; Date: Wed, 15 Dec 2004 08:01:50 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 15-12-04 (A New Dance [7]) ; Id: <1.5.4.16.20041215080338.2b576eea@pop.mindspring.com> ; --------- ; ; FOTD -- December 15, 2004 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; I was thinking of returning to the MandelbrotMix4 formula for ; today's fractal, but before I did, I decided to have another go ; at the HyperMandelbrot formula. In the end, I was glad I did. ; ; I found today's curious circular object at the center of a small ; bud on the southern shore of East Valley of the M-set. It is ; unlike anything that I know of in the classic Mandelbrot or ; Julia sets, which is why I named it "A New Dance". ; ; It is not surprising that the HyperMandelbrot set should hold ; new and unsuspected features. After all, the hyper-set is ; actually a 4-dimensional thing, with unlimited angles at which ; to cut 2-dimensional slices. Unfortunately, these slices will ; necessarily miss most of the HyperMandelbrot set. The most they ; can give in a single image is a vague idea of the richness that ; actually exists. ; ; When a 2-D slice passes close to an attracting element of the ; HyperM-set, the slice will be distorted by that element, giving ; the impression of a heavy cloth draped over what lies beneath. ; Today's image is composed mostly of such distortions. Many of ; the features in the hyper-vicinity are not in the image, but ; merely close to it, and those that pass through it, do so only ; coincidentally. ; ; Because it illustrates some truly new features, I rated today's ; image at a 7. It could just as easily have been rated at an 8. ; I was feeling conservative when I decided on the rating. When ; adjusted for the render time of 3-1/2 minutes, the rating adds ; up to an overall worth of 200. ; ; The image is available, already rendered, on the FOTD web site ; at: ; ; ; ; Brisk winds and a temperature of 39F 4C kept the fractal cats ; safely indoors on Tuesday. The duo actually seems to realize ; that winter has arrived, and there will be few pleasant outside ; days for the next few months. An extra serving of tuna assured ; their good moods. Today is starting sunny but even colder. And ; a few flurries of snow fell during the night. I hope the duo is ; as adjusted to indoor life as they seem. ; ; For me it looks like a day with an average amount of work. This ; means an early afternoon finish and several hours for fractals, ; the next of which will appear right here in 24 hours. Until ; then, take care, and how many Mandelbrot sets could fit on the ; head of a pin? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= A_New_Dance { ; time=0:03:30.49--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot passes=1 float=y center-mag=+0.27135683244730280/-0.006228258974698\ 45/138988.3 params=0/0/0.9/0/1e-020/0 maxiter=1500 inside=0 outside=imag logmap=190 periodicity=0 colors=000TQ9SQASQBRRCRRDQRFQTGQTHQTIRTJRTLSTMRTNR\ TOQUPPURPVSOWTOXUNYVNZWP_YR`_TaaVbbWcdYdf_ehafibgk\ dhmfjnhkpjmrkntmouoqwqryrszonwmiukdsh_qfVocQmaLkZG\ iWBgU6eS0eU2cV4bW6aY8`ZA__CZaEYbFXcHVdJUfLTgNShPRj\ RQkTPlUOmWMoYLp_KqaJscIueHwgGzgHzhFORWMRTLRQJQNHQK\ GQHEQE7UADQCJNDOKEUGGZDHdAIi7JfBNdFQbIT_MWYQZWTbUX\ eR`hPckNgnHkuLjqOjmRjjUjfXjc_j_bjXeiThiPkiMniIqiFt\ iBzm5wi8tfAqbCn_FkXHhTJeQLbNO_JQXGSUDVR9XO6ZL0ZM3`\ N6aN9bOBcOEdPHeQKfQMgRPhRSiSVkTXlT_mUbnUeoVgpWjqWm\ rXpsBkcXrt1u`3o_5j_7eZ9`ZBWYDRYFMXHHXJCWI6ZK7WM7UN\ 7SP7PR8NS8LU8IW8GX9EZ9B`99_32a97bECcJHeOMfTRgZWic`\ jhekmjjwrlrnmmjohfpcbqZZsUVtPRvHLuKOuMRtOTtRWsTZwY\ bsV`qRapS_oSZnTYmTXlUWlUVkVTjVSiWRhWQgXPeTKgXOh_Si\ cWjf_kjclmgmpknnhnmenlbnj_niXnhUnfRnePndMnbJnaGn`D\ nZAnY7oV4nX5nZ6m`7mb8ld8lf9khAljBmkBmmCmoDmqEmsEmu\ FmwGmyHmzHmzFmzDmzCmzAmz7 } frm:HyperMandelbrot {; periodicity must be turned off a=(p1),b=(0,0): q=sqr(a)-sqr(b)+pixel, b=(p2+2)*a*b+p3, a=q, |a|+|b| <= 100 } ; END PARAMETER FILE========================================= ; ;