; Date: Thu, 10 Apr 2008 17:16:29 -0400 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 11-04-08 (Renormalization [Rating Normal]) ; ; Id: <1.5.4.16.20080410171858.2adf65ac@pop.mindspring.com> ; --------- ; ; FOTD -- April 11, 2008 (Rating Normal) ; ; Fractal visionaries and enthusiasts: ; ; Today's image is yet a third view of the scene that appeared two ; days ago on April 9. But whereas in yesterday's reimage we tore ; the original image to shreds, in today's view we 'renormalize' ; it into a reasonably symmetrical object. ; ; I named today's image "Renormalization". As far as I know, ; renormalization is something physicists do when the numbers ; behind their theories add up to infinity or zero, or something ; else absurd. They simply insert arbitrary terms into their ; formulas, which result in the formulas accurately describing the ; ideas they are trying to prove. I'm not sure if this band-aid ; approach actually proves anything, but it sure eliminates a lot ; of headaches for the theorists, especially those still searching ; for that elusive theory of (almost) everything. ; ; In today's image I renormalized things by simplifying the ; orientation parameters to 90,0,0,90, which conveniently draws ; the 'Rectangular' direction, defined by the imag(c) and imag(z) ; axes. After much stretching and skewing, this simplification ; produced a near-symmetrical pattern around the hole at the ; center, which once was a perfect minibrot. Since the scene was ; renormalized, the rating could be nothing but 'normal'. ; ; But things in the image are not quite as normal as they first ; appear. Today's orangish pattern has only two rounded points, ; whereas the Mandelbrot version of the same scene has four ; points. Where did the other two points go? Most likely, they ; rolled off into the fourth dimension. ; ; The calculation time of today's image is a blessedly brief 34 ; seconds, fast enough to bring joy even to the hearts of those ; who don't get the point of fractals. ; ; The trip to view the finished image on the FOTD web site at: ; ; ; ; is equally fast. ; ; With a high temperature of 72F 22C, gentle winds, and brilliant ; sun, Thursday was the best day so far this spring. The fractal ; cats must have agreed. They got into a spat over who should sit ; in the sunniest window. ; ; My day was moderately active. Tomorrow will probably be the ; same. The next FOTD image will be created sometime during the ; next 18 hours and posted in 24 hours. Until that semi-glorious ; moment breaks upon the waiting world, take care, and renormalize ; yourself. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Renormalization { ; time=0:00:34.74-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 center-mag=+0.000000003\ 13126323/-0.0000000643364187/2.29769e+007/1.4265/\ -86.5334566310032614/83.7362695773166621 logmap=181 params=90/0/0/90/-1.749446905449293/6.834887985e-0\ 07/-1.749446905449293/6.834887985e-007/2.0000001/0 float=y maxiter=1800 inside=0 periodicity=10 colors=0000850966A79B8BC9ED9HEAKFBOFBRGCWHD`IDeNEl\ TFoaOuiYvrVzxSzxQzyNzyXzzgzzpzzzI00GA0EK0BUT9_O6_K\ 4_F2_B7XCCVDHTDMQEOXCROEWMFewcdoZcgUb_PaSKfEsdGjcH\ bbIVaJNI`RKZQLYPNXOOWNPUMRTLSSLTRKVQJWOIzzzzzztwso\ rnkieg`XkSOzXLvVLqSHjOFeMF_ic``V`SNo_9lXAjUBgSCePD\ bMELhzNevOcrPanR_jSYfTWbVUZWSVXQRZON_MJiF0hG2gG3fH\ 4fH5eH6dI7dI9cJAbJBbJCaKD`KEL5kTDVxy9vvAtsArpBqmBo\ jCmgCldCjaDhZDfWEeTEcQFaNF`7l`9h`Ad`C``DX`FU`GQ`IM\ `JIsSNoQLkOJgNIcLGjzJgoIedHbUGYtjZqgZoeZlcZjaZg__e\ Y_bW_`T_YR_WP`TN`RL`OJ`MHLk9MiANgAOeBPdBQbBR`CSZCT\ YCUWDVUDWSEXREYPEZNF_LFkmzjjuigqhdlgbhf_deX_dUWcSS\ bPNaMJlVFjTFhRFfQFeOFcNFaLF0OR4NP7NOBMNEMMHMLLLKOL\ JRLIVKHYKGxQ0vP1uP2sO3rO4pP5oQ6mS7lU8jW9iYAg_BfaCd\ cDceEagFiicgk_fmWeoTcqPbsMauIUwIWxHXyHYzGZzG_zFQzf\ UzXYzORzuSzqTzmUzjVzfWzcWz_XzWYzTZzP_zM`zICzzPzbtz\ rozhjzZezPDzrHzkLzdPzZTzS } 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