August 2013 - Fractint - mailman.xmission.com

FOTD 08-08-13 (Almost the Best [A-8,M-8])
by Jim Muth 08 Aug '13

08 Aug '13

FOTD -- August 08, 2013 (Rating A-8,M-8) Fractal visionaries and enthusiasts: Today's image shows the center of what I consider the best anti-minibrot yet. The location of the action is in a seahorse tail on the east edge of the north branch of Seahorse Valley of the parent Mandelbrot set. An everyday Mandelbrot minibrot would normally lie in this area, but it has been obliterated by the tiny bit of Z^(-4) stuff infesting the entire parent fractal. The image clearly shows the center of the hill of anti- bifurcation, the peak of which is actually a seamount lying quite a distance (467 iterations) undersea. A quick count will show the anti-bifurcation, which increases from the inside out. The name "Almost the Best" shows that I consider the image to show continued improvement, while always leaving room for further improvement. The art and math ratings concur with this opinion. The calculation time of 10-1/2 minutes is slow, I admit it. But relief is at hand on any of the FOTD web sites. To view the image without the task of calculating it, check one of the following web sites: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Heavy clouds again blocked the sun today here at Fractal Central, while the temperature of 81F 27C kept things reasonably comfortable. The fractal cat forgot the lack of sun as soon as I produced the laser pointer and gave him a good chase that soon had him panting in exhaustion. The fractal people, who were not panting in exhaustion, had one more typically busy day. The next FOTD will be posted when humanity achieves immortality, or possibly a little sooner. Until this happens, take care, and I hear that some people expect that by the year 2045 we will be able to download our conscious self-aware unique selves, complete with our varied emotions, into robot-like machines that will endure indefinitely, granting virtual immortality. This appears well enough, but I wonder exactly what information we will download into the robot machines. I also wonder if immortality will be for everyone, rich and poor alike, or only for those wealthy enough to pay for the process, which obviously will be hugely expensive. If immortality will be only for the wealthy, how will the impoverished feel? Will the common people simply sit idly by and watch the wealthy allow them and their loved ones to die, while the wealthy reserve immortality only for those they deem worthy (that is with enough money) to live forever? Or will there be a revolution against the wealthy that would put an end once and for all to privileged-class thoughts of immortality? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Almost_the_Best { ; time=0:08:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.7444863811241328/+0.1622564474808734\ /1.895244e+010 params=1/2/1e-025/-4/0/0/0/0 float=y maxiter=1500 inside=255 logmap=-470 periodicity=6 mathtolerance=0.05/1 colors=000SkkSjgSjdUi`miYghUbhR_gNWgKSfGSfDSe9Se6R\ c8Qa9P_AOYBNWCNUDMSELQFKOGJMHIKIFKF9LD6KB0K93LD6MJ\ 9OKBPNEQRHSUKTYMU`PWdSXgUYjWVhYTg_Re`PdbNcdLafJ`gH\ _hF`iEajDbkCclBdmAen8eo7fp6gq5hr4is3jt2jm1ef1`_1WT\ 1RM1MF1H81DC7BFD9JJ8MP6PU5QQBQNHRJNRGTSCZS9dS6iZ6U\ e6Fl60jH5hR9gaEekIduMdqPdnSdkVdgYdd_dabdYedVhdSjgT\ fjUbmVZoVWlQjiLyhMxhMxgNxgNxgOxfOxfPxfPxeQweQwdRwd\ RwdSwcSwcTwcTwdVveWufYugZth`siasjcrjdrkfqlgpmipnjo\ olnpmnqomqpmplkphipdgo`foXdoTboP`nL_nHYnDWn9VmATlB\ SkCRkDQjEPiFOiGNhGMgHKgIJfJIeKHeLGdMFcNEcNDfRGhUIk\ XLm_NobQreSthVvkXlPUc2S`6VY9XVCZTG`QJcNMeKQgITiFWl\ C_n9bp7er8gq9ipAjoBloCnnDomEqlFslGtkHvjIwjGviFvhEv\ gDvfCveBueAud9uc8ub7ua6uaAsdErfHpiLokPmnSlp6mD8jBA\ gACd9Db8F_7HX5IV4KS3MP2NN1MO4LO6LO8KPBKPDJPFIPHIQK\ HQMHQOGQQFRTFRVERXERZGSaIScKTeMTgOUiQUkSUmUVoWVqYW\ s_Wu`Ww_Zr_amZdhZgcYjZYmU } 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 07-08-13 (Better Yet [A-8,M-8])
by Jim Muth 07 Aug '13

07 Aug '13

FOTD -- August 07, 2013 (Rating A-8,M-8) Fractal visionaries and enthusiasts: Today's image shows what I consider to be the best example yet of an anti-minibrot. It lies in the debris in a tiny minibrot on the north shore of East Valley of the parent Mandelbrot set. The name "Better Yet" implies that even better anti-minibrots may be yet to come. The art and math ratings of 8 indicate that I consider both aspects of the image to be above normal. The calculation time however is a dragging 10 minutes. This delay may be bypassed by viewing the image on one of the web sites. <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Heavy clouds hung on all day here at Fractal Central today, though it remained dry. The temperature of 75F 24C would have seemed better if there had been sun. The fractal cat slept through most of the day, while the fractal humans kept busy doing human things. The next FOTD will be posted in a number of hours. Until that ambiguous length of time passes, take care, and if nothing, not even light, can escape from a black hole, how does the gravity get out to pull everything into the hole? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Better_Yet { ; time=0:10:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.2927628248663804/+0.015094370223889/\ 7.020676e+009/1/-35/0 params=1/2/1e-016/-2/0/0/0/0 float=y maxiter=1600 inside=0 logmap=-300 periodicity=6 mathtolerance=0.05/1 colors=000fSoaPlXLjSIhNFeIBcD8`85Z32XHDWUOWmTTfYW`\ bYVf`OkbIoeCtg6xiAvgDufGtdKscNqaQp`UoZXnY_lWckVfjT\ iiSllYnobpqgrtmtwrvywussumptgltbisXfsRbrL_rGXpIYoK\ YnMYmNZlPZkRZiS_hU_gW_fX`eZ`d``bkeca`cTWdJRdAMd1H_\ 1FV1ER1CM1BH1AD188174165575885C95FA5JB5MC6PD6TE6WF\ 6_G6bH6eI7fK8gM9hOAhQBiSBjUCjWDkYEl_FlaFmcGneHngIo\ iJpkJpl9YR0F56MCBSIGZOLdUOo`Qj_SfZZbY`ZYaVXhQWjMWq\ IVsEUm7ToAUpDVrFVsIWoLWqNXrQXsTYpVYqYZr_Zsa_sb_td_\ te_uf_uh_vi_vj_wl_wm_xn_xp_yq_yr_qmXjhUbcSW_PPVMHQ\ KALH3HF7GEAEDAAAAAA000ArzApzAnzAkzAhzCezEczGczIZzK\ TzMUzOUzQUxSTvUTtWTrXVqWSpWQoVPnVNnVKmUJlUHlTGkTDj\ TBjSAiS8hS7hOKdKWaJXdIYgIYiHZlH_nG_qG`sFavEvzFaxBJ\ xFIvIIuLItPIsSHrVHqYHpaHodHngGmkGlnGkqGjxJqtGipDbl\ AWh8Pd5I`2BX04Z26_48a6Ab8CdAEeCGfEIhGKiIMkKOlMQnOS\ oQUpSVaZVNdV0kR9jVIiYRha_gdhfhrfjqekqdlqdmqcnqbnqb\ oqapqaqq`qq_rq_sqZtqZtkVq } 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

Under-iterated parent fractal of FOTD for Aug 4th, '13 fixed
by Hal Lane 07 Aug '13

07 Aug '13

This zoom into the parent of Jim's FOTD for August 4th, 2013: http://www.emarketingiseasy.com/TESTS/FOTD/2013/F130804W.jpg was under-iterated when I used Jim's FOTD maxiter of 1,000. Here's the same fractal with maxiter=10,000: http://www.emarketingiseasy.com/TESTS/FOTD/2013/F130804V.jpg Method for Comparing the Differences Between Two Images ------------------------------------------------------- Here's a nifty way to compare the difference between two different versions of a fractal or other pair of similar images: Put the two different images into adjacent tabs in your browser. I do this by right clicking each link and choosing "Open link in new tab". If your browser has scaled the images down to fit your browser window, click the upper left corner of each image once -- to keep your browser from resampling (and possibly repositioning) the images. Then quickly alternate between viewing each of the two images in their respective tabs. This lets you see differences in the images quite clearly, by using the eye's sensitivity to motion. Many browsers accept the key combination <ctrl><n> to view their <n>th tab. Using the keyboard allows you to not have to move your gaze away from the images to aim your cursor at each of the two tabs to click on them. I'm able to hold down the <ctrl> key and alternately press the "3" and "4" keys (or wherever the two tab's locations are) to "blink" back and forth between viewing each of the two different images. The differences between the images literally jump out at you. I got this idea from the method used by Clyde Tombaugh to discover Pluto. He blinked between viewing two different photographic plates of the night sky taken on successive nights. Pluto moved as the photos were blinked. The instrument he used to do this is called a "blink microscope." This "blink" method is not limited to fractal image comparison. It can be used to compare of any pair of images with slight differences. For example, one could compare the change in quality of two or more versions of the same image saved with differing amounts of JPEG compression. If you're a member of the [Fractint] email list serve, please let me know whether you're able to "blink" a pair of images from my description above. Thanks, - Hal Lane ######################## # hallane(a)earthlink.net ########################

1 0

FOTD 05-08-13 (Anti-Minibrot [A-8,M-9])
by Jim Muth 06 Aug '13

06 Aug '13

FOTD -- August 05, 1013 (Rating A-8,M-9) Fractal visionaries and enthusiasts: Today's image bears an artistic rating of 8 and a math value of 9. This is because it is the most spectacular anti-minibrot I have yet found, a fact that obviously also inspired its name. The image shows the exact opposite of a minibrot, or what I call an anti-minibrot. Instead of a basin at the center, the image has a hill; while instead of doubling in number as the center is approached, the number of elements is cut in half. The scene lies in left-over debris cluttering a minibrot that lies rather deep in an elephant trunk of East Valley of the parent fractal, which on the surface is an everyday Mandelbrot set, but in its depths is corrupted by quintic energies. Except for a minor tweaking of one register, the extremely busy color palette was created by a random strike of the <enter> key. The calculation time of 1-1/2 minutes is fast enough for most fractalists, but a bit of time may still be saved by checking the web sites. Various renderings of today's image are posted on the following web sites: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Today brought increasing clouds and a temperature of 75F 24C to Fractal Central. The fractal cat noticed the gradually weakening sun; the humans noticed the work. The next FOTD will be posted when I get a round tuit. Until the tuit appears, take care, and the rest of the world knows that the people in the U.S. are a bunch of gun-loving fast-shooting racists. But why then did we racists twice elect a black president by such a sizable margin? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Anti-Minibrot { ; time=0:01:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+0.3007751526060126/-0.0201684395807311\ /2.544126e+010/1/47.5/0 params=5/1000000000000.0\ /0/0 float=y maxiter=1500 inside=0 periodicity=6 colors=000`bf_ZgZUhYQiXLjWHkVClU8mT4nW5kY5i_5gb5ed\ 5bf5`i6Zk6Xm6Up6Sr6Qt6Oq8Mn9LlAJiCIfDGdEFaFDZHCXIA\ UJ9RK7PM6MN4JO3HP2GU9GYFGaMGeSGiZGmdGqkGuqGywEqoI9\ 8CihAa`8VU6NM4FF277LMGIIDFFBCC9996664332yHnlDc`AUO\ 6KC3Ay0Js0Hn0Fi0Ed0C_0BV09P07K06F04A03501tUVSFFnXU\ jURfSPcPN_NLWLJTIHPGFLECIBAE98A767443225Yg4Vd4Ta4R\ Z3PX3NU3LR2JO2HM2EJ1CG1AD18B0680450223Sf2MY1GP1BH0\ 58a`KtYVSHFQ3pK2eF1VA1L50AwUcrR`nPYjNVeLSaJPYHMUFK\ PCHLAEH8BC68845422Se`LVRELI7A9ovKkrIhnHejGbgFZcDW_\ CTXBQTAMP8JM7GI6DE59B3672331lqNW_FGI7uSppQllOhhMdd\ K``IYXGUTEQOCMKAIG8FC6B847zzztt0ee0SS0EE0EoKCgHA`E\ 8TB6M84E52728gA7c96_86X75T64P54M53I42E32B2171030MC\ WKATI9QG8NE7KC6HA5E84B638425212D8BB799688566454343\ 22111bjfZfbWbZTZWQVSMRPJNLGJHDFE9BA677333r1Aj08b07\ V05N04F02701Gunjo0mVdDkmBfhAac9XZ7SU6OP5JK3EF29A14\ 5W0CS0AP09M08J07G06C04903 } 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=========================================

1 0

Anti-aliasing uncovers hidden features in Aug 4, '13 FOTD.
by Hal Lane 05 Aug '13

05 Aug '13

In Jim's FOTD for August 4, 2013, many features which are hidden in the chaotic areas of the original image, pop into visibility in the anti-aliased version. Original: http://www.emarketingiseasy.com/TESTS/FOTD/2013/F130804.gif Anti-aliased: http://www.emarketingiseasy.com/TESTS/FOTD/2013/F130804J.jpg Method for comparing the differences between two images: -------------------------------------------------------- Here's a nifty way to compare the difference between the anti-aliased and non-anti-aliased versions of the fractal: Put the two different images into adjacent tabs in your browser. I do this by right clicking each link and choosing "Open link in new tab". If your browser has scaled the images down to fit your browser window, click the upper left corner of each image once Â to keep your browser from resampling (and possibly repositioning) the images. Then quickly alternate between viewing each of the two images in their respective tabs. This lets you see differences in the images quite clearly, by using the eye's sensitivity to motion. Many browsers accept the key combination <ctrl><n> to view their <n>th tab. Using the keyboard allows you to not have to move your gaze away from the images to aim your cursor at each of the two tabs to click on them. I'm able to hold down the <ctrl> key and alternately press the "3" and "4" keys (or wherever the two tab's locations are) to "blink" back and forth between viewing each of the two different images. The differences between the images literally jump out at you. I got this idea from the method used by Clyde Tombaugh to discover Pluto. He blinked between viewing two different photographic plates of the night sky taken on successive nights. Pluto moved as the photos were blinked. The instrument he used to do this is called a "blink microscope." This "blink" method is not limited to fractal image comparison. It can be used to compare of any pair of images with slight differences. For example, one could compare the change in quality of two or more versions of the same image saved with differing amounts of JPEG compression. If you're a member of the [Fractint] email list serve, please let me know whether you're able to "blink" a pair of images from my description above. Thanks, - Hal Lane ######################## # hallane(a)earthlink.net ########################

1 0

FOTD 04-08-13 (No Minibrots Here [A-7,M-8])
by Jim Muth 04 Aug '13

04 Aug '13

FOTD -- August 04, 2013 (Rating A-7,M-8) Fractal visionaries and enthusiasts: Today's scene shows what I call a 'hill' of anti-bifurcation situated inside the second bud of the north radical of the large minibrot on the main stem of the tiny parent M-set. The generating expression adds an infinitesimal amount of Z^(-2.2) to 100 parts of Z^2, producing a tiny Mandelbrot set with left-over debris at the center of the buds. The fractional part of the exponent has generated a discontinuity in the northeast part of the image. As the name implies, there are "No Minibrots Here". At least, I have not yet found any in the area, though similar 'hills' abound. The artistic rating of a 7 indicates average worth, while the math rating of an 8 indicates exceptional mathematical value. In fact, the 'hill' is one of the finest I have yet stumbled upon. The calculation time of 1-1/2 minutes is fast enough to keep impatience at bay. And the finished image is always available on the FOTD web sites. The finished image is or soon will be posted on the following web sites: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Near perfect midsummer weather prevailed here at Fractal Central today, with photoshop blue skies, cotton-candy clouds and a temperature of 77F 25C. The fractal cat enjoyed the conditions while sleeping in the laundry basket. The fractal humans enjoyed the fractal cat enjoying the conditions while sleeping in the laundry basket. The next FOTD will be posted when I find it and write about it. Until that glorious moment arrives, take care, and show the world that your pet conspiracy theory is true. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= No_Minibrots_Here { ; time=0:01:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.01757933078094727/+0.000158504568805\ 81/1804502/1/75/0 params=100/2/1e-016/-2.2/0/0/0/0 float=y maxiter=1000 inside=0 periodicity=6 mathtolerance=0.05/1 colors=000AmNDPDf97c86a76Z66X55U45S45P35N24K14I04Y\ GsXFpWEmVDjUChzzzzzzhcz09YP8cO7fU6zYIzL5KK4HJ3EI2C\ H19G06GzaGtYGnVGhSGcPGYMGSJGMGGHDGBAG57v86k65`45Q2\ 4wlrshnpejmagjZcgV_dSXaOTYLPVHMSEIPAEM7BF37amzaWgH\ LV9AH0Fz1Em2Dc3CW4BU5AS69P78N87L96JA5HB4EC3CD2AE18\ F06TP2SN3RL3QJ3PH3OG3NE3MC3LA4K84J74I54H34G14o7Gk6\ Eg5Dd4C`4BY3AU28Q27N16J05BeMzXhpQ_gJSYDKP6CQu7Pr6P\ o6Ol6Oi6Ng6Nd6Ma6MZ5LX5LU5KR5KO5JM5JJ5IG4ID4HB4H84\ G54G24fyKdvJcsIbqIanH65G63H61H74I86J98K9ALACMBENCG\ OCIPDLQENRFPSFRTGTUHVVIXWIZWPROVJGaB8g31Mdf61qL`bL\ Y_KUXKRUJNQJKNIHKIDHHADH6AG37C5`D4YD4WD4UD3SE3QE3O\ E2ME2KF2IF1GF1EF1CG0AG08G06Y6hX5eW5cV5aU4ZT4XS4VR3\ TQ3QP3OO2MN2JM2HL1FK1DJ1AI08H06S7bR6`Q6ZQ5XP5WP5UO\ 4SN4QN4PM3NM3LL3JK2IK2GJ2EJ1CI1BH19H07G05WxIUsHToG\ SkFRgEQcDP_COWBNSAMO9LK8KG7JC6I85H446jP8`KASGCICE9\ 8rcimZchUZcPUZKPUFJPAEK59 } 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 02-08-13 (Reasonable Result [A-7,M-7])
by Jim Muth 03 Aug '13

03 Aug '13

FOTD -- August 02, 2013 (Rating A-7,M-7) Fractal visionaries and enthusiasts: In today's image we add only 0.000000000000000000000000000001 part of Z^(-5) to 100 parts of Z^2. The resulting tiny M-set still has a few remnants of the negative exponent lurking in the depths of its buds. Today's scene lies in a bit of this leftover debris in the center of the main bud of the large minibrot on the main spike of the tiny parent M-set. I rated both the art and math interest at a 7, making the image notably average. I leave it to the individual fractalist to decide whether the name "Reasonable Result" accurately describes the image. There is nothing super spectacular about the image, but it renders in a mere 30 seconds, making the calculation a breeze. The fickle winds can be avoided by checking the image on one of the web sites. The image is or soon will be posted on the following web sites: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> The day began pleasant enough here at Fractal Central, with blue skies and white cottonball clouds, but heavier clouds moved in during the afternoon and the humidity increased, making the temperature of 82F 28C feel a bit muggy. The fractal cat, now over 10 years old, crawled under a slip cover and spent the afternoon appearing as little more than a breathing lump, while the fractal humans made it through another day with nothing going wrong. The next FOTD will be posted on a day in the near future. At this time the best bet is August 04. Until whenever, take care, and even when a person knows something, there is no guarantee of its truth. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Reasonable_Result { ; time=0:00:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.01773008927479706/0/8.195031e+012 params=100/2/1e-030/-5/0/0/0/0 float=y maxiter=1000 inside=0 logmap=40 symmetry=xaxis periodicity=6 mathtolerance=0.05/1 colors=00000K00L00M00N00O00P00Q00S00U00W00Y00_40a9\ 4cE9cFEaGG`HK`HPfHUiHZoHctEhwEmzCrzCvzKzzUzzczzmzz\ zzwzzwzzwzwwzrwzktrftict`YtTTtQKzMQtKToHWiEYfC``9c\ W6fT4iM1oH0rE0t90w40z10z00z00z00z00z00z00z00z00z01\ z04w06t09t0Cr0Er0Ho0Ew0Ko0Mi0Tc0WY0YT4cM9fHCiCHo6M\ r1Qw0Wz0`z0cz0iz0oz0zz0rz0ct1MiH9Y`0Qr0Ez0Cz06z04z\ 01z00z00z00w00t00o00i00c00Y00T00M00Q00K00H00E00C04\ 90E60Q40Y06i0Er0Mz0Wz0cz0kz0tz0zz0wz0rz0oz0ir0ff0`\ Y1Ym6Tm9QmCKmEHmHCmK9mM4mY4mQ1mK0mE0m90m40c00t00z0\ 0z00z00z00z00z00z06z6HzEQzMYmCQmEWmKcm0zm0zm1zm4zm\ 0zm0im0Km00z01z01z01z04z04z04z04z06z06z06z06z09z09\ z09z09z04z01z00z00z00z00z00z00z00f00o00w00z00z00z0\ 0z00z40t90iH0`M0TW0H`09i01o09i0Hf0Mc0WY0`W4iTEoQQw\ KczHozEzz9zz6zz4zz1zz9zzEzzKzzQztWzk`zcfzTkzKrzCww\ 4zt0zo0zi0zf0zrHtz`fzkfztWzzKzz9zz0zz0wz0oz0iz0kz0\ kz0oz0oz6ozErzMrzWtzctzkt } 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 01-08-13 (Planetary Nebula [A-7,M-7])
by Jim Muth 01 Aug '13

01 Aug '13

FOTD -- August 01, 2013 (Rating A-7,M-7) Fractal visionaries and enthusiasts: In today's image we *subtract* 0.0000000000000001 part of Z^(-2) from 100 parts of Z^2. This combination creates a tiny Mandelbrot set 1/100 of the normal size, which, when blown up, appears on the surface to be perfectly normal, but does strange things in its deepest depths. And at a magnitude of over 10^15, you can't go much deeper, at least with DOS Fractint. Today's scene lies in the East Valley area of the large minibrot on the west branch of the filament extending from the period-3 bud on the north side of the main bay of the tiny parent M-set. Traces of East Valley stuff abound in the scene, but the overall donut-like pattern is quite unexpected. The four brilliant red areas are fine examples of what I call 'peaks of anti-bifurcation', where the iteration count grows smaller as the center is approached, while the number of elements is cut in half instead of doubling. I named the image "Planetary Nebula" when I was reminded of the gaseous shells puffed off by dying stars. The art and math ratings are both a 7, indicating near average interest. The calculation time of 2-3/4 minutes can be avoided by checking one (or all) of the FOTD web sites. FOTD images are available on the following web sites. <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Lots of clouds and occasional periods of rain prevailed here at Fractal Central today. The fractal cat enjoyed the near perfect temperature of 79F 26C. The humans, not being quite as fractal as the cat, spent the day doing what needed to be done. The next FOTD will be posted soon. Until we find out now much time 'soon' implies, take care, and since all the world's problems are caused by someone else, no one needs to do anything about the problems. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Planetary_Nebula { ; time=0:02:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.00153754810877916/+0.010303790076819\ 72/1.344536e+015/1/-70/0 params=100/2/-1e-016/-2/0\ /0/0/0 float=y maxiter=1500 inside=0 logmap=190 periodicity=6 mathtolerance=0.05/1 colors=000z0Lx0Lm0Mc0MU1OK230000000000000000010120\ 2303404505606707808919A2AB3BC4CD6DE8EGAFICGKCILBKM\ BNLAQK9UJ9ZI8cH8hGDjHIlINnISoJXpJaqKksXku`mwdrzhzz\ lzzptzdovTmrImmHmhGhcFcZEZUDUPDQKIMKNILSFOWCU`F_eH\ ejJknGlqElsClvAlx8lzDktIjoNiiShdXgZafUfeOjdJdbL_`M\ U_NPYOJWQEVR8TS3STAYRGcPMhOQjUTl_WmdZoj_qnapobopdn\ qemqflrhksijttemlnxjitieqh`ngXkkRihShfThdThbUh`UhZ\ VhtbhXVhANhBSgBXgBagBfgBkgBpgBug5uhIlYVdOfXENdJ4kO\ l5EKoVRePYWJdMDjC7nRHreRdZVSTZEMb1GeoeneiiWmdNp_Vn\ UblPjjKrhFpkJVZWoEgdQaVaWAqSGoRLmQQlPVjO_iOddXh`dl\ XlrNvqQupTtoWsoZsnarmdqlbsmgqmkojkymonosdtyPqwVou`\ ltfjrlgprdwxeowehwfawfVwgOwgHwgAwhGqiLkjQekV`l`Vme\ PnjJrnHnoEkoCho9dp7ap4Wu1Zp2ak3df4fa5iX6lS7oN8xT0t\ O5qJ9mFEjAIg6Me9SdCXbFbaIgkQm`LlRGkGBj67jLHdPGh_Q_\ i_RqpAshJuaRwU_yNgfrRpZczGojLdWQVHVLN`OTeQZjSUYaPM\ kLAuPWjVueTq`SmXQjSPfO1zA } 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

Three Details
by Brian Prentice 01 Aug '13

01 Aug '13

Here are three monochrome details of the fractal discussed here recently: http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_26a.png http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_26b.png http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_26c.png Brian Prentice

3 3