Fractal visionaries and enthusiasts:

In today's FOTD I have another go at the 'Minibrot for the Ages' that appeared as the FOTD for May 21.  Well, actually it's not the same minibrot.  The May 21 minibrot has an exponent of 1.08, while today's version has an exponent of 1.0745.

As the exponent is reduced, the prominent hook changes into an arch, and the entire minibrot moves toward the main bay of the parent fractal, where it is quickly swallowed up.  Today's image catches it as it plows through the fine grit on the shore line of its parent's main bay, shortly before it dives into the bay.

To get top detail, it was necessary to render today's image at a maxiter of 32,000, which increases the calculation time to an annoying 40 minutes.

The image was rendered with the outside set to 'fmod'.  This is a mistake, since I wanted to try the scene in the normal outside=iter manner.  But by the time I had realized the error, 40 minutes had passed, and the image was finished, and it even looked rather pleasing, so I let it go as FOTD for May 25.

The name "Demystified Midget" indicates that all those strange holes around the base of the hook of the original version are actually parts of the second half of the minibrot peeping through.  Today's image removes all doubt that half of the original minibrot is actually obscured from view.

The rating of a 6 is for artistic value.  The mathematical value is closer to a 9.

A mix of sun and clouds, and a summer like temperature of 81F 27C made Tuesday a near ideal day here at Fractal Central.  The fractal cats must have agreed, for they spent an unusual amount of time watching the outside world, which is a cat's TV.

The humans had an uneventful day.  This is always a good thing, and if tomorrow is just as good, the next FOTD will be posted in 24 hours.  Until then, take care, and never say never.  If things keep going as they are, one of these days we may find that one plus one suddenly equals three.

Jim Muth
jimmuth@earthlink.net


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

Demystified_Midget { ; time=0:40:43.14-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=recip passes=1
  center-mag=-0.20382948/+1.15808753/112/1/-105/0
  params=1.0745/0/16/525 float=y maxiter=32000
  inside=255 outside=fmod periodicity=6
  colors=000QDgQDgQEgPEgPEgPEgPFfPFfPFfOFfOGfOGfOGfO\
  GfOHfNHfNHfNHfNIfNIfNIfMIfMJfMJfMJfMJfMKfMKfLKfLKf\
  LLfLLfLLfLLfKMeKMeKMeKMeKNeKNeJNeJNeJOeJOeJOeJOeIP\
  eIPeIPeIPeIQeIQeIQeHQeHReHReHReHReHSeGSeGSeGSeGTdG\
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  cA`cAacAacAacAacAbc9bc9bc9bc9cc9cc9cc8cc8dc8dc8dc8\
  dc8ec7ec7ec7ec7fb7fb7fb6fb6gb6gb6gb6gb6hb6hb5hb5hb\
  5ib5ib5ib5ib4jb4jb4jb4jb4kb4kb3kb3kb3lb3lb3lb3lb4l\
  c3hb2db2Xa1Pa1H`09K01K12K23K23K34K45L45M56N67O67P7\
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  jaUjaUjaUkaTkaTkaTkaTlaSlbSlbSlbSmbSmbRmbRmbRnbRnb\
  QnbQnbQobQobPobPocPpcPzzz }

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