Fractal visionaries and enthusiasts:

Today's image shows one of the many holes that lie near the base of the hook in the image of May 23, when the exponent of the image is lowered from 1.08 to 1.078 and the minibrot tracked down.

I named today's image "An Incredible Hole" because in some ways the attributes of the central hole are as unbelievable as some of the kooky claims now circulating among the credulous.  (But remember that a claim is not necessarily false simply because rationalists disbelieve it.)

To emphasize the hole's unusual qualities, I brought it to active life by rendering the scene with the inside set to 'bof61'.  (When the hole appears as a flat black area, some of its impact is lost.)  The bluish-pink coloring of the hole is unintentional.  It came about by lucky accident.

The hole is a true hole, and not simply an artifact of too low a maxiter.  I tested the scene with a maxiter of 1,000,000 and found the hole unchanged.

The amazing thing about this hole became obvious when I decided to count the number of large lobes around its edge.  After several failed attempts to get an exact count, I realized that I would never get the count correct, for the large and small lobes with all their sub- and sub-sub-lobes, are of one and the same series.  The total number of lobes is therefore infinite.

The inside of the hole in today's image is actually an extension of the minibrot in the original 'minibrot for the ages' image.  The original minibrot extends invisibly under the surface debris of the original image, well beyond the hook.

The rating of an 8 seems justified.  If I had put a bit more effort into the coloring, I might have rated it an 8-1/2.

Thursday turned into a midsummer-like day here at Fractal Central, with enough heat, haze and humidity to satisfy the most ardent hot weather lover.  The high temperature of 90F 32C totally satisfied the fractal cats, who stretched to their full cat lengths to show their pleasure.  As of post time, a warning on the TV Weather Channel (I call it the Commercial Channel) of possible tornadoes in the area had proved to be a scare rather than a forecast.

The humans had a relatively slow day, which was good in some ways, but not so good in others.  If nothing goes wrong, which is usually the case, the next FOTD will be posted in 24 hours.  Until then, take care, and yesterday's kookiness sometimes proves to be today's scientific fact, but before the question is settled scientifically, how does one tell the true kookiness from the kooky kookiness?

Jim Muth
jimmuth@earthlink.net


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

An_Incredible_Hole { ; time=0:08:12.85-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=recip passes=1
  center-mag=-0.000750885846/+1.174041344618/144809\
  /1/-47.5/0 params=1.078/0/16/525 float=y
  maxiter=4000 inside=bof61 logmap=-250 periodicity=6
  colors=000zf0ze0ze0zc0yb0yb0wa0va0v_0tZ0tZ0sX0qX0q\
  W0pW0pU0oT0mT0mR0lR0zhvjQ0iO0zaohN0hM0zUhfK0eI0vNU\
  cH0oFNoF0h7F_E0a07ZC0Z07aB0W00W00U70U00T60R00R40Q2\
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  00300800A00H00H20N40N60O70Q90QB0RC0TC0TE0UF0UH0WI0\
  XK0XM0ZN0_O0_Q0aR0aT0eU0hW0mX0rX0vZ0z_0za0zb0zd0zg\
  0zi0zl0zm0zm0zm0zm0zm0zm0zm0zl0zk0zj0zi0wh0wh0yh0y\
  h0zh0zh0zh0zh0zh0zh0zh0zh0zh0zh2zh2yh4wh4ehZehZfh_\
  fh_hh_hhaihaihaihajhbjhbjhblhblhblhcmhczUczUczUczU\
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  _izZizXizWizUizTizRjzQjzOjzNjzMjzKlzIlzHlzFlzElzCl\
  zBmz9mz7mz6mz4mz2oz0oz0oz0oz0zz0zzKzzKzzKzzKzzKzzK\
  zzKzzKzzKzzKzzKzzKzzKzzKzzKzzKztKzvKzvKzvKzwKzwKzw\
  KzyKzyKzzKzzKzzKzzKzzKzzKzzKzzUzzUzzUzzUzzUzzUzzUz\
  zUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzU\
  zzUzzUzzUzzUzzUzzUzzUzzUz }

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