[Fractint] FOTD 23-09-05 (Square Root of 2-1 [7])

23 Sep 2005

      FOTD -- September 23, 2005 (Rating 7)

Fractal visionaries and enthusiasts:

Due to an unexpected small but rushed job, which needs to be 
delivered by this afternoon, today's discussion will be brief.

Starting with today's image we will begin a series of FOTD's 
that explore scenes in the fractals created by the formula 
Z^(sqrt(2))+C.  These fractals are infinite in number, and all 
are broken by discontinuities, but the midgets in them are 
relatively easy to find, and though not as varied as those in 
the classic Mandelbrot set, the midgets still have much variety. 
The names will merely indicate the number of each image in the 
series.  The name of today's image is "Square Root of 2-1", 
which indicates it is the first in the series of images based on 
the square root of 2.

Today's parent fractal is the one at ground level of the 
MandelbrotBC2 formula.  In future FOTD's we will investigate 
other levels reached by this formula.

The rating of a 7 is the seventh consecutive such rating.  The 
render time of 1-1/2 minutes is blessedly brief.  The finished 
image is posted on the FOTD web site at:

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

With lots of sun, reasonable humidity, and a high temperature of 
86F 30C, Thursday turned out virtually perfect here at Fractal 
Central, especially for the cats, who spent the afternoon hiding 
in the holly thicket, making sure the cat from two doors down 
the hill kept his distance.  With only a moderately heavy load 
of work to finish, my day was not quite perfect, but it came 
close.  Today is starting with some clouds and quite warm.  
Possible showers are forecast for later.  We'll see how it goes. 
The next FOTD will appear in 24 hours.  Until then, take care, 
and dream of fractals.

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

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

SquareRoot_of_2-1  { ; time=0:01:30.66--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC2
  center-mag=+0.56788044566820710/+1.699692341050198\
  00/884217.7/1/-10/4.03226944195589354e-009
  params=1.414213562373/0/0/0 float=y maxiter=4200
  inside=255 logmap=67 periodicity=10
  colors=000G5CC6DE7EG8FI9GJAHKBILCIMDJNEK9FMAGNBHOC\
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  m6zm6zm6zl6zl6zl6zlgzWszs }

frm:MandelbrotBC2   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*floor(p/(2*PI))
  r=real(p2)-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=========================================