Fractal visionaries and enthusiasts:

In today's image we venture into the parent fractal that comes about when the formula Z^(1.15)+C is calculated at a level 11.5 turns down the complex logarithmic hyperspiral when no function is applied.

The name "Blithe Eidolon", is a fancy way of saying 'happy ghost'.  It refers to the parent fractal, which resembles a chubby but happy ghost flitting merrily off to the east-northeast, its short plump arms protruding through its sheet.  Today's image is located in a stream of chaotic debris extending from the ghost's upper arm.

Actually, it's a bit incredible that such fractals exist at all.  The value of iterated Z in today's generating expression is 1.15, which is perilously close to unity, a value that cannot create fractals unless it is combined with some other value.

There might or might not be a minibrot at the center of today's image.  The signs are there, and all the way down it has appeared as though a minibrot would become visible on the next dive, but here we are at the limit of resolution and no minibrot has yet appeared.

Actually, we need no minibrot.  The image stands on its own merits, and rates a 5, which on the old scale would be a 7.

The calculation time of 4-1/3 minutes borders on slowness, leaving it to the individual fractal visionary to decide whether the result might be worth the effort.  For those in doubt, the finished image may be viewed on my FOTD web site at:

     http://www.crosscanpuzzles.com/Archives.html

The image is also available for viewing on Hal's web site at:

http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html

Paul's venerable FOTD web site is still up at:

     http://www.Nahee.com/FOTD/

Though it is currently inactive.

Another fine spring day prevailed here at Fractal Central on Friday, though with a temperature of 61F 16C, it was not quite as warm as on Thursday.  The fractal cats did not concern themselves with the outside conditions, but enjoyed the inside conditions to the best of their ability.  Their only excitement came in the afternoon, when Nicholas sensed a stray cat passing through the yard and leaped to the window to be sure the cat continued on its way.

The day of the humans was about average.  The next FOTD will be posted in 24 hours.  Until then, take care, and when was it determined that ghosts do their haunting wearing old bed-sheets instead of regular clothes?

Jim Muth
jamth@mindspring.com


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

Blithe_Eidolon     { ; time=0:04:20.68-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident passes=1
  center-mag=-0.8500552192825902/+1.261034003596572/\
  2.19456e+011/1/-157.25/0 params=1.15/0/-11.5/36
  float=y maxiter=640 inside=255 logmap=375
  periodicity=6 mathtolerance=0.05/1
  colors=000HTMGSLFRKEQJEPIDOHCNGCMFBLEAKD9JC9IB8HB7\
  GA7FA6E05C04B0490370260240130010YZJxVzpRrhNjaJbUFV\
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  C1mA0m70m50m20mICmGAmE9mD8mB7m96m85m64m43m32m11uP6\
  uN5uM5uL5uK4uJ4uI4uH4uG3uZDpfJpnPpmSplVpkXpjUpjUpi\
  UphUpgUpgUpfUpeUpdUpdUpaUpZUpXUpUUpSUpPUpNXpKTp53z\
  HPpFMpCIzAEz7Bz57z23zfGpbEpZDpWCpSApP9pL8pH6pE5zA4\
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  pAapAZp9Xp8Up8Sp7Qp6Np6Lp5Jp4GpmUzmUzmUzmUzmUzmUzm\
  UzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUz\
  mUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmU\
  zmUzmUzmUzmUzmUzmUzmUzmUz }

frm:MandelbrotBC3   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)+PI-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a }

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