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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal lies in the same area of the same parent as the images of the past 2 days. And like those two images, it consists of an intricate network of filaments. The cubic minibrot at the center of today's image is well beyond resolution, though the mixture of quadratic and cubic effects surrounding it is apparent. I named the image "Land of Loopiness" because so many of the filaments form closed loops. Then I rated it at a 7. The calculation time of 1-1/3 minutes is brief enough to keep everyone happy. And of course, the finished image is or soon will be posted on the FOTD web site at: Sunday morning, when FL asked if I felt like going to visit a new antique emporium that just opened about 75 miles away, I reluctantly said yes. This is why the FOTD for September 1 is so late. I guess I can't see what is so fascinating with the 'junque' other people have the sense to throw away, but it makes FL happy if I am there with her, looking bored, so I just can't say no to her. Luckily, or unluckily, we found nothing worth picking up. With maximum sunshine, low humidity, and a temperature of 82F 28C, Sunday was a near perfect day here at Fractal Central. The fractal cats celebrated the fine weather, as well as the apparent departure of the manx cat, by giving themselves a thorough grooming. (And that's no tall tail!) Like some ovens, cats are self-cleaning. My day was fair enough, despite somehow being drawn into the antiquing expedition. The next FOTD, with a new theme, will be posted within 8 hours. Until then, take care, and the question is not, "why is there something instead of nothing", it is "why is it impossible for absolutely nothing to exist". Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Land_of_Loopiness { ; time=0:01:22.56-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideJulibrot passes=1 periodicity=10
center-mag=-3.94470157911456/+0.00001549964882567/\
8.2e+012/1 maxiter=1800 float=y inside=0 logmap=154
params=0/0/0/0/0/0/0/0/3/3 mathtolerance=0.05/1
colors=0007VN8WO9XPBYQCZRD`TEaUFbVHcWIdXJeYKfZLg_N\
iaOjbPkcQldRmeTnfUogVqiWrjXskZtl_um`vnawobxpZskWog\
TkcQg_NcWJZRGVNDRJANF5GA6IB7JB7KC8LC8MC9ND9ODAQEBR\
EBSECTFCUFDVGDWGEXGFZHF_HG`IGaIHbIHcJIdJIeJPbMW_Ob\
zR`z_ezWizTzzPzzMzzJzzHzzGzzEzzDzzBzzAzz8zz7zz5XQ4\
VT2TV1SW4SW6SW9SWBSWERWGRWJRWLRXORXQRXTQXVQXYQX_QX\
bQXdPZeQXfRVfRTgSSgTQhTOhUNiVLiVJjWHjXGkXEkYClVDqX\
CnYBl_Bi`AgaAdc9bd8_f8Yg7Vh7Tj6Qk5Om5Ln4Jo4Gq3Er2B\
t29u16v14r57o89lCBiFDeIFbMH_PJXSLUWNQZPNaRKeTHhVDm\
WEkXFjXGiXHhXIgXJfXKeXKdXLcXMbYNaYO`YP_YQZYQYYRXYS\
WYTVYUUYVTZWSZWRZXQZYPZZOZ_NZ`MZaLZT2QYBVaKZeTbxjw\
i`fVRQJDAHH9FK9DO9BR9AU98Y86`84d82g81j83iB4iE6iH7h\
K8hNAhQBhTDgWEgZFgaHgdIfgKfjLfmMfpJfsHfuKgsMhrOiqR\
jpTkoVlnQmeLnYGoPCpHBqGBrGBrGBsGBtGBtGBuGBvGBvGBwG\
BxGBxGByGBzGBzGHxNNvUSt`Yrgbpngojlofqncvn_znXqiShd\
N__JRVEIQAPMEWJHbGLiCOp9S }
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)+0.00000000000000000000001),
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.
