Fractal visionaries and enthusiasts:

Mandelbrot sets come in all sizes and shapes, but the parent fractal of today's image, which came into existence when I combined 0.72 parts of Z^(1.4) with 0.72 parts of Z^(-1.4) and added (1/C) on every iteration, is the most distorted Mandelbrot set that I have yet found.

To begin, it is rotated 180 degrees so that its East Valley lies on the west side of its main bay.  To add to the strangeness, its apparent main bay is filled with debris of all sizes and shapes, and to complete the weirdness, the inner outline of this debris field is the true shore line of the bay, with all the expected buds in fragmentary form.

Despite all the attention I have given to the parent fractal however, the parent is not the FOTD for today.  Today's fractal is a scene in the East Valley area of the parent, well inland from the traditional shore line.

When I first saw today's image, it reminded me of a fantastic radio antenna, perhaps broadcasting fractal information throughout the galaxy.  I immediately named it "Interfractal Antenna" and rated it at an 8-1/2, with the extra half point being a reward for the coloring.

As far as I have examined, there are no minibrots in today's image, which is unfortunate.  If minibrots were lurking in the depths, they would be of a most interesting variety.  The nest of various sized circles filling the antenna mesh partly make up for the lack of minibrots however.

The calculation time of under 1-1/2 minutes will be no problem for dedicated fractal fans.  The brief calculation time will also make quick work of checking the parent fractal, which I have made such a fuss about.

It might be windy in southern California, but once the fog and frost cleared off today here at Fractal Central, the weather was quite peaceful, with a mix of clouds and sun.  The temperature of 45F +7C was just about average for the start of December.  The fractal cats approved of these conditions, while the humans had another uneventful day.

The next FOTD is scheduled to be posted in 24 hours, though it could be later if a shopping expedition arises.  Until whenever, take care, and in the song 'The Twelve Days of Christmas', the gift given on the fourth day is four *calling* birds.  I have never been able to determine exactly what kind of birds are or once were known as calling birds.  Could the word 'calling' originally have been 'collied', meaning blackened by coal soot, perhaps in thoroughly polluted 19th Century London?

Jim Muth
jamth@mindspring.com


START PARAMETER FILE=======================================

InterfractlAntenna { ; time=0:01:25.00 SF5 at 200MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=recip
  center-mag=-6.903338839/+0.123290986/1382/1/127.5/0
  params=0.72/1.4/0.72/-1.4/0/0/0/0 float=y
  maxiter=1800 inside=0 periodicity=6
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  l8Gh7Ie5La4PZ3TX2ZV2eU2lT }

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