Fractal visionaries and enthusiasts:

Today's image is named "Squarely Rooted".  This is because the image was generated by the expression Z^(sqrt(2))+C calculated 14 turns up the complex logarithmic hyperspiral with the 'recip' function applied.

The parent fractal is a Mandeloid with a teardrop-shaped main bay, rotated so that its main bud faces southeast.  It has only one period-3 bud, but the usual higher order buds.  The scene of today's image is in a field of debris located where the second period-3 bud might normally be expected to lie.

The rating of a 7-1/2 includes the standard 1/2-point bonus for my color work.  The image itself is merely average.  To achieve the flat-background effect, I rendered the scene with the logmap set to an artificially high 67.

The shape of the minibrot at the center mirrors the shape of its parent, which is a quite common thing in fractals with exponents of Z between 1 and 2, where the parent fractals can assume most any shape they wish, especially when calculated with alternate values of the logarithm.

The calculation time of 32 seconds is blessedly brief, so why not run the included parameter file and see what you might have missed.

The partly cloudy skies were fair enough, and the temperature of 70F 21C was agreeable enough here at Fractal Central today.  But the frequent showers made it a day to be forgotten.  The fractal cats, ever forgetful, had already forgotten the day when it began.

After almost 3 inches, 7cm, of rain overnight, the humans were glad they had installed the sump pump.  A floor with a few puddles is far better than a basement filled with 100cm of water.  The next FOTD will be posted in 24 hours.  Until then, take care, and if you would like to become wealthy in this sour economy, open a shoe store for bigfooted sasquatches.  It must be quite uncomfortable for them, stomping around in the cold mud in their bare feet.

Jim Muth
jimmuth@earthlink.net


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

Squarely_Rooted    { ; time=0:00:25.01-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=recip passes=1
  center-mag=-1.4597524206/-0.4141910317/25206/1/85/0
  params=1.414213562/0/14/0 float=y maxiter=2000
  inside=0 logmap=67 periodicity=6
  colors=00000KxZJzwCzzzFmC9qz9gz9Yz9Pz9Fm96g8D`7JV6\
  PP5WJ4aD3g72m16cBAVKEMUIDbM4kZIWkVHwg2ubCtYMrTWqOe\
  mW_tlXslXslXslXsmXsmXsmXrmXrmXrmWrmWrmWrmWrmWqmWqm\
  WznWznWznVznVznVznVznVznVzmVznVzoVzoUznVzmWzlXzkXp\
  kYpjZpi_ph_ph`pgapfapebpecpddpcdpbepafpafp`gp_hpZi\
  pZipYjpXkpWlpWlpVmpUnpTnpSopSppRqpQqpPrpPspOspNtpM\
  upMvpLvpKwpJxpJxoLwnMvmNulOtkPsjQriRqhSpgTofUneVmd\
  WlcXkbYjaZi`_h_`gZafYbeXcdWddVecUfbTgaSh`Ri_QjZPkY\
  OlXNmWMnVLoUKpTJqSIrRHsQGtPFuOEvNDwMCxLCzLDzKEzKFz\
  JGzJHzJIzIJzIKzHLzHMzHNzGOzGPzFQzFRzFSzEfzzfzzfzzf\
  zzfzzfzzbzzZzzWzzSzzPzzNzzMzzLzzJzzIzzHzzFzzDzzBzz\
  Azz8zz6zz5zzCzzIzzOzzUzzSzzRzzQzzPzxXzjczXkzJrz5qz\
  8pzAozCnzEnzGrzkNzXLz_KzaJzcHzfGzhFzjEzlLzhSzeZzae\
  zZlzVszSgzNWzIKzD8z9PzDdzGtzJtzKtzLtzMtzMtzNtzOtzP\
  tzPmzSfzV_zYUz`NzcGzfAzhEzfIzdLzbPzeTzgXzj_zlczogz\
  qkztnzvizWdz6YzHSzSLzaFzl }

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