[Fractint] FOTD 25-07-08 (Into the Depths [7.5])

25 Jul 2008

      FOTD -- July 25, 2008 (Rating 7.5)

Fractal visionaries and enthusiasts:

With today's image we continue the explorations of minibrots in 
the Mandeloids of very low order, going down from yesterday's 
1.075 to 1.05.  The parent fractal is a grossly oversized thing, 
shaped rather like a comet, with debris fields on both sides of 
its squared-off outer extremity.  It was produced by calculating 
the formula Z^(1.05)+C at a level 13 turns up the logarithmic 
hyperspiral.

Today's image is located at the edge of the southern debris 
field at the outer extremity of the parent.  The exact spot is 
impossible to recognize on the surface, and I needed to use my 
not-so-secret method of identifying minibrots to ferret out the 
elusive little midget.

In fact, I never did reach the minibrot itself.  The resolution 
breaks down well before the minibrot becomes visible.  But the 
pattern around it is quite interesting -- perhaps the best de-
fined pattern I have yet found around a minibrot in a fractal of 
such a low order.  Or maybe it's just that I put a bit of effort 
into the coloring.

I named the image "Into the Depths", which is a fair description 
of the impression I get while studying it.  I rated it at a 7.5, 
mostly because it is surprisingly rich for a scene in a fractal 
of such a low order, but also to give myself a pat on the back 
for the coloring.

The calculation time of just under 2-1/2 minutes on a fireball 
2000mhz machine should bring tears to no one's eyes.  But compu-
ters are notoriously prone to stubbornness, so to guarantee dry 
eyes, I recommend visiting the FOTD web site at:

       <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and viewing the finished image there.

The next FOTD will appear in 24 hours, most likely continuing 
the same theme with an exponent even closer to unity.  Until 
then, take care, and take no fractal for granted.

Jim Muth
jamth@mindspring.com
jimmuth@aol.com

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

Into_the_Depths    { ; time=0:02:24.45-SF5 on P4-2000
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC3 function=ident passes=1
  center-mag=-14.84534363332544/-23.4626947348403/\
  4.554307e+010/1/-21.75/0 params=1.05/0/13/1500
  float=y maxiter=1500 inside=0 logmap=228
  periodicity=10 mathtolerance=0.05/1
  colors=0000FTWQh00fKDZWLa00ZGIZOHYWFSE4JUCZRAbW9JT\
  QJUFdzuJwcLUL`UJeQUQRNSUGjT9dT3WU9bVFqzLnzMoVMoVNz\
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  cnUbmXblZbkaajcajeaihahj`gl`fo`fq_es_dv_cx_czX`wVZ\
  tTXqRVnOTkMRhuAPXXrWVoWTm }

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