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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: NEW FORMULA ALERT! The DivideJulibrot formula included in today's parameter file is a new version that has been slightly changed from the earlier version. The earlier version will still work, but the version in today's parameter file is somewhat faster. As for today's image, take it or leave it. For some reason I dislike perfection, probably because it leaves no room for improvement. And this afternoon when I took another look at yesterday's image, it struck me as being just a bit too perfect. A tiny rotation took care of the perfection however. A rotation of a mere 0.0005 degree from the Julia orientation wreaked total havoc on yesterday's image. (A slightly larger rotation makes the rectangle go away completely.) But the wreckage struck me as being good enough to serve as FOTD for August 11, especially since I had little time for a further fractal search. The color palette is the same as yesterday's, with only a slight change. Since yesterday's image was the real thing, I gave no rating to today's image, which is a parody of yesterday's. The name "No More Perfection" explains itself. The parameter file runs in 1-1/4 minutes, about the same time it takes to view the finished image on the FOTD web site at: Monday here at Fractal Central was actually a bit too chilly for perfection, and the heavy thunder-shower in mid-afternoon made it even cooler. An afternoon temperature of 63F 17C is hardly ideal for mid-August in the northern hemisphere, but the day was salvaged in the evening by a lovely double rainbow spanning the eastern sky. The fractal cats enjoyed the few intervals with brilliant sun, and endured the periods of rain. My day was rather busy, yet pleasant enough. I expect a repeat tomorrow. The next FOTD will be posted in 24 hours. Until then, take care, and the farmers must be praying for rain. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
No_More_Perfection { ; time=0:01:14.44-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideJulibrot logmap=136 maxiter=3500
center-mag=-0.0000104151/+0.002511651686/798281.4
params=89.9995/0/89.9999/0/-1.7435/0/0.00019/0.073\
88/2.003/0.0003385 float=y periodicity=10 passes=1
inside=255
colors=000EJMILNNNOSQQXTUaWYmdftiongjj`cdUW_NOUHGE\
2DJ7BOBATG9hF6mK9mPBmUDmZFmcHmkImhJmfKmdLmbMmcNmhO\
mcPcVQcTRcRScPTcNUcLVcJWcIacHXcHScHOmHJgHEsG5mHAgI\
FaJKWKPQLUONTKMYHMbEMgBMl6Ds7Ir8Mq9Qp9UoAZnBbmCflC\
jlzauzcpzelzghziczk_zmWzoUzqSzsRzuPzwOzxNzyLzzKzzI\
zzHzzGzzLzzPzzUzzYzzbzzfzzkzzozznzznzzmzzmzzlzzlzz\
kzzkzzjzzjzzizzizzhzzhzzgzzgzzfzzfzzYzzezzezzdzzdz\
zczzczzbzzbzzazzazz`zz`zz_zz_zzZzzZzzYzzYdzXezX9zz\
BzzCzzDzzEzzFzzGzzHzzIzzJzzKzzLzzMzzNzzOzNPzNQzORz\
PSzPTzQUzQVzRWzSXzSYzTZzT_zU`zVazVbzWzzWzzzzzFzzzz\
zGzzzzzHzzzzzHzzzzzIzzzzzIzzzzzJzzzzzJzzzzzKzzzzzL\
zzzzzLzzzzzMzzzzzMzzzzzNzzzzzNzzzgzOgzzfzPfzzfzPfz\
zfzQfzzfzQfzzfzRfzzfzRfzzfzSfzzzzTzzzzzTzzzzzUzzzz\
zUzzzzzVzzzzzVzzzzzWzzzzzXzzzezXTzzUzXUzzUzXUzzVzX\
VzzVzXVzzWzXWzzWzXWzzWzXXzzXzXXzzXzXYzzYzXYzzYzXYz\
zZzXZzzZzXZzz_zX_zz_zX_zz }
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.
