smoothness from 256 colors. The name "Evaporation" refers to the bluish clouds, which to me appear to be clearing away, perhaps after a fractal storm. The calculation time of just over a minute will bring grief to no one if, in their opinion, the image lays an egg. For a little fun, try changing the exponent part of the real(p4) parameter a few orders of magnitude in either direction and watch the blue cloud totally evaporate or thicken. The already-calculated image is available on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Typical October weather prevailed here at Fractal Central today, which made for a not too pleasant afternoon. The sun was blocked most of the time by dark lumpy clouds scudding from the west, (stratocumulus), which dropped occasional sprinkles, while the temperature remained stuck in the mid 50's F around 12C, and the wind gusted to 20mph, 30kph. Not being weather wise, the fractal cats ignored the marginal conditions and concentrated on deciding who would own the new chair. FL put a heavy afghan over the chair to thwart their scratching efforts while they bickered for ownership. The next in the apparently unending series of fractal images will be posted in 24 hours. Until then, take care, and if I don't exhaust the supply of fractals in this world, I'll keep finding them in the next. But I still wonder how I'll continue posting them to the list. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Evaporation { ; time=0:01:08.27-SF5 on P4-2000 reset=2000 type=formula formulafile=basicer.frm formulaname=MandNewt06a passes=1 float=y center-mag=-0.0587134/0.29352/32.89674/1/-135/0 params=-1.82/-1.79/2.48/-1.18/1.28/1.63/1e-030/0 inside=bof60 logmap=yes periodicity=0 sound=off colors=000xaNw`Nv_MuZMtYLsXLrWKqVKpUKoTJnSJmRIlQIk\ PIjOHiNHhMHgLHfKGeJGdIFcHFbGEaFD`EB_D9ZC5YB0UA0Q80\ N60wzzwyzwwzwvywvxwvwwvvwvuwvtwvswvqwvowvmwvlvvkvu\ luukuumuuluumtunsunrunquopuoouonuomuokupjupiuphupg\ upfupdupcupbupaup`up_uqZuqYuqXuqWuqVuqUrqTrqSrrQbr\ PbrObrNbrMbrLbrKbrJbsIasHNnGNnFNnENnDNnCNnCNnBNnAM\ mAMmALmAKm9Km9Km9Km9Lm8Km8Lm8Lm7Mm7Mm7Nm7Pm6Tl6Sl6\ Sl6Rl5Rl5Ql5Ql4Pl4Pl4Ol4Ol3Nl3Nl2Ml2Ll2Kl1Jl1Il1Hl\ 0Um1Sm1Rm3Rm4Pm5Nm6Lk7Jk8Ij9GjAFiBCiCAiEHhGFhIDgKB\ gL9fM7fIIpJHpKFpLEpMDpNCpOBpPApQ9pR8oS6oT5oU4oV3oW\ 2oX1oY0oZ0o_0o`0o`0oa0nb0mb0lc0kc0jd0id0he0gf0ff0e\ g0dg0ch1ch1bi1ai2`j2_k2Zk2Yl3Xl3Wm3Vm4Un4Tn5So5Rp5\ Qp6Pq6Oq6Nt5Lq6Mn6Ok7Ph8Qe9Rb9T_AUXBVUCWRCYODZLD_I\ E`FFaCFc9Gd6He5He4Hf6Gc8E`ADYCBVEASF8PH7MJ5JL4GN3D\ N38N39O2AO2BP2DP1EP1FQ1GQ0HR0IR0JR0KS0MS0NT0OT0PT0\ QU0RU0SV0TV0TV0TU0UU0UU0U } frm:MandNewt06a {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=p3*z^2+c-1 z=z-1*a/b p4 < |a| } END PARAMETER FILE=========================================

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FOTD 22-10-11 (Platinum Oxide [7.5])
by Jim Muth 23 Oct '11

23 Oct '11

FOTD -- October 22, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: The October 22 image is late because I spent extra time today trying to get the 2000mhz fractal computer to run. The machine has always been questionable, and this morning, when it came on with a blue 'something's wrong' screen, I decided to try only one more time to get it running. Reseating all the cards did nothing, so I said farewell to the 9-year-old 2000mhz unit, stored it in the closet, and brought the 13-year-old 200mhz machine out of retirement. The older machine booted up perfectly, and now has the position of honor on the fractal desk top, where it will remain until replaced by the next currently active machine to be retired. The failed machine will live on however through its video card, which handles the Fractint DOS video modes perfectly, and which I will install in the replacement machine. Today's image is a quickie that I found on the old fractal computer after the newer unit stopped working. The very fast image is a mixture of Z^2 and Z^5 created by the FinDivBrot-2 formula. The rating of a 7.5 includes an unusual 1.5-point bonus for my coloring work. The basic fractal shape has appeared several times previously as FOTD's, but I did devote a considerable time to achieve the slate-gray effect, which was only inspired by the program and needed much hand work. The central shape is filled with quintic minibrots, all of which are virtually identical and not worth the trip down. The parent minibrot is one of those deceptive Mandelbrot sets that at first glance appears normal, but develops more quintic-like features the deeper one dives into it. The name "Platinum Oxide" refers to the overall color cast. The calculation time of 35 seconds is an estimate. The image actually took 2 minutes and 13 seconds on the 200mhz unit. On the 2000mhz machine, which runs 4 times, (not 10 times}, as fast, I assume it would finish in 35 seconds. The already-calculated image is available on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic web site may be accessed at: <http://www.Nahee.com/FOTD/> Today's weather here at Fractal Central was a repeat of yesterday's, with more dry but dark clouds, raw winds and a temperature of 52F 11C. The fractal cats took the day in stride, and were distracted only by a major cat fight that broke out in the back yard when two prowling tomcats crossed paths. The humans had a routine day, though I became quite annoyed when the 2000mhz fractal computer went on the blink again. The next FOTD will be posted in 24 hours. Until then, take care, and the most qualified does not always win. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Platinum_Oxide { ; time=0:00:35.00-SF5 on a P2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+0.3596259397545952/+0.6447633584097521\ /3515559/1/-30/0 params=5/100000/0/0 float=y maxiter=1500 inside=0 periodicity=6 colors=000fdLhdKjcJkcImcGocFqcErcDn_FjWHfSIbPKZLLV\ HNREOUKNWQMYWL`aKbgJdlJJhLKQPNSRPUTRWVTYXV_ZXa`Zcb\ `edbgfdihgkkimmkoonqrpstruvtwxzzzvvvrrrmmmhhhcccZZ\ ZUUUPPPKKKFFFAAA55500000000000000000000U00cQNmSUmN\ SqIRwGOsEMpCKmAIi8Gf7Ec8Gd8Hd9Id9JeAKeALeBMfBNfCOf\ CPgDQgDRgVzrEShEThFUhFVhGWiGXiHYiHZjI_jI`jJakJbkKc\ kKdlLelLflMgmMhmNimNjmOknOlnPmnPnoQooQpoRqpRrpSspS\ tqTuqTvqUwrUxrVyrJsvPwtzksylrxlrwlrwmrvmrumrunrtnr\ snrrorrorqorpprpproprnqrmqrmqrlrrkrrkrrjsrisrhsrht\ rgtrftrfureurdurcvrcvrbvrawrawr`wr_xrZxrZxrYyrXyrX\ yrWzrVzrt`FrbIpdKoeNmgPkiSjjUhlXgmZeoacqcbrf`thZvk\ YwmWypboKapMapNaqP`qQ`rS`rT_sV_sW_tYZtZZu`ZuaYubYv\ dYveXwgXwhXxjWxkWymWynVzpVzqJC3MPGPaTSneCCWDEXDFYE\ GYEHZFIZFK_GL_GM`GN`HOaHQaIRbISbJTcJUdKVdKXeKYeLZf\ L_fM`gMbgNchNdhOeiOfiOhjPijPjkQklQllRmmRomSpnSqnSr\ oTsoTupUvpYeS_dQadPcdOddN } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 20-10-11 (Fantasia in Blue [8])
by Jim Muth 21 Oct '11

21 Oct '11

FOTD -- October 20, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today we return to the warhorse formula, the MandAutoCritInZ, where we check the parent fractal created when 3 negative parts of Z^(neg(sqrt2)) are combined with 1.5 negative parts of Z^(2*(neg(sqrt2))) and (1/C) is added on every iteration. This parent consists of two large bays, one on each side of the X-axis, with a large minibrot-filled field of debris scattered to the east. Today's image lies in a smaller patch of chaos just south of a large bud on the east side of the large north bay. Two tricks were involved in creating the effects in the image. To begin, I reduced the bailout radius to an unusually small 7, then I rendered the resulting image and its ballooning elements with the 'outside' set to 'tdis'. The name "Fantasia in Blue" was inspired by the overall blue cast of the image, though I have toned the blue down a bit since naming the image. The rating of an 8 is what I felt the image was worth at the time I rated it. The calculation time of 3-1/2 minutes is well within reason. To avoid all calculation hassle, view the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And view it in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic, web site may be accessed at: <http://www.Nahee.com/FOTD/> Saturday was ruled by heavy clouds here at Fractal Central, though the rain for the most part stayed to the west. The fractal cats, who pay far less attention to the weather than the humans, ignored the temperature of 57F 14C and had a lazy day, taking turns sleeping on the new chair instead of fighting for it. The humans, FL and I, had an uneventful day also. With the graphic design work slowing down, more and more days are becoming uneventful. The one thing not slowing down however is the FOTD, which I now have more time to work on. The next FOTD will be posted in 24 hours. Until then, take care, and if the climate changes, will the change be for the better or worse? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Fantasia_in_Blue { ; time=0:03:37.29-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.300193586061464/+0.4252430675353652/\ 2.728e+011 params=-3/-1.4142/-1.5/-2.8284/0/-93/0/0 float=y maxiter=1500 inside=0 outside=tdis periodicity=6 mathtolerance=0.05/1 colors=000dD7iG5oJ2uM1uP0uS2uT4rW5qY7m`8kb9idBgfCd\ iEbjFalHdb9gQ2jG0_K9QPNFT_5Ym0`uCdiTiSjn9uq0ro0jn7\ blEajL_iT_g_ZfgXdoXcu_dkadbdfTffKigBjg1mi0oi0jf0fd\ 4bcCZbNV`XS_fkHqu3uFfVCsbBzkCymEooFfqHYrIPsKGuK7u2\ T_0oH5uX9raEofIliNimSfqXjoaomfrkkwjqziuzguiLuP0uM2\ kJ5bH7TF90BI08O0ER0KY0Ta0`j0hp0mp0jp0ep2_n9VlGPgMK\ dMFbKCeIAgD7iN3iL3jI3kE3k13j03a03N03809u5DuEHuOMuX\ QufTsbPuaMu_QuZTuXWuW_uVcuTfuSiuQluOquNsuLwzczzczz\ mzzmzzqzzIzzLzzOzzSuuVqjXlZZgTacNd_HgVBjQ5mM0oJ0kN\ 0jQ0iV0gY0db0bd0ai0_l0Zq0Ws0Vy0Tz0Sz0Qz0Ow4NlBL`IK\ QQKGXIJaIMdIPgHSkHVoHYrF`uFcuFduK_uOVoSQiWMbZHXbDQ\ f9Kj4Em38r32u30u30u30u30u30u30u30u30u30u30u30u30u3\ 0r32k45gC7aK9WTBS`ELiFFrIBzK5zN1zO7zSCzVIzXNzZTzaZ\ zdbzfiziozkszmowojrqfnqairkuisiau_WsYTmWQgWNaVKWTH\ QTEKSBES9LVFSYLZ`SdcXjfbriiulouoskqfWqTEqF0q20q00s\ 00w00z00z0C3HI3EN4CT7BZA8 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 19-10-11 (Mandala-Head [8])
by Jim Muth 20 Oct '11

20 Oct '11

FOTD -- October 19, 2011 (Rating 8) Fractal visionaries and enthusiasts: For today's image I turned to a built-in Fractint formula, the type=manzzpwr, a formula I rarely if ever bring up, which on every iteration raises Z to the power of previous Z then adds Z^(n). In today's image 'n' equals -12. After a few minutes of tweaking and experimenting with the formula, I turned up today's image, which for obvious reasons I named "Mandala-Head". The image resembles one of those surreal paintings by Rene Magritte in which people have things such as apples where their heads and faces would be expected. Today's image has a mandala instead of a head. (A mandala is a devotional symbol representing the eternal cycles that fill the universe, especially the cycle of birth and death believed in by most eastern religions but considered heathen doctrine by the western religions, where the doctrine of only one chance to achieve salvation is accepted as truth.) Most of the image's effect was achieved by rendering the scene with both the inside and outside parts set to 'atan'. The peach-turquoise color scheme adds to the effect, since the peach areas somewhat resemble the color of skin. The rating of an 8 might be a little liberal, but why not, since today I'm in one of my more liberal moods. And there will be no trouble at all with the calculation, since the time is a fireball-fast 25 seconds. For maximum convenience, the image has already been calculated and posted to the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> It is posted in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> The day began with clouds and mist here at Fractal Central. The foul weather continued for the rest of the day, never quite dry and never quite wet. The fractal cats approved of the temperature of 66F 19C, but Cassie approved a bit too much when she took her claws to the upholstery of the new chair and got herself scolded. The humans had another near normal day, with nothing out of the ordinary to report. The next FOTD will appear in 24 hours. I'll leave it to the individual fractalist to figure where it will appear from. Until then, take care, and if reincarnation is true, then about half the people on earth hold false beliefs; if it is false, then the other half hold false beliefs. In either case, the religious beliefs of at least half the people on earth are false. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Mandala-Head { ; time=0:00:25.26-SF5 on P4-2000 reset=2004 type=manzzpwr passes=1 params=0/0/-12 center-mag=0.430612/0/0.5657059/1/-90/0 float=y maxiter=1500 bailout=10000 inside=atan outside=atan logmap=yes periodicity=10 colors=000gaVgbWgbXhcXhcYhdZidZie_ie`ie`jfajfbjgck\ gckhdkhelielifljgljhmkhmkimljnljnmknmlonlonmoonooo\ ppoppppqqqqqqrrqrssqrrrsqrsqrsprsprsorsorsnrsnrsmr\ smrslrskrskssjssjssististhsthstgstgstfstestestdstd\ stcttcttbttbttattatu`tu_tu_tuZtuZtuYtuYtuXuuXuuWuu\ WuuVuuVuuUuuTuuTuvSuvSuvRuvRuvQuvQvvPvvPvvOvvNvvNv\ vMvvMvvLvvLvvKvwKvwJvwJwwIwwHwwHwwGwwGwwFwwFwwEwwE\ wwDwwDwwCwwDxxCwwCvvCvvCuuCtuCttCssCrsBrrBqrBqqBpp\ BopBooBnoBmnAmmAlmAllAklAjkAjjAijAhiAhi9gh9fh9fg9e\ f9ef9de9ce9cd8bc8ac8ab8`b8`a8_`8Z`8Z_8YZ7XZ7XY7WY7\ VX7UX7TW7TW7SV6RV6RV6QU6QU6PW6PW6PV6PU6PU5PU5PU5PU\ 5PU5PU5PU5PU5PT4PT4PS4PR4PQ4PP4PO4PQ5OU6NU7NUAOUDQ\ VGU_JYdMaiPenSisVnxUmxTlxSlxRkxQkxPjxOjxNixMixLhxL\ hxKgwKgwKfvJfvJfuJeuIetIetIdsIdsHcrHcrHcqGbqGbpGbp\ FaoFaoF`nF`nE`mE_mE_lD_lDZkDZkCYjCYjCYiCXiBXhBXhBW\ gAWgeZQeZRe_Sf_Sf`Tf`UgaU } END PARAMETER FILE=========================================

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FOTD 18-10-11 (Down in the Boondocks [All math])
by Jim Muth 19 Oct '11

19 Oct '11

FOTD -- October 18, 2011 (Rating All Math) Fractal visionaries and enthusiasts: Today's image rates All Math. The mathematical interest is just about all it has going for it. The image itself is little more than a passing scene in an infinite world of fractals. And the calculation time of nearly 2 hours is far beyond reason. In addition, the exponent of Z that created the image is 1.0005, so close to unity that no one in his right mind would enter it as a parameter with any expectation at all of finding much more than smooth and straight band edges. Questioning my own sanity, I did enter this value as the exponent of Z, and in addition I felt fairly confident of finding something of interest. Today's image is what popped up where nothing should exist. The scene is neither a Julia set nor a Mandelbrot set, but something in between. The detail in the image is not the organized chaos that makes most fractals so interesting. The detail in today's image consists of countless discontinuities arranged into half-orderly elements. If any part of the image is zoomed into, a flat featureless area will ultimately be arrived at. In ordinary fractal chaos, the chaotic features continue without limit. The name "Down in the Boondocks" refers to the exponent of Z, which is by far the closest to unity of any FOTD fractal so far. A price must be paid for seeing detail in a fractal so close to unity however. The price is the need of a very high maxiter, resulting in a calculation time of 1-3/4 hours, which is tedious indeed for such an unartistic image. But help has arrived in the form of the FOTD web sites. All the tedious calculating may be avoided by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> It may be seen in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic web site may be accessed at: <http://www.Nahee.com/FOTD/> The day began with clouds here at Fractal Central, but the clouds cleared off before noon, leading to an afternoon of sunshine, balmy south breezes and a temperature of 70F 21C. With rain and colder weather forecast, today might have been the last near-perfect day of the fall. The fractal cats passed a good part of the day sharing the new chair. The humans disagreed a bit about politics (as is standard) but the day passed uneventfully. The next FOTD will be posted in 24 hours. Until then, take care, and liberal thinkers know that conservative policies are the cause of the problems, while conservative thinkers know that liberal policies are the cause of the problems. Neither side appears able to recognize that their conflicting views of the solution are also a part of the problem. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= DownInTheBoondocks { ; time=2:05:44.73-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=1 maxiter=120000 center-mag=+2.723099067722828/+0.02123607283229285\ /6919/1/5/0 params=37.5/0/37.5/0/1.1513/0/0/0/1.00\ 05/0 float=y inside=0 logmap=-15900 periodicity=9 colors=000zdCzeEzfGzgIzhKziMzjOzkQzmSznUzoWzpYzq_z\ razsbzs_zsXysUwsRurOsqOqpOooNmnNkmNilMgkMfjMeiLdhL\ cgLbfKaeK`dK_cJZbJYaJX`IWZIVXIUVHTTHSRHROGQLGPIHOF\ GNDKMDKLFKKIKJKKINKHPKUKzTKzTKzTKzTKzTKzTKzTKzSKzS\ KzSKzSKzSKzSKzSKzRKzRKzRKzRKzRKzRKzRKzRKzQKzQKzQKz\ QKzQKzQKzQKzPKzPKzPKzPKzPKzPKzPKzOKzOKzOKzOKzOAzOA\ zOAzOAzPAzQAzRAzSAzSAzTAzUAzVAzWAzWAzXAzYAzZ1z_1z_\ 2z`2za3zb3zc4zc4zd4ze5zf5zg6zg6zh7zi7zj7zk8Wk8Yl9_\ m8an6co4eq2gr0is0ku0mv0ox0qz0sy0ux0ww0ww0ww0ww0ww0\ ww0ww0ww0ww0ww0uw0sw0qw0ow0mw0kw0iw1gw1ew2ew2ew3ew\ 4fw4gw5gw5hw6hw6iw7iw7jw8kw8kw9lwAluAmsBmqBnoComCo\ mDpmDpmEqmEqmFrmEsmFrmFqmFpmGomGomGnmHmmHlmHlmIkmI\ jmIimJimJhmJgmKfmKfmKemLdmLcmMczOazQ`zS_zUZzWXzYWz\ _VzaUzcTzeRzgQziPzkOzmMznLzpKzpJzpIzpGzpFzpEzpDzpB\ zpAzp9zp8zp7zp5zp4zp3zp2zp1zp2zp2zpfzpezpezpdzpczp\ czpbzpazpazp`zp`zp_zpZzpZ } frm:SliceJulibrot5 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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