Fractal visionaries and enthusiasts:

Today's image is an almost Julia set of the 4th valley beyond Seahorse Valley out the main spike of the Mandelbrot set.  I call it an *almost* Julia set because its orientation is rotated 0.4 degree toward the Rectangular direction.

The valley itself appears as the open stripe down the center of the image.  The north and south branches of the valley are seen edge-on, and appear as the brilliant blue-white areas flanking the open area and filling the outer Julia shape.

The name "Troubled Julia Set" indicates that the Julia set is askew.  This close to the over-extended Julia orientation of the Julibrot, a small rotation makes a big difference.

The rating of a 7 might not fully justify the calculation time of just under 6 minutes, but the image is still an interesting one.  The finished image might be posted on the FOTD web site at:

       http://www.Nahee.com/FOTD/

but I am not sure Paul has the site up-to-date quite yet.

Sunday turned into a perfect day here at Fractal Central.  The blue sky, mare's-tails cirrus and temperature of 61F 16C kept both cats and humans happy.  I passed some time walking to the nearby Susquehanna River, where a large number of Canada geese were resting on the water before flying south.  FL kept busy doing other things.

The next FOTD will be posted in 24 hours.  Until then, take care, and old age is the time when a person has the money to do what he always wanted to do but is no longer able to do it.  (Hey, don't tell me my attitude is negative.  That's the way I see it and I'm not the one who designed it.)

Jim Muth
jamth@mindspring.com


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

Troubled_Julia_Set { ; time=0:05:58.08-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot2 center-mag=0/0/26.83367\
  /1.0692 params=90/0/89.6/90/-1.3996313761/0/0/0
  float=y maxiter=250000 inside=0 logmap=35
  symmetry=yaxis periodicity=6
  colors=000REQSESUEUWEXYFZ_G`aHbcIeeJigKmiLqkMtmNwk\
  OziPygQxeRwcSvaTu_UtYVqWWnUXkSYiQZfOZcMYaKXZIWWGVU\
  EURCTOASM8RJ6QG4PE5OF5NF5MF5LF5KG5KG5KG5KG6KH6KH6K\
  H6KH6KI6KI6KI6KI8KH9KGALGBNFDQEESEFUDGWDIZCJ`BKbBL\
  dAMfAQbET_IWXMZUQbQTeNXhK`kHdnEgoFfoFepFdpGdqGcqGb\
  rGarHasH`sH_sH_uL`vO`wR`xVayYaz`azaYzaUzbRzbNzcKzc\
  GzdDzd9zd5zdFzdPzeZyecxehwfhvfduectdbscarb`qa_p`Zo\
  _YnZWmYVmXUmWTmVSmURmTQmTPmXOm`OmdNmdNmdRlcCkcDjcC\
  icChcCgcCfcCecBdcBccBcbBcbBcbBcbAcaAcaAcaAc`Ac`Ac_\
  Cc_DcZEcZFcYHcYIZXJUXKPWMKWNFVOAVP5UR3SS3RT3RU3SW3\
  TX4VY4V`4Wc4Wh4Xm4Xr4Zv4`z4az5dz5ez5gz5iz5jz5jz5lz\
  5mz5nz3pz5qz6qz8rz9rzBrzCszDszFszGtzItzJtzKuzMuzNu\
  zPvzQvzSvzTwzUwzWwzXwzZwz_wz_wzaxzbxzcxzdxzexzfyzh\
  yziyzjzzkzzlzzmzzozzpzzqzzqzzqzzqzzqzzrzzrzzrzzrzz\
  szztzzuzzvzzwzzvzzuzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:SliceJulibrot2   {; draws most slices of Julibrot
  pix=pixel, u=real(pix), v=imag(pix),
  a=pi*real(p1*0.0055555555555556),
  b=pi*imag(p1*0.0055555555555556),
  g=pi*real(p2*0.0055555555555556),
  d=pi*imag(p2*0.0055555555555556),
  ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
  sg=sin(g), cd=cos(d), sd=sin(d),
  p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
  q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
  r=u*sg+v*ca*sb*cg, s=v*sin(a),
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=sqr(z)+c
  |z|<=9 }

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