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Fractal of the Day
by Jim Muth
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FOTD -- January 10, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Today's fractal is a simple Julia set of the East Valley area of the large minibrot on the infinitely divided main stem of the Z^(2.003)+C Mandeloid. The corresponding Mandelbrot point is at the edge of one of those curious rectangles that I occasionally mention. Yes, the rectangles also exist in the Mandelbrot aspect of the Z2.003 fractal. In fact, today's image is filled with tiny rectangles. Today's image is extremely sensitive to very small changes of some parameters, while other parameters may be changed to any value with no effect on the image. I named the image "From the Abyss", probably thinking of one of those great old sci-fi movies, where creatures like Godzilla emerge from abysses. I rated it at a 7.5 because I can see nothing in it worth more. The fast calculation time of 1-1/2 minutes will leave lots of time for non-fractal activities. As always, the finished image is or soon will be posted for instant viewing bliss on the FOTD web site at: Partly cloudy skies, a temperature of 30F -1C and a biting northwest wind made the outdoors unpleasant here at Fractal Central on Saturday. The fractal cats do not go outdoors however, and there was enough afternoon sun to keep them happy. But we'll see how they take to the foot or so of snow forecast for the FC area tomorrow. My day was too busy to be pleasant. The next FOTD will be posted in 24 hours. Until then, take care, and be careful of the creatures in the abyss. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
From_the_Abyss { ; time=0:01:33.55-SF5 on P4-2000
reset=2004 type=formula formulafile=basic.frm
formulaname=SliceJulibrot4 passes=1 float=y inside=0
center-mag=0/0/920/1/-37.5/0 logmap=226 maxiter=800
params=90/90/90/90/-1.743488082976184/3.24124320102\
5422e-007/0/0/2.003/0 periodicity=10
colors=000JFFKEKLDPMCTOBYQ9bS8fT7kT6pR5tW0v`3tc2rf\
1pi0nlAmmCmnEmoGmpImqKmqMmqOmqQmqSmqUmqWmrYmramsem\
thnulnvpnvsnvrlvrjvrivqgvqfvqdvpbvpavp_vpZnkYgfY`a\
XTXXMSWFNW8IWAKZCMaEOdFQgHSjJTlLVoMXrOZuQ`xRazYLWY\
42_96`E9aJCdOFgSIjXLmaOrfRvkUzoXzrVzrTzrRznPzkOvgM\
rfKmeIhdGccFZaDW`BY_9_Z7`Y6bW8cUAdSCeQEgOFhMHiKJjI\
LkGMbLLVPLNTKFXK7`KA_PDZTGYXJXaLWeOViRUnUTrXSvZRzj\
UoZZqObrCgt1ku4gu6du8auAZuCWuFTuHQuJNuLKuNHuLHrKHo\
JHlHHiGHgFHdEHaCHZBHWAHU8HR7HO6HL5HJAMOERTIVYMUbRU\
fVUkZUpbUufUyjWfU6OU7QU7RUCTUHUUMVUQWjVXg_YgZWecZc\
g`acb_cdYcf_cgWchTciQcjNckKllGilDfmAdn7ao4Zp1Xp4Yn\
7YmAYlDZjGZiJZhMZgO_eR_dU_cX_b_``b`_e`ZeXZg`YidXkh\
WmkVooUqsTrvSprTnnTmjTkfTjcTh_UfWUeSUcOUbLUZRWVWXS\
`ZOf_KkaHpzMXYRkTzzzzuzzzzTkURlWQnZOp`NrcLseKuhIwj\
HxlJtmKqnLnoNjpOgqPdrR`sSYtTVuUSuyPIrSPkVVdY`Y`gRc\
mLhrKfsKesKdtJ55U99cDCmHF }
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=========================================
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times.
