; Date: Sun, 28 Feb 2010 22:41:54 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 01-03-10 (Rectangularitis [6]) ; Id: <1.5.4.16.20100228224309.2b9f77f0@pop.mindspring.com> ; --------- ; ; FOTD -- March 01, 2010 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; Just when I thought I had seen all aspects of the Z^2.003 ; rectangle and had a vague comprehension of its full 4-D shape, ; I made a slight parameter change and the rectangle went crazy. ; It became a zig-zag thing better seen than described. ; ; The rectangle exists in its most perfect form in the Julia ; plane. Similar much smaller rectangles exist in the patterns ; around the minibrots in the Mandelbrot plane, but the original ; Julia rectangle totally vanishes in the Mandelbrot orientation. ; The Julia rectangle also extends into the Oblate and Rectangular ; orientations, and in the rotations between these orientations, ; though some degree of stretching and skewing is necessary to pre- ; serve the rectangular shape. I have not yet carefully checked ; the Elliptic and Parabolic planes, though I have no reason to ; doubt that traces of rectangularity exist there also. ; ; Such rectangles exist only in fractals with exponents of Z very ; close to 2.003. I have checked the Julia sets of the same area ; of the Z^4.003 Mandeloid and found no traces at all of a rectan- ; gle. As to why the Z^2.003 Julia sets seem so blessed with rec- ; tangles, I have no idea. Only the deity of numbers knows why, ; and he isn't talking. ; ; I named today's image "Rectangularitis" and rated it at a 6, ; which in my perhaps too-humble opinion is what it's worth. The ; calculation time of just under 3 minutes seems to be pretty ; standard for rectangle views when the maxiter is set at a some- ; what excessive 32767. ; ; All this calculation may be avoided however by viewing the ; finished image on the FOTD web site at: ; ; ; ; But keep alert if you view the images on the FOTD web site! The ; internet address of the site will change in about one week. ; ; Sunday here at Fractal Central began with a heavy snow shower ; that left 2 inches or 5cm of fresh fluffy snow on the ground. ; But when the sun came up, the snow melted away as fast as it had ; fallen, and by midday the streets were totally clear. The ; fractal cats took it in stride. ; ; My day was acceptable; FL spent most of the day watching the ; earthquake coverage on TV-Chile. The next FOTD, maybe or maybe ; not more rectangular stuff, will be posted in 24 hours. Until ; then, take care, and except for those who put their faith in ; reason, it's irrational to believe that all questions have a ; rational answer. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Rectangularitis { ; time=0:02:53.85-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/4508.257\ /0.0159/90/-55 params=0/90/0/90/-1.7435/0/0.00019/\ 0.07682/2.003/0 float=y maxiter=32767 inside=0 logmap=63 periodicity=6 colors=000CD6DE7DF8DG9DHADIBDJCEKDELEEMFENGEOHBPID\ QJERKFTNGWRIYVJ`ZKccLehNhmOkrPnvHpzMqzQqzUrzYrzasz\ mzzzzzetzarvYmrUjmRfhNbcJZZFVUBSP8PK9MF9KA9I8FG6KE\ 4PC3UF5ZI6cK8hN9mPBrSCvUEzXFzZGvZHrZImZJhZKcZKZZKU\ YLSXLTXLVWMXWMYVM_VMaUNbTNdTNfSOgSOiROmSGjROgQWdPc\ aOkRCwWIt_NrcSohYmlbjpghxnktlfqjanhYkfThdOtw0ecKRK\ bCEaC1uE6pGBkIGgKLbMQZOVUQ_QSdLUiHWnCZt2Ys8YrEYqKY\ pQYpVYo`YnfYmlcuuYmqSfmMZiGSeAKa4AX5DY5GZ5JZ5M_5P_\ 5S`5V`DZXLbUTfR`iNhmKpqHzzAxwCwtEvrGuoItlJsjLrgNqd\ PjwMmlOpbQsSRvITx8Ux7Rx6Px6Mx5Kx4Hx4FpCGhJHaRIUYJZ\ q1NdK9UfBTdCSbER`FQZHPXIOVJNTLMRMLPOKNPJLhHNZILQJJ\ 29RAEMHJHOOCTP4jfllbjm_inXhoUgpRfqOevEatIcrLdpOfnR\ gmUikXji_lgbmdjsegpfengblh`jiZhjcfkcdlcamc_ncYocWp\ cUqcSrmQpmOnmMmmKkmIimGhmEfmCzzAzz8zz6zz3zz5zz6zz8\ zz9zzBzzCzzEzzFzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; draws all 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=z^(p5)+c |z|<=9 } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint