; Date: Sun, 06 Jan 2008 15:44:20 -0500 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 06-01-08 (This is not a Julia Set [No Rating]) ; ; Id: <1.5.4.16.20080106153402.2a571624@pop.mindspring.com> ; --------- ; ; 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: ; ; ; ; 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========================================= ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint