; Date: Mon, 28 May 2007 22:35:38 -0400 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 29-05-07 (Once a Rectangle-- [5]) ; ; Id: <1.5.4.16.20070528224015.2b87ecd6@pop.mindspring.com> ; --------- ; ; FOTD -- May 29, 2007 (Rating 5) ; ; Fractal visionaries and enthusiasts: ; ; There is a curious rectangle in the Julia set of the formula ; Z^(2.003)+C with initial C set to -1.7453,0. Its Z coordinates ; are 0.00019,0.07388. It is best seen at a magnitude around 100. ; I have featured this Julia rectangle and various distortions of ; it many times over the 10-year life of the FOTD. ; ; Not surprisingly, similar rectangles surround the Mandelbrot ; midgets in the -1.7453,0 area of the Z^(2.003)+C Mandelbrot set. ; But there are an infinity of other directions in which the ; 4-dimensional Julibrot can be sliced at this point. Does the ; rectangle exist in any of these odd slices? As today's image ; shows, it most certainly does exist in at least some of the odd ; slices. Today's scene is sliced very near the Oblate direction, ; and the rectangle, if anything, is even more spectacular. ; ; The appearance of origin symmetry in the image is deceiving. A ; close examination reveals subtle differences at the corners. ; But if the slice had been exactly in the Oblate direction, the ; symmetry would have been preserved. ; ; I rated the image at a 5, since there are only so many times the ; same fractal object can be shown and rated above average. I ; named the image "Once A Rectangle--", because no matter how the ; orientation is twisted, the rectangle is always hiding somewhere ; nearby. ; ; The calculation time of under 3 minutes on the P2000 would be ; around 12 minutes on the P200 unit. But why calculate when the ; finished image is posted for viewing on the FOTD web site at: ; ; ; ; Near perfect weather prevailed here at Fractal Central on ; Monday. Only a slight bit too much humidity kept it from being ; absolutely perfect. Of course, weather perfection is a ; subjective thing. With almost no rain for the past month, the ; local farmers certainly are not calling the weather perfect. ; ; The fractal cats spent the day being cats. I spent the day ; trying but not quite succeeding avoiding activity. The next ; FOTD will appear in 24 hours. Until then, endure. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Once_A_rectangle-- { ; time=0:02:54.25-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=1 inside=0 center-mag=-0.00000638398529728/-0.000133749671322\ 46/3892.894/0.01489/92.009718764060608/76.75397332\ 36568793 params=0/90/2/90/-1.7435/0/0.00019/0.0738\ 8/2.003/0 float=y maxiter=10000 periodicity=10 colors=0001In1In2Jo2Jo2Jo2Jo3Jo3Ko3Ko3Ko4Ko4Ko4Ko4\ Lo4Lo5Lo5Lo5Lo5Lo6Mo6Mo6Mo6Mo7Mo7Mo7No7No7No8No8No\ 8Oo8Oo9Oo9Oo9Oo9OoAPoAPoAPoAPoAPoBPoBQoBQoBQoCQoCQ\ oCQoCRoDRoDRoDRoDRoDRoCSpCSpCSqCSqCSqCTrCTrCTsBTsB\ TsBUtBUtBUuBUuBUuBVvAVvAVwAVwAVwAWxAWxAWyAWyAWyCYx\ EZxF_wH`wIawKbvMdvNevPfuQguShuTitVjtXltYms_ns`osbp\ rcqresrgtqhuqjvqkwpmxpnyplvnjtlhrjgphengclebjc`haZ\ f`YdZWbXU`VSZURXSPVQOSONRNMQMKOLIMJHKHFIFDGEBECACA\ 8A8687565343O21YASiDUiDTjESjERkERkEQlEPlFOmFNmGMnI\ MnKLoMKoOJpQIpSHqUHqVGrWFrXEsYDsZCt_Ct`BuaAub9vc8v\ c7uc4vc5vc6vc7vd7ve8vf9vg9vhAviBvjBvkCvlDvmDvmEvmF\ vmFvmGvmHvmHvmIvmJvmJvmKvmLvmMvmMvmNvmOvmOvmPvmQvm\ QvmRvmSvmSvmTwmUwmUwmVwmWwmWwmXwmYwmYwmZwm_wm_wm`w\ mawmbwmbwmcwmdwmdwmewmfwmfwmgwmhwmhwmiwnjwnjwokwpl\ wplwqmwqnwrnwrowspxtqwspwspvsovrovrournurnurnvrmvr\ mvrmwrmwrmwrmgDXhDWhDWiDV } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } ; END PARAMETER FILE========================================= ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint