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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I'm starting to discover the potential of the DivideJulibrot formula. Today's image is a Julia set of East Valley of the large minibrot on the main stem of its parent fractal. This parent fractal came about when I divided Z2 by (Z^(16)+10). On the surface it resembles an oversized Mandelbrot set, while deep inside it takes on Z16 characteristics. The image is a splendid blending of quadratic East Valley elements with the more circular Z16 elements. It rates a full 9.5, 1/2 point of which is due to my marginally expert coloring efforts. I named the image "Hexidecimal Quad" in recognition of the mixture of elements of two different orders. The calculation time of a superluminal, (which is possible in the world of fractals), 23 seconds, will make running the included parameter file a pleasure. An equal pleasure may be experienced by visiting the FOTD web site at: The Sunday weather here at Fractal Central was so good that the digital thermometer read 'comfort' from sunrise to sunset. Lots of sun, low humidity and a temperature of 82F 28C in the middle of the dog days must be considered near perfection. The fractal cats were more interested in a squirrel that was in the yard all morning, gathering nesting material. I did little but take it easy most of the day, though far busier days are in sight. The next FOTD will be posted in 24 hours. Until then, take care, and forget philosophy for a day -- a lack of philosophical pondering leads to less wisdom but more peace of mind. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Hexidecimal_Quad { ; time=0:00:23.00-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideJulibrot logmap=11 periodicity=10
params=90/90/90/90/-17.4231/0/0/0/16/10 maxiter=1600
center-mag=0/0/0.891266/1/-90/0 float=y
colors=000FA2HA0LA0OA5S8CXAJaCQfEXkGcpIjuKqiJnYJkN\
JhKYLHk0Fd0DZ0BT09N08H0zh4zc8zECmCJcBOUAQK9QJAPKAK\
LBKMBKNCMOCSMKULRZKYaJeaIldHthKvmMurPxzRzzTzzXlz_`\
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.
