June 7, 1997: Seahorse Valley Angle | June 6 | June 8 | 1997 | FOTD Home |
Fractal
visionaries:
Sometimes familiar things appear like new when seen from a new
perspective. Such is the case with today's fractal.
We all
know and love Seahorse Valley, located at -0.75 0n the Mandelbrot
X-axis. It is one of the most prolific areas of the entire
M-set. We are also familiar with the Julia set associated
with
this point -- a symmetrical series of buds sprouting from buds.
But there are four other perpendicular planes through this area, and
some of these are quite attractive. Today's fractal is a view
of
Seahorse Valley sliced along the YZ axis of the four-dimensional
Julibrot figure. I realize that it looks nothing at all like
Seahorse Valley, but that's because we're viewing it from an entirely
new direction.
Tomorrow, I'll show another slice of this most interesting area of the
Julibrot figure. I have not yet found all slices,
however.
I'm still working on the formulas that display some of the oblique
slices. A few directions have so far eluded me, but every
failure
brings me a bit closer to a complete mapping.
Jim Muth
jamth@mindspring.com
START PARAMETER-FORMULA FILE FOR 19.6======================
SeahorseValleyAngl { ; time=0:00:11.15-SF5 on P4-2000
reset=1960 type=formula formulafile=basicer.frm
formulaname=Man-YZ-XZ passes=1
center-mag=-4.44089e-016/2.22045e-016/0.8503401
params=0/0.75/0/0 float=y maxiter=100000
bailout=100 inside=0 logmap=yes
symmetry=xyaxis periodicity=10 sound=off
colors=000gGEP0HR0KT0MV0OX0QZ1S`2Ub3Wd4Yf5_i6ak7cn\
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EQZESZFUZFXZGZZG`YHbYHdYIVyLWxLWzLXzLXzKYzKYzKZzK_\
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zzMzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:Man-YZ-XZ {; Jim Muth
; 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 PARAMETER-FORMULA FILE FOR 19.6========================