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