FOTD -- December 28, 2002 (Rating 9) Fractal visionaries and enthusiasts: Somehow, I once again survived the first and biggest of the two seasonal holidays. (Is it politically correct to use the word 'Christmas'?) The tree was lovely, the turkey dinner delicious, the presents were exchanged peacefully, the conversation was not controversial, and most importantly, the fractal cats concealed their bad moods. All this pleasantness left me in a highly- charged fractal-finding mode. (Fractals are really not hard to find.) The fractal I found appears as today's FOTD image. The formula I used is an old one, which has been lying dormant for many years and which for some forgotten reason I had named 'cascade'. As is the case with most of these old formulae, I have totally forgotten what it was originally intended to do. (Why do I neglect to add comments?) The formula appears to have some vague relation to the mysterious 'Ikenaga' function, though I wrote it at least one year before I began working with the 'Ikenaga' function. The image that I found, with its rating of a very impressive 9, is one of the best of the year. Like so many works of art that unfold in time, the 2002 series of FOTD images has reached its peak near its end. I named the image "Cascade of Bubbles". I chose this name when I noticed that the bof60 bubbles appear to be cascading down into the depths of the picture. This cascading effect might be what inspired the original name of the formula, which, unlike most of my formulae, has no variable parameters. There are as many holly leaves as bubbles in the image, all cascading downward, but bubbles are more poetic, so I chose the bubbles. The image renders in exactly 4 minutes on my machine, accurate to 1/100 of a second. There is nothing unusual in this time. It is simply a coincidence. After all, a time of exactly 4 minutes has just as much chance of coming up as a time such as 0:04:16.37. The 4-minute render-time wait can be cut by more than half by downloading the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> It was a cold week here at Fractal Central, with 4 inches of snow on Christmas day giving the first white Christmas in 33 years. Needless to say, the dynamic duo of fractal cats disapproved of such conditions and needed several treats of left-over turkey to soothe their ruffled tempers. As for me, I somehow have managed to get almost all the work caught up, and find myself with little to do but search for the next fractal, which will appear in 24 hours. It will be hard to find one that equals or exceeds today's image, but I'll try. Check tomorrow to see if I succeed. Until then, take care and relax. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Cascade_of_Bubbles { ; time=0:04:00.00--SF5 on a P200 reset=1950 type=formula formulafile=jim.frm formulaname=cascade passes=1 center-mag=+0.2605319\ 14765418/+0.9301176063963406/890.8654/1/162.5/-3.6\ 0000224075562869e-012 float=y maxiter=250 bailout=100 inside=bof60 logmap=yes periodicity=0 colors=000zzzzmmwcUqX0mTHkPOjLMiJLhHKgFIfDHeBGd9Fc\ 7Db5C`3BZ4CX5CU5DR6DO6EJ7EJ7EUUtUUtUUoUUoqaapaaoba\ obanbambalcakcajcajcaidahdaafZUpVNtSFoO8nL8nN8nQzq\ SpnVmnXdn_anabmdamfcmiclkckndjpehsgftidzkbzn`zqZzu\ QztCprEhpGbnHSkJViLXgN_ePacQdaSf_UiYWkVYnTZpR`sPbu\ U_nZWgbT_gPTlMMjPMhSMfVMdYLb`L`cL_fLYhLWkLUnLSqKQt\ KOwKMzKKxLJuMHsMGqNEnOClPBjP9hQ7eR6cS4aS3ZT1XU4ZS6\ `R9bPBdOEfMGhKJkJLmHOoFQqETsCVuBYw9_y8`t9ap9bl9chA\ ddAe`AfXAgTAhPAiLBjHBkDBk9BnKJqVRtdYrdVpeSnePlfMkf\ JifFggCeg9ch6ah3`h0Zj3Yl6Xm9VoBUpETrHSsKQuMPvP7hh6\ ce5Zb4U_3PX2KU1FR3WP5mMt8jbFeLN_LUaL_bLfdLleLsgMzi\ KveIraFnXDjTAfP8bK5ZG9aICcLGfNMTRSEVY0ZZ1Z`2Ya4Yb5\ Yd6Xe7Xa8VY9TUAQRCONDMJEKFFHBGFDJDENCGQAIT8JW6L_5M\ b3Oe1Ri9TmGWqOYuV`ybXuaUp_QlZMhYIcWF_VBVT7RS7SO6TK\ 6UH5VD5W9Cz5gOjjadhKolUnocmsmleLpeWqdfrdqsiAhn9`_J\ nUSkN`iHiffPrgctirwb9o_8n } frm:cascade {; Jim Muth z=c=pixel: a=sqr(z)+(c-1)*z-c b=3*sqr(z)+c-1 z=z-2*a/b, .000000000000000000000000000001 <= |a| } END 20.0 PAR-FORMULA FILE==================================