Fractal visionaries and enthusiasts:

The exponent of (-Z) in today's image is 1.05, a value that would be expected to create little in the way of interesting fractals.  But it is negative Z that we are iterating today, not positive Z, and when it comes to fractals with an exponent of Z between 1 and 2, negative Z wins hands down.

The parent fractal, with an exponent only 0.05 above unity, already has some halmarks of the Mandeloids -- a prominent period-2 bud on the negative X-axis and a very well-defined Seahorse Valley.

To produce today's image I found the Julia set of this valley, which is an empty featureless figure-eight shape, and double rotated the view 0.5,0.5 degrees.  The result is a figure eight nearly filled with the bloated Mandelbrot valley.

Searching for interesting semi-chaos, I increased the maxiter to 500000, but when I saw that no chaos was to be found, reduced it to the present 75000, which is still quite large enough.

The name "An Old Smoothie" refers to the smooth edges of everything in the scene.  Since the image is the second similar one in a few days, I declined to give it a rating.  The result is probably not worth the calculation time of 11-1/2 minutes, so thank goodness for the FOTD web sites.

A series of heavy thunder-showers plagued Fractal Central through the night and most of today, with about 3 inches, 7.5cm of rain falling in that time.  The fractal cats checked the window several times, but when the thunder grew too sharp, they ducked for cover in the closet.  FL simply endured the conditions, while I rather enjoyed the action.  At least, the temperature of 64F 18C pleased human and cat alike.

The next FOTD will be posted in 24 hours.  If an antiquing expedition arises, it might be late however.  Until whenever, take care, and don't worry about who might be the next U.S. president.  You'll never notice a difference.  The international corporate conglomerate is actually running things and will continue doing so.

Jim Muth
jimmuth@earthlink.net


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

An_Old_Smoothie    { ; time=0:11:29.48-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot5 center-mag=-0.3568/0/1
  params=89.5/0/89.5/92/-0.736/0.03/0/0/1.05/0
  float=y maxiter=75000 inside=0 outside=tdis
  logmap=75 periodicity=9
  colors=000Q86R56R26R06Q17Q27Q28Q38Q49Q49Q5AQ5AQ6BQ\
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  OFYNCZM9_L7_KUE1UD2UD2UC2 }

frm:SliceJulibrot5   {; draws all slices of Julibrot
  pix=pixel, u=real(pix), v=imag(pix),
  a=pi*real(p1*0.0055555555555556),
  b=pi*imag(p1*0.0055555555555556),
  g=pi*real(p2*0.0055555555555556),
  d=pi*imag(p2*0.0055555555555556),
  ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
  sg=sin(g), cd=cos(d), sd=sin(d),
  p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
  q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
  r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=(-z)^(real(p5))+c
  |z|< esc }

END PARAMETER FILE=========================================