; Date: Tue, 08 Apr 2008 22:03:28 -0400 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 09-04-08 (Perfect Proportions [6.5]) ; ; Id: <1.5.4.16.20080408220556.2b472d30@pop.mindspring.com> ; --------- ; ; FOTD -- April 09, 2008 (Rating 6.5) ; ; Fractal visionaries and enthusiasts: ; ; Although the minibrot at the center of today's image looks like ; a quadratic one, it is not. The parent fractal was generated by ; the formula Z^2.0000001+C rather than the classic Z^2+C. On the ; surface, the parent cannot be distinguished from a perfect clas- ; sic Mandelbrot set, but down deep, especially along the negative ; X-axis, things are quite different. ; ; The little minibrot in today's image lies at the edge of the ; infinitely divided X-axis in the vicinity of East Valley of the ; large minibrot at -2.475 on the X-axis. ; ; Yes, I know that the large minibrot is centered at -1.75 of the ; negative X-axis, and not -2.475, but today's parent is not the ; standard Mandelbrot set. It is the fractal I call the shadow ; Mandelbrot set, which lies in the same Julibrot figure as the ; classic M-set but is double rotated 45 and 45 degrees toward the ; Julia orientation. ; ; This less-familiar shadow set has twice the area of the classic ; set, and the linear dimensions are therefore 1.414 times those ; of the classic set. As for double rotation, don't waste mental ; energy trying to picture it. It's a four-dimensional thing im- ; possible to visualize in three dimensions except in a projection. ; ; With its near-perfect square pattern, the minibrot in today's ; image is quite striking in its own right. Enjoy it while you ; have it, for we will see another view of it in tomorrow's FOTD, ; when we see what a difference a little rotation can make. ; ; The image rates a not-too-bad 6-1/2. The name "Perfect Propor- ; tions" refers to the strikingly perfect square pattern, which ; will not remain perfect for long however. ; ; The calculation time of only 35 seconds makes running the ; included parameter file a pleasure. Equally pleasurable is the ; trip to the FOTD web site at: ; ; ; ; where the finished image is posted for instant viewing. ; ; A dull, dreary morning gave way to a brilliant blue sky at noon, ; followed by a balmy sunny afternoon with a temperature of 63F ; 17C. The cats enjoyed the balminess from their shelf in the ; front window. ; ; My day was busy, but still well under control. The next FOTD, a ; shocking scene indeed, is already in the bag and will be posted ; in 24 hours. Until then, take care, and be ready for the big ; change. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= PerfectProportions { ; time=0:00:34.89-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 center-mag=0/0/\ 2.154207e+008/1/-179.25/0 params=45/0/45/0/-1.749\ 446905449293/6.834887985e-007/-1.749446905449293/\ 6.834887985e-007/2.0000001/0 float=y maxiter=1800 inside=0 logmap=181 periodicity=10 colors=0003966A79B8BC9ED9HEAKFBOFBRGCWHD`IDdNEkTFl\ aOikYftVmzSrzQvzNzzK_PHNYnLYjIYeGZaEZXBZT9_O6_K4_F\ 2_B7XCCVDHTDMQEOXCROEWMFewcdoZcgUb_PaSKfEsdGjcHbbI\ VaJNI`RKZQLYPNXOOWNPUMRTLSSLTRKVQJWOIXNHzzztwsornk\ ieg`XcSOzXLvVLqSHjOFeMF_ic``V`SNo_9lXAjUBgSCePDbME\ LhzNevOcrPanR_jSYfTWbVUZWSVXQRZON_MJiF0hG2gG3fH4fH\ 5eH6dI7dI9cJAbJBbJCaKD`KEL5kTDVxy9vvAtsArpBqmBojCm\ gCldCjaDhZDfWEeTEcQFaNF`7l`9h`Ad`C``DX`FU`GQ`IM`JI\ sSNoQLkOJgNIcLGjzJgoIedHbUGYtjZqgZoeZlcZjaZg__eY_b\ W_`T_YR_WP`TN`RL`OJ`MHLk9MiANgAOeBPdBQbBR`CSZCTYCU\ WDVUDWSEXREYPEZNF_LFkmzjjuigqhdlgbhf_deX_dUWcSSbPN\ aMJlVFjTFhRFfQFeOFcNFaLF0OR4NP7NOBMNEMMHMLLLKOLJRL\ IVKHYKGxQ0vP1uP2sO3rO4pP5oQ6mS7lU8jW9iYAg_BfaCdcDc\ eEagFiicgk_fmWeoTcqPbsMauIUwIWxHXyHYzGZzG_zFQzfUzX\ YzORzuSzqTzmUzjVzfWzcWz_XzWYzTZzP_zM`zICzzPzbtzroz\ hjzZezPDzrHzkLzdPzZTzSXzL } 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