[Fractint] FOTD 16-05-09 (Unity and a Half [6.5])

16 May 2009

      FOTD -- May 16, 2009 (Rating 6.5)

Fractal visionaries and enthusiasts:

The complex logarithm is multi-valued, so how then do we know 
which value is the correct one?  The answer is that they are all 
'correct'.  The square roots of 4 are plus-2 and minus-2, and 
they are both 'correct'.  We use the root that works best in the 
situation at hand, which is almost always the plus-2 root.  The 
same is true with the complex logarithms, but the other values 
are always there, and they also make fractals.

The MandelbrotBC3 formula makes use of these other values of the 
complex logarithm.  Each value draws a different fractal, even 
when the exponent of Z remains unchanged.  In today's image we 
have gone 30 levels up the logarithmic ladder to a level where 
the Z^(1.5)+C parent Mandeloid is totally changed.  Today's 
image is located in the 'Seahorse Valley' of its parent.

Since most of the effect is a result of the coloring, which I 
put at least 10 minutes work into, I have added the usual 1/2 
point bonus for the coloring, bringing the overall rating to a 
less-than-inspiring 6-1/2.  The name "Unity and a Half" refers 
to the exponent of Z.

The calculation time of a shockingly fast 44 seconds will bring 
no discomfort to even the most fastidious.  The trip out to the 
FOTD web site at:

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

to see the finished image there will be equally enjoyable.

The showers moved out of the Fractal Central area early Thursday 
night, leading to a foggy start for Friday.  By 10am the fog 
cleared out however, and the rest of the day was near perfect, 
with blue skies, puffy clouds, and a temperature of 77F 25C.  
The fractal cats enjoyed the weather conditions, but they were 
not happy when a lovesick tomcat wandered by and sprayed the 
wall right beneath their favorite window.  A quick squirt from 
the hose removed the offensive odor and restored the cats' good 
moods.  My day was busier than expected, in fact it was barely 
under control.

Unless FL gets an antiquing urge, the next FOTD will be posted 
in 24 hours.  Until then, take care, and be conservatively 
liberal.

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

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

Unity_and_a_Half   { ; time=0:00:44.80-SF5 on P4-2000
  reset=2004 type=formula formulafile=basic.frm
  formulaname=MandelbrotBC3 function=ident float=y
  center-mag=+0.1641879378341295/+0.775442975243285/\
  200823.9/1/-5/0 params=1.5/0/30/0 maxiter=1800
  inside=0 logmap=105 periodicity=10
  colors=0000HU000K0U0000KU000N0U0000HU000K0Ul0fi1cf\
  2`c3Y`4VY5SV6QS7NP8KM9HJAEWU2UR4SP5QN6OL7NJ8LH9JFA\
  HDBzm8wi9te9qb9n_AkXAgUAcRB_NBWLBSICOGCKDCoMMfJJYG\
  HPDEZOFYNEXMEWMEVLEVLEUKETKESJERJDRIDQRzPHzOGtNGmN\
  KcMFcLEZKEUJDPJDKICFHCCGBCcuAaqB_mBYiBWeBUaBSYBQUC\
  OQCMMCKICIECz5Az6Bz6Bz6Bv6Br7Bm7Bh7Bc7BZ8BU8BP8BK8\
  BJ9CI9CI9CI9CIACHACHACHACGBCGBCGBCf5Ga6FY7ET8EP9DK\
  ACH09G2AG3AG5BG6BG7BG9CGACPu`OrZOpYNnXNlWMiVMgTMeS\
  LcRL`QKZPKXNJVMJSLJQKIOJIMHHJGHHFGFEGDDF5mG6lH7lJ9\
  lKAkMBkNDkOEkQFjRHjTIjUJiVLiXMiYNh_Ph`QhaRhm`kxjnv\
  hotgosfoqeopdoncombokaoj`oh_ogZoeYocXpbWp`Vp_UpYTp\
  XSpVRpUQpSPpROpPNpOMpQOnRQlSSjTUhUWfVYdW_bXa`Zc__e\
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  nHcmGbmGbmGblFblFalFakEakEakEdzMezOezPezQfzRfzSfzT\
  gzUgzVgzXhzYhzZhz_iz`izaizbizc`zYSzSJzM0z7LzuJzeHz\
  RZzEXzDWzDVzDTzDSzDRzDQzD }

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