; Date: Sun, 03 Sep 2006 00:15:33 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 03-09-06 (Seahorse Valley-02 [6]) ; Id: <1.5.4.16.20060903001625.0daf4806@pop.mindspring.com> ; --------- ; ; FOTD -- September 03, 2006 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; Today's colorful image is another unfamiliar view of Seahorse ; Valley, which appears as the straight-edged bluish horizontal ; band extending nearly the full width of the frame. If the ; Mandelbrot set were expanded to include the part of the Julibrot ; extending behind and in front of the screen along the real-Z ; axis, today's view would be looking down from above. (Yester- ; day's view was looking from the left.) Being a four-dimensional ; object, Seahorse Valley has more different views than can be ; imagined. And even when all the views have been studied, the ; viewer will have no better idea of the actual overall shape of ; the valley than he did at the start. ; ; Four-dimensional objects are not mere everyday three-dimensional ; objects with extra complex shapes. They are totally and ; absolutely different. The most basic feature of 4-D things is ; that their surfaces are three-dimensional, with 3-D volume. ; When looking at the surface of an opaque 4-D object, a 4-D man ; would see a 3-D volume projected onto his 3-D retinas. When ; observing a 4-D hypersphere, he would see what we would consider ; every point on the inside of a normal 3-D sphere. ; ; Rotation in four dimensions is about a plane as axis, and a 4-D ; object may be subject to two totally independent rotations ; simultaneously, with the gyroscopic effect of one rotation ; having no effect on the other rotation. All this is entirely ; unimaginable, but may easily be confirmed with mathematics. ; ; I named today's image "Seahorse Valley-02". I rated it at a 6. ; The render time of 1-1/2 minutes is brief enough to cause no ; one impatience. But the image has been posted anyway to the ; FOTD web site at: ; ; ; ; Heavy rain fell all day here at New Fractal Central on Saturday. ; The fractal cats watched with some interest for a few minutes, ; then got about their normal cat business. My day was accept- ; able. The next FOTD will appear in 24 hours. Until then, take ; care, and step likely. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Seahorse_Valley-02 { ; time=0:01:36.83--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=flip/ident center-mag=-0.0375587/0/13.33333/0.06756/90/6.3997\ 41848e-014 params=90/0/2/0/0/0/-0.75/0.1 float=y maxiter=16000 inside=0 logmap=yes periodicity=10 colors=000qcUoXVmQWkJXiCYh6YlAeoDlrGsuJzpLtlNogPic\ QdZSZVUUQWOMXJHZDD`89a3Cc6Fe8HgAKiCNkEPmGSoIUqKXsM\ _uOawQdySfzUhuVjqWkmXmiYneYpaZqX_sT`tP`vLawHbyDcz9\ cyHcyOcyWcybcyjcyqcyxcsu`msYgqVanSWlPQjMKgJEeG8cD2\ aAhANkPancolbmkakj`jh_hgZgfYeeXdcWbbVaaU_`UZZVYYVX\ XVWWWWUWVTWUSXTRXTPXSOYRNYQMYQRVWWT``QfeOkjMpfPobR\ o_ToWWoSYnP_nLbnIdnEfmAim7km3mm0om8hkGbjOWiWQgcJmk\ DrbHvVKzNNz`NzOAzkdziezhezffzefzdfzbgzagz`gzZhzYhz\ XhzXgzYgzYfzYfzZezZezZdz_dz_cz_cz`bz`bz`az`azWYzSU\ zOQzKNzGJzCFz8Bz48z7AzABzDCzGDzJEzLFzOGzRHzUIzXJzZ\ KzaSzd_zggzklzoqzsuzrvzUwz6xzPyzgzzizzjzzkzzlzznzz\ ozzpzzqzzrzzdzzfzzgzzizzjzzlzzmzzizzfzzbzz_zzZzzZz\ zZzzYzzYzzYzzYzzXzzXzzXjzXkzWlzWzzWzzWzzXzzYzzZzz_\ zz`zzazzbzzczzdzzezzfzzgzzhzzizzizzjzzkzzlzzmzzzzz\ lzzVzzDzzHzzKzzNzzQzzTzzVzzXzzZzz`zzbzzgzzlzzqzzvz\ zszzqzzozzmzzkzzizzgzzdzz } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } ; END PARAMETER FILE========================================= ; ;