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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Between reassuring FL that the end is not yet nigh, pondering the fourth dimension, and finishing an unexpectedly large pile of work, I had less time to devote to the FOTD on Wednesday than I would have liked. But all is not lost. FL is reassured for at least a day that the end is not yet here, and the work is behind me. As for the fourth dimension -- that continues to puzzle me. Some things supposedly possible in 4-D space are logically impossible. I read recently in a book of four-dimensional geometry that when a hypersphere is subject to double rotation and the two rotations are equal, then all points of the hypersphere except the single point at the center move in a circle. The puzzle is what happens to the points at the centers of rotation of the circles. Are these points moving in circles also? The description of double rotation, says that they must be. But if they are, then the points circling them are being carried along, and not moving in perfect circles at all. As I said above, it's logically impossible. But one thing certain is that the fourth dimension is fascinating. It's too bad that, even though my mind is capable of pondering 4-D, I'll never get to see it -- at least not in this world. I will get to see more fractals however. In fact, today's image is a grossly overblown sample of one. I named it "A Flawed Jewel" because I feel it has potential, but due to the lack of time I was unable to bring out its full luster. As it is, the colors are far too gaudy, so much so that I dared not give the image a rating. Most of the gaudiness was achieved by rendering the scene with the outside set to 'real' and the inside set to 'fmod' with a proximity of 0.75. A good part of the image consists of this glorified inside stuff. The little minibrot at the center suffers from an insufficient maxiter, a flaw that is easily remedied at the cost of a little slowdown by raising the maxiter to 3600. With the maxiter at 1800, the image calculates in 2-1/3 minutes. A maxiter of 3600 adds about one minute. All such problems may be eliminated however by surfing out to the FOTD web site at: After the early morning fog cleared off, perfect early autumn weather prevailed here at Fractal Central on Wednesday. Total sun and a temperature of 75F 19C can hardly be surpassed. The fractal cats' thrill came in the afternoon, when seven, yes seven, half-grown cats appeared in the yard next door. A half hour later the seven cats were gone and the fractal cats had settled to sleep. As stated earlier, my day was quite busy. Tomorrow will likely be slower. The next FOTD will appear in 24 hours. Until then, take care, and though the country is a clown show, don't lose the faith. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
A_Flawed_Jewel { ; time=0:02:20.52-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=recip passes=1
center-mag=-1.801058963211113/+5.410777958127436/3.\
52828e+010/1/4/0 periodicity=10 mathtolerance=0.05/1
proximity=0.75 maxiter=1800 outside=real inside=fmod
params=-0.88/-1/0.176/-5/0/-95/0/0 float=y
colors=0005g`DbXKZTRVQP`VNf_LldJriIwmJvlKvlLulMulN\
tlNtlmJ7IXdHS`GNYFJUEERD9ND5KH7PL9UPBYSCbWEg_GkcIp\
fJtcKsaLr_MqYNqWOpUPoSPoZWYeaHkg0ce6WdBObHGaM8`RBP\
XEDaEF`DG`CH_CJ_BKZBLZAKZ9KZ8KZ8KZ7JZ6JZ6JZ5JZ4IZ4\
IZ3IZ2IZ2HZ1HZ0HZ0HZj`DdYI_UMVQRPNWKJ`FGdGPYHXRIdK\
4WX7ZYAaZDd_Gf`JiaMlbPncSldVjdYhd`fdcdefbei`el_ehY\
YdWRaUKTPTLKaDGiQP0VN2_M4dK6iJ8nHAsGCxFEuJCsMApP8n\
T7kW5iZ3ga2i_3kY3mW3oU3qS4sQ4uO4wM4rW3nd2jm1fv0`o0\
Vh0Qa0KV0EO09H0DF5GDAJBFM9KP8OT6QW5SaBQfHOkMMpSKuY\
IzbGxYFwUFvPEtLEsGDrCD`XEKpE49V9BUECTJDTOESTFSYGRa\
HRPZgDpxChtC`qCTnCLkCDhC5ezXwvVtsTroRplPniNleLjbJh\
_IfVJgRJgNJhIKhEKiAKiIgWGYIEO4DO3CO2CO1AUA8ZI6cR4h\
Z2mfHncWnajn_kockpfkqjkrmlsplttluwluzeouZipSckMZgi\
TsjTtkTulSqlRnlRklQhmPdmPamOZmOWA43FB8KHCONGPL`OMT\
OOKNQCNR4PNIQKVSGhTDub35XN4Rf4My4XyFgyPcqQ`jQXcRUX\
RQQSNJSKCSwpCw2miDiWNfIYc }
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.
