; Date: Wed, 20 Oct 2004 10:07:05 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 20-10-04 (Elephant-Seahorse [6]) ; Id: <1.5.4.16.20041020100811.38ff8818@pop.mindspring.com> ; --------- ; ; FOTD -- October 20, 2004 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; Today's FOTD takes us to the hypercomplex formula of Fractint, ; which draws a four-dimensional version of the Mandelbrot set. ; At one time I used this formula quite extensively, but since ; then I have written my own formula, the HyperMandelbrot, which ; draws all the same images plus many new images that the hyper- ; complex formula does not. ; ; The hypercomplex formula is not to be cast aside as outmoded ; however. It still draws some very interesting images, and it ; draws them faster than my own formula. In a case like today's, ; where the image takes over one hour to render, speed becomes ; quite important. In addition, the hypercomplex formula is the ; only one in which the various functions can be applied. ; ; Being four-dimensional, the overall shape of the hypercomplex ; Mandelbrot set is impossible to visualize, but when the function ; is 'sqr', it can be taken as two familiar Mandelbrot sets partly ; overlapping. The position of the overlapping sets is controlled ; by the Z parameter. The other functions produce different ; figures, but the figures behave in pretty much the same way. ; ; The most interesting parts of the fractals drawn by the hyper- ; complex formula are the places where different parts of the two ; overlapping M-sets intersect. One such place is seen in today's ; image, which shows an intersection of Elephant Valley and ; Seahorse Valley. ; ; When two elements intersect, the element with the lower itera- ; tion count always obliterates the higher. In today's image, ; Seahorse Valley appears as the brownish shaft shooting up the ; center of the frame, while the rest of the scene is a part of ; Elephant valley. Examine the brownish elephant-trunk features ; just above the center of the frame. The elephant spirals do not ; go on indefinitely, as would be expected. Instead, as their ; iteration count increases, they grow more diffuse as they grow ; smaller, until their iteration count finally becomes higher than ; the count of Seahorse Valley, which until now they have been ; obscuring, and they vanish entirely. The moral of all this is, ; 'once a point escapes, it is not coming back'. ; ; I named the image "Elephant-Seahorse", because it is a combina- ; tion of both valleys. I rated it at a 6, more for its mathema- ; tical interest than its artistic worth. ; ; The unusually slow render time of 1 hour 18 minutes reduces the ; overall worth to a pathetic 7.6. But that abysmal worth can be ; ignored by downloading the file of the completed GIF image from ; the FOTD web site at: ; ; ; ; A chilly rain here at Fractal Central on Tuesday, with a temper- ; ature of 52F 11C, kept the dynamic duo of fractal cats indoors ; all day. They accepted their confinement stoically, though an ; extra treat of tuna was needed to help them find their stoicism. ; Today is starting chilly and cloudy, but at least it is dry. ; What the cats will make of this is anybody's guess. ; ; My guess is that the next FOTD will appear in 24 hours, and it ; is a pretty fair guess that the image will be memorable. Until ; that glorious moment arrives, take care, and search for the ; hidden meaning in fractals. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Elephant-SeaHorse { ; time=1:18:35.73--SF5 on a P200 reset=2003 type=hypercomplex function=sqr passes=1 center-mag=-0.22062180436286390/-0.029775589430454\ 16/607.5435 params=0/0/0/0.53 float=y maxiter=27000 bailout=9 inside=0 logmap=25 periodicity=10 colors=000OSVPTVQUWRVWSWWUXWVYXWZXX_XY`XZaY_bYacYb\ dYceZdfZegZfhZgi_ij_jk_kl_lm`mn`no`opapqaop`nn_lmZ\ kkYjjXiiWggVffUedUccTbaSa`R`_QZYPYXOXVNVUMUSMTRLSQ\ KQOJPNIOLHMKGLIFKHEIFDJGEKHELHFMIFNIGOJGPKHQKHRLIS\ LITMJUNJVNKWOKXOKYPLZQL_QM`RMaRNbSNcTOdTOeUPfUPgVQ\ hWQiWRjXRkYRkZRj_9i`BhaCgbEfcFedGceIafJ_gLYhMWiNUj\ PSkQQlSQmRRnRSnRToQUoQVoQXpPYpPZpP_pP`qOaqObqOdrNe\ rNfrNgsMhsMisMktNjsMjsMjsMjsMjsMjsMjrMjrMirLirLirL\ irLiqLiqLiqLiqLhqKhqKhpKhpKhpKhpKhpKhpKhrIhpKhoMhm\ OhlQhjShiUhgVhfXhdZhc`habh`dhZehYghWihVkhTmhSohRpg\ SofTofToeUneUndVncVncWmbWmbXmaYmaYl`Zl_YmZXnYWoXVp\ WUqVTrUSsTRtSQuRPvQOwPNxOMyPLzPKzQJzQIzQHzRGzRGzSH\ zSIzTIzTJzTKzUKzULzVMzVMzWNzWOzWOzXPzXQyYQyYRyZSxZ\ SxZTx_Ux_Uw`Vw`Ww`Ww_VuZVtYUsXUrWTqVToUSnTSmTRlSRk\ RQiQQhPPgOPfNOeMOcLNbLNaKM`JM_ILYHLXGKWFKVEJUCISEJ\ TFKTGLTHMUINUJOUKPUMQVNRV } ; END PARAMETER FILE========================================= ; ;