FOTD -- March 01, 2005 (Rating 4) Fractal visionaries and enthusiasts: Every so often my interest in the fourth dimension surges, and I start exploring the odd slices of the Z^2+C Julibrot, which just happens to be a four-dimensional mathematical object containing both the Mandelbrot set and all the Julia sets. For today's image I went to the large midget on the negative X-axis of the Mandelbrot set, where I calculated a slice in the Oblate direction, (real[z],imag[c]), through the 'Seahorse Valley' area of that midget. Don't search for the name 'Oblate' in any book about fractals. It is a name I invented myself for slices cut in this particular orientation through the Julibrot. It is not a straight and simple slice, since the imag(z) para- meter is not zero. The small imag(z) value of 0.025 gives the entire scene an interesting skew to the left. The skewing is in the scene. The image itself, though stretched in the vertical direction, is unskewed. Unfortunately, the final result, which I did not put adequate work into, rates only a 4. After two tens and an eight, today's 4-rated image might seem a big come down, but the 'passes=b' option renders the image in a blazingly fast time of under 20 seconds, which means that little time will be spent in rendering the ho-hum image. I named the image "Little Oblate Seahorse", which is a descrip- tion of the area and direction in which the image is found. The parameter file calculates very fast, but a download of the image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is nearly as fast, and for those with over-qualified computers, it is far more convemient. The snow started later than forecast here at Fractal Central on Monday, but when it finally did come, it came heavy, and by the time it wound down well after dark, over 7 inches (18cm) were on the ground. The fractal cats, being wise as all cats are, took their outside time early. By the time the snow began, they were safely ensconced on their shelf, watching with satisfaction the big flakes falling outside. A surprisingly small tuna treat was needed to keep them happy. This morning is starting with partly cloudy skies and sub-freez- ing temperatures. The snow covering the ground and clinging to the trees is making a winter wonderland of the surroundings, but cats of the fractal variety do not like snowy paws, so it is yet to be seen what kind of day they will have. I'll have a day of clearing away the snow however, which will take about an hour and leave ample time for the next FOTD, which will appear in 24 hours. Until then, take care, and be of high faith. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= LitleOblateSeahors { ; time=0:00:19.88--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=b center-mag=0/0/55.71368/0.1391 maxiter=3750 params=0/90/2/0/0/0.025/-1.768529748533/0 float=y inside=255 logmap=yes symmetry=origin periodicity=9 colors=000QMcQMcQMcQMcQMcQMcQMcQMbQMaQM`QM_QMZQMYQ\ MXQMWQMVQMUQMTQMSQMRQMQQMPQMOQMNQMMQMLQMKQMJQMIQMH\ QKGPJFONJOQNNTQNXUM_YMb`LfdLigKlkKpoJsrJvvJyyLquMi\ qOamPUiRMeSEbZYhepnkzsozlrsevl_ydTzXMzQGwWNoaUgg`_\ mgchigckkZmnUnrPpvKryFsuLnrQioVdl__hdVeiQbnL_sGbpF\ dmFgjFihEleEnbEp`EsYDuVDxSDzQCzNCzKCzICm_PVp`Xq_Zq\ Z`qYbqXdqXfqWhqVjqUlqUnqTpqSrqRtqRoiQkbPgVOcONbRQb\ UTbXVb_Yba_bdbbgeajgamjaolaroauraxtazwazyhzpnzgkt_\ inTfhMdbFbX8iaGofOukVzpbzujzyqzxozxmzxkzxizwgywevw\ ctwaqv_ovYlvWjvUhvTiuYHkVHkWHkYHkZRjd`jjjiptivuguv\ fuweuxduycuzauz`uz_uzZuzYuzWuzVuzUuzTuzSuz`vzhvvqv\ ryvozvowtonroepoXnoOloFjqNjsUjuajvhjxpjzwjzzjzzjyz\ huzgrvfnqdjlcggbcb`_Y_XTZTOXPJWMEVRKSVPQ_UNcZLhcIl\ iGqnDusBzx8zz6zz4zzBwzIqxPluWktZjs`irbirdhqfgphfoj\ folenndmpclrcltorpsufwxXzzQzzHzzJzzLzzMzzOzxQzwRzu\ TzsVzrWzpYzn_oFSlCCnFD000 } 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=========================================