; Date: Sat, 08 Oct 2011 08:07:03 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 07-10-11 (The Forgotten Sets [7]) ; Id: <1.5.4.16.20111008080704.145fbc22@pop.earthlink.net> ; --------- ; ; 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: ; ; ; ; It will also be posted, and in high definition at that, at: ; ; ; ; The original and now classic web site may be accessed at: ; ; ; ; 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========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ;