; Date: Mon, 01 Jun 2009 16:16:29 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 01-06-09 (Seahorse Valley-01 [6.5]) ; Id: <1.5.4.16.20090601161744.2b2fc1e0@pop.mindspring.com> ; --------- ; ; FOTD -- June 01, 2009 (Rating 6.5) ; ; Fractal visionaries and enthusiasts: ; ; Very slow image alert!! Run parameter file at your own risk! ; ; We have not had a FOTD theme month for quite a while, so I have ; decided to make Seahorse Valley the FOTD theme for the month of ; June. Not only will we explore the well-known Mandelbrot and ; Julia aspects of the valley, we will check the four remaining ; aspects as well. ; ; Seahorse Valley of the Mandelbrot set is actually a four- ; dimensional thing, which includes not only all its Julia sets, ; but the scenes in the Oblate, Parabolic, Elliptic and ; Rectangular directions, as well as the oblique scenes sliced at ; unimaginable four-dimensional angles. I have included a short ; chart of the six mutually perpendicular planes of the Z^2+C ; Julibrot: ; ; real(C) and imag(C) = Mandelbrot aspect ; real(Z) and imag(Z) = Julia aspect ; imag(C) and real(Z) = Oblate aspect ; real(C) and real(Z) = Parabolic aspect ; real(C) and imag(Z) = Elliptic aspect ; imag(C) and imag(Z) = Rectangular aspect ; ; The names of the four additional aspects are my own invention. ; ; The orientation of today's image is within 1/100 of one degree ; of the Julia orientation. The tiny rotation is toward the ; Rectangular orientation. The outer edge of the fractal is the ; familiar Julia set with a C-value of -0.75,0. Cut the maxiter ; to 100 to see it. ; ; The strange-looking stuff inside the familiar Julia set is a ; gross enlargement and distortion of the Mandelbrot aspect of Sea- ; horse Valley. As far as I know, this is the smallest deviation ; from the actual Julia orientation of Seahorse Valley that I have ; yet seen. ; ; The familiar Julia set of Seahorse Valley calculates in a few ; seconds, but today's slight rotation raises the calculation time ; to over three hours. The incredible increase in time is due to ; the stuff on the inside of the fractal, most of which has an ; iteration count in the millions, and also to the fact that the ; periodicity must be turned off for the image to generate ; properly. ; ; The name "Seahorse Valley-01" is a catalog number, since I will ; be doing many more Seahorse-Valley images in the month to come. ; Luckily, no more images will take anywhere near today's 3 hours ; to calculate. The rating of a 6-1/2 implies that I feel there ; is too much mathematical interest and too little artistic worth ; in the image. Also, I have posted several images very similar ; to today's in the past, though the images were nowhere near as ; extreme. ; ; Those with a few hours to spare may see the image by starting ; the included parameter file and coming back several hours later. ; Those with more pressing things to do may see the finished image ; on the FOTD web site at: ; ; ; ; Another perfect day prevailed here at Fractal Central on Sunday, ; with sunny skies and a temperature of 77F 25C. The fractal cats ; spent most of the day in the side window, watching the other ; cats in the neighborhood wander by. ; ; My day was pleasant enough. If all goes well, the next FOTD ; image will be posted in about 6 hours. Until then, take care, ; and when does the beginning end? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Seahorse_Valley-01 { ; time=3:09:55.05-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=1 center-mag=0/0/0.862069 params=90/0/89.99/90/-0.75\ /0/0/0/2/0 float=y maxiter=3500000 inside=0 logmap=yes symmetry=yaxis periodicity=none colors=000HazJczLezNgzPizRjzTkzVmzXnzZoz`qzbszduzf\ wzhzzjzzlzznzzpzzrzztzzvzzxzzzzzzzzzvzzrzzmzzhzzcz\ zZzOj_NibMidLifKihJhkIhmHhoGhqFgtEgvDgxCgzIfuOepTd\ kZdfccaibXnbTi`Vd_X_YZVX__YZdZZi_Zn`ZsaZwbZtYRqUJn\ QCpVKqZRrbYsgdtkkuorrmmpkinjdlh`jgXdi_ZjaTkcNmfHnh\ Boj6pl7mk8jk8gj9ejAbjA_iBYiBVhCShDQhDNgEKgEIgILiLN\ jOPkRRlUTmXWn_YoNfLcfZtfkp`lmWliQlfLlbGl_AlW5lT0lQ\ 6nOBpLGqJMsGRtEWvC`wFdqHgkJjfLm`OpVQsQSvKUyFTuKTqP\ SmTSiYReaRafRZjPWhNTfLQdKNbIK`GIZEFXDCVB9T96R73P61\ O76R8BU8GX9L_9QbAUeBZhBckChnCmqDrtDvvFruHotJksLhrN\ dqPapRYoSVnUSmWPlYMk_JjaDicAhd7g`CeYHdULcRQbNUaKZ`\ HcZDgYAlX6rW3xV0zU2xS3tR4pP5mO6jM7gL8eJAbIB_GCXFDU\ DERCFOAGM9KPBORCSTDWWE_YFc_GgaHkdIofJshKvjLulOumQu\ nTuoVupYuq_trbtsdttgtuitvltwnnxmiymczlczlczlczkczk\ czjczjczjczkczlhzlmzmrzmvznzznzzozzpzzpzzqzzqzzrzz\ rzzizz`zzSzzJzzBzzIzzOzzU } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint