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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal is a new view of an old friend. The friend is the classic Mandelbrot set, which is one of only two of its kind. Actually, since the Z parameter is equal to the C parameter, today's fractal is a scene in the second M-set, the one I call the shadow set. The strangely stretched and twisted object is an unfamiliar view of the last midget out on the negative tail that is within reach of the double-precision math routine. This midget is located at C=-1.999999117... on the tail. When seen as a Mandelbrot midget or a Julia set, this object is surrounded by the neat, symmetrical pattern of a midget near the escape radius, with features bifurcating in a 2,4,8,16... series as they approach the midget. But today's picture is neither a Mandelbrot midget nor a Julia set. The plane of today's image is oriented within a few degrees of the Rectangular direction of the Julibrot. This Rectangular plane is determined by imag(z) and imag(c). At this odd angle, (which is the name I gave to the picture), the nice neat 2,4,8... series has been stretched and twisted into a grotesque parody of itself. Even the 2,4,8... series has been obliterated, and replaced by an indescribable series of ever-smaller features. The whole thing makes more of a mathematical curiosity than a work of art, so I could rate the image at only a 4. But despite the low rating, it is not without its merit, and the render time of 11 seconds is fast enough to make the parameter file the most efficient way to view the image. For those who would prefer to download the GIF image, that image is available at: The fractal weather today was perfect, with brilliant Autumn sun and a temperature of 70F (21C), which pleased the two fractal cats immensely. Today in the Fractal Central neighborhood we had one of those grand ceremonial funerals that I find so impressive and moving. As I heard the tolling bell, wailing bagpipes, and watched the hour-long procession in honor of two fallen policemen file past, my thoughts were those of life and death, and the meaning of it all. It was just the kind of experience I needed to get my philosophical energies stirring once again. It also put me behind in my work, which explains the unusually fast FOTD image. But the inspiration I received was worth the time spent. Some of that inspiration may appear as soon as tomorrow, but more likely sometime over the weekend. The cats are still pleased, but they would be even more pleased if I were to feed them, so I guess it's time to shut down the fractal shoppe and call it a day and a night. Until the next time, which is coming in 24 hours, take care, and exalt in your fractals. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
The_Oddest_Angle { ; time=0:00:11.50 -- SF5 on a P200
reset=2001 type=formula formulafile=multirot.frm
formulaname=multesc4-XZ-YW passes=t center-mag=-0.00\
000000000271445/-0.00000000001024659/5.033505e+011/0\
.07201/106.91/-79.243 params=99.3/107.3/-1.999999117\
587294/0/-1.999999117587294/0 float=y maxiter=550
inside=0 outside=real logmap=36 periodicity=10
colors=000RYbXcY_jSZbJZXAUK0cMEgIRmFbqBomIUwSozkczzS\
nrNafIOUDBF87MH4OO2SX0Vc0Zk0as0cz8RvQFqNHoMUoJZnIMmF\
NmEOkBQkARj2F03H03I23I44J84KD4KF6MJ6NN6NQ7OU7QY7Q_8R\
c8SgYegXci<3>RaiQaiO_iN_iMZiKZiKYjJYjjN8qNA0zw_6izez\
0SkMKqiDvz4zgDkKKY0RJAZKKfKXmMfuMqzMoeKoJJo0J8z0Hz0N\
w4VrBamHggNobSvYZzSczQjzNqzMvvRw<3>akwXqwRvwMzw<2>2Z\
r0Qq0Ho0QfBZYKgOMaUMXYMRaNKf<2>N4rZDejJSvQFzX2gEifHc\
<3>fMJfNEeMEbKDaKD_JBSoaXrbZubbwcfzeizemzfozfgsb_cZU\
OXM8SF0QUAegQsuczDIE8JF6JF2KF0KF0MF0MF0MF0RSAVeJZrJX\
nJUkJSi<2>Q8II8XA8j38w4Hs4Oo4Vm6bi6if6qb6w_Ayc<2>Mzm\
QzqUzsXzv0UX6X_HYbHYbHXbFXcFXcFXcEVe<2>DVfDVfBUgBUgB\
UgAUiASiASi8Sj8SjzzHzzJzzKwzMuwNquQnsRjqSgnUcmVajYYi\
ZVf_RcaObbQzYNuV<2>JeNMfOOgQRiRSjR<2>_nVym8siAnfBjcB\
eaD_ZEXXEbaUifinky6_fESaMMYUFUa8Qg2M_MkHXS0e830z87zE\
EuIKnNRi
}
frm:multesc4-XZ-YW {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p2, c=e*imag(pixel)+p3:
z=sqr(z)+c,
|z| < 4 }
END 20.0 PAR-FORMULA FILE==================================
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