[Fractint] FOTD 29-09-11 (Squarely Rooted [7.5])

29 Sep 2011

      FOTD -- September 29, 2011 (Rating 7.5)

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 finished image is posted at:

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

for effortless viewing.

It is posted in high definition at:

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

The original FOTD web site may be accessed at:

      <http://www.Nahee.com/FOTD/>

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\
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  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=========================================