; Date: Wed, 03 Mar 2010 18:43:13 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 04-03-10 (Half-and Half [7]) ; Id: <1.5.4.16.20100303184431.368f78ca@pop.mindspring.com> ; --------- ; ; 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: ; ; ; or ; ; ; 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========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint