Fractal visionaries and enthusiasts:

In yesterday's image we set the real(z) axis perpendicular to the Mandelbrot plane at the -0.75 limit of Seahorse Valley.   In today's image we do the same with the imag(z) axis, which gives us the Rectangular aspect of the valley.   The question then immediately arises, which Z axis is actually perpendicular to the Mandelbrot plane.   The answer is that they both are.   And every other line in the Julia plane is perpendicular to the Mandelbrot plane as well.   The two planes are absolutely perpendicular to each other, with every line in both planes perpendicular to every line in the other.   Absolute perpendicularity is one of those strange unvisualizable things that cannot exist in spaces with dimensions less than 4.

Seahorse Valley is filled with holes that resemble crossed peanuts, which I call peanut holes.   Today's image shows one of these holes in its full glory, with many other holes scattered about.   These holes are not true areas of trapped points, but bottomless pits of ever increasing iteration count.   In today's image the maxiter is 110,000, but even this value leaves the peanut hole wide open.   A much greater maxiter of 1,000,000,000 or so would totally close it however, greatly increasing the already very slow calculation time in the process.

The unlikely values in the parameter file show that the image has been greatly stretched and skewed to bring the large peanut hole to a reasonably undistorted state.   Such distortion that needs to be undone is very common in the Rectangular and other odd planes.

 I gave today's image no rating.   After all, how could a mere peanut hole earn a rating?   In addition, the calculation time of 1-1/3 hours will try the patience of even the most patient fractalist.   I strongly recommend viewing the finished image on the FOTD web site at:
Heavy clouds blanketed the Fractal Central area on Thursday, but no rain fell during the daylight hours and the temperature hovered around a very comfortable 73F 23C.   The fractal cats had nothing to say about things.

My day was occupied with work.   But the efficiency eventually paid off and the work was finished by 4pm.   The next FOTD will be posted in 24 hours.   Until then, take care, and no comment at this time.


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

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

Seahorse_Valley-12  { ; time=1:22:37.96-SF5 on P4-2000
  reset=2004 type=formula formulafile=slices.frm
  formulaname=Rectangular inside=0 maxiter=110000
  center-mag=-0.79070618646798470/+0.0004412500501707\
  6/5.971931e+007/0.0001521/0.0745896617071803714/-89\
  .9801123768401396 float=y periodicity=10
  params=0/0/-0.75/0
  colors=000BJDBIEBHFBFGBEHBDIBCJBAKB9LB8MB7N84LB6ND\
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  e`Gg_GiZHkXHkWIjWJjWIiVHiVGcVEYWDTWBNWAHWAFWBDWBCW\
  ADUADSCDQFDPHDNJDLMEJOEIR }

frm:Rectangular {; Jim Muth  imag(z),imag(c)
  z=flip(real(pixel))+p1,
  c=flip(imag(pixel))+p2:
  z=sqr(z)+c,
  |z| <= 16 }

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