Fractal of the Day
by Jim Muth

Anatomy of a Midget ©
Jim Muth's fractal image in GIF format (640x480).

FOTD -- August 28, 2006   (Rating 8)

Fractal visionaries and enthusiasts:

I have always wondered what a midget in the Z^sqrt(2)+C fractal looks like up close and personal.   Today I decided to find out.   I calculated the Z^sqrt(2)+C Mandeloid as it appears 414 levels down the logarithmic ladder, and found the smallest midget I could that was within range of resolution.   I set the maxiter at a very high 50000 and let the image rip.   The unusually high maxiter is necessary to show all the detail in the more chaotic areas surrounding the main bay.

Surprisingly, or perhaps not so surprisingly, the midget mirrors the appearance of its parent fractal.   The sharp, jagged elements radiating from the midget have divided and sub-divided until they have lost definition.   I would like to more closely examine the chaotic areas of the image, but sadly, these lie beyond resolution.

I named the image "Anatomy of a Midget".   After all, the picture is basically a study of a midget.   I rated it at an 8, perhaps a bit high but not beyond reason.

The render time of 27-1/2 minutes is true when the parameter file is run on my fastest machine, a P4-2300, with the passes set to 1.   On my usual P200 unit, the image takes about 1/1-2 hours, not nearly the 11-1/2 times as long as might be expected.

All this concern about render times may be avoided by downloading the finished image from the FOTD web site at:
Heavy rain fell all day Sunday here at New Fractal Central on the banks of the Susquehanna River in Central Pennsylvania.   By the time the day ended, near 4 inches, that is 10cm, of rain had fallen, causing some flooding of small streams and streets.   The fractal cats stopped chasing each other long enough to glance out the window once or twice to watch the rain.   But they are not outside cats, and they don't worry about wet weather.

My day started slow and finished slow.   The next FOTD will appear in 24 hours.   Until then, take care, and what is more unreal, a dream or a fractal?


Jim Muth
jamth@mindspring.com
jimmuth@aol.com

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

AnatomyOf_A_Midget { ; time=0:27:30.35-SF5 on P4-2300
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC2 passes=1 inside=0
  center-mag=-0.35216497790502230/+0.096774058667879\
  18/2.68731e+011/1/117.5/-0.000214201607454139742
  params=1.4142/0/-414/0 float=y maxiter=50000
  logmap=650 periodicity=10 mathtolerance=0.05/1
  colors=000kwUlvSmuQnsNorLpqJqoGrnEsmCokDljDhhDegDb\
  eDZdDWbDSaDP_DMZDIXDFWDBUD8TD5SDFWGOZIYbLfeNohPmeN\
  kcMiaKh_JfYIdWGbUFaSE_PCYNBWL9VJ8TH7RF5PD4OB3SDDVF\
  NZGXaIfdJpZZeTmVSnXRnZRn_QoaPobPodOoeNpgNpiMpjLqlL\
  qmKqoKqpOmlRiiUffXbb`__cWXfTTiPQlMNjLPiKRgJTfJVdIX\
  cHZaG``GbZFdYEfWDhVDjTClSBnQApPArREoTHlULiWOfYScZV\
  ``ZYbaVceSehPglMhoJjsGkvEnoOqhXtafwVozPxlYp_fiddbh\
  cXlaRq`LuZFyY9`XBsbCpeDngEkjFhlGfnHclGakFksFYiEVhE\
  TgDRTCPXCMXBKbBIaAG`AKbEOdHReKVgNZiQajUelXin_lobpq\
  esrhpofnmdkjbih`ffZdcXaaV__TXXRVVPSSNQQLNOJLLHIJFG\
  HEEPCCXABc99k78r6AnCCkHDhMFdRGaWIZ`JVeLSjMPoi0gfJi\
  dakbtm`tYZtIYt3_kA`cHaWObOV_QSYRQWSOUTMSUJQVHOWFMX\
  DKYBJXFJXIJWMIWPIVTIVWIU_HUbHTfHTiHSmGSpGRtGRwGRzG\
  UyGWxGYxG_wGawGcvGewGgxGiyGkzGmzGozGqzGszPnzXizedz\
  m_zuVzW0zX2zX4zX6zX8zYAzYCzYEzYGzYIz_LzaOzcQzdTzfV\
  zhYzi_zkbzmezngzpjzrlzjyz }

frm:MandelbrotBC2   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*floor(p/(2*PI))
  r=real(p2)-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=========================================




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Go to my Fractal Links webpage,
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Plus, to my hostings of:
O's Fractal Art Gallery.

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