; Date: Wed, 30 Mar 2005 09:50:07 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 30-03-05 (Extremely Deep [9]) ; Id: <1.5.4.16.20050330095057.29c790b8@pop.mindspring.com> ; --------- ; ; FOTD -- March 30, 2005 (Rating 9) ; ; Fractal visionaries and enthusiasts: ; ; Caution. Today's image is the slowest of all time. Unless you ; can afford several days of computer time, do not attempt to ; generate today's image from the included parameter file. ; Download it from the FOTD web site. ; ; In yesterday's FOTD discussion I announced that I had found a ; scene extremely deep in Seahorse Valley, but that it would take ; several days for my fastest computer to render it at full size. ; Well, I underestimated the ability of my fast P4-2300 machine ; when it is running straight DOS. When I booted it with DOS 6.22 ; and set it to the task of calculating the full sized image, it ; finished the job in under 3-1/2 hours, running at about 23 times ; the speed of the P200 and not needing to be kick-started back ; into high speed mode every half hour or so. This speed is ; somewhat of a surprise, since 2300 divided by 200 equals 11.5, ; which is only half of 23. I guess the 2300 does twice the work ; per cycle, at least with the high-speed Mandelbrot formula. ; ; The render time in the parameter file has been adjusted to ; reflect the time it would have taken my standard P200 unit to ; calculate the same scene. Needless to say, very few will wish ; to devote almost 3-1/2 days computer time to the calculation of ; today's image, which is why I sent it on ahead to the FOTD web ; site at: ; ; ; ; where it may be viewed at once. ; ; Today's image is located extremely deep in Seahorse Valley, at a ; distance of only 0.00000799... from the mystical point on the ; X-axis. It shows a midget on the west shore of the valley. The ; almost unbelievable narrowness of the valley at this point is ; demonstrated by the X-value of the scene, -0.7500000000975. ; ; The iteration count of the large areas of purple is over ; 1,100,000, which is one of the reasons the image is so slow. ; The other reason is the maxiter, which at 450,000,000 is over ; 1/5 of the absolute maximum of which Fractint is capable. And ; even this extreme maxiter fails to close all the spurious holes ; in the image. The magnitude of 3*10^12 is not all that unusual, ; but I have included the mathtolerance entry in the parameter ; file to insure that anyone who decides to render the image from ; the parameter file does so at the correct magnitude. ; ; Searching for seahorses in the image is futile. I have no idea ; where they have gone, but they have totally vanished. What we ; have instead is a midget surrounded by a spider-web network of ; filaments, organized into nodes with peanut-holes at the center. ; The pattern of filaments around the midget is also surprisingly ; irregular. The expected powers-of-two organization of elements ; is there, but it appears to be breaking down. I wonder whether ; the 2-4-8-16... arrangement breaks down entirely even deeper in ; the valley. I rather doubt it, but I also doubt that I will ; soon be going deeper into Seahorse Valley. ; ; I named today's image "Extremely Deep", which is nothing more ; than a description of its location. The rating of a 9 reflects ; the mathematical interest. The artistic merit alone is probably ; closer to a 6. ; ; I think that with today's image I have satisfied my curiosity ; about what lies hidden this deep in the Mandelbrot valleys. ; Tomorrow's FOTD will return us to the world of more conventional ; fractals. I have yet to conclude the tour of the Elliptic ; orientation of the Julibrot, but I might stop off briefly in the ; MandelbrotMix4 formula for a bit of refreshment before returning ; to the fourth dimension. ; ; A perfect early spring day on Tuesday brought out the playful- ; ness in the neighborhood kids and the fractal cats as well. The ; duo actually started chasing each other around the yard, much as ; they did many years ago when they were young cats. It brought a ; twinge of nostalgia to me as I wondered if this was the last ; time I would see the nearly 15-year-old pair carrying on like ; kittens. Even though I had to call a few extra times to coax ; them indoors when evening came, I gave them an extra treat of ; tuna. They ended the day sleeping side-by-side on the couch. ; This morning is starting hazy but even milder. I expect another ; good day for the duo. ; ; For me it will be work first, then fractal play. The next ; fractal will playfully appear in 24 hours. Until then, take ; care, and be at ease in the abstract realm of numbers. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Extremely_Deep {; time=80:45:00.00--SF5 on a P200 reset=2004 type=mandel center-mag=-0.75000000009746660/+0.000007999957331\ 57/2.927877e+012/1/14.9973484273890882/-0.00159468\ 292361711339 params=0/0 float=y maxiter=450000000 bailout=9 inside=0 periodicity=10 mathtolerance=/1 colors=000zvuzttzrszprznqzlpzjozhnzfmzdlzbkz`jyZix\ XhwVgtUfqTenSdkRchQ`ePZbOW_NUYMSVLQTKNQJLNIJLHHIGE\ GFCDEABE8FIAILBLPCOSDRWEUZFXbG`eHciIflJipKlsLowMrz\ NuzOtzNswMstLrqKqoJqlIpiHofGodGqgFriEskEtnDupCvrCw\ tBxwAyyAzz9zz9xzEvzItzNryRoxWmw_kvciuhftldsqbru`qy\ YmwWivUetSasQZqOVpMRnKNmIJkGGjMLlRPnXToaYqgasletjh\ mikghnagqWftQewKdyEcwFcuFcsFbqFboFbmFakFaiFagFaeFZ\ hGXjHUmHSoIQqINtJLvJJxKGzKEzLCzLLmLMoSNpZOqePrlQss\ QtzTstWrnZqhapcdoYgnSjmMllHmhLmePmbSm_WnW_nTbnQfnN\ jnKm9fF8cG8`G8YG8WH8TH8QH8OHERJJTLPVMUYOZ_PdaRicSn\ fUthVyjXzlYroUfqRVtNKvKGn_Hm`HlaIlaIkbJjcJjcKidKhe\ LheLgfLgfPjiTmkXpm`rpdurhxtlzvjzuhztfzsdzrbzq`zpZz\ oYznWzmUzlSzkQzjOziMzhKzgJzgMzfPzfRzfUzfWyfZwf`ufc\ tffrehpeknemmepkerieugewfevjgvmhvpiutjuwkuzluzmtzn\ sznrzofzDdzBazA_y9Xy8Vy7Ty6Yz9bzBgzDlzFqzHvzJzzLzz\ NzzRwzUszXoz_htiltlotomup } ; END PARAMETER FILE========================================= ; ;