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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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=========================================