FOTD -- June 19, 2009 (Rating 7)
Fractal visionaries and enthusiasts:
Today we have a scene very near the Julia set of Seahorse Valley
of the (-Z)^(2.5)+C Mandeloid. Actually, the image has been
rotated 6 degrees from the Julia orientation toward the Oblate
orientation.
Instead of being at -0.75 on the X-axis, the seahorse singular-
ity in this Mandeloid lies near -0.760037363. To see the pure
Julia set, which is far less interesting, change real(p1) to
zero and reduce the maxiter to 150 to save time.
The first thing I notice about the image is the open slit along
the X-axis. This is the area near the singularity between the
north and south arms of the valley.
Next, I notice the many proto-peanut holes. Most have only two
lobes, but the two at the left end of the fractal appear to have
developed four lobes, and the brilliant open area on the X-axis
just left of center is certainly a peanut hole in the making.
Actually, I'm not sure that the image is mathematically correct.
The X-axis symmetry might be an artifact of the math routine.
To see the problem, set real(p1) to something like 0.0000000001.
The image still has X-axis symmetry. Then set real(p1) to zero,
and the right half of the resulting fractal totally changes.
Such a small parameter change cannot possibly make such a large
change in the resulting image. But real or an artifact, today's
image rates a 7.
The calculation time of 2-1/2 minutes is quite reasonable even
for the most fanatical rationalists. And never forget that the
finished image is available on the FOTD web site at:
<
http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
Thursday started with rain here at Fractal Central, but just
after noon the sky brightened and the rain ended. One final
sprinkle fell at 2pm, but after that the sun appeared and it was
a fine day, with a temperature of 77F 25C. After chasing away a
couple unwanted stray cats with their fierce glares and mighty
growls, the resident fractal cats spent the day sleeping and
ignoring the weather.
My day was average. It's not boring; it's peaceful. The next
FOTD will be posted in 24 hours. Until then, take care, and be
fractalish.
Jim Muth
jamth@???
jimmuth@???
START PARAMETER FILE=======================================
Seahorse_Valley-19 { ; time=0:02:27.18-SF5 on P4-2000
reset=2004 type=formula formulafile=basic.frm
formulaname=SliceJulibrotMin4 center-mag=-0.056338\
/0/1.03 params=84/0/90/0/-0.760036373/0/0/0/2.5/0
float=y maxiter=50000 inside=0 logmap=yes
periodicity=10
colors=000hKdhLehMfhNghOihQjhRkhTmhVnhWphYqh_rh_th\
auhavhcwhcwhcwhdwhdwhewhewhfwhfwhfwhfwhfwT22V68X9D\
ZDI_GNaKScNXdQacP`bP_bO_aOZaOY`NY`NX_NWZMWZMVYMVYL\
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FJOFJNEINEHMEHLDGLDGKDFKCEJCEJCDIBCIBCHBBGABGAAF99\
F99E98E87D87D86C76B75B74A64A63962952851640851951B6\
2C62E72F73H83I83K84L94N94OA5QA5RB5TB6UB6WC6XC7ZD7_\
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xhDqmCmmBmmBmmAmlAmk9mj1mi5mh9mgDmfGmeKmaOv_SwYRwW\
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aWC`XC_XC_XBZYBZYAYYAYYAX_9W`9Va9Uc8Td8Se8Rf8Qh7Pi\
7Oj7Nk7Mm6Ln6Ko6Mp6Oq7Qr7Ss8Ut8Wu8Yv9_w9axAcyAezAg\
zBizBkzBmzCozCqzDszDuzDwzEyzEzzEzzFzzFzzGzzGzzHzzH\
zzLzzPzzUzzZzzczzhzzmzzrzzvzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:SliceJulibrotMin4 {; 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=(-z)^(p5)+c
|z|<=9 }
END PARAMETER FILE=========================================
