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June 9, 2010: Beyond the Horizon June 8
June 10 2010 FOTD Home
 Rating 7

beyond

Fractal visionaries and enthusiasts:

Today's formula, the FinDivBrot-2, certainly creates some interesting and unexpected parent fractals -- and it's only 4 lines long.  (I have always avoided those overblown formulas with 40 or 50 lines, most of which are devoted to coloring tricks.  I much prefer the coloring tricks to come from the fractal math, not the fractal artist.)

Today's formula, along with the type=Mandel, MandAutoCritInZ, MandelbrotBC3, and SliceJulibrot4 formulas (formulae) are the ones I turn to almost automatically when I boot the Fractintprogram.  They rarely disappoint me.

In today's FOTD, the FinDivBrot-2 formula produced a parent fractal that resembles a Mandelbrot set pretty closely until its main stem is examined.  Instead of one main stem, this parent has two main stems, both of them infinitely divided into ever-smaller curled stems.  Today's image is located in the East Valley area of the minibrot on the northern main stem.

I named the image "Beyond the Horizon" because I did go a bit beyond the limit of perfect definition to find the scene.  The rating of a 7 means the image is kind of good, but nothing to get excited about.

Another picture perfect day prevailed here at Fractal Central on Tuesday, an exact repeat of Monday.  The fractal cats, now convinced that the unwanted intruder cat has moved on, spent most of the day sleeping.  My day was busier than Monday, but still left lots of time for fractal diversions.  The next FOTD will be posted in 24 hours.  Until then, take care, and pass the time pleasantly.

P.S.  If a Klein bottle is given an extra twist, the result is a surface known as a 'projective plane', which needs a full five dimensions to be seen in its full unsquashed, non-intersecting glory.  But don't ask me to describe the shape of this surface.  Describing the Klein bottle is hard enough.  And unless I'm mistaken, a projective plane may also be created by widening a Mobius strip until the single edge closes on itself to form a single-sided edgeless surface.

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


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

Beyond_the_Horizon { ; time=0:03:54.18-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=FinDivBrot-2 function=recip logmap=506
  center-mag=-1.418212964957334/+0.03225319123708284\
  /1.626e+013/1/167.5/-0 params=-0.05/-10/0/0 float=y
  maxiter=1500 inside=0 mathtolerance=0.05/1
  colors=000L1UK1SK1QJ1OJ1MI1KH1IH1GG1EG1CF1AE19E18D\
  07D06C05B04B03A02001A00900800800700700600500500400\
  40030020020010010000000000000000000000000000000000\
  0000000000000000000000000000000000000000000000IwzF\
  zxCzw9yv6xu3wsGuqEsnDojCjfBfbAbZ9YV8UR6QN5LJ4HF3DB\
  207hhZzzhrrZmoPhkFci5Zf0Ud0Sa0Q_0OY0NV0LT0JQ0HO0GL\
  0EJ0CH0AE08C0790570340120BqVAmT9jR9gP8dN7aL7YK6VI5\
  SG5PE4MC3JA3F92C7195163031Ave8o`7hW6bS5WN4QI3JE2D9\
  1640SO0OL0LI0IG0FD0CA098065zczw`zsZzoXzkUvhSrdQm`N\
  hXLcZJhSGbMETOBWF9FB7A74z32zB5V94z73K52F31A105aZuY\
  VoUSiQOcMLYJHTFENBAH77B335PvWOtVNrUNqTMoSLnRLlRKkQ\
  JiPJhOIfNHeMHcMGbLG`KF_JEYIEXIDVHCUGCSFBREAPDAOD9M\
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  7Uz5Uz3Uz1UzUUzTUzSUzRUzRUzzzEzzEzzEzzDzz1zz1zz0zz\
  0zz0zz0zz0zz0zz0zz0zz0zz0 }

frm:FinDivBrot-2   { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
esc=(real(p2)+16), b=imag(p1):
z=(b)*(z*z*fn1(z^(a)+b))+c
|z| < esc }

END PARAMETER FILE=========================================