Fractal visionaries and enthusiasts:

To find quadratic minibrots lurking in fractals, the first step is to look for areas of two-way symmetry.  But some fractals defy this rule.  Today's image has no symmetry at all around the largest and obviously quadratic minibrot.  To find it I simply toggled in and out of color mode on the previous screen and checked the tiny blinking points that indicate minibrots.  The lack of symmetry surrounding the large minibrot does not hold for the smaller ones that dot the image however.  These smaller minibrots are surrounded by the symmetry expected of a proper quadratic minibrot.

The minibrots in the image are curiously arranged so that they appear to lie only within the brilliant yellow areas, which are actually broken bits and pieces of filaments.  Minibrots do exist within the blue and peach-colored areas on the left however, but as tomorrow's FOTD will show, they lie at a considerably greater depth.

The parent fractal was created by combining 0.75 negative parts of Z^(sqrt2) and Z^(-sqrt2), then adding (1/C).  This parent is a grossly oversized thing, mostly a network of zigzagging filaments shaped like an arrowhead, with Mandelbrot bits and pieces scattered throughout.  Today's scene is located close to the negative X-axis.

I named the image "Where is the Symmetry?", which refers to the pattern around the largest minibrot.  The parameter file has insufficient space to include the question mark.

The rating of an 8 is about what I consider the image to be worth.

The calculation time of 2-1/4 minutes will pass quickly once the brilliant colors appear at the top of the screen.

Crystal blue skies, a brisk temperature of 50F 10C and copper leaves falling from the trees made today a fine one here at Fractal Central.  The fractal cats were intrigued by the falling leaves, which they might have mistaken for passing birds.

The humans had an average day.  FL is still a bit out of sorts from the local influenza bug, which caused us to cut short the regular Saturday afternoon antiquing trip.  The next FOTD will be posted in 24 hours.  Until then, take care, and keep posted.

Jim Muth
jamth@mindspring.com
jimmuth@aol.com


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

WhereIsTheSymmetry { ; time=0:02:15.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandAutoCritInZ function=recip passes=1
  center-mag=-1.845750542/+0.000320033/17403/1/-145/0
  params=-0.75/-1.4142/-0.75/1.4142/0/0/0/0 float=y
  maxiter=1200 inside=0 logmap=80 periodicity=10
  colors=000zmozlnzkmzjlzikzhjzgizfhzegydfxcewbdvacu\
  `bt_asZ`rY_qXZpWYoVXnUWmTVlSUkRTjQSiPRhOQgNPcMOaLN\
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  A0zC0zE0zE0zG0xI0rI0nK0gK0aM0WO1QO5MQ7GS8ASA5UC0UE\
  0YC0_C0aC0eC0gC0iC0nA0oA0rA0vA0xA0zA0zE0zA0z80z70x\
  50x31v17v0At0Gt0Kl8ScK_YWgQioKvxCzz1zz7zzAzzEzxIzo\
  MziQzaUzWYzOazGezAiz3nz0rz0tz0vz0vz0xz0xz0zz0zz0zz\
  3zz5zz8zzCzzEzzIzzMzxOzvSzvYzvUzvSxvQrvOivKcvIYvGS\
  vEKvAEv88v70t03v5QxElxOKt7Uo8clAlgAvcCz_EzUIzWEzYA\
  z_7za5zc1zc0ze0zg0zi0zl0zl0tQ0W70000800M8IYSelnzxz\
  zvzztzzrvzrnzoizneznazlYziUzgQzgMveMrcMmcMh_KccUZc\
  UUcUUcUUcUUcUUcUUcUUcUZcUZcUc0cz0cz0cz0cz0mz0mz0mz\
  0mz0mz0zz0zz0zz0zz0zz0zz3zzCzzMzzWzzezzozzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

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