; Date: Tue, 08 Mar 2005 09:56:14 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 08-03-05 (Parabolic Horse [6]) ; Id: <1.5.4.16.20050308095650.29bfbae8@pop.mindspring.com> ; --------- ; ; FOTD -- March 08, 2005 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; Today, we shift our attention to what I call the Parabolic ; slices of the Julibrot, which are determined by the real(c) and ; real(z) axes. To visualize the orientation of these slices, we ; must imagine the three-dimensional section of the Julibrot that ; exists in our space when the Mandelbrot set is on the screen and ; the real(z) axis is perpendicular to the screen. The Oblate ; slices that we have been examining for the past seven days are ; what we would see if we were to view this three-dimensional ; object from the left of the screen. The Parabolic slices that ; we will be examining for the next seven days are what we would ; see from above the screen. ; ; In the image, the vertical direction is the east-west direction ; of the Mandelbrot set, with east on top and west on bottom, ; while the horizontal direction is the in-out direction when the ; M-set is on the screen and the Julibrot is oriented so that the ; real(z) axis is perpendicular to the screen. The left half of ; today's image is the part of the Julibrot section behind the ; screen, the right half is in front of the screen. ; ; In today's image I have sliced the Julibrot through the upper ; branch of Seahorse Valley. Yet no valley is visible on the ; screen. Nor is anything visible resembling the Julia sets of ; the valley. The Valley has been transformed into the bright ; horizontal ribbon that appears near the top of today's image. ; Actually, the Seahorse ribbon is actually much narrower than it ; appears in today's image, which has been stretched in the ; vertical direction to 15 times its normal width. ; ; The narrow bright horizontal line lower in the image is one of ; the small valleys on the western shore of the large period-2 ; bud of the M-set. The broad area below that is the start of the ; Mandelbrot mainland in the vicinity of Scepter Valley. ; ; I named this orientation the Parabolic direction because it is ; filled with parabolas. In fact, the Parabolic slice through the ; origin of the Julibrot starts as one great parabola, which is ; actually the graph of the function X^2. Checking the Parabolic ; slice through the origin of a fractal is one way of finding the ; critical points of that fractal's formula, and is one of the ; methods I sometimes use. ; ; I named today's image "Parabolic Horse". No, I have never seen ; such an oddly shaped land-horse, but a valley named after the ; sea-horse does appear in the image, and the image most certainly ; is filled with parabolas, so I suppose the name is justified. ; ; I rated the image at a 6. Most of the rating is due to the ; colors, which I spent a little extra time on, and are rather ; intense. The render time of 2-1/2 minutes is quite reasonable ; for such an image, but so is the minimal effort required to ; download the completed image from the FOTD web site at: ; ; ; ; The time for the completion of the philosophy, which I abruptly ; discontinued, is drawing near. It should appear within a week. ; I will say little about my views at this time other than to ; state that I consider myself bound by neither scientific nor ; rational correctness. ; ; Warm sun and a high temperature of 70F 21C gave the fractal duo ; of cats nearly an entire day in the yard on Monday. They passed ; most of the time lurking in the holly bushes, but when the ; obnoxious gray-and-white cat from up the hill intruded in the ; yard, Thomas sprang into action, and with a mighty yell, sent ; the intruder scurying back where he belongs. Tippy watched the ; action with interest. When the day ended, I rewarded both of ; them with a generous serving of tuna. ; ; Today is starting rainy and windy, with rapidly falling tempera- ; tures and talk of snow on the way. It looks like the cats' good ; day will not be repeated. For me the day looks like it will be ; on the slow side, which means lots of time for the next fractal. ; Until that next fractal appears in 24 hours, take care, and why ; does 0! equal 1 instead of 0? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Parabolic_Horse { ; time=0:02:25.50--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-xz-yw-new passes=1 center-mag=0/-1.30045/13.90355/0.06894 params=0/0/2/0/0/0/0/0.051 float=y maxiter=40000 inside=255 logmap=11 symmetry=yaxis periodicity=10 colors=000MY0S_0U_0Yb0ee0ug0zg0zj0xe0m_0eU0YP0SH4M\ CCK6HE4PC6UH9SMCPPHPUMMYSMbSKeSKjSHmSHrSErSCuSEuSH\ uSHuSKuSKuSMuSMuSPuSSuSSuSUuSUuSYuSYxU_xYbx_bxeexg\ exjgxmgxrjxumxxmxzpxzpxzrzzxxzrrzpmzmgzjbzg_zbUz_P\ zYKzUEzS9zP6zK1zH0zE0zC0z90z60z40x44r49j4Ee4M_4SU4\ _M4eH4jC1r41x01z01z01z01z01z01z01z09z0Ez0Kz0Su0Ym0\ be0j_0pS0uK1zC4z46z0Cz0Ez0Hz0Kz0Mz0Pz0Sz0Uz0Yz0_z0\ bz0ez0gz0jz0mz1pz4rx6uu9xp9zmCzjEzgHzeKzbMzYKz_Hz_\ Ez_Cz_Cz_9z_6z_4zb1zb1zb0zb0zb0zb0zb0ze0ze0ze0ze0z\ e0ze0zg0zj0zm0zp0zr0zu0zx0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz4zz6zzCzzEzzKzzMzzSzzUzz_zzbzzgzzjzzpzzrzz\ xzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzxzzuzzrzzmzzjzzez\ zbzz_zzUzzSzzPzzKzzHzzCzz9zz6zz1zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz4zz6zz9zzEzzHzzMzzPzzSzzYzz_zzezzgzzjzzpzzrz\ zxzzzzzzzzzzzzzzzzzzzzKPZ } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } ; END PARAMETER FILE========================================= ; ;