Fractal of the Day
by Jim Muth

A New Dance ©
Jim Muth's fractal image in GIF format (640x480).

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=========================================




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