; Date: Sun, 13 Jan 2008 19:42:51 -0500 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 14-01-08 (New View of Seahorse [7]) ; ; Id: <1.5.4.16.20080113193240.0dd7f7ae@pop.mindspring.com> ; --------- ; ; FOTD -- January 14, 2008 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; Today we introduce a new formula, which draws the slices of the ; Julibrot that are missed by the other odd-slice and oblique- ; slice formulas. This formula draws only the oblique slices in ; which there is no annoying stretching or skewing that must be ; unstretched to be properly seen. ; ; I named the image "New View of Seahorse", and indeed, this is ; what it is. In the image we see the entire Julia set of ; Seahorse Valley as well as an enlarged view of a deep part of ; the valley itself in the same frame. And don't miss the peanut ; holes where the vertical valley meets the edges of the Julia ; parts of the image. ; ; The blank outer shape is immediately recognizable as one of the ; Julia sets of Seahorse Valley, while the colorful vertical inner ; stripe is a grossly enlarged but unstretched view of Seahorse ; Valley as it appears at a depth of y=0.004. The sides of the ; valley are parallel not because it is stretched, but because it ; is sliced at a depth where its sides actually are parallel. ; ; The inner part of the image is enlarged for the same reason that ; a 2-D slice of a circular cylinder can appear as anything from a ; circle to a stripe with straight and parallel edges. A cross- ; section of a similar 4-D cylinder is a sphere, and the cylinder ; can be sliced by a 2-D plane in a direction that stretches the ; projection equally in 2 dimensions. Such a two-dimensional ; stretching appears as a simple magnification. ; ; I rated the image at a nominal 7, a fair rating for an image ; with a rather slow calculation time of around 22 minutes. But ; why not forget about calculating by going to the FOTD web site ; at: ; ; ; ; and viewing the image there? ; ; Sunday turned out pleasant but a bit colder here at Fractal ; Central. The clouds that moved in during the afternoon held the ; temperature to 43F 6C and led to a cold rain mixed with snow ; after nightfall. The fractal cats and myself as well spent most ; of the day taking it easy in front of the TV. The next FOTD ; will appear in 24 hours. Until then, take care, and I wonder ; what happened to all the wonder I once felt as I read those ; early books about the wonders of science and the physical world. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= NewViewOf_Seahorse { ; time=0:21:58.54-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MoreSlices passes=t center-mag=0/0/0.86 params=-0.7500101/0.004/0.00014/0/0/0 float=y maxiter=40000 inside=0 outside=tdis logmap=yes symmetry=none periodicity=10 colors=000LQmKPjJNhIMeHKbGJ_FHX8FXCIWFLVJOU_LnaNld\ PjXdTVbVS`XQZZNX`LVbNWcOXcPXcQYcRZdSZdT_dU_dV`eWae\ XaeYbeZbeYcbXc`XcZWcXWcVVdTVdRUdPUdNTdLTdJSbNR`QQZ\ UPXXOV`NTcMRfLPjKNmJLqIJtIHwHJtHLrGNpGPmFRkFTiEVgE\ XdDZbD``DbZEZaEWcETeFPgFMiFJkGFmGCoG9qEDrDGrBKrANs\ 8Qs7Us5Xs4_t2ct1ft0itBblMWdXPYgIQrBJnAMj9Pf9Sb8VZ8\ YV7`R7cN6fJ5iF5lB4o74r33u03x5At9HpDOlHVhLadPgaNcVL\ _OJYHHSAFk4DmcHc`K8YNBVQESTHPWKMZNJaQGdTDgWAjY7nbB\ rgFzmJvfLvaMvXUvScvNmvJmuKmuLmuMmuMmuNmtOrtOvtPztQ\ ztQzsRzsSzsSzsTzsUzsUztSzuQzvOtwMrxKqyIpyHouKpqMqn\ OrjQrgSscUt`WtXYuT_vQavMcwJexFgxCiy8kz5mz7Zz9YzAXz\ BWzDVzEUzFTzGSzISzJRzKQzLPzNOzONzPMzQMzOOzNQzMRzKT\ zJUzIWzGXzFZzE_zCazBbzAdz9ezCbzF_zIYzLVzOTzRQzUOlX\ Lj_IhbGfeDdhBbk8`n6_oDYoJWpPUpVTq`RqfPrlNrrMkmKdiJ\ ZeISaHLXFFTE8PD2LC6JGAHJDGMHEQLCTOBWS9_W7bZ6eb4if2\ li1okBgmL_oVSqdKO_vNYsMXp } frm:MoreSlices {; Jim Muth ; P1 -- M-center of slice ; P2 -- angle of slice ; P3 -- J-center of slice z=pixel+(p3), c=p1+(pixel*p2): z=sqr(z)+c, |z| < 16 } ; END PARAMETER FILE========================================= ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint