Fractal visionaries and enthusiasts: 

Today's image lies in the parent fractal that results when the expression Z^(1.7)+C is iterated 11 levels up the complex logarithmic hyperladder with the recip function applied.  (The 'hyperladder' could more correctly be called a hyperspiral or hyperhelix.)

This parent fractal resembles a distorted Mandelbrot set that has been rotated so that its East Valley lies on the northwest side of the main bay, while its main period-2 bud sprouts from the southwest side.  A long, twisting filament with a large minibrot extends southwest from this bud, but we are not interested in this filament.  For today's image we check the southeast shore line of the misplaced East Valley.

We find some curious elephant pieces in this area, but we bypass the pachyderms to check a high-order star, where we find today's scene.  The rating of an 8 indicates that I consider the image to be an above average one found in the range of exponents between 1 and 2.

The name "Shattered Dreams" is un-necessarily foreboding.  The image is actually rather bright and cheerful.  The calculation time of 6 minutes drags a bit, but relief lies at the web sites.

The morning fog cleared off by 10am, leading to a sunny hot afternoon with a temperature of 91F 33C.  The fractal cats remained in full summer mode all day, except for a brief moment of excitement when Nicholas got wind of an unwanted tomcat in the area.  The humans spent much of the day preparing for the big week-end.  The next FOTD is not scheduled to be posted until September 4, but even then, no guarantee is given or implied.  Until whenever, take care, and be extremely cautious before you believe the promises of the political candidates.

Jim Muth
jimmuth@earthlink.net


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

Shattered_Dreams   { ; time=0:06:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=recip passes=1
  center-mag=-0.1238618515707104/+0.2069993477786224\
  /2.660665e+007/1/-177.5/0 params=1.7/0/11/0 float=y
  maxiter=5000 inside=0 logmap=702 periodicity=6
  colors=000000988AA9BCACEBDFCEGDFIEGKFHMGFOHEQICSJB\
  UBJPNRJYZDhf8sfAqfCofEmfGmfImhKmjMmmOmpQmqSmuSmrQe\
  oLYjHQgCIe8Ac43dCEiKOnRZsZhwertbpr_opXnmUmkRliOkfL\
  idIhbFg_CfY9eW7dUAaTC_SFYRHWPJUOMSNOQMQOKTLJVJIXHH\
  _FFaDEcBDf9Ch7Bj5sksohplfniclfajcZh_XeXUcUSaRP_ONY\
  PMXQMWQMVRMURMTSLSSLRTLRULQULPVKOVKNWKMWKLXKKXKKZM\
  J_OI`QHbRHcTGdVFfWFgYEh_Dj`DkbCldBmeBldCkcDjbEiaFh\
  `Fg_GfZHeYIdXIcWJbVKaUL`TL_SMZRNPQ`QR`RT_SV_yJQzMS\
  oURdaQUiQJqP9xP8`mITaRMQ`EEi73kE9lKFmRLnXRpbXqibro\
  hsunopikkegfacaX_XTXTPYNMZIJ_CG`7D`2BpVHevMoyiMuhD\
  ShN`hNbhOehOahLbgIcfGcfDdeBde0ikEejRbjc_jpXjkdhfkg\
  aszXzzRrzMkhGUjBKl6Am8Kh9UdBc_CcWDwSFwNzzJzrFzdazR\
  wsOuqLspIqnFomCmk9kj7jmFhoMfqTes`cugbwn`yu_0cs1cp2\
  cm2ckAcjImiQmhYmgemflmemmanmYnzUozQozNizSczWYz_Tzd\
  NzhzzlzzpzzqzzqzzqzzrzzrzzrczXbzXbzWazW`zMczIgzEjz\
  Anz6qz2kzIpzGuzEvzHwzKxzN }

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