Fractal visionaries and enthusiasts: 

Today's image is the parent fractal that results when the expression Z^(1.09+C is iterated at ground level of the hyperladder with no function applied.  I rarely use parent fractals as FOTD's, but today's parent struck me as having enough bite to earn the honor of being declared FOTD for 25-11-13.  The reason for the name "Toothache" is now obvious.

As the exponent of Z is decreased toward unity, the resulting parent fractals tend ever closer to a circle.  But this tendency can be avoided for a while by calculating the fractal as it appears on one of the remote levels of the hyperladder.  In today's image however, we need no remote level.  The fractal is interesting enough right at the ground level, where we find a Mandeloid that resembles nothing as much as a newly extracted tooth.

Despite surface appearances, the image is filled with well hidden and quite hard to find smaller minibrots.  I will present a few of these in future FOTD's, though do not expect any paradoxical images to magically appear.

The art rating of the image is a reasonably respectable 7.  The math rating is a very respectable 8, mostly due to the unexpected richness of the outer filaments of the fractal.

The calculation will cause no problems.  The image will finish in less than one minute on most units, at least those that do not panic at the sight of a DOS prompt.  Panicky units can be spared the panic by checking the finished image on the FOTD web sites.

After a morning low of 16F -9C the temperature rose to a not very warm afternoon peak of 34F +1C.  Helped by hazy sun, it felt almost comfortable after the biting winds of yesterday.  The fractal cats agreed, as did the fractal humans.

The next FOTD will be posted when both it and I are ready.  Until that marvelous moment arrives, take care, and how could one communicate the directions of left and right to an alien imprisoned in a ship in outer space, with no knowledge of the outside universe?

Jim Muth
jimmuth@earthlink.net


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

Toothache          { ; time=0:00:55.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident
  center-mag=-3.94562/-2.28956/0.2032885/1/-45/0
  params=1.09/0/0/525 float=y maxiter=13000
  inside=0 logmap=7 periodicity=6
  colors=00000E00I00M00Q10U20Y30`40g50i60m70q80q90sA\
  0rC0qE0oG1nI2mK3kL4jM5iN6gO7fP8eQ9cRAbS9aTBZUCWVEU\
  WFRaHPmIMzJKzLHrMEzOCrP9zR7rS4zT2rW4mY6m`8mbAmeCmg\
  EzzGzzIzzKzzMzzOzzQzzOzzNzzMzzLzzJzzIzzHzzGzzEzzDz\
  jCziBzh9zg8zf7ze6zjKznYzrkzvyzJXzKZzL_zLazMbzNdmUe\
  mOgmUhmUjmQkmUmmUnmUomUpmUpmUpmUqmUqmUqmUqmUmccicc\
  fccbcc_ccWccTccPccMccIccFccBcc8cc4cc1cc4cc6Im8ImAI\
  mCImFImHImJImLImNImQImSImUImWImYIm_ZmXomUmzWlzXjzY\
  izZgz`fzaezbczcbze`zf_zgZzhXzgVzgTzgRzgPzzNzzLzzJz\
  zHzzFzzDzzBzzZzzZzzZzzZzzZzzZzzZzzZzzczzczzczzczzc\
  zzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczz\
  czzczzczzczzczzczzczzczzczzczzczzmzzmzzmzzmzzmzzmz\
  zmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

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