Fractal visionaries and enthusiasts:

The parent fractal of today's image was created by iterating the expression Z^(sqrt(3))+C with the MandelbrotBC3 formula at a level of 12 turns up the complex logarithmic hyperspiral with the 'round' function applied.  This parent consists of a large circular main bay, with strangely enough, two large period-2 buds, one on the northwest shore line, the other on the northeast shore, with the whole thing resembling the head of Mickey Mouse.  Today's scene is located on the western edge of the northwest period-2 bud.

The MandelbrotBC3 formula takes advantage of the multi-valued nature of the complex logarithm.  Unlike the expression Z^2+C, which, regardless of the value given real(p2), always draws the Mandelbrot set, an expression such as Z^(sqrt(3))+C has no single fractal associated with it.  It has instead an infinity of different fractals, every one of which is the result of iterating the expression Z^(sqrt(3))+C.  Asking which fractal is the correct one is meaningless.

Today's image is named "Square-Root-of-Three Minibrot".  The reason for the name is obvious.  The rating of an 8-1/2 might be a bit liberal, but I did do some extra work on the coloring, and I feel I deserve the reward.

Lots of sun and lower humidity made Wednesday a rather pleasant day here at Fractal Central.  The fractal cats were up and about most of the day, getting into various kinds of mischief -- a good sign that they approved of the drier conditions, if not the higher temperature of 88F 31C.

My day was acceptable, if not great.  The next FOTD will be posted in 24 hours.  Until then, take care, and if you're a serf, be faithful to your lord and master.

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


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

SqrtThree_Minibrot { ; time=0:01:45.08-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=round passes=1
  center-mag=-0.9914563737440867/+0.4862853210787398\
  /1.758179e+011/1/-67.5/0 params=1.732051/0/12/0
  float=y maxiter=3000 inside=0 logmap=162
  periodicity=6 mathtolerance=0.05/1
  colors=0004Kp5Kn6Kl6Kj7Kh8Kf8Kd9Jb9I`9HZ9GX9FV9ET9\
  DRzzzzzzzzzzzzzzzzzzzzzzhzzUfzGpzwVzs_mpcDh_JaWPVS\
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  czzazzUzmUknqgkjjicmgXpeRrgWqh_qicqjgqllpmppntpoxp\
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  zPAzTBzZCzcDzhDzmHzrLzvPzzTzzSzzRSzQQzPPzONzNLzMKz\
  LIzKHzKKzJKzIzzIzzHzzGzzGzzFzzEzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzz8zd8ze8zf8zg9zh9zi9zj\
  9zk9zlAzmAznAzoAzpAzqGzqLzqRzqWzqazqfzqkzqgzrdzr`z\
  rYzsVzsRzsOzsLztHztazYjzi }

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