[Fractint] FOTD 19-12-13 (Grounded in Zexpe [A-7,M-6])

19 Dec 2013

      FOTD -- December 19, 2013 (Rating A-7,M-6)

Fractal visionaries and enthusiasts:

Today's image takes us to the fractal that many years ago was 
named the Zexpe fractal by Lee Skinner, who did extensive work 
on it.   The Zexpe is the fractal that results when the 
expression Z^(epsilon)+C is iterated in the Mandelbrot mode.  
The usual Julia variations also exist, but we are not concerned 
with these in today's image.

The Zexpe fractal is just one of an infinity of fractals that 
can be created by the manzpower formula of Fractint when the 
value of the exponent is varied.  But the manzpower calculation 
involves complex logarithms, which are multi-valued and when 
calculated by the MandelbrotBC3 formula, can create an infinity 
of fractals for every possible fractional value of Z.  So there 
are actually an infinity of Zexpe fractals to be explored.

Today's image lies in the Zexpe Mandeloid fractal that comes 
about when the expression Z^(e)+C is iterated by the 
MandelbrotBC3 formula at ground level of the hyperladder with no 
function applied.  This parent resembles a quadratic M-set 
rotated 90 degrees, with an ersatz main bud on the north side 
and an ersatz East Valley on the south side.  There is some kind 
of pathological growth on the southwestern side of the main bay, 
but this does not enter into today's image, which lies in the 
East Valley of the parent.

The name "Grounded in Zexpe" implies that the image lies in one 
of the Zexpe fractals and was calculated at ground level of the 
hyperladder.  The art rating of a 7 and math rating of a 6 
indicates that the artistic worth is about average and there is 
little new stuff to be found in the math aspect of the image.  
Luckily, the calculation time of 1-3/4 minutes is fast enough to 
keep fidgetiness and impatience at bay.  The web sites can 
eliminate the fidgetiness.

Enjoy the finished image at:

      <http://www.crosscanpuzzles.com/Archives.html>

Where the image may be seen without the chore of calculating it.  
And be sure to check the variations at:

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

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

  <http://user.xmission.com/~legalize/fractals/fotd/about.html>

The sunshine was dimmed by haze today here at Fractal Central, 
but the temperature of 41F +5C was the warmest in two weeks.  
New fractal cat Jazzy celebrated the thaw by starting a tussle 
with Nico, but when Nico forgot his strength and got a bit too 
rough, Jazzy called it quits and ducked under the bed.  The 
fractal humans simply had another normal day.

The next FOTD will be posted in the appropriate time, whenever 
that might be.  Until then, take care, and before we condemn the 
evil big greedy corporations who care only about their profits 
and don't concern themselves with poverty, let's check to see 
who is giving them the money that makes them so profitable.

Jim Muth
jimmuth@earthlink.net

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

Grounded_in_Zexpe  { ; time=0:01:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident float=y
  center-mag=+0.0911597350623097/-0.3661580031587182\
  /1.7e+011 params=2.71828182845905/0/0/0
  logmap=249 maxiter=5000 inside=0
  periodicity=6 mathtolerance=0.05/1
  colors=0000KH0KH0KH0KH0KH0KH0KH0KH0JG0JG0JG0IF0IF0\
  IF0HE0HE0HE0GE0GD0GD0FD0FC0FC0EC0EC0EB0DB0DB0DB0CA\
  0CA0CA0B90B90B90A90A80A809809709709708708708607607\
  60750650650650540540540430430430330320320220210210\
  11011010000000zp0zo0zn0zm0zl0yl5xkAxjFviKuhOthNrgN\
  qfMpeModMndLmcLkbKjaKi`Kg`Jg_JfZIeYIdYHcXHbWHbVGaU\
  G`UF_TFZSFYREXQEWQDVPDUOCTNCSMCRMBQLBPKAOJANIALG9J\
  E9GC8EA8B97887577065053041030020010000000000000wzz\
  rzzmzzjzzgzzdvzarz_mzYhzWfzUdzTbzSazR`zQZzQZzPXzPW\
  zOVzOUzNTmMSzMSzLSzLSzKSvKTrJSmJRhIQcIQZHRUHRPGROG\
  TNFXNE`MEcLKZKUUJcSJcRIcQHUPGUOFUMFUKEQIDMGCKEBICB\
  GBAEA9C98A87877666555444333223112111000zzczzczzczz\
  czzUzzKzzAzz0gU7jT6mS6pR6sQ6vP5zO5zN5zM5zL4zK4zI4z\
  H4zG3zF3zE3zD3zC2zB2zA2z92z81z71z61z51z40z30z20z10\
  zZDzYCzXCzXCzWCzWCzVBzVBzUBzUBzTBzTAzSAzSAzRAzRAzQ\
  9zP9zP9zO9zO9zN8zN8zM8zM8 }

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