; Date: Fri, 27 Mar 2009 18:55:29 -0400 ; ; To: fractint@mailman.xmission.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 28-03-09 (Hypersphere Scene [8]) ; ; Id: <1.5.4.16.20090327175547.0d278ce4@pop.mindspring.com> ; --------- ; ; FOTD -- March 28, 2009 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; Today's image shows a series of four-dimensional hyperspheres ; caught in the act of passing through our three-dimensional ; space. (The additional networks of twisting filaments and ; flying clouds of fractal sand can be considered extra bonuses.) ; ; If a 4-D hypersphere were to pass through our space, we would ; see a tiny sphere appear, which would grow in size, reaching ; maximum size as the center of the 4-D hypersphere passed through ; our space, and then shrink at the same rate as it grew until it ; finally vanished. Today's image shows a series of hypersphere ; intersections from the first 3-D slice to the largest. ; ; Of course, I invented this analysis. The image is a pure ; abstraction that could represent almost anything one wanted to ; see in it. It is actually a scene in a fractal created by the ; MandNewt06 formula, a formula I wrote about 10 years ago and ; soon forgot about. I have a whole series of these formulas, ; which are equally as forgotten. ; ; Most of today's image consists of 'inside' stuff made visible by ; the 'bof60' inside fill, a fill that has a tendency to create ; 'bubbles'. The rating of an 8 might be a bit overblown, but I ; kind of like the image. The name is self-descriptive. ; ; The calculation time of 2-1/2 minutes is fast enough to prevent ; boredom and slow enough to give time to enjoy the rendering ; precess. The image is also available on the FOTD web site at: ; ; ; ; The rain ended during Thursday night here at Fractal Central, ; leading to a foggy start on Friday. But the strong spring sun ; cleared away the fog by 10am, and the rest of the day was hazy ; and mild. The fractal cats found the afternoon sun on their ; shelf just warm enough for comfort. ; ; My day was peaceful but rather busy -- not a bad combination. ; The next FOTD will be posted in 24 hours. Until then, take ; care, and if you see it with your own eyes, it might or might ; not be real. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Hypersphere_Scene { ; time=0:02:28.62-SF5 on P4-2000 reset=2001 type=formula formulafile=basic.frm formulaname=MandNewt06 passes=1 float=y center-mag=0.274128/-1.06927/24.13934/1/-67.5/0 params=-2.37/2.17/-1.56/-1.05/3.29/-3.17 maxiter=254 inside=bof60 logmap=yes periodicity=0 colors=000pzznyxlxwjvuhtsfrqepodnmclkaji`ig_geZecY\ caXa_V`YUZWTXVSWTRUSQSQOQPNPNMNMLLKKJJJIIEEGGEGFCH\ EBID9JC7K94LA6MB7NC8OD9PEAQFBRGCSHDTIEUJFVKGVJHVKI\ VLJVLKVbLRdMSfNUhOVjPWlQYmRZoS_qTasUbuVcwWexXfxYgr\ ZdkZadZ_XZXQZVJZSAYRCZQDaNFeKGhHIlEInBJoCKoCKoCLoC\ LoCMoCMoCNoCNoDOoDOoDPoDQoDQoDRoDRoDSoESoEToEToEUo\ EUoEVoEWoEWoFXoFXoFYoFYoFZoFZoF_oF_oF`mG`lH`kIajIa\ hJagKafLbeLbdMbbNbaOc`Oc_PcYQcXRdWRdVSdUTdSUeRUeQV\ ePWdMYeOWeQVeRTeTSeUQeWPeXOeZMe_LeaJebIedHeeFegEeh\ CejBekAdj9dj9cj9cj8cj8bj8bi8bi7ai7ai7ai7`i6`i6`h6_\ h6_h5_h5Zh5ih4ih4ig4ig4ig3hg3gg3fg3fg2ef2ef2df2df1\ cf1cf1bf1be3ad4ad5`c6`c7_b8Zb9YaBXaCW`DV`EU_FT_GSZ\ HSZJSYKSYLRXMRXNRWORWPRVQRUSRUTRTURTVQSWQSXQRYQR_Q\ Q`QQaQPbQPcQOdPOePNgPNhPMiPMjPLkPLlPKmPKnRMmTNmUOm\ WQmXRlZSl`UlaVlcWkdYkfZkh_kiajkbjlcjnejpfiqgisiitj\ iukhvmhwnhxohyphzqhzrhzsh } frm:MandNewt06 {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=p3*z^2+c-1 z=z-1*a/b 0.000000000000000000000000000001 <= |a| } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint