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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today is the next to last time we will meet the fractal beast that has been prowling the neighborhood for the past two days. The beast is actually a four-dimensional thing with more aspects than it has fleas. I named today's view of the critter "Triple Beast" because the beast appears to have been stretched in three different directions. Most of the features that appear in the Mandelbrot aspect of the scene are still recognizable, though some have been stretched almost beyond recognition. And one of the green inner spirals has apparently split into a double spiral. The double spiral is only an accidental effect. It appears because the calculated slice of the Julibrot that we see on the screen cuts twice through a curved four-dimensional tube-like feature something like a rolled-up scroll that has been bent in the middle. Since the beast is starting to become boring, and we have seen such distorted Mandelbrot features quite a few times before, I could rate the image no higher than a 5, which is average. But the beast is near the end of its life, and will make only one more appearance before being sent to the oblivion where all the undiscovered fractals are awaiting it. The beastly fractal may be glimpsed by running the included parameter file, or by downloading the finished image from the FOTD web site at: The next installment of philosophy is but two days off. So be patient. Enlightenment is nigh. Tuesday was another perfect day for this time of year here at Fractal Central. Warm sun and a temperature of 39F 3C made conditions near ideal, at least in the places where the snow had melted and the ground was bare. The fractal cats enjoyed conditions to the best of their ability, and when they finally came indoors, were ready to curl up and sleep. Today is starting the same. Another good day would appear to be in store for the duo. For me, the work is normal. It looks like the day will be neutral. This means ample time for the last of the beastly images. Until the final beast appears in 24 hours, take care, and be ready for new ideas. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Triple_Beast { ; time=0:02:41.04--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot2 center-mag=-0.000003485\
49440916/-0.00000142882743436/518039.3/0.05033/\
156.558086503412028/-40.9116101381892818
params=55/-157/-81/166/0.288136932805/0.4826454054\
09/0.288136932805/0.482645405409 float=y
maxiter=5000 inside=0 logmap=288 periodicity=10
colors=000SYsSXrSWqSVpSUoSTnSSmSQlTOkUMjVKiWIhXGgY\
Ef_CeaAdcAceAbgAaiA`kC_mEZoGYqIXrKWsMTrOSqQRpSQpUP\
oWOnXNnYMmZLl_KlaJkcIjeHjgHkhGkgFlfEldDmbCm`BnZAnX\
9kV8hT8eR8bP7_N7XL7UJ6RH6OF6LD5IB5FC5CC49D46D43D45\
E57F59G6AH6CI6EJ7FK7HL8JM8KN8MO9OP9QQARRATSAVTBWUB\
YVC_WC`XCaYEbZGbZHc_Jd`Kd`MeaNebPfbQgcSgdThdVheWif\
YjgZjh`kiakjclkdmlfmlgmmimminmjomjpmjqnjrojtpjuqjv\
rjwsjxtlxujwtivshurgtqftpdsocrmbqlapk`oj_oiYnhXmgW\
lfVkdUjcTjbRiaQh`Pg_OfZNfYMgXKgVJgUHhTGhREhQDiPBiN\
AiM8jK7jJ5jI4kG2kF1kE0gH1dJ1aM2ZO2WR3TT3QY4Na4Kf5U\
o5cs2mz5mz8mzBhtEcrHZqKUoNPnQLmTMkWNjZOiaPidQhgRhj\
SgmTgpShsTgrTfrTfqTeqUepUbpU_pUZoUUoVTnVTnVSnVSmVR\
mWRnWQoWQpWPqWPsXOuXOwXNxXNzXMzYMzYLzYLzYKzYKzVOzS\
SzQWzN_zLczPgzUkzZozcszhvzmuzmwzmvzmvzmuzmuzmtzmtz\
mszmszmrzmrzmrzmqzmqzmpzmpzmozmozmnzmnzmmzmmzmmzml\
zmlzmkzmkzmjzmjzmizmizmiz }
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=========================================
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