; Date: Wed, 24 Sep 2008 22:33:37 -0400 ; ; To: fractint@mailman.xmission.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 25-09-08 (A Flawed Jewel [No Rating]) ; ; Id: <1.5.4.16.20080924223457.2b1f9b6e@pop.mindspring.com> ; --------- ; ; FOTD -- September 25, 2008 (No Rating) ; ; 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 rota- ; tions 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: ; ; ; ; and enjoying the already-calculated GIF image posted there. ; ; 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 params=-0.88/-1/0.176/-5/0/-95/\ 0/0 float=y maxiter=1800 inside=fmod proximity=0.75 outside=real periodicity=10 mathtolerance=0.05/1 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========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint