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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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=========================================