; Date: Thu, 02 Jul 2009 23:48:15 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 03-07-09 (Fast and Slow [No Rating]) ; Id: <1.5.4.16.20090702234955.2b576e94@pop.mindspring.com> ; --------- ; ; FOTD -- July 03, 2009 (No Rating) ; ; Fractal visionaries and enthusiasts: ; ; There are two versions of today's scene, calculated by two ; different formulas, one sliced in the Mandelbrot direction, the ; other sliced in the almost-Julia direction, give or take a ; fraction of one second of arc. The fast Mandelbrot version ; takes under 3 minutes to calculate, the slow Julia version takes ; 4-1/2 hours. Since the images are virtually identical, I advise ; running the fast version and taking my word that the slow ; version appears identical. The slow version is the topic of ; this discussion however. ; ; In three-dimensional space two planes must intersect in a line, ; and lie at a certain single unique angle to each other. In four- ; dimensional space two planes intersect in only a single point ; and lie at two independent angles to each other. When the two ; angles are equal, every point in one plane in a circle around ; the point of intersection is at the same distance from the other ; plane. It makes no sense to a 3-D programmed mind, which ; visualizes a conic section, but that's the way it is. ; ; Today's fast image intersects the Julia plane at a double angle ; of 90,90 degrees. The slow image intersects the Julia plane at ; a double angle of a tiny fraction (about 1/50th) of one second ; of arc from the actual Julia direction, yet the change from ; Mandelbrot to Julia features has not yet appeared. The change ; will appear in the next 0.000001 degree of double rotation ; however. Some pretty abstract thinking is needed to figure out ; what's happening here. (It's beyond me!) ; ; All this abstraction prevents me from rating the image, though ; the calculation time of the fast version of under 3 minutes ; makes it relatively simple to see the image. Masochists who ; want to assure themselves that both images are virtually ; identical may start the slow version and wait half a day or so. ; ; The best way to see and compare both versions is to view them on ; the FOTD web site at: ; ; ; ; Partly cloudy skies and a temperature of 82F 28C made Thursday ; near ideal here at Fractal Central. The fractal cats enjoyed ; things as much as they could, while my day was average. ; ; The next FOTD is due to be be posted in 24 hours, but we expect ; a big rush job on Friday, so don't be surprised if the FOTD is ; late. Until whenever, take care, and keep searching. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Fast_Version { ; time=0:02:50.81-SF5 on P4-2000 reset=2004 type=mandel center-mag=+0.2500000999954\ 752/-0.00000000004996773/8.672315e+011/1/-165/0 params=0/0 float=y maxiter=500000 inside=0 symmetry=xaxis periodicity=0 mathtolerance=0.05/1 colors=000EpADq9Cs8d4ge5fe6ef8ef9dfAcgBbgCahEahF`h\ G_iHZiIYjKYjLXkMWkNVkOUlQUlRTmSSmTRjMLlQOmURoXUp`X\ rcZsgaujdvngzujxsiwqiuoitmhrkhqjhohhnfgldgkbgiagh_\ ffYfeWfcUfbSe`Re_PeYNeXLdVJdUIdSGdREcPCcOAcSeAPPPN\ 9cO8eP8fQ8gR8hS8iS8jT8kU8lV8nW8oW8pX8qY8rZ8s_8t2Mx\ JFv_8uo0xp1vp1tp1rp1pp1np1lp1jp1hp1fp2dp2bp2`p2Zp2\ Xp2Vp2Tp2Rp2Pp3Np3Lp3Jp3Hp3Fp3Dp3Bp39p37o13p35p47p\ 68p7Ap8BpADpBEpDGpEHpFJpHKpIMpJNpLPpMRpOSpPUpQVpSX\ pTYpV_pW`pXbpZcp_evXnsZjp`fnbbkdZifVjeUkeUldUldTmc\ TncTnbSobSpaSpaRq`Rr`RyXOuZQr`RnbSkcUheVdgWahYZjZV\ l_SmaOobLqcIreEtfBvg6zg8whAuhBriDpiEmjGkjIhkJfkLcl\ MalOZmQXmRUnTSnTPqUQnVQlWQjXQgYReZRc_R``RZaSXbSVcS\ SdSQeTOfTLgTJhTHmUIkTGiTFhTEfSDdSCcSBaRA_R9cU9`S8Z\ R8XQ8VO8TN8RM8PL8NJ7LI7JH7HG7FE7DD7BC78769979B79C8\ AE8AF8AH9BI9BKABLACNACOBCQBDRCDTCDUCEWDEXDEZEF_EFa\ EFbFGdFGeGGgGGhGGjEFlDEnC } Slow_Version { ; time=4:31:16.93-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 center-mag=-0.002030815\ 15044265/-0.0022062339955831/15067.5/1/-105/0 params=89.999999/0/89.999999/60/0.2500001/0/0/0/2/\ 0 float=y maxiter=500000 inside=0 symmetry=xaxis periodicity=0 mathtolerance=0.05/1 colors=000d4ge5fe6ef8ef9dfAcgBbgCahEahF`hG_iHZiIYj\ KYjLXkMWkNVkOUlQUlRTmSSmTRjMLlQOmURoXUp`XrcZsgaujd\ vngzujxsiwqiuoitmhrkhqjhohhnfgldgkbgiagh_ffYfeWfcU\ fbSe`Re_PeYNeXLdVJdUIdSGdREcPCcOAcSeAPPPN9cO8eP8fQ\ 8gR8hS8iS8jT8kU8lV8nW8oW8pX8qY8rZ8s_8t2MxJFv_8uo0x\ p1vp1tp1rp1pp1np1lp1jp1hp1fp2dp2bp2`p2Zp2Xp2Vp2Tp2\ Rp2Pp3Np3Lp3Jp3Hp3Fp3Dp3Bp39p37o13p35p47p68p7Ap8Bp\ ADpBEpDGpEHpFJpHKpIMpJNpLPpMRpOSpPUpQVpSXpTYpV_pW`\ pXbpZcp_evXnsZjp`fnbbkdZifVjeUkeUldUldTmcTncTnbSob\ SpaSpaRq`Rr`RyXOuZQr`RnbSkcUheVdgWahYZjZVl_SmaOobL\ qcIreEtfBvg6zg8whAuhBriDpiEmjGkjIhkJfkLclMalOZmQXm\ RUnTSnTPqUQnVQlWQjXQgYReZRc_R``RZaSXbSVcSSdSQeTOfT\ LgTJhTHmUIkTGiTFhTEfSDdSCcSBaRA_R9cU9`S8ZR8XQ8VO8T\ N8RM8PL8NJ7LI7JH7HG7FE7DD7BC78769979B79C8AE8AF8AH9\ BI9BKABLACNACOBCQBDRCDTCDUCEWDEXDEZEF_EFaEFbFGdFGe\ GGgGGhGGjEFlDEnCEpADq9Cs8 } 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