; June 8, 1997: Broken Arches 
;
; arches
;
; 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\
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}

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=========================================
;