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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: There is something about perfection that annoys me, so when I took another look at the FOTD for August 4, which is as close to perfection as the FOTD comes, I felt a twinge of annoyance. I felt that I must do something to spoil that image, which rates a lofty 9.5. To wreak my havoc, I rotated the view about 0.25 degree from the Julia orientation. This tiny rotation totally changes the image. Instead of circular perfection, we now have something that more closely resembles an alien sun rising above an alien horizon. I named the image "Phantom Sunrise". The change in orientation does not improve the original image, indeed, despite using virtually the same color palette, the rotation drops the rating from a 9.5 to a 7. Today's image is therefore more a mathematical curiosity than a work of fractal art. Thankfully, the image calculates in a blinding fast 25 seconds, so little time will have been wasted if the result is found disappointing. And never forget that the finished image is always available on the FOTD web site at: Only two degrees kept the weather from being perfect here at Fractal Central on Wednesday. Even though the humidity was lower, the high temperature of 88F 31C was just a bit too warm for the spoiled fractal cats, who spent the day stretched under the cool air vent. Much of my day was spent meditating on the fourth dimension and the meaning of fractals. The next FOTD will be posted in 24 hours. Until then, take care, and follow in the footsteps of the great fractal. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Phantom_Sunrise { ; time=0:00:25.02-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideJulibrot sound=off periodicity=10
center-mag=0/0/0.891266/1/-90/0 float=y maxiter=1600
params=90.01/0/90.24/0/-17.4231/0/0/0/16/10 passes=1
logmap=11
colors=000SIKTHJUGKVEKWCKXAKaCQfEXkGcpIjuKqiJnzzkz\
zzzzmzy0zt0zm0yh0xc0wZ0uU4sK8pEAnCAkBAgAAb9AZAAUAA\
QBAOBCMCKLCPMKULPZKWaJbaIjdHthKumMurPxzRzzTzzXlz_`\
zdZqO_UNYTMWSLURKSQJQPJOOMZJWbFcfBci8mn4mu1zzCVXNb\
NYjDhlCbnBYoASq9Ns8Ht7CrAGpDKnFOmISkLWiN_gQcfSggcd\
hnaiyZhydgyjXqbMiWBaO0VH8TEFRCNQ9UO7`M4hL2oJ0vI0uJ\
6uKFtLOtMWnbfhrqikojemjZkkTjlMhlGfm9dm3ch9YcESZKMV\
PGFcnJXnNRnRLnVFnZ9nY7cX5TW3JV18V00Y70`E1bK2TGHKDV\
BAhUsnNq`GoO9mA3l0LZ9bMLs9WtGRuMMuSHvYCvc7liMbo`Ut\
o_X4cR7gLAkFDoAGrMKuXNxhRzsUzzMzzEzz6zz0zz0cm1ar2`\
v3_z4WwCTtJQqRNnYKke4SV3PS2MP1KN4GV7Db8Ea8Ea9F`9F`\
AF_AG_BGZBGZ65h8Be9GbAL_BQYCWVD`SEePFjNPeLY`KgWJpS\
IeYEWbALg6Bl3FkAJjGNiMRhSVgYZfcbeifeo`hpWjqRlrLosG\
qtBsu8cf5OT29F3MI4ZK4kMDkRLkVUkZakbjkfrkjricrgXreQ\
rdKrbDr`6r_0jS4cL8XECQ7GJ0KNBGQMCUW9Xf5_p2XmCVjLSg\
UQdbObkTfiXihalgeofFZ6GR4 }
frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots
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),
aa=real(p5)-2, bb=imag(p5)+0.00000000000000000001,
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)/(z^(-aa)+bb)+c
|z| < 1000000 }
END PARAMETER FILE=========================================
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times.
