FOTD -- January 06, 2008 (No Rating) Fractal visionaries and enthusiasts: The FOTD is late today because I was volunteered for a trip to view old junk at a remote antique mall on Saturday. Today's image is a scene in Seahorse Valley. But it is not a miniature Julia set. Nor is it a miniature Mandelbrot set, nor an Elliptic set, nor a Rectangular set, nor a Parabolic set. It does come within 1-tenth of a degree of being a miniature Oblate set however. (There are six independent kinds of sets in the Julibrot because in four-dimensional space there are six mutu- ally perpendicular planes through a single point.) Also, the Seahorse Valley in which today's image lies is not the main one of the M-set. It is the Seahorse Valley of the large minibrot at -1.75 on the negative X-axis of the M-set. An Oblate set is a slice through the four-dimensional Z^2+C Julibrot figure in the plane determined by the imag(c) and real(z) axes. The miniatures in Oblate sets can be shaped like anything but miniature Mandelbrot sets. They often take the form of Julia sets, but just as often do entirely their own thing, making figures that could never be found in a Julia set or the classic Mandelbrot set, (though I have seen Oblate-type miniatures in perturbed Mandelbrot sets). To visualize the location of today's image, start at the point at -1.768... of the M-set as being centered on the screen. This is the point where the two branches of Seahorse Valley meet. Then imagine the entire 4-D Julibrot in which the valley lies as being rotated so that the real(z) axis is perpendicular to the screen. The object in today's image then lies about 6 inches behind the point on the screen and is being viewed from the left. The object in question is not artistically very attractive, but it does show that Seahorse Valley, the FOTD theme for January, has more potential than can even be imagined. I gave the image no rating, though I did name it "This is not a Julia Set", a fact that is immediately apparent. The calculation time of 36 seconds is brief enough to inconven- ience no one. And as always, those who would rather download than render may do so at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed image is or soon will be posted. Milder temperatures arrived here at Fractal Central on Saturday, but so did clouds, and in the evening, rain. The fractal cats made the best of conditionss by sleeping most of the day, while FL and I spent most of the day down in Dillsburg. The next FOTD will appear in 8 hours. Until then, take care and stay with it. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= ThisIsNotAJuliaSet { ; time=0:00:36.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=-0.00210532115066575/+0.525784551738717\ 90/121.4231/2.0567/90/3.88578058618804789e-016 params=0.1/90/0/90/-1.76852957968/0/0/0 float=y maxiter=10000 inside=0 logmap=11 periodicity=10 colors=000JGCHDBGB9E98D77G89I9BKADNBFPCHRDJUELWFNY\ FO_IN`LNbONcRNeUNfXMh_MibMkeMlhMojKmkMlkOklQjlRilT\ hmVfmXenYdn_cnacobcodcpfcphcpicqkcrmcspctncsmcslcr\ kcqjcoicmhckgcifcgecedccccbccacc`bc_acZ`cY_cXYaWW`\ WX_WXZVXYUXXTXWSXVRXVQXUPWTOVSNURNTQMSPKROIQOGPNGP\ MFOLFNKFMJFLIFKLFKNFKPFMRFOSEPUDQWCRYASZ8T`6Ub4Vd2\ We0Xb3Y`5ZZ7_X9`UBaSDbQFcOHdLKeJMfHOgFQhCSiAUj8Wk6\ Yl1Tl4_m6em9lmBrmGpjLohQnfPhpSkjVmdYoZ`qTcsOdpRdnT\ dlVdiXdgZde`dcbd`cdZcdXcdUcdScdQcdOcdLcdJcdHcdFcfG\ cgHciIcjKclLbmN_oNWqPSsQNuSJwUFyVBzY5zW6yV7xU8wS8v\ Q9uNAtLBsJBrICqHDpGDoEEnDFmCGlBGkAHj8Ii7Jh6Jg5Kf4L\ e4Hd3Kc3Kb3Ka3K`3K_3KZ2KY2KX2KW2KV2KU0KT2KV4KX6KZ8\ K_AKaCKcEKeGKfIKhKKjMKlOKmQKoSKqUKrUKrUKrUKrUKrUKo\ TKmRKjOKhMJeKIcIE`GAZE7MPQ6Yi9_gB`fEaeGbdJdbLeaOf`\ Hb_Me_Qg_Ui_Zk_bm_fo_ltajq_hoZgmXejWchUbfT`dSZaQY_\ PWYNVWMTTLRRJQPIOMGMKFLIE } frm:SliceJulibrot2 {; 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=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================