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