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.

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\
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  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=========================================