Fractal visionaries and enthusiasts:

Today's FOTD image is late, but it's still worth the effort of a trip to the FOTD web site.  In the image we venture ever closer to the point of total linearity.  In fact, since yesterday's image we have gone half-way to unity.

The value of the exponent in today's image is 1.0045, yet it still creates fractals with interesting detail.  There must be something special about the point 4.45 levels up the log ladder when the 'recip' function is applied.

Regardless of which mathematical quirk the image came from, it is worth a rating of an 8, much of it due to the mathematical factor.

If I had had more time to work on the coloring, I might have raised the image to a rating of an 8-1/2.  As it is, I devoted most of the color work to creating the 3-D effect in certain areas.

The name "Into the Depths" describes the fall toward unity.  Though today's image is quite close to the limit, I would not be surprised if tomorrow's is even closer.  Check back to see.

Tuesday was a bit chilly but otherwise very pleasant here at Fractal Central, and the clouds were spectacular.  The fractal cats thoroughly appreciated the temperature of 66F 19C, reverting to curl-up mode for their afternoon siestas.  The humans, who were out of town all afternoon, let them sleep undisturbed.  The next FOTD will be posted in just a few hours.  Until then, take care, and what will those who base their world view on the reality of the material universe do, if it turns out that everything is an illusion?

Jim Muth
jimmuth@earthlink.net


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

Into_the_Depths    { ; time=0:16:58.75-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=recip passes=1
  center-mag=-2.100288591283524/-1.442130840681714/\
  528.8877/1/115/0 params=1.0045/0/4.45/3600 float=y
  maxiter=5200 inside=255 logmap=966 periodicity=6
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  DKVDLUCFU3IU7LUCNMKMMKLMK }

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