FOTD -- October 30, 2007 (No Rating)

Fractal visionaries and enthusiasts:

Today's image takes us once again to one of the infinity of 
fractals created by the formula Z^sqrt(2)+C, this time to the 
fractal that appears 1.4142 levels up the logarithmic ladder, a 
fractal that resembles a limbless torso with a head attached 
-- a perfect parent fractal for the day before Halloween.  The 
scene is located in the chaos on the eastern side of the head.

The image shows a small minibrot and its surrounding pattern.  
As must always be the case in fractals where the power of Z is 
fractional, the features in the image are broken and scrambled.  
But the broken features make a rough kind of symmetrical pattern 
around the midget, which is barely striking enough to raise the 
image to FOTD status.  I can give no logical reason for the name 
"Square-Root Picnic".

Since I have done so many of these scrambled fractals with 
exponents of Z between 1 and 2, and achieved only a modicum of 
success, I could not give the image an honest rating, but it is 
still worth a look.  The calculation time of 7 minutes is 
slightly slow for such a less-than-splendid image.  To save time 
and frustration, I recommend going to the FOTD web site at:

       

and viewing the finished image there.

After a foggy and frosty start, Monday turned quite pleasant 
here at Fractal Central, with sunny skies, light winds, and a 
high temperature of 55F 18C.  The fractal cats were more con-
cerned with something in the hallway than with the weather.  
They must still remember the mouse that popped out of the hole 
in the floor by the radiator last year around this time.  When 
no mouse appeared on Monday, I comforted the disappointed duo 
with a treat of tuna and cheddar cheese.

The next FOTD will appear in 24 hours.  Until then, take care, 
and don't get caught up in a non-local fractal field pattern.


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


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

Square-Root_Picnic { ; time=0:07:06.50-SF5 on P4-2000
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC2 center-mag=-0.1110651380\
  7892870/+1.444879230159444/5.566726e+010/1/-52.5/\
  0.0361740551652163 params=1.4142/0/1.4142/0 float=y
  maxiter=3000 inside=0 logmap=848 periodicity=10
  colors=000cAqcApcApcAncAmcAkcFkhKjmPhrUgvZgzcfzhdz\
  mgzrdztczvaxt`vqZtpYsnXpkVnjTkgSjfRhdPfaOd`MaYL`XJ\
  ZVIXSHVRFSOERMCOJBMI9LH8IE6HC5E93C82B6183062030020\
  0100200300500600800900B00C00E00F00H00I00J00L10M10O\
  10P10R11S11T11V21X21Y22Z22`22a22c33e33g33i33k33m35\
  o35q55s55t56u56v56w56x28y36z56z65z85z95zB3zC3zE3zF\
  2zH2zH2zI1zJ1zL1zM0zO0zP0zR0yS0xT0wT0vV0uX0tY0tZ0t\
  `0ta0tc0td0tf0xd0tf0pg0mg0hh0fh1aj3Yj5Vk8Rm9OpCJqE\
  FtHCvI8xL3xO5zM6zM8zM9xMBwMCvMEtMFsMHqMIsMJvMJxMLz\
  MMzMOzMPzMRzMSzMTzMVyMXxMYwMZvRYuOYqMYmJYkIYiHYgEY\
  eCYc9Ya8Y_6YY3YW2YU0YS0XQ0YO0YM0ZK0ZgzZqz`zz`zz`zz\
  awzamzaczca0ca0c`0d`0d`0dZ0fZ0fY0zY0zg0zn0zn0zg0zV\
  0zT0zT0zS0vS0nR0gR0`R0TP0FPgFOgFOgFMgFMgFMgFLgc9zc\
  AzcEzcIzcMzcQzcUzcYzcazcezcizzmzzozzqzzszzuzzwzzyz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzwzzxzzzzzzzzzzzzzzz\
  zzzzzzxzzwzzwzzvzztzztzzs }

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|

**************************************
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