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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: In today's image we return to the parent fractal of recent days, where we examine one of the two branches of the seahorse-type valley of the Mandeloid, the two-branched valley that appears where one would expect a single-branched east-type valley. To add extra interest I have evaporated the scene and rendered the resulting screenfull of 'inside' stuff with the inside=bof61 option. In this case, the option works quite well. We all know from geometry class that it is impossible to geometrically square the circle. It's impossible because the number (pi) is irrational. But despite this impossibility, in today's fractal we have a greenish square inside a skeletal circle. This square does not actually square the circle that surrounds it, but I kind of like the idea, so I named the image "The Circle Squared". When I saw the results of the day's fractal work, I decided to rate the image at an 8. The calculation time of 3-1/2 minutes is well within reason, as is the even briefer time required to drop in at the FOTD web site, where the completed image is posted for instant pleasure. The FOTD web site may be accessed at: Unacceptably hot weather spoiled Wednesday here at Fractal Central. A temperature of 93F 34C with blazing sun is too hot most everywhere, except perhaps in Yuma, Arizona. The fractal cats spent the day taking it easy. At an age of 4 years, they are still young cats, but those old-age cat habits are already sneaking into their behavior. My day was reasonably average. Unless something extraordinary happens, tomorrow will be the same. The next FOTD will appear in 24 hours, a length of time also known as one day. Until then, take care, and even though the day is 24 hours long, the earth turns on its axis once every 23 hours and 56 minutes. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
The_Circle_Squared { ; time=0:03:32.29-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=recip float=y
center-mag=+18.78498568713734/-0.3110130853796065/\
1439432/1/32.5/-3.34062104436622098e-006
params=2.5/-1.05/0.35/-5.05/0/1e+100/0/0
maxiter=3600 inside=bof61 periodicity=10
colors=000ecRgXNhRKlKGmEEo5Aq05r00t00l0Gc5VXEhNNuE\
Xz5czEZzMTzTNzZKueEol7hr0aw0Vz0Nz0Gz07z0Et3IjEN_NR\
PXXEe_0me0uh0zl0zj0zh3zhCzgMzeTze_zcgzaozauz_zzZzz\
Zzz_wz_qz_lz_gz__z_Vo_NzaIzaCza3za0za0za0za0za0zhA\
zoNtuajzmZzzMzzAzz7zz7zz7zz5zz5zz5zz5zz3zz3zy3zw3z\
w0zu0zt0zt0zw7zyEzzKzzPzzVzz_zzezzjzzozztzzozzhzza\
zzXzyPzuIzqAzm3zj0zg0zc0ya0wa0ua0ta0r_0q_5o_Am_ElZ\
IjZMhZPgZTeZVcVcaRl_NtZKzXIzVbyTCsRAoR5qP3zN0zN0mM\
0zM0zK0zI0zG0zE0zC0zA0z70z50z30z00z00z00z00z05z37z\
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zzzuzwqzrjzmezh_zcVzZNzTIzNCzI5zC0z50z00z00z00j00_\
00P33E7C0AE7AGEAGKCIPCIVCK_EMeEMjENoENrCTqCZoCamCg\
lAljAojAthAyg7ze7zc7za7za5z_3tZ3jX0_V0PT0ER00P00N0\
0M00R00X03a3Eg5MlzTq7azzhzAKzpyzKgzgzzTrwVztVzqVzm\
Vzj_zghzcqy_yuXzqTzmPzjMzeIzaEzZCzqIzqNzzTzzZzzczz\
hzzmzzr_zwazzazzazzazzZzz }
frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
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times.
