[Fractint] FOTD 20-08-10 (From Epsilon to PI [7])

19 Aug 2010

      FOTD -- August 20, 2010 (Rating 7)

Fractal visionaries and enthusiasts:

On Thursday I was occupied with the 'Zexpe' series of formulas 
(formulae is the plural word for the over-educated) and tried 
one of my own.  Using the MandelbrotBC3 formula, I checked to 
see what the Zexpe fractal looks like at a level of PI steps up 
the complex logarithmic hyperladder.

The parent fractal that I found there looks pretty much like the 
minibrot at the center of today's image, though it is rotated 
180 degrees, and as today's image shows, it is quite interesting 
in its depths.

Today's scene lies in a valley of its parent that corresponds to 
the small valley near the center of the eastern shore line of 
the main bay of the minibrot at the center of the image.

The rating of a 7 means I consider today's image to be a bit 
better than yesterday's, yet nothing to get over-excited about.

The name "From Epsilon to PI" fairly describes the math behind 
the image.

The calculation time of 1-1/2 minutes is fast by any standards.  
But viewing the finished image on the FOTD web site at:

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

is less work and more fun.

Perfect weather prevailed here at Fractal Central on Thursday -- 
sunny skies, low humidity and a temperature of 84F 29C.  The 
fractal cats had a thrill when a very loud fight broke out 
between two cats in the yard next door, but they seemed a bit 
disappointed when one cat, presumably the loser, made a cautious 
retreat before the dispute could escalate to physical violence.  
My day was slow, which gave more time to waste before searching 
for fractals.

The next FOTD will be posted in 24 hours.  Until then, take 
care, and I found a mind lying on the basement stairs.  Did 
anyone lose theirs?

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

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

From_Epsilon_to_PI { ; time=0:01:28.70-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident
  center-mag=-0.1738289076076641/+0.3463464790189864\
  /9.098551e+008/1/152.5/0 params=2.71828182845905/0\
  /3.14159265358979/0 float=y maxiter=3600 inside=0
  logmap=129 periodicity=6
  colors=000E28F3BG4EH5HI6KJ7NK8QL9TMAWNBZOCaPDcQEcR\
  FcSGcTGcUGcRGcOIcKJcIJdGJeEJfCKgAKh8Kk6Kn7Lq8Nt9Qw\
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  3oS2bL1QE0D7upgpkckg_fbXaZTXUPTQMOMIJHEEDB987443w1\
  mw0hw0cx0Zx0Ux0Px0Ky0Fy0Ay05yI5zC3z6zzEszCzzBhzAzz\
  8Zz7zz6Pz0zzE9zDzzDAzDzzDCzCzzCEzUzzCFzUzzKCzUzzR9\
  zUzzY7zUzzk9zUzzbIzUzzTRzUzzNSzMzzLMzKzzIHzHzzGBzF\
  zzJGzNzzMTzLzzLdzKzzJpzJz }

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