Fractal visionaries:

As promised, todays fractal, which I named "Arches", is another view of Seahorse Valley.  But whereas yesterday's image showed Seahorse Valley as it might be viewed from the X-axis, at the left edge of the screen, today's image shows the valley as it might be viewed from the top of the screen on the Y-axis.  In both cases, the Mandelbrot set must be imagined as a three-dimensional object existing in space on both sides of the screen.

But one might ask, "where in the picture is the Seahorse Valley?  I see nothing but a few arches."  Look again at the picture, notice the straight horizontal ribbon of chaos toward the top of the screen.  That straight band is Seahorse Valley.  Viewed from this angle, it's totally unrecognizable.  Even more unrecognizable is the valley at -1.25.  That's it -- that straight-edged band of chaos nearly buried in the rubble toward the bottom of the screen.

The odd slices of the Julibrot figure are filled with perfectly straight bands of high-iteration chaos such as those in today's fractal.  When I first saw these bands, I thought the formula wasn't working.  But the bands are real features, since they correspond to features in the classic M-set.

Before I go, I must thank Benno Schmid for those 4-D formulas he sent a couple days ago.  They gave me just the hints I needed.  I had been struggling with similar formulas for several months, but I just couldn't get them right until I saw how Benno had solved the same problem.  After I made a few minor corrections in my formulas, they worked perfectly.

For tomorrow, we'll leave the world of four dimensions and return to the familiar and easy to comprehend world of the two dimensional screen.  I've got a good fractal waiting to be posted.

Jim Muth
jamth@mindspring.com


START COMBINED FILE FOR 19.6===============================

Broken_Arches      { ; time=0:00:11.21-SF5 on P4-2000
  reset=1960 type=formula formulafile=basicer.frm
  formulaname=Man-YZ-XZ passes=t
  center-mag=0/-1.38484/1.908986/0.5157
  params=0/0.18/1.06/0 float=y maxiter=3600
  inside=253 logmap=7 symmetry=yaxis periodicity=10
  colors=000WpKNtSTnQPkOLhMHdLF_JEWHCRFBNE9LC8KA7J99\
  IAAHBDGDFFFHEHJDJLELNGNQIPSKRUMTWOVYQX_SZZUaYWcYYe\
  X_gWajWclVenUgpUgrOdhJ`ZEYRCSZBUNAQJ8WH7aG6gE5mD8n\
  CAoCCpCEqCGrCJsCLtCNuCPvCRwCTxCRwFQvHPuJOtMNsOMrQL\
  qSKpVJoXInZHm`GlcFkeEjgDiiHgeLeaPcYTbVX`R`ZNdXJhWG\
  gZJfaLfdOegQejTdmVcpYcs_bvbbxdftWiqOlnGggJbaMYWOUQ\
  RPKUKEWF8ZB2`haneZmbXl_UlXSkVPkSNjPKjMIiKFiHDhEAhB\
  8g96gCBdEGbHK`lUDpYBMToNUoOUoOUoPVpQVpRWpRWpSXpTXq\
  TYqUZqV_qW`qWarXbrYcrZdrZes_fs`gsahsaisbjtcktcltdm\
  tentfoufpugquhruisvitvjuvkvvlwvlxwmywnzwnzwozwpzxq\
  zxqzxrzxszytzytzyuzyvzywzzwzzxzzyzzyzzxzyxzyxzyxzy\
  xzyxzyxzyxzywzywzywzywzywzywzywzywzzwzzvzzvzzvzzvz\
  zvzzvzzvzzvzzuzzuzzuzzuzzuzzuzzuzzuzzuzztzztzztzzt\
  zztzztzztzztzzszzszzszzszzszzszwszwszwszwrzwrzwrzw\
  rzwrzwrzwrzwrzwqzwqzwqzwqzwqzwqzwqzvqzvqzvpzvpzvpz\
  vpzvpzvpzvpzvpzv00Zmz6lz7 }

frm:Man-YZ-XZ {; Jim Muth (thanks to Benno)
; p2 = 0 = Julibrot YZ plane
; p2 = 1 = Julibrot XZ plane
; p2 = >0 <1 = Oblique planes
z=real(pixel)+flip(real(p1)),
c=imag(pixel)+flip(imag(p1)),
a=p2, b=flip(cos(asin(p2))):
z=sqr(z)+((a+b)*c),
|z| <= 25 }

END COMBINED FILE FOR 19.6=========================================