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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's Julibrot image pictures an Oblate view of a midget that lies on the negative stem of the Mandelbrot set, very near the point where the stem joins the main body of the M-set. The next five FOTD images will also show Oblate views of the Z^2+C Julibrot. Mandelbrot midgets, or atoms, as they are sometimes called, are shaped like miniature versions of the Mandelbrot set. Julia 'midgets' are shaped like miniature versions of the particular Julia set in which they lie. Oblate 'midgets', which may be better described as holes, have no definite shape. Sometimes they look like Julia sets, at other times, such as in today's image, they have no definite shape, and resemble stretched and distorted, almost tortured bits of perturbed M-sets. Oblate midgets can never resemble intact Mandelbrot midgets however. Today's rather unsettling image reminds me of a face that has just witnessed a horrible scene. I have named it "Something Horrible". The parameter file renders in under 4 minutes, and when the rendering is finished, the resulting image has a rating of an average 5. Rendering may be avoided by downloading the ghastly image from the not-at-all-ghastly FOTD web site at: Don't give up hope, philosophy fans. The next outburst of philosophy will appear in the near future. The temperature reached 39F 4C here at Fractal Central on Tuesday, but the yard remained snow covered, keeping the fractal cats confined to the porch. They spent over an hour lounging in the sun, which is just now starting to clear the holly trees at the bottom of the yard. They must have been satisfied with their time outside, for the normal evening serving of tuna kept them happy. Unfortunately, today is starting notably colder with high wind, and the cats' happiness is in doubt. The work in my department is normal. I should be finished soon enough to leave ample time for the fractals, the next of which will appear in 24 hours. Until then, take care, and regardless of how hard one searches, they will never find the fourth dimension of space. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Something_Horrible { ; time=0:03:42.18--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=multirot-XY-ZW-new function=ident/flip
passes=1 center-mag=+0.00000000001018554/-0.000000\
00008617887/9.050939e+009/1.5291/-171.386570340830\
417/-11.1781883317050372 params=0/90/2/0/-1.748659\
111815974/0.01381380513990133/-1.748659111831792/\
0.0138138052283043 float=y maxiter=5000 inside=0
logmap=-188 periodicity=10
colors=000ITKITKITKITKITKITKITKITKITKITKITKITKJTLK\
UMLVNMWOMXQMYSNZTN_VN`XObZOc_OeaPfcPgePdfQ_`RRWNMN\
KEMS6H_BGgGFoLEwPDrNEnLFjKGfIGbHHYFIUDIQCJMAKI9KMB\
JPDJSFIVHIYJI`LHcNHfOHbRIZUJVWJRZKN`LJcLFeMBhN7jNC\
dQG_SKVUPZSTaRXdQ`gPejOimNmpMqsMuvOrqQolSlgUibWfYY\
dU_aVaZVcWVeTWgQWiOWkLXmIXoFXqCYs9Yu7YwjIzgMzeQzcT\
zaXz__zXczVfzTjzRmzPqzNtzMozMkzMgzMczM_zMWzMSzLOzL\
KzLGzLCzL8zL4zL0zM1zN1zN1zO2zP2zP2zQ2zR3zR3zS3zS3z\
R5zR7zQ9zQBzPDzPEzPGzOIzOKzNMzNOzNPzMRzMTzMUzLWzLX\
zLZzK_zKazKbzN`zP_zRZzTYzVWzXVzZUzaTzcSzeQzgPziOzk\
NzmMzlOz9WzAXzBXzDYzEZzFZzG_zH`zJazKazLbzMczNczMaz\
M_zMYzMWzMUzMSzMQzMOzMMzLKzLIzLGzLEzLCzLAzL8zL6zL4\
zJ7zHAzGCzEFzDHzBKzAMz8Pz7Rz5Uz2Vz4Wz5Xz7Xz8YzAYzB\
ZzDZzE_zG_zH`zJ`zKazMazNbzPbzQczSczTdzVdzWezYezZfz\
n`zfcz_fzTizMlzFoz8rz0wz1uz1sz2qz2pz3nz3lz4kz4iz5g\
z5ez6dz0qz7nzElzKizRgzXdz }
frm:multirot-XY-ZW-new {; draws 6 planes and rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4:
z=z^(p2)+c,
|z| <= 36 }
END PARAMETER FILE=========================================
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times.
