FOTD -- October 07, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows one of the forgotten sets -- those that lie in the Julibrot at orientations other than the Julia or Mandelbrot. Today's image happens to lie in the Oblate direction, which is determined by the imag(c) and real(z) axes of the Julibrot, and is a name of my own invention. The image is a sideways view of Seahorse Valley of the large minibrot on the main spike of the largest minibrot on the main spike of the Mandelbrot set. The scene is not centered in the Mandelbrot plane however. It is located at a distance of -1.786117 in the real(z) direction, which means it is part of the shadow M-set, a phantom set with a linear size 1.4142 times that of the classic M-set. The name "The Forgotten Sets" gives recognition to the sets in the four odd planes of the Julibrot figure, as well as those in the countless rotations. In fact, calling these things 'sets' is basically a mistake. All Z^2+C fractals including the Mandelbrot set are mere 2-D slices through a far more monstrous figure -- the 4-D Julibrot. The rating of a 7 is getting to be boring, but I must rate the fractals as I see them, and today's impresses me as being of only average quality for a FOTD. The calculation time of 54 seconds will pass quickly, even though not in a flash. If the official FOTD web site host can recover from the hack attack, the finished image will soon be posted at: <http://www.crosscanpuzzles.com/Archives.html> It will also be posted, and in high definition at that, at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original and now classic web site may be accessed at: <http://www.Nahee.com/FOTD/> Absolute perfection prevailed here at Fractal Central today. Both the humans and the fractal cats agreed, enjoying the day as much as possible. With a large anticyclone, (one of those things with an 'H' in the center that the TV weather people put on their maps), parked right overhead, not a single cloud was seen and the temperature reached a very pleasant 68F 20C. The next FOTD will be posted in 24 hours. Until then, take care, and if neutrinos really do exceed the speed of light as claimed in a recent issue of 'Time' Magazine, what would happen if we sent a burst of them to the moon, where they would be reflected back to earth? As I see it, they would return a few seconds before they were sent and could then trigger a device that would cause them not to be sent out in the first place. Faster-than-light neutrinos would also give a glimmer of scientific respect to the paranormal claim of precognition, a currently 'impossible' thing that I already know does in fact exist. This does not imply that I put faith in the ramblings of Madam Zucchini, the fortune teller down at the corner. But it does mean I am convinced that, in some strange way, the future may affect the past, thus violating the law of causality. If this makes me a superstitious true-believer in the paranormal, so be it. Now it's time for the useless information of the day. The formula for the hypervolume of the curved 5-D hypersurface of a 6-D hypersphere is very simple -- (pi^3)*(radius^5). Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= The_Forgotten_Sets { ; time=0:00:54.82-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 periodicity=6 center-mag=+0.00010515898520233/0/3801.206/1.2576 params=0/0/90/0/-1.786117/0/-1.786117/0 float=y maxiter=12000 inside=0 logmap=27 symmetry=xaxis colors=000B1QC2QD3QD4RE5RF6SF7SG8TG9THAUIBVICWJDXK\ EYKFZLG_LH`NIaOIbPIcQJcSJcTJcUJcVKcWKcYKcZLc_Mc`Nc\ aNccObdPaePcfQehPfiQgjRgkRglRgmRhmRhmRhmShmSimSimS\ ilSikSijSjiTjhTjgTjfTkeTkdTkcTkcUmbTkbSiaSgaRf`Qd`\ Qb_P`ZP_YOYWNWUNUSMTRLRQLPPKNOKONKMMILLGKKEJJCIIAH\ H8GE6FE4EF8FFBGFFHFIIGLJGPKGSLGVMHZNHaOHdPHhQIkRIn\ SIrTIuUJzVIxUIwUHuUHtTGrTGqTGpTFnSFmSEkSEjSEiRDgRD\ fRCdQCcQCbQB`QB_PAYPAXP9UOAWPBXQCYRD_SD`TEaUFcVGdW\ HeXHgYIhZJi_Kk`LlbLmdMofNphOqjOrlLngJlcHi`FgXCcUA`\ Q8YN6WK8XJ9ZKA_LBaMCbNDcOEdPFfQGgRHhSIjTKjULkVMlWO\ mXQnYSoZUo_Wp`YqaZrb_sc`scarcbqdcp_doOenKfmFfmAgm7\ hm7im8jm8mm9rm9vmAzmAzmBzmBzmCzmBzmCzmDzmDzmEzmEzr\ FzrGzrGzrHzrHzrGzrGzrFzrFzwEzzEzzDzzDzzCzzCzzBzzBz\ zAzzAzz9zz9zz8zz8zz7zz7zz6zz6zzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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=========================================