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: <http://www.Nahee.com/FOTD/> 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=========================================