Fractal visionaries and enthusiasts:

Today's image is a hastily done tweaking of an image originally posted several years ago.  Since it is a re-used image, I could rate it no higher than a 6.  But the image is not as poor as the rating implies.  The colors have been improved and the cropping changed, making it at least a pseudo-new image.

On its surface, the parent fractal is a Mandelbrot set, while in its depths it is an order-11 fractal.  Today's scene lies on a side shoot of the western branch of the filament extending from the large northern bud of the parent M-set.  It is located a short distance east of the East Valley of the large minibrot on the filament.

The image clearly shows the 4-way quadratic symmetry around the outer part of the fractal, while the inner part shows order-11 symmetry.  The 4-way symmetry is imperfect however.  A close examination of the four outer filamentary complexes reveals small irregularities, the most obvious of which are the 9 small white dots surrounding the outer edge of the donut ring.  I have no idea how the number 9 fits into the mathematics of the image.  All I can make of it is that the number 9 lies between 4 and 11. (Inside the donut ring, all is in order, with the proper 11 white dots.)

The name "Ring Around Eleven" refers to the fractal ring encircling the minibrot at the center, looking almost like a bluish donut divided into 11 raspberry-filled segments.

The image might not be a fully new one, but it is still worth the thrifty 30 seconds required to finish the calculation and stand in awe of the image.

The day began cloudy here at Fractal Central, but patches of blue appeared by mid-morning, and by noon it was sunny.  The temperature of a mild 54F 12C would have given a preview of spring if the winds had not been so brisk.  The fractal cats presumably spent the afternoon in the sun.

The humans spent the afternoon at a very atmospheric antique emporium.  By the time we left the shop, we were rather spaced out by the intense aura radiating from the genuine 200-year-old stuff we saw there.  We are now un-spaced, so the next FOTD, the one for March 5, will be posted in 24 hours.  There will be no FOTD for March 4.  Until then, take care, and Einstein claimed that God does not play dice with the universe.  But then, who was Einstein to tell God what to do?  (Einstein has since been proved wrong.  It appears that God does play dice.)

Jim Muth
jimmuth@earthlink.net


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

Ring_Around_Eleven { ; time=0:00:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basic.frm
  formulaname=AllNewDivideBrot function=recip float=y
  center-mag=-0.1500652732064654/+1.02814534759123/\
  1.549192e+012/1/5/0 params=11/1e+020 periodicity=6
  maxiter=400 inside=0 logmap=48 mathtolerance=0.05/1
  colors=000zzznwzfozakxSjnSipPipQhpRgmSeiTceUacV``W\
  _YXYWTXTTVRUTOURMSPJQLHNIEKFCGDADC9BB6AAAEA2MB2TF2\
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  zbdzfezjfznfz_WzMMz8CzEGz0CzJJzbCzcJzdQzeWzfbzgizj\
  sziqzhozgnzflzejzolzjjzeizagzXfzSdzOczJazF`zJYzMWz\
  ZDzWHzSLzPPzMTzJXzKbzKhzLnzLtzJrzIpzHozGmzFkzEjzD_\
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  zqqzqpzqozqnzqmzqlzqkzLoztmzqjzohzmfzkdzW9zVDzVHzV\
  LzVPzUTzUXzU`zUdzP`zKXzJZ }

frm:AllNewDivideBrot   { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
b=imag(p1)+0.00000000000000000001:
z=b*(z^2*fn1(z^(a)+b))+c
|z| < 1000000 }

END PARAMETER FILE=========================================