Fractal visionaries and enthusiasts:

Today's image rates a mighty 9, and I think it's worth it.  The parent fractal is an almost-Mandelbrot set rotated 180 degrees so that the main spike points east along the positive X-axis instead of west along the negative X-axis.

I call this parent fractal an 'almost' Mandelbrot set because it has an extra bud beyond its East Valley, (which is on the west side of the main bay), and also a very unusual mini-something where the large minibrot on the main stem would be expected.  Beyond this strange 'something' the main spike splits into two branches.

The parent came about when I subtracted 11 parts of Z^(2.1) from 11 parts of Z^(1.9) before adding straight C on each iteration.  It's an unlikely combination that results in a fractal with far more in its depths than would first be expected.

Today's scene ignores the strange 'something' on the main spike of the parent, which I might examine tomorrow, and dives into the northern branch of the East Valley.  The image is actually a mix of inside and outside stuff, with the inside parts brought to life by the 'bof61' fill.

The name "Leaves of the Ages" simply popped into my head as I studied the image. I have no idea what the name might refer to, though it does seem poetic enough to be the name of a fractal.

The calculation time of 3-3/4 minutes is rather slow, but once again the warhorse web sites are ready to trot to the rescue.

The weather took a turn for the worse here at Fractal Central today, as heavy clouds moved in overnight and light snow began at 9am.  With the temperature around 36F +2C, the snow never amounted to much and changed to rain before noon.  The fractal cats soon forgot an afternoon in the sun and retired for the day to their shelf by the heat.

The humans, FL and I, had a day with little to remember, which is how it goes when the adventurous days of childhood turn into the routine days of adulthood.  The next FOTD will be posted in 24 hours.  Until then, take care, and when the going gets tough, the tough guys let a woman solve the problem.

Jim Muth
jimmuth@earthlink.net


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

Leaves_of_the_Ages { ; time=0:03:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandAutoCritInZ function=ident
  center-mag=+0.0528755229234613/+0.00726740883032/\
  3.48016e+010/1/-2.5/0 params=11/1.9/-11/2.1/0/0/0/0
  float=y maxiter=1000 inside=bof61 periodicity=6
  colors=00004E05F06H07I28J39J5AK6BK8CL9ELBGLCIMEKMF\
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  q5Qq6Tq7Xq8_q9cpAgpBjpCnpDqpEupFxoEtoDqoCmnBjnAfn9\
  cm8_m7Xm6Tm6QhAWcD`ZGeUJjQMoSPpTSqUVrVXsW_tXbtZeu_\
  gv`jwamxbpycryhmflhOpd6WoCCyIEuLGrOHoRJlTKiWMfZNc`\
  P`cRYfSVhUSkVPnXMpYJs_Gv`DxZIqXNkVSeTX_S`Uhbbe_abX\
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  6Qn69o5Aq5Bq5Cq7Do9EkAFfCGbEHZFIUHJQILMFMICMF9MC6K\
  83I50G20E40C60A708906A04C }

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