FOTD -- March 04, 2010 (Rating 7) Fractal visionaries and enthusiasts: If the Julia set of a Z^(2.003)+C Mandelbrot rectangle is an octagon, what would we see if we checked half-way between the Julia orientation and one of the other orientations -- a hexagon? Actually, when the octagon is double-rotated halfway toward the Mandelbrot direction, it has long since become a perfect rectangle. In fact, it morphs into a rectangle well before the double rotation reaches one degree from the Julia plane. Today's image shows how our Julia octagon appears when its orientation is rotated only 0.000065 degree toward the Rectangular direction. It certainly does not appear as an octagon, though the eight vertices are still vaguely discernible, and it is nowhere near appearing as a rectangle. In fact, it is hard to believe that the weird shape will ever morph into a rectangle. But strangeness is a way of life in the world of fractals, and with quite a bit of stretching and a bit of skewing, the pointed shape in the center of today's image will be a near-perfect rectangle by the time it is rotated to the Oblate direction. The name "Half-and-Half" does not refer to coffee creamer. It means that the shape in the image is halfway between its Julia shape and the Oblate shape. The rating of a 7 is above average, which makes the image's calculation time of just under 2 minutes reasonable enough. The most reasonable way to view the finished image however is to view it on the FOTD web site, which for another 10 days or so may be accessed at both the following addresses: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or <http://www.Nahee.com/FOTD/> Wednesday began with light snow here at Fractal Central. The snow ended by midday, leading to a cloudy afternoon with occasional sprinkles of rain and a temperature of a seasonable 43F +6C. The fractal cats would have preferred more sun, but a special treat of salmon (we were out of tuna) eased their disappointment. My day was normal. FL is still watching the continuing 24-hour earthquake coverage on TV-Chile. (It looks riveting; it's too bad I don't understand Spanish.) If all goes well, and why should it not, the next FOTD will be posted in 24 hours. Until then, take care, and if one wants nothing, he is certain to get everything he desires. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Half-and-Half { ; time=0:01:51.21-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=-0.000001843\ 04564558/-0.00000312570156525/33523.52/1/-120/0 params=89.999935/0/90/0/-1.743397953167458/1.66204\ 6652e-005/0/0/2.003/0 float=y maxiter=1800 inside=0 colors=000pYRr`TsdVthXulZvo`vmavkbvibvgcvedvddvbev\ `fvZfvXgvVhvUhsRiqPioNilKijIihGieDicBia9i_7iZAfZCc\ YE`YGZXJWXLTWNQWPOfQMXVWN_dDdmHYbKRTPXUTaVYfWakX_l\ WYlVWmVUmUSmTQnTOnSNnSLoRJoQHpQFpPDpOBqO9WW8VW7UW7\ TW7SW7RW7QW7PW7OW7MX7JY7DZ8GX8IW8LU8NT8QR8SQAVOEXN\ I_LMaKQaIY_HbYFgWElU9qS5mQ6gP7aO8XN9RLAMKBKJCKIDK9\ 7K11K34K56K78K9AKBCKDFJFHHHJFJLEKNHNMKQMNTLQWLSYKV\ `KYcJ`fJbhIekIhnHkqHnvDmsHlpLlmPkkTkhXje`jcci`giYk\ hWohTsgQwgOzbMuZKpVIkRGfMEaICXEASA9OAANBBLBCKBDJBE\ IBFHBGGe`mZWfTS_NOTHKMLL9JKBHJCFIDDUE1YA2`B3_B4YC5\ WC5UC6SD7RD8PE8NE9LEAJFBHF85L98JAAIACHBEGahXZeVXbT\ U`SSYQPVONTNKQLzNJzLIzIGzbpzXfzRYzzOzzJzzIzzIzzHzz\ HzzGzzGzzFzzEzzFzzFzzFzzFzzFzzFBOFBKFsGAoGBlGBhGCe\ GCaGCZGDVGDSGEOGELGEHGFEGF1sA4iC6_D9QEyFewGduGcsGb\ qGaoG`nG_lGZjGYhGXfGWdGVcGUaGT_GSYGRWGQVGPTGORGNPG\ MNGLLGKKGJIGIGGHmMLnQNoUP } 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=========================================