; Date: Fri, 19 Nov 2010 18:19:46 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 20-11-10 (Manipulated View [No Rating]) ; Id: <1.5.4.16.20101119181939.150f31fa@pop.mindspring.com> ; --------- ; ; FOTD -- November 20, 2010 (No Rating) ; ; Fractal visionaries and enthusiasts: ; ; In yesterday's image a segment of the classic Mandelbrot shape ; appears in the background as the brilliant blue stuff. But the ; shape is so distorted that it is almost impossible to recognize ; the part of the M-set shape that is showing. In today's image ; we have taken yesterday's scene, rotated, twisted, and skewed it ; until we have restored the Mandelbrot shape to recognizable ; familiarity. ; ; Much to our surprise, we find we have cut a slice through the ; M-set shape that covers the main period-2 bud, the northwest ; part of the Main Bay and the northern period-3 bud. To find the ; slice, I totally winged it by eye. It might be possible by ; complicated trigonometry to determine the correct anti-distor- ; tion mathematically. It works quite well with simple single ; rotations, where all that is required is to enter the cosine or ; the reciprocal of the cosine of the angle as the X-magnification ; factor. But in yesterday's image, where four angles are ; involved, the mathematical method is too complex, at least for ; my Arithmetic-101 level of knowledge. ; ; At this point, I am left wondering which version of the same ; slice is more correct, yesterday's or today's. The actual ; Mandelbrot part of the Julibrot is a 4-D thing, kind of a nest ; of hypercylinders shaped like the M-set in the C-plane, but ; extended to infinity in the Z-plane. (Don't try to visualize ; the entire shape, it's impossible.) This Mandelbrot hyper- ; cylinder nest becomes distorted when it is sliced at an angle, ; as we did in yesterday's image. ; ; Today's image, which corrects this natural distortion, is ; actually the more distorted, and therefore the least correct ; image. But at the same time, it is almost impossible to tell ; our position when viewing yesterday's image, so I suppose this ; makes today's image the more correct one. ; ; All math and almost no artistic value equals no rating. The ; name "Manipulated View" tells it like it is. The calculation ; time of under 2 seconds is incredibly brief, and should be not ; be a factor. The finished image may also be seen on the FOTD ; web site at: ; ; ; ; Conditions here at Fractal Central on Friday were acceptable, ; with partly cloudy skies, a temperature of 48F +9C and cats that ; were fairly contented. The commercial work was about average, ; while the FOTD, is more a curiosity than a work of art. The ; next FOTD will be posted in 24 hours. Until then, take care, ; and try to uncover the alien plot before we end up on a slave ; ship to Arcturus. ; ; ; Jim Muth ; jamth@mindspring.com ; ; ; START PARAMETER FILE======================================= Manipulated_View { ; time=0:00:01.88-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=0.177576/\ -0.440939/0.5850274/0.3595/142.341509490465285/\ -74.8871977088931544 params=152/105/-64/49/-1/0/\ 1.118/0 float=y maxiter=1800 inside=0 logmap=yes symmetry=none periodicity=6 colors=000C36D47E58F69G7AH8BI9CKADMCEOEFQGGTIHWKIZ\ NJbQKfWKi`KleKngKljKjjKhfKgcKe`Kc_KbZKcYKdXKeXKfXK\ gZKg`KkaKnaKqbKnbKlcKjcKhdKfdPdeUbaZ_gcYkhVpmTtrQy\ vOzzMzzJzzHzzFzzDzzAyz8xz6vz4uz4zzJzzXzz8zzWzzrrzb\ rzOrzLrzJrzHrzFrzDrzBrzCrzCrzCrzDrzDrzDrzErzErzErz\ MrzErzFrzFrzFrzGrzGrzGrzHrzHrzHrzHrzIrzIrzIrzJrzJr\ zJrzKrzKrzKrzXzzWzzWzzVzzVzzUzzUzzTzzTzzSzzSzzRzzR\ zzQzzQxzPwzPuzOszOrzNpzNnzMmzMkzLizLhzKfzKdzTdzScz\ RczQczQczPczOczNczNczMczLczKczeVzdWzcWzbXzaXz`Xz_Y\ z_YzZYzYZzXZzWZzV_zV_zU_zT`zS`zR`zQazPazPazObzNbzM\ bzLczKcz_zzXzzUwzSrzPmzMhz`zz_zzZzzZzzYzzYzzXzzXzz\ WzzVzzVzzUyzUxzTwzTvzSuzRszRrzQqzQzzPzzPzzOzzNzzNz\ zMzzMzzLzzLzzKzzGzzHzzHzzIzzIzzJzzJzzKzzKzzSzzPzzM\ zzNzzMzzLzzKzz6zz7zz8zz8zz9zz9zzAzzAzzBzzBzzCzzCzz\ DzzDzzEzzFzzFzzGzzGzzHzzHzzIzzIzzJzzJzzKzz4zz5zz6z\ z7zz8zz9zzAzzBzzPzzOzzNzz } frm:SliceJulibrot2 {; 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=sqr(z)+c |z|<=9 } ; END PARAMETER FILE========================================= ; ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ;