FOTD -- January 25, 2013 (No Rating)
Fractal visionaries and enthusiasts:
I named today's image "The Seahorse Valley", and why not.
That's what the image shows. Yes, I know it looks nothing like
Seahorse Valley, but it's not the familiar Mandelbrot or Julia
views of the valley. Its orientation is off in some remote 4-D
orientation not too far from the Julia aspect of the valley.
The close-to-Julia nature is apparent in the outer shape of the
figure. The more interesting inside stuff exists because the
angle of the slice has been rotated six degrees toward the
Oblate orientation and one degree in another unimaginable 4-D
direction.
I declined to rate the image, since Seahorse scenes are so
common in FOTD history. If the image had not been such a slow
one, I might have rated it at a 7, but 15 minutes is quite a
wait for an image to finish, especially when it lies out in a
hyperspace no-man's land. Those who view the image on one of
the web sites will avoid the calculation wait and get quite a
bargain.
The finished image is posted in its full glory at:
<http://www.crosscanpuzzles.com/Archives.html>
and in even fuller glory at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The glorious back images are online at:
<http://www.Nahee.com/FOTD/>
The 24th brought a mix of sun, clouds and more cold weather to
Fractal Central. Today brought clouds and snow. At post time
about 1-1/2 in. or 4cm had fallen and the snow was still falling
lightly. The fractal cat spent the day watching the flakes come
down and lying by the heat. The humans spent the day getting
the work finished and readying the snow shovel.
The next FOTD will be posted in 24 hours. Until then, take
care, and why doesn't the other side see that it is wrong?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
The_SeahorseValley { ; time=0:15:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot4 passes=t
center-mag=0/0/1.037/1/-35/0
params=84/0/90/1/-0.75/-0.005/0/0/2/0 float=y
maxiter=32767 inside=0 logmap=yes periodicity=0
colors=000hKdhLehMfhNghOihQjhRkhTmhVnhWphYqh_rh_th\
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zzLzzPzzUzzZzzczzhzzmzzrzzvzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=z^(real(p5))+c
|z|< esc }
END PARAMETER FILE=========================================
FOTD -- January 23, 2013 (Rating 8)
Fractal visionaries and enthusiasts:
Today's unusually colored image is a near-Julia scene in the
Seahorse Valley area of the (-Z)^(2.5)+C Mandeloid. To
visualize the Julia set, mentally remove the highly colored
inside stuff while retaining the outer shape, which is the Julia
set. To see the actual Julia set, change the real(p3) parameter
to 0.
The thin open slit across the center of the image is a sideways
view of the space between the two branches of Seahorse Valley.
The angle of the slice is rotated 6 degrees from the Julia
direction toward the Oblate direction.
The rating of an 8 is largely earned by the coloring, which was
created effortlessly by the Fractint program. My part was to
tweak a few registers to make the colors blend more smoothly.
The calculation time of 3-1/2 minutes is a fair price to pay for
the image. (Most of the time is spent calculating the final two
lines.) But it is still a bother to set up and run the
parameter file. The web sites can eliminate any parameter-file
set-up anxiety.
For immediate relief view the finished image at:
<http://www.crosscanpuzzles.com/Archives.html>
And don't forget the hi-def variations at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
or the back images at:
<http://www.Nahee.com/FOTD/>
Some clouds, some sun, a little less wind and a still chilly
temperature of 18F -8C made for another bone-chilling day here
at Fractal Central today. The fractal cat had an exciting day,
surviving his regular trip to the doctor. The humans had
another in the endless string of passing days.
The next FOTD will most likely be posted in 24 hours. Until
whenever, take care, why can't we think four-dimensionally, when
even an unconscious computer can do it.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Shade_of_Antiquity { ; time=0:03:30.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot5 passes=1
center-mag=-0.056338/0/0.91876 params=84/0/90/0/\
-0.760036618323/0/0/0/2.5/0 float=y maxiter=250000
inside=0 logmap=yes symmetry=xaxis periodicity=12
colors=000hKdhLehMfhNghOihQjhRkhTmhVnhWphYqh_rh_th\
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zzLzzPzzUzzZzzczzhzzmzzrzzvzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:SliceJulibrot5 {; draws all 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), esc=imag(p5)+9
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=(-z)^(real(p5))+c
|z|< esc }
END PARAMETER FILE=========================================
FOTD -- January 22, 2013 (Rating 8)
Fractal visionaries and enthusiasts:
Today's 8-rated image is based on the unlikely expression
Z^11+(1.1*Z)+C. The expression seems innocent enough, but when
it is iterated 800 times, it creates a parent fractal that
appears as a distorted Mandelbrot set with its stem facing
northeast and a star burst radiating from its East Valley, which
lies on the southwest side of the main bay. Today's scene lies
about halfway out the center ray of the starburst.
The name "Reiterated Numbers" is a fitting description of
today's image as well as almost all other fractals.
The rating of an 8 might be a bit overdone. A 7-1/2 might be
more accurate.
The calculation time of 45 seconds will cause no one distress,
especially after the interminable hours-long calculation time of
yesterday's image.
Make life easy. Dump the calculation wait. View the finished
image at:
<http://www.crosscanpuzzles.com/Archives.html>
And view the hi-def variations at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
plus the back images at:
<http://www.Nahee.com/FOTD/>
Conditions more typical of winter in central Pennsylvania
arrived with a bang here at Fractal Central today, with an inch
(2cm) of snow on the ground, a sky filled with wind-torn clouds,
and a high temperature of a bone-chilling 16F -9C. The fractal
cat survived the day by the heat; the humans simply survived.
The next FOTD will be posted when the time is right. (The most
likely time is 24 hours from now.) Until whenever, take care,
and I still say we should pass a law to stop this climate change.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Reiterated_Numbers { ; time=0:00:45.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=ident float=y
center-mag=-0.1254246947312831/-0.038926514109924/\
1.570419e+012/1/12.5/0 params=1/11/1.1/1/0/0/0/0
maxiter=800 inside=0 logmap=82 periodicity=6
mathtolerance=0.05/1 colors=00003B04C05D06E07F08G0\
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TZzzTzzNzzHzzIzzJzzKzzOzzRVzVRzYNz`IzdEzgAzjBzgCze\
DzzEzzEzzBzz9zz7zz5zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
tzzqzzozzlzzjzzgzzezzSzzEzzLzzSzzZzzdzzUzz`zzg }
frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
FOTD -- January 22, 2013 (Rating 8)
Fractal visionaries and enthusiasts:
Today's 8-rated image is based on the unlikely expression
Z^11+(1.1*Z)+C. The expression seems innocent enough, but when
it is iterated 800 times, it creates a parent fractal that
appears as a distorted Mandelbrot set with its stem facing
northeast and a star burst radiating from its East Valley, which
lies on the southwest side of the main bay. Today's scene lies
about halfway out the center ray of the starburst.
The name "Reiterated Numbers" is a fitting description of
today's image as well as almost all other fractals.
The rating of an 8 might be a bit overdone. A 7-1/2 might be
more accurate.
The calculation time of 45 seconds will cause no one distress,
especially after the interminable hours-long calculation time of
yesterday's image.
Make life easy. Dump the calculation wait. View the finished
image at:
<http://www.crosscanpuzzles.com/Archives.html>
And view the hi-def variations at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
plus the back images at:
<http://www.Nahee.com/FOTD/>
Conditions more typical of winter in central Pennsylvania
arrived with a bang here at Fractal Central today, with an inch
(2cm) of snow on the ground, a sky filled with wind-torn clouds,
and a high temperature of a bone-chilling 16F -9C. The fractal
cat survived the day by the heat; the humans simply survived.
The next FOTD will be posted when the time is right. (The most
likely time is 24 hours from now.) Until whenever, take care,
and I still say we should pass a law to stop this climate change.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Reiterated_Numbers { ; time=0:00:45.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=ident float=y
center-mag=-0.1254246947312831/-0.038926514109924/\
1.570419e+012/1/12.5/0 params=1/11/1.1/1/0/0/0/0
maxiter=800 inside=0 logmap=82 periodicity=6
mathtolerance=0.05/1 colors=00003B04C05D06E07F08G0\
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DzzEzzEzzBzz9zz7zz5zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
tzzqzzozzlzzjzzgzzezzSzzEzzLzzSzzZzzdzzUzz`zzg }
frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
FOTD -- January 21, 2013 (Rating 8)
Fractal visionaries and enthusiasts:
Today's image is a scene on the east shore line of the north
branch of Seahorse Valley of the Mandelbrot set. The scene is
rather deep in the valley, requiring a maxiter of 1,500,000,
which makes its calculation quite slow, in the range of several
hours on older machines. On S.O.T.A. (state-of-the-art) units,
with DOS capability, the calculation is much faster, more like
15 minutes, but there is still no denying that the image is a
slow one. The individual viewer must decide if the result is
worth the wait.
I rated the image at an 8, mostly because it is a reasonably
unfamiliar scene in the all-too-familiar Mandelbrot set. I
named it "Underwater Scene" because it is located deep in the
'watery' Seahorse Valley.
Those with slow computers can save a couple hours by viewing the
finished image on the official FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
Those with S.O.T.A. units can still save several minutes.
High-definition versions of recent images are online at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The thousands of back images and discussions may be seen at:
<http://www.Nahee.com/FOTD/>
Clouds, light snow and a temperature of 30F -1C made for a
winterish scene today here at Fractal Central. The fractal cat
spent much time by the heat, trying to persuade the humans to
turn it up. The humans spent lunch time watching the
inauguration ceremonies and the rest of the time keeping busy
with the regular work.
The next FOTD will be posted when the time is right. Until
whenever, take care, and I noticed much less enthusiasm in
today's ceremonies than I saw four years ago. Maybe people are
disappointed.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Underwater_Scene { ; time=0:15:00.00 SF5 at 2000MHZ
reset=2004 type=mandel center-mag=-0.7499986559107\
32/+0.002303751935777/1.1e+011/1/177.5/0 params=0/0
float=y maxiter=1500000 inside=0 logmap=120000
periodicity=6 passes=t mathtolerance=0.05/1
colors=000RlmRmlRnlPjjOfiMcgL_fJWdITcHPaFL`EIZCEYB\
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sczrmzrmzqmzpmzpmzomznmzn }
END PARAMETER FILE=========================================
FOTD -- January 20, 2013 (Rating ?)
Fractal visionaries and enthusiasts:
Fractal trees are nothing new in the FOTD series, but I have
never posted a tree with such simplicity as is seen in today's
image. The scene is a Julia set of the (-Z)^(1.618034)+C
Julibrot. The corresponding Mandelbrot point lies where the
X-axis meets the western edge of the main bud of the Mandeloid.
The full Julia set resembles an 'infinity' symbol, a figure
eight lying on its side, with an infinity of fractal trees
along its edge. The tree in today's image is the largest one,
which lies on the X-axis on the east edge of the figure eight.
The simplicity was created by lowering the maxiter to 112. This
cuts off the finer tree branches, leaving only the most basic
tree shape.
The name "Fire Tree" refers to the color of the tree. The
calculation time of 15 seconds is due to the unusually small
maxiter.
The finished image is posted at:
<http://www.crosscanpuzzles.com/Archives.html>
The high-definition renderings are at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The back images are at:
<http://www.Nahee.com/FOTD/>
A sunny day with a temperature of 46F +8C was spoiled by a
blustery wind here at Fractal Central today. The fractal cat
spent most of the time basking in the sun on his shelf, watching
things blowing by in the wind. The humans took it easy most of
the day.
The next FOTD will be posted in a reasonable time. Until then,
take care, and don't wait for a second coming. It isn't coming.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Fire_Tree { ; time=0:00:15.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot5 center-mag=0.2398/0/15/\
0.922/90/0 params=90/0/90/0/-1.15/0/0/0/1.618034/0
float=y maxiter=112 inside=255
logmap=69 periodicity=6
colors=0000mzqNIqMFpMDpLAkK7lK5mzwnyvoxupwtqvsrurs\
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3aB3`D3_E3YG2XI2WK2VM20mz }
frm:SliceJulibrot5 {; draws all 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), esc=imag(p5)+9
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=(-z)^(real(p5))+c
|z|< esc }
END PARAMETER FILE=========================================
FOTD -- January 18, 2013(Rating 7)
Fractal visionaries and enthusiasts:
Today's image is another 'almost' Julia set. The parent
Julibrot was created by iterating the expression
(-Z)^(1.618034)+C. The area of the image lies deep in the west
branch of the valley enclosing the large bud on the northeast
shore line of the main bay of the associated Mandeloid.
The image very clearly illustrates the hairline spirals that lie
in the Julia sets of the areas just inside Mandelbrot valleys.
The name "Broken Julia Spirals" refers to the spirals on the top
side of the grossly enlarged Mandelbrot valley fragment cutting
diagonally across the inside of the open area in the image.
These spirals are broken because of the limited resolution of
the image, which causes many pixels to totally miss the very
narrow body of the spirals and print it as an open area. This
breakup can be eliminated by the process of anti-aliasing, which
calculates the image at a higher resolution, slightly blurs the
result then shrinks it down. Unfortunately, the process can be
quite time consuming.
The rating of a 7 is FOTD average. If such images had not been
posted so frequently lately, I might have rated the scene as
high as an 8.
The calculation time of 7 minutes is a bit excessive. To save
time, I recommend checking one of the FOTD web sites.
The finished image is online at:
<http://www.crosscanpuzzles.com/Archives.html>
A sample of what anti-aliasing can do for hairline spirals is
posted at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The FOTD back images are at:
<http://www.Nahee.com/FOTD/>
Today brought lots of sun to Fractal Central, but the
temperature never rose above 30C -1C. The fractal cat basked in
the sun all afternoon, having the best day so far this winter.
The humans passed the very bright day getting organized.
The next FOTD will not be posted before January 20, since I'm
going back to Old Fractal Central tomorrow to finish a few
things that need to be done. Until whenever, take care, and
since everyone claims to do what is right, why does so much
wrong exist in the world?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
BrokenJuliaSpirals { ; time=0:07:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot5 passes=1 periodicity=6
center-mag=0.10596/0.159292/0.8912656/1/46.75/0
params=89.8/0/89.8/0/0.3125/0.5702/0/0/1.618034/0
float=y maxiter=5000 inside=0 logmap=yes
colors=000B36701812923A33B34C44D55E66F66G77G87H98I\
98JA9KBALCAMCBNDBOECNFBOECOECPECPEDQEDQEDREEREEREE\
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IhRGhSGjSFhTFfTFeUFcUEbVE`VEZVEYWEWWDVXDTXDSYDQYDO\
YCNZCLZCK_CK`CKaCKbCKcCKc }
frm:SliceJulibrot5 {; draws all 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), esc=imag(p5)+9
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=(-z)^(real(p5))+c
|z|< esc }
END PARAMETER FILE=========================================
FOTD -- January 17, 2013 (Rating 6)
Fractal visionaries and enthusiasts:
Today's FOTD is one I found almost automatically in the brief
periods of free time that somehow worked their way into an
otherwise very busy day. The rating of a 6 might be considered
a gift, since I can see little of note in the image.
The image is a near-Julia scene in the easternmost East Valley
of the Z^9+C Mandeloid. (The parent Mandeloid has eight East
Valleys.) The name High-Order Hijinks" refers to the order-9
Julibrot as well as the orientation of the slice, which lies
only 0.00003,0.00003 degrees from the true Julia orientation.
The 'outside' parts of the image were colored by the 'imag'
option, which adds somewhat more life than the flat straight
'iter' coloring. The calculation time of 7 minutes is more than
the image is worth. I strongly recommend trying one of the FOTD
web sites.
Be free of calculation inefficiency! View the finished image
online at:
<http://www.crosscanpuzzles.com/Archives.html>
And enjoy the hi-def versions at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
Thousands of back images are at:
<http://www.Nahee.com/FOTD/>
A mix of sun and clouds with a temperature of 41F +5C made today
bearable if not exactly pleasant here at Fractal Central. The
fractal cat was more interested with the unwanted cats prowling
about than with the weather. The humans had another average day
-- pleasant to live through but boring to write about.
The next FOTD will be posted within a reasonable time. Until
whenever, take care, and always do good, but before doing it, be
sure to find out exactly what defines good.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
High-Order_Hijinks { ; time=0:07:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot4 passes=1 float=y
center-mag=0.13128/0.748246/8.950949/1/-87.5/0
params=89.99997/0/89.99997/0/0.67545/0/0/0/9/0
maxiter=5000 inside=0 outside=imag periodicity=12
colors=000nZqmYplXokWnjWmiVlhUkgUjgTifSheSgdRfcQeb\
QdaPc`Ob`Na_N`ZM_YLZXLZWKYVJXUJWUIVTHUSHTRGSQFRPEQ\
OEPNDONCNMCMLBLKAKJAJI9IH8HG6FH8HH9IHAJICKIDLIEMIG\
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acNbdNceOdfOfgOghOhiPjjPkkPllPmmQnjQnhRnfRodSoaSo_\
TpYTpWUpTUpRVqPVqNWqKWrIXrGXrEYsBYs9Zs7_u4Zs5Zr5Zq\
6Zp6Zo7Zn7Zl7Zk8Zj8Zi9Zh9Zg9ZfAZdAZcBZbBZaBZ`CZ_CZ\
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qLDqKCsIDqJDpJDoJDnJDmJElJEkJEjKEiKEhKFgKFfKFdKFcK\
FbKFaLG`LG_LGZLGYLGXLHWLHVMHUMHTMHRMHQMIPMIOMINMIM\
NILNJKNJJNJINJHNJGNKDOJENJFNJFMJGMJGLJHLJILIIKIJKI\
JJIKJIKIILIIMIIMHHNHHNGHOGHPGHPFHQFHQEHREGRDGSDGTD\
GTCGUCGUBGVBHUCGVBGWBGWBGXBGYBGYAGZAF_AF_AQKKJFANH\
FQJJTLNWNSZPWaR_dTdgVhjXl }
frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=z^(real(p5))+c
|z|< esc }
END PARAMETER FILE=========================================
FOTD -- January 16, 2013 (No Rating)
Fractal visionaries and enthusiasts:
Today's image is an almost-Julia set of the East Valley of the
large minibrot on the northern main spike of the Mandeloid that
results when the expression (-Z)^(2.5)+C is iterated.
The reddish stuff inside the large open hole is grossly enlarged
Mandelbrot stuff. The outer bluish stuff is Julia in nature.
I enjoy 'almost' Julia images because they are much more varied.
In pure Julia images, every small hole is basically identical,
while in the 'almost' images, no two holes are the same.
The name "The Unseen World" does not refer to the supposed abode
of spirits. It describes the high-iteration Mandelbrot stuff
that lies hidden beneath the low-iteration surface Julia stuff.
I gave the image no rating, but if I were to rate it, I would
have chosen something like 6-1/2. When the calculation begins,
it looks like the image will be finished in less than a minute,
but things slow down considerably once the central open area is
reached, and the calculation will drag on for about 5 minutes.
Save energy! Save time! View the finished image at:
<http://www.crosscanpuzzles.com/Archives.html>
and see the high-definition versions at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The back images are online at:
<http://www.Nahee.com/FOTD/>
About 4-1/2 inches (12cm) of sloppy snow fell overnight here at
Fractal Central, making for a very unpleasant day with heavy
clouds. The temperature of 34F +2C melted just enough snow to
fill the gutters with water and make dry feet impossible. The
fractal cat, who always keeps his feet dry, had an active day of
tearing up old newspapers. The humans had an average day.
The next FOTD *will* be posted. The best bet is to look for it
in 24 hours. Until whenever, take care, and why is the massacre
of 26 people killed together by a single gun more outrageous
than 1000 killed one-at-a-time by cheap hand guns every month?
Would someone please explain the current politically correct way
of thinking. I'm a little befuddled by it.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
The_Unseen_World { ; time=0:05:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot5 passes=t periodicity=12
center-mag=0.202471/-0.225264/56/1/-57.5/0 float=y
params=89.898/0/89.898/45.5/-1.422159233/0.2244159\
71/0/0/2.5/0 maxiter=32767 inside=0 logmap=8
colors=00000H00L10O20S30V40Z50a60e71h82l93oA4sB5vC\
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mramrbmrcmrcmrcmrcmrcmrcmrcmrcmwczwczwczwczwczwczw\
czwczwczwczwczwczwczwczwczwczwczwczwczwczwczwczwcz\
wczwczwczwczxczyczzczzczzczzczzczzczzczzczzczzczzc\
zzczzczzczzczzczzczzczzcz }
frm:SliceJulibrot5 {; draws all 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), esc=imag(p5)+9
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=(-z)^(real(p5))+c
|z|< esc }
END PARAMETER FILE=========================================
FOTD -- January 15, 2013 (No Rating)
Fractal visionaries and enthusiasts:
I began the day with a question -- when a three-dimensional left
hand glove is viewed from the fourth dimension, does it appear
as a left or a right hand glove? A few minutes pondering
convinced me that the question is meaningless. In 4-D space
both left and right hand 3-D gloves are the same shape. They
simply lie in different positions. Now on to the important
topic -- the fractal for today.
Today's image has something strangely familiar about it. In
fact, this is the name I gave it. The familiarity arises
because the image is actually a view of the familiar Seahorse
Valley of the Mandelbrot set. The unfamiliarity exists because
in today's image the valley is viewed in the Oblate orientation,
centered at the point -0.6 on the imag(z) axis. The scenes of
this particular orientation bear no resemblance to either the
Mandelbrot or the Julia aspects of the valley.
Seahorse Valley is actually a thing with four spatial
dimensions, which means it has six mutually perpendicular planes
cutting through it, each of which can be translated in an
infinity of perpendicular directions.
With such a familiar object as the source of the image, I could
give it no rating. The calculation time of 5 minutes is longer
than I would have preferred, but the new view of an old object
that will result will make the effort worthwhile. Those who do
not calculate may view the finished image on the web sites.
Avoid calculation by viewing the completed image on the official
FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
And check the hi-def versions at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
Don't forget the back images at:
<http://www.Nahee.com/FOTD/>
Thickening clouds and a temperature of 36F +2C made today less
than ideal here at Fractal Central. The forecast of ice and
snow later tonight and tomorrow makes the future look even less
ideal. The fractal cat passed the day in the front window,
watching the world go by and in the back window, watching the
stray cats go by. The native humans spent the day watching the
work go by.
The next FOTD will be posted when the appropriate time has
passed. Until whenever, take care, and let's give our congress
a kick in the butt. Tell them to pass a law requiring that all
our silly disagreements be solved.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Strangely_Familiar { ; time=0:05:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot4 passes=1 maxiter=27000
center-mag=0/0/7.466019/1/-36.75/0 params=0/0/90/0\
/-0.75/0/0/-0.6/2/0 float=y maxiter=27000
inside=0 logmap=-13 periodicity=0
colors=000enldmmclmbkmajn`im_hmZglYfkXekWdjVcjUbiS\
aiQ`hO_gMZgKYfIWfGVeEUdCSdARc9Qc8Pb7Na5Ma5L`4J`4I_\
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NV6OV4OU6PV7QV9RWARWCSWDTXFTXGUYHVYJVYKWZMXZNX_PY_\
QZ_SZ`T_`U`aW`aXaaZbb_bbaccbdccdcaca`b_ZaYY`WW_UUZ\
SSYUQZRO_NM_OK_PJ_PK_QK_QL_RN_SP_TQ_US_UU`VV`WX`XZ\
`Y_`Za`_c``d`af`biaag`bf`be`bc`bb`ba`b``bZ`bZ`cZ`c\
Z`cZ`cZadWbeRckMipInuKotMptNqtPqtRrtSstUttVtt_nkci\
cgdWlZOpUGtP8pS9mV9jYAg`AdcAafBZiBWkBTlDUkEVjGWiHX\
hJYgKZfG_eC`d8ac4bbIcaNd`Re_WfZ_fYdfXhfZl`YfWXaRWX\
MVSHUNCTI7SD8YJ9bPAgVBl`CqfEpXFpOGlSHiWHf_IccJ`gJY\
kKVoKSsNZnQdjSjfVpbXvZYsXYpVZnTZkSZhQ_fO_cM_cLYcQW\
cVVc_TccSchQcmPcqTcmXcj`cgdcdzcazcZzcXzcUzcSzcOzcK\
zcHzcLzcPzcTzcXzc`zcdzchzc1zz2zz2zz2zz3zz3zz3zz3zz\
DzzGzzIzzLzzNzzQzzSzzOzzK }
frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=z^(real(p5))+c
|z|< esc }
END PARAMETER FILE=========================================
