; Date: Thu, 21 Oct 2004 09:49:11 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 21-10-04 (Antarctic Fractal [6]) ; Id: <1.5.4.16.20041021095017.2aafc51c@pop.mindspring.com> ; --------- ; ; FOTD -- October 21, 2004 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; Today's formula, the 'hypercomplexj', draws the Julia sets that ; correspond to the Mandelbrot sets drawn by the 'hypercomplex' ; formula. These formulas use 4-part hypercomplex numbers, which ; draw four-dimensional M-sets and J-sets. These two four-dimen- ; sional collections of sets are oriented so that they intersect ; in single points, with an entire 4-D Julia set corresponding to ; every individual point of the 4-D M-set. For this relation to ; be possible, fully eight dimensions are needed. So when we ex- ; plore with the 'hypercomplexj' formula, we are actually explor- ; ing an eight-dimensional Julibrot figure. ; ; In eight-dimensional space, there are six mutually-perpendicular ; directions that are at the same time perpendicular to a two- ; dimensional plane, such as that of the screen. All six direc- ; tions can be explored with the six variable parameters of the ; 'hypercomplexj' formula. (For some reason, the 'hypercomplex' ; formula ignores the 'warped' M-sets.) My dream formula would be ; one that draws every possible orientation through this 8-D Juli- ; brot. Unfortunately, my math ability is not up to the task of ; writing such a formula, so the formula will remain a dream. ; ; When I first saw today's image, it reminded me of something ; familiar that I could not quite recall. Then I recognized a ; resemblance to the continent of Antarctica, and named the image ; "Antarctic Fractal". ; ; The image is one of the Julia sets that corresponds to yester- ; day's 'Elephant-Seahorse' Mandelbrot image. In the 8-D Julibrot ; not all Julia set slices are symmetrical, as they are in the ; more familiar 4-D Julibrot. In today's image, which shows the ; entire Julia set, I emphasized this lack of symmetry. ; ; As was the case in yesterday's image, today's image has places ; where different elements overlap, and the lower-iteration ele- ; ments are obliterating the higher-iteration ones. What we have ; is two distinct Julia sets fighting to be displayed on the ; screen, with the lower parts of each set winning. It strikes me ; as much like human nature, where we know what is right but are ; prevented from doing it by our baser instincts. ; ; With so much calculating to do in each cycle and a maxiter of ; 27000, today's image is a slow one, taking an hour on my tired ; old workhorse 200mhz machine. (On the new 2200mhz machine, a ; test-rendering took 8 minutes, but that unit is for real work, ; not fun.) ; ; Today's image has much mathematical interest but lacks artistic ; beauty. I rated it at a 6, mostly for its math interest. When ; the one-hour render time is figured in, the overall worth equals ; a humble 10. ; ; My recommendation is to avoid such excessive humility by down- ; loading the completed GIF image from the FOTD web site at: ; ; ; ; But if your machine is a fast one and is Fractint compatible, be ; humble. Take a few minutes to enjoy the coming-into-existence ; of a tiny part of an unimaginable 8-dimensional world. And un- ; less I am mistaken, our universe is currently theorized to con- ; tain 11 dimensions. ; ; A chilly, dreary, misty day here at Fractal Central on Wednesday ; kept the fractal cats confined to their shelf by the window. ; For some unknown reason, their moods were not bad however. As a ; reward, they received extra tuna for their evening dinner. ; Today is again starting dreary and chilly. More tuna will be ; needed. ; ; In my department, the commercial work is still caught up, and ; the FOTD fractals will keep coming every day. The next one will ; appear, not quite by magic, at this same time and place 24 hours ; from now. Until that ecstatic moment, take care, and don't dis- ; turb the fractal peace with excess exuberance. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Antarctic_Fractal { ; time=0:12:09.08--SF5 on a P200 reset=2003 type=hypercomplexj function=sqr passes=t center-mag=-8.88178e-016/-0.132743/1.173709 params=-0.2218959949992792/-0.03077554360265753/0/\ 0.53/0.25/0 float=y maxiter=27000 bailout=9 logmap=yes symmetry=none periodicity=0 colors=000POePXeOZeO`eOdeNheOleOoeOqeWrd_sdctdeudf\ vefwgbwiZwkVwmRxpNxrKxsKwqKuoKsmKqkKoiKmgKkeKicKha\ Kh_FgYAgWDeUFcSHaQJ_OLYMOWLQUMSSMUQNWOOZMO`KPbIQdG\ QfERhDReCQcBPaBO_ANX9MV9LT8KR8JO7IM6HK6GI5FG5FH9JI\ CNIFRJIUKMYKPaLSeLVhMYgN_gNbgOdfOgfPifQleQneRqeRsd\ SvdSxdYugcriiokolnuipzfrzdtzeotejnfehgabhXXjSRkOLk\ JFjEAhACf9Dd8Eb7G`6HZ5IX4KV3LT2MR1NP0ON6PLCQKIRMOS\ NUTOUUPUWQVXRVYSVZTV_UW`VWaWWcXWdYXeZXf_Xg`XhaYibY\ kcYldYmeZnfZogZphZqi_sj_tk_ul_vm`wn`xo`ypazqayp`xn\ _vmZukYtjXsiWqgVpfUodUmcTlaSk`Rj_QhYPgXOfVNdUMcSMb\ RLaQK_OJZNIYLHWKGVIFUHESFDTGEUHEVHFWIFXIGYJGZKH_KH\ `LIaLIbMJcNJdNKeOKfOKgPLhQLiQMjRMkRNlSNmTOnTOoUPpU\ PqVQrWQsWRtXRuYRuZRt_9s`BraCqbEpcFodGmeIkfJigLghMe\ iNcjPakQ_lS_mR`nRanRboQcoQdoQfpPgpPhpPipPjqOkqOlqO\ nrNorNprNqsMrsMssMutNtsMtsMtsMtsMtsMtsMtrMtrMsrLsr\ LsrLsrLsqLsqLsqKsqKsqKsqK } ; END PARAMETER FILE========================================= ; ;