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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Fractals are for fun. True, they have other uses, and perhaps deep meanings that we are yet to fathom. They might even be a mathematical manifestation of God, but above all else, fractals are fun. And today's fractal is total fun. I was in a fun mood when I found it, and with its gaudy colors, the image looks like pure fun. The image is actually a scene in the fractal that results when various portions of Z^(-1.6) and Z^(-6.1) are combined and (1/C) is added. The formula, like the last two, is whimsical. (Most likely, tomorrow's FOTD will be a play on the fractions 1.7 and 7.1.) The parent fractal of today's image is a Mandeloid with four main bays, the easternmost of which appears the most critical, with lots of Mandel-buds and filaments that terminate in rings. Several disconnected features lie a small distance to the west and north of the main Mandeloid, but these play no part in today's FOTD. The midget in today's image is located near the point where the filament of an eastern bud intersects its terminal ring. To add a bit of 'zip' to the scene, I rendered it with the outside set to 'tdis'. Then I named the whole thing "Just For Fun", which, after all, is what fractals are the best at. The rating of a 6 is boringly average, though the render time of 3 minutes is thankfully short. And the image may be seen even faster by downloading it from: Once we got our act together here at Fractal Central on Thursday, the day went very well. There was lots of sun and the temperature reached 50F 10C, just mild enough to keep the cats happy during their afternoon in the holly thicket. In the evening, and against my better instincts, I went to a New Year's dinner at the home of the Fractal Lady's brother -- the second outing in 24 hours. I would rather have spent the evening in search of fractals, but all went well and now, when someone tells me to 'get a life', I can reply that I have one. But today is starting rainy, the dinners are past, and the cats already look sullen. Check back in 24 hours to see how things turn out. Until tomorrow take care, and if searching for fractals is not 'having a life', then what is? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Just_For_Fun { ; time=0:03:00.43--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+1.62834596524853100/+0.561897474119188\
30/32042.8/1/-35/-1.25182780807975291e-011
params=1.6/-6.1/6.1/-1.6/0/0 float=y maxiter=1000
inside=0 outside=tdis logmap=yes periodicity=10
colors=000zzNp`QndSlhVjkYho_fsbevdcsbbqa`o`_l_YjZX\
hYVfXUcWSaVR_TPYSOVRMTQLRPJPOIMNGKMFILABLCEKEGKFJK\
HLKJOKKQKMTKOVKPYKR_KTbKVfGUeIUdKUcMUbOUaPU`RU_TUZ\
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dsXcqYbp_ana`lc_keZigYghXfjWdlVbnUapT_rSYzT`vSZsRX\
pRVlQTiQRfPPbPN_OMXNKTNIQMGNMEJLCGLADK89I4AK7BL9CM\
BDOEEPGFQIGSKHTNIUPJWRKXTLYWM_YN`_OaaPcdQdfRehRfhQ\
ghPhhOgfRfaUdZWbW_`VbZSdXJfVIiTHkRGnPFqNErLEoKDkKD\
hKCdKC`KCYKBUKBQJBNJAJJAFJACJ98J94K65J96IC6IF7HH7H\
K8GN9GQ9FSAFVAEYBE_CDbCCeDChDBjEBmFApFAtGFwGKxHPyH\
TzJXzL`zNLkONjPOhPPfQQeQRcQSbRT`RUZRVYSWWSXVTYTTZS\
T_QU`OUaNUbLVcKVdIgpMVdHJUC3H87J7AL7EN7HP7LR7OT7SV\
7VX7ZZ7a`7eb7hd7lf7oh7sj7vk7wfBwbEwZHwVLxQOxMRxIVx\
EYxA`vC_tE_rFZpHZoIZmKYkMYiNYgPXfQXdSWbTW`VWZXVYYV\
W_VU`USbURcUPfQMiMKlIHoEFrBIqCKqDMqDPpERpETpFVoGYo\
G_oHanHcnIfnJhmJjmKvQItUK }
frm:MandelbrotMix4 {; 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,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END 20.0 PAR-FORMULA FILE==================================
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