; Date: Fri, 15 Oct 2004 09:52:50 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 15-10-04 (The All-Seeing Eye [8]) ; Id: <1.5.4.16.20041015095352.39078256@pop.mindspring.com> ; --------- ; ; FOTD -- October 15, 2004 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; Today's unusual fractal takes us to the fn(z*z) fractal formula, ; a formula that at first glance appears to have little to offer, ; but proves quite rewarding when explored. Like yesterday's ; formula, today's formula draws some images that consist mostly ; of blank 'inside' stuff that does not come to life until it is ; activated by a suitable non-flat rendering method. Today's ; image consists almost entirely of 'inside' stuff brought to life ; by the 'fmod' inside fill. Only the brilliant center 'sun' and ; the brilliant turquoise center dots surrounding it are made of ; 'outside' material. ; ; Quite surprising is the effect the 'fmod' inside fill has on ; today's image. This fill normally produces overlapping bubbles, ; but in today's image it creates virtually the entire fractal ; with its spider-like arms and smoothly gradated background. ; This is the best job I have yet seen the 'fmod' fill do on a ; fractal. I must one day check to see what additional surprises ; this fill has hidden in it. ; ; In the fn(z*z) formula the function is obviously a major part of ; the calculation. To generate today's image I chose the cotanh ; or hyperbolic cotangent function. When the bailout radius is ; set to 1, this function fills the screen with an unsurprising ; hyperbolic pattern. As the bailout radius is increased, the ; solid pattern breaks down into separate bits and pieces that ; grow smaller as the bailout is increased further, until they ; finally vanish entirely, leaving a blank black screen of ; 'inside' stuff. For today's image, I settled on a bailout of ; 1600, where the bits and pieces have grown quite small, but have ; not yet entirely vanished. ; ; When I am in scientific mode, I call such blank or nearly blank ; screens 'virtual fractals' because they resemble sub-atomic ; virtual particles that are caught halfway between existing and ; not existing, and need only some extra energy to bring them to ; full existence. In today's case, the 'fmod' inside fill ; supplies that energy. In mystical mode, I call such blank ; screens ghost images, because they resemble ghosts or spirits ; that really exist but are invisible to our everyday sight. In ; this case, the 'fmod' fill gives us the psychic sight needed to ; see the ghosts. ; ; Today's image resembles nothing as much as a great eye. I named ; it "The All-Seeing Eye" I leave it to the viewer to decide the ; owner of the all-seeing eye. ; ; With its rating of 8, today's image is the highest rated image ; yet of my tour through Fractint. The render time of under 2 ; minutes raises that rating to an overall worth of an impressive ; 430. ; ; As always, the minor job of image rendering may be avoided by ; downloading the completed GIF image from the FOTD web site at: ; ; ; ; A nondescript day here at Fractal Central on Thursday left the ; fractal cats in an ambiguous mood. Variably cloudy skies and a ; temperature of 64F 18C, with light winds, were pleasant enough ; for humans, but the duo could not decide how they wanted to ; spend the afternoon. They finally divided their time between ; the porch and the holly thicket. The clouds are thick this ; morning, and rain is threatening, so I doubt that the cats will ; have a better day. ; ; For me, even if it rains, the day will be fair enough once the ; work is finished. And if all goes very well, I'll find a great ; fractal. Whatever happens, I'll return in 24 hours with the ; next FOTD. Until then, take care, and a great fractal is better ; than a flu shot. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= The_All-Seeing_Eye { ; time=0:01:51.78--SF5 on a P200 reset=2003 type=fn(z*z) function=cotanh passes=1 center-mag=-1.5342/-1.53559/5.268201/0.9415/45/\ -2.50563458870090017e-014 float=y maxiter=255 bailout=1600 inside=fmod proximity=1 logmap=yes symmetry=none periodicity=10 colors=000BTgzztTxyQwxNuwLsvKqtKorKmpJknJilJgjJfhI\ dfIbdI`bHZ`HXZHVXHUVGSTGQRGOPFMNFKLFIJFHHGJKHKMHMO\ INQIPSJQUJRWKTYLU_LWaMXdMZfN_hN`jOblPcnPepQfrQgtRf\ vReySdxTcwUbvVauW`tX_tYZsZYq_Xo`WmaVkbUicTgdSeeRck\ KYpESu7Mz1Gw4Iu6Kr9MpBOmEQkGRhJTfLVcOXaQZZT_XVaUYc\ S_ePbgNdiKgjIilFlnDnpAqr8ssApqCmoEkmGhlIejJehLgfLi\ eLkcLmaMo_MqYMsWMuUMwSMyQNx9OwFOvLPuRQtXQsbRrhSqnT\ pzSqtRqoRqjQqdQq_PqVPqQOqKOqFNqANq5Qn8SlBUjEWgHYeJ\ _cMb`PdZSfXUhUXjS_lQbqPenOdlNcjMbgMaeL`cK_aKZZJYXI\ XVIWTHVQGUOGTMFSKERHEQFDPDCOBCNCDQDESEFVFGXGH_HIaI\ IdJJfKKiLLkMMnNNpGOpNNrTNt_MveMxkMzlOylPymQxmRxnTx\ nUwoVwoWwpYvpZvq_uq`urburctsdtsettgsthsuirujrvlrvm\ qwnqwoqpljiicbfYWcRP`LIYEAY6CW8EVAGTCISEKQGMPIONKQ\ MMSKNUJPWHRYGT_EVaDXcBZeA`g8bl5gi7cf9_dBXaDT_EQXGM\ UIISKFPMBOO9NN8MM8LL8LL8KK7JJ7II7II7HH6GG6FF6FF6EE\ 5DD5CC5CC5BB4AA49948A1994 } ; END PARAMETER FILE========================================= ; ;