Fractal visionaries and enthusiasts:

The theme of August is fractals from deep in the Mandelbrot set.  Today's image is not from the Mandelbrot set however.  It is from the fractal that results when Z^(2.25)+C is iterated 1/2 level up the complex logarithmic hyperladder, (actually more of a hyperspiral).  I had to depart from the theme of the month for one day to get caught up.  The very deep images are quite slow, and I have been falling behind.

The parent fractal appears as a distorted M-set rotated so that its distorted main period-2 bud lies on the north side of the main bay.  There is a small valley on the east side of this bud, with today's image lying in that valley.

I named the image "Half a Spider".  Spiders have eight legs, but there are only four spidery legs radiating from the central minibrot in the image.  Since four is one-half of eight, the name is quite appropriate.  (The circular disk closer in around the minibrot holds nine legs however.)

The rating of a 7 places the image just about at the center of FOTD ratings.  The calculation time of under 1-1/2 minutes assures that no precious time will have been wasted if the eager fractalist is disappointed with the image.

Threatening clouds moved in here at Fractal Central on Saturday morning, and a heavy thunder-shower arrived at 3pm, putting a finish to any outdoor activities.  The fractal cats' outdoor activities are limited to gazing out the windows anyway, so they had no problem with their outdoor activities.  If the day had been dry, the temperature of 79F 26C would have been pleasant.

The humans, with no outdoor activities planned, had a typical day indoors.  The next FOTD should be posted in 24 hours, which is the typical interval.  Until then, take care, and be a rational skeptic who believes that no physical aliens are visiting earth in flying saucers.  Such a belief is irrational.  Due to the cosmic speed limit of light, (186,000mps), such visits are impossible.  If you must believe in something irrational, believe in ghosts.  Though they are quite disturbing to skeptical rationalists, at least they are not impossible.

Jim Muth
jimmuth@earthlink.net


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

Half_a_Spider      { ; time=0:01:25.03-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=recip passes=1
  center-mag=-0.1522280397550513/+0.9940388789985681\
  /7.345366e+010/1/32.5/0 params=2.25/0/0.5/0 float=y
  maxiter=1800 inside=0 logmap=141
  periodicity=6 mathtolerance=0.05/1
  colors=0000Xy0Wt0Uo0Sj0Qe0Na0KX0HS0EN0BJ08E059024f\
  LC`IAWF9QD7LA6G74A53521I9yG8rE7lC6fA5`94V73O52I31C\
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  B84T73Q63O63M52K52I42G42E31C31A2182061041020r_PnXN\
  kVLgTKdRI`OHYMFUKERICOFAKD9HB7D96A64643321CzzBuuAq\
  q9mm8ii8ee7``6XX5TT4PP4LL3GG2CC188044DnNBiLAeJ9aH8\
  YF7TD6PB5L94H73C5283141GTjEPdCM_AJV8GQ7CK59F36A135\
  IDYC8M64BqKlmIhiHefGbbEZ_DWWCTSAQP9ML8JI6GE5DA4972\
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  mJzmEzm9zm4zmYzzgzzhzzhzzhzzhzzhzzhzzhzzhzzhzzhzzh\
  zzhzzhzzhzzhzzhzzbzzXzzRzzLzzFzz9zz8zz7zz7zz6zz5zz\
  5zz4zz3zz3zz5zz2zz1zz1zz0 }

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