Fractal visionaries and enthusiasts:

One should always be prepared for the unexpected, even when it seems impossible.  Today's slice through the Julibrot is a good example.

The slice is centered on East Valley of the Mandelbrot set, and oriented 0.1 degree from the Oblate direction, which means the Mandelbrot stuff is stretched about 573 times its normal extent in one direction.

In the image that I found before today's, I unstretched the Mandelbrot parts, but in so doing, I stretched the Julia parts about 573 times.  The grossly stretched Julia stuff is visible near two corners of today's image.  When I did this stretching, I had almost no hopes of finding any of the Mandelbrot stuff that I had presumedly returned to its normal proportions, but much to my surprise, I found one tiny open spot lurking in the upper left corner.

When I closed in on the tiny spot, I found the better part of one of the twisted minibrots that fill East valley.  At first I could not believe that any Mandelbrot features at all could remain when the Julibrot is sliced 89.9 degrees from the Mandelbrot orientation.  But pictures do not lie, (unless they have been manipulated on a computer), and the twisted object at the center of today's image is most certainly the remains of an East Valley minibrot.

The rating of a 6! means that almost all the interest lies in the mathematical aspect of the image.  The artistic worth is minimal, though not entirely absent, and the features surrounding the chopped-off minibrot certainly are curious.

The name "Expect the Unexpected" relates my adventures on the way to finding today's image.

The calculation time of 21 seconds takes almost all the work out of running the included parameter file.  The calculation work can be eliminated entirely by viewing the finished image on the FOTD web site at:

       http://www.Nahee.com/FOTD/

The sun departed and the clouds moved in here at Fractal Central on Monday, while the temperature hovered around a mild 55F 13C.  The fractal cats took it all in stride, concerned only about their next food treat.  My day was uneventful.  Until next time, take care, and beware of global warming -- it's got me worried.  How long will it be before we wake up one morning up to our knees in the rising seas and find polar bears extinct?


Jim Muth
jamth@mindspring.com


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

ExpectTheUnexpectd { ; time=0:00:21.31-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot2 center-mag=-0.023260073\
  46855092/-0.00735188243689156/2294.688/0.002601/\
  -179.929980454595068/89.7871683432740895
  params=0/0/89.9/0/0.277/0/0/0 float=y maxiter=2400
  inside=0 logmap=22 periodicity=6
  colors=000A0OA0PA0QA0RA0SA2TA4UA6WA8YAA_ACaAEcAGeA\
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  L95E6273USSPOOLKKHGGCCC888444PUvGKb8AJyfVnZPdSKVLF\
  KEAA752Tg1JT09E8yM7rJ6kH5dE4YC3R92K71D4062jcxdZq_V\
  jVQcQMXKHRFDKA8D546amLYhJVdHS`FPXEMTC_oGbeIeXJhOLj\
  FMeFOaFPYFQUFSQFTLFUHFVDFX9FY5FZ1F_4M`6Sa9ZbBdcEkd\
  GqdEpfDogCniAmj9ll8km7kn9loAlpBlpDmqEmqFmrHmsInsJn\
  tLntMnuNovPovQowRowUkuXgsZcqa`odXmfTkiPilMgnIeqEct\
  Aav7`uAYuCVtETtGQtJNsLLsNIsPGiRD`TBSU9NV8IW7EW79X6\
  4Y50Y56bABgEGkILpMQtQQuSQvUQwWQxYQy_cz`czbczdczfcz\
  hcziczgczemzcmzamz_mzYmzWmzUmzSmzzmzzmzzmzzmzzrzzv\
  zzzzzzzzzzzzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzznzzkzzgzzczz_zzXzzTzzPzz\
  MzzLzzKzzJzzIzzHzzHzzFzzE }

frm:SliceJulibrot2   {; draws most slices of Julibrot
  pix=pixel, u=real(pix), v=imag(pix),
  a=pi*real(p1*0.0055555555555556),
  b=pi*imag(p1*0.0055555555555556),
  g=pi*real(p2*0.0055555555555556),
  d=pi*imag(p2*0.0055555555555556),
  ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
  sg=sin(g), cd=cos(d), sd=sin(d),
  p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
  q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
  r=u*sg+v*ca*sb*cg, s=v*sin(a),
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=sqr(z)+c
  |z|<=9 }

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