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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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=========================================