FOTD -- March 15, 2013 (Rating ?)
Fractal visionaries and enthusiasts:
Today's image is a variation on a minibrot. I named it
"Minibrot Madness" because the minibrot is unlike any I have
seen so far in Fractal Land. Actually, the image is a
continuation of the recent explorations in the 4-D
HyperMandelbrot set created by hypercomplex numbers.
The 'stuff' condensing around the edges of the bays and buds of
the minibrot is just as much a mystery as the eroded 'stuff'
that obscures the minibrot in the image of March 04. It has no
right to be there, but there it is anyway, violating all the
rules of common-sense math.
This 'stuff' is sensitive to the value of the real(p3) and
real(p4) parameters. And if the maxiter is increased, the
'stuff' expands and soon fills in the remaining open areas
inside the minibrot.
The image might be a real fractal; it might be an artifact of
math imprecision. But until I find out exactly what is going on
with these hyper-images, I will rate them with a question mark.
One thing not in doubt is the speed of the parameter file, which
on the modern day speed-demons will finish in 45 seconds or
less. Of course, the simplest way to see the image is always to
check it on one of the FOTD web sites.
View the finished image at leisure at:
<http://www.crosscanpuzzles.com/Archives.html>
And check the high-definition renderings at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The thousands of FOTD back images are at:
<http://www.Nahee.com/FOTD/>
Clouds and a temperature of 45F +7C prevailed today here at
Fractal Central, while the fractal cat prevailed in my favorite
chair. The humans simply prevailed, which requires no further
elaboration.
The next FOTD will be posted in the appropriate time. Until
whenever, take care, and they say heaven exists in four-
dimensional space. No wonder we can't spot it with our three-
dimensional scientific devices. All we can see are 3-D slices.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Minibrot_Madness { ; time=0:00:45.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=HyperMandelbrot2 center-mag=-0.7329986\
40931621/+0.2212681808037857/4510/1/-158.75/0
params=0/0/0/0/0.135/0/1e-070/0 float=y
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frm:HyperMandelbrot2 {; periodicity must be turned off
a=(p1),b=(p2):
q=sqr(a)-sqr(b)+pixel,
b=(p3+2)*a*b+p4,
a=q,
|a|+|b| <= 100 }
END PARAMETER FILE=========================================
FOTD -- March 14, 2013 (Rating ?)
Fractal visionaries and enthusiasts:
Today's date is 3-14, which makes it international PI day. In
two years it will be 3-14-15, which will make it an even more
accurate PI day. And in three years it will be 3-14-16, which
is the rounded value of PI that I learned in elementary school.
In honor of the number PI, today's image has absolutely nothing
to do with 3.141592654....
In the last FOTD, I said I was finished with the hypercomplex
stuff for a while. I lied. I am becoming so fascinated with
the theme that I'll probably continue with it for a number of
days. I will give no rating to the images because I have no
idea what I am dabbling in.
Today's image shows another scene that should not be there. The
location is at the center of the main bud of a minibrot in an
elephant on the southern shore line of East Valley of the parent
HyperMandelbrot set.
The eighteen arms are arranged around the center in six groups
of three. But the six groups are not identical, with each group
having its own particular arrangement of its arms.
The name "Hyper Something" indicates that the appearance of the
image indicates that it involves hypercomplex numbers, but at
the same time I have no idea what the period of the arms means.
Regardless of what is going on, the image is a pretty good one,
which, if I had given it a rating, would have rated an 8.
The calculation time of 40 seconds will pass quickly, leaving
ample time to ponder the mathematical mysteries of the image.
For even more pondering time, check the completed image at:
<http://www.crosscanpuzzles.com/Archives.html>
and the high-definition versions at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The FOTD back images are at:
<http://www.Nahee.com/FOTD/>
Today came on like a day in mid-January here at Fractal Central,
with biting winds, scudding clouds and a temperature only a
degree or two above freezing. The fractal cat took advantage of
the sun while it was shining, and found comfort in my favorite
chair when the sun failed him. The humans simply had another
day with nothing to report,
The next FOTD will be posted in the proper time. Until whenever
that might be, take care, and now is the time for action.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Hyper_Something { ; time=0:00:40.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=HyperMandelbrot2 center-mag=+0.2536635\
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params=0/0/0/0/1/0/1e-075/0 float=y maxiter=600
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frm:HyperMandelbrot2 {; periodicity must be turned off
a=(p1),b=(p2):
q=sqr(a)-sqr(b)+pixel,
b=(p3+2)*a*b+p4,
a=q,
|a|+|b| <= 100 }
END PARAMETER FILE=========================================
FOTD -- March 12, 2013 (Rating 7.5)
Fractal visionaries and enthusiasts:
Today's image is another, and probably the last, of the present
series of ventures into the world of the four-dimensional
HyperMandelbrot set. To create the image I took the image of
March 4 and decreased the value of the real(p4) parameter to
1e-170. As a result I found that the number of arms surrounding
the center point, which is the pseudo-origin of the underlying
minibrot, has increased.
I'll make no effort to explain the number of elements around the
center, since I have no idea what determines this number. But
the number does appear to increase by increments of two as we
venture deeper into the apparently limitless center point.
The color palette is the same one that appeared in the March 4
image, with a few tweakings to smooth some rough breaks. The
rating of 7-1/2 is a bit conservative, but this is the third
image based on the same theme, which detracts from its worth.
The calculation time of 2-1/2 minutes is a fair price for the
image. And as always, the web sites are even more fair.
The completed image is posted at:
<http://www.crosscanpuzzles.com/Archives.html>
Variations are online at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
back images are available at:
<http://www.Nahee.com/FOTD/>
The day began with rain here at Fractal Central. The rain
ended by midday, but the clouds hung on all afternoon. The
temperature of 50F 10C was pleasant enough. The fractal cat
spent the morning watching the world go by and passed the
afternoon wrapped in an afghan and visible as only a lump. The
humans passed the day pondering existence.
The next FOTD will be posted in a day or two. Until whenever,
take care, and let a smile be your umbrella on a rainy day, but
don't start complaining when you get wet.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
More_Vacuum_Energy { ; time=0:02:30.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=HyperMandelbrot2 center-mag=+0.2587410\
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frm:HyperMandelbrot2 {; periodicity must be turned off
a=(p1),b=(p2):
q=sqr(a)-sqr(b)+pixel,
b=(p3+2)*a*b+p4,
a=q,
|a|+|b| <= 100 }
END PARAMETER FILE=========================================
FOTD -- March 11, 1013 (Rating 7.5)
Fractal visionaries and enthusiasts:
Today's image is a scene in the Scepter Valley of the same
oversized parent Mandelbrot set that created the March 9th image
of two days ago.
The overwhelmingly obvious minibrot at the center combines the
quadratic elements closer to the minibrot with the heptic (I
guess that's the word) elements farther out, to create an
entirely new world of high-order images.
I named the image "More Heptic Stuff" in the hope that 'heptic'
is the right word for Z^7 stuff. (As I see it, the series goes
. . . linear, quadratic, cubic, quartic, quintic, hexic, heptic,
octic, nonic . . . etc.)
The rating of 7-1/2 seems about right while viewing the image,
but the rating appears too high when the calculation time of a
dragging 20 minutes is considered. Viewing the finished image
on one of the FOTD web sites can raise the rating a point or so.
The finished image is posted at:
<http://www.crosscanpuzzles.com/Archives.html>
High-definition renderings are at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
Back images are at:
<http://www.Nahee.com/FOTD/>
With near total sunshine and a temperature of 59F 15C, yesterday
was infested with spring here at Fractal Central. The fractal
cat caught the lazy bug early and stretched on his shelf in the
southwest window most of the afternoon to take advantage of the
sun, which at this time of the year is as strong on his shelf as
it ever gets. Today turned out cloudy but with another quite
mild temperature of 55F 13C. The humans had average days both
days.
The next FOTD will be posted whenever it is. Until then, take
care, and I hear from some in the media and also from FL that
there is a war against women. But I am uncertain just which
group of people is supposed to be waging war against just which
group of women. Is it all men against all women, or only right-
wing men against left-wing feminists, or is it the entire male-
dominated culture itself that is at war against women? I have
always assumed there are fewer women in high-paying top
executive offices because women have the common sense to avoid
the life-shortening dog-eat-dog race to the top, and not because
there is a male-created glass ceiling holding back all the
aspiring women.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
More_Heptic_Stuff { ; time=0:20:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MultiExp function=recip passes=1
center-mag=-18.7620116655262/+0.3566079766580704/\
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frm:MultiExp { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
b=imag(p1)+0.00000000000000000001:
z=z*z*fn1(z^(a)+b)+c
|z| < 100000000 }
END PARAMETER FILE=========================================
FOTD -- March 09, 2013 (Rating 8)
Fractal visionaries and enthusiasts:
Today's image shows that heptic minibrots need not always be the
dull high-order things one would presume. The parent fractal is
an oversized Mandelbrot set that has been corrupted not very far
from its surface with order-7 energies.
The scene is in the East Valley area of the parent's large main-
stem minibrot, which is already well on the way to becoming an
order-7 minibrot. This minibrot's East Valley has already
vanished and been replaced by burgeoning order-7 lobes, which
are surrounded by loosely connected spirals. These spirals
still abound in today's image, which lies rather deep in one of
the larger spirals.
The rating of an 8 is my estimate of the image's worth. The
minibrot really is quite unusual. Foe comparison, try to find
as interesting an order-7 minibrot in the straight Z^(7)+C
Mandeloid.
The name "Forever Seven" indicates that from the magnitude of
today's image all the way to infinity the order-7 minibrots will
prevail.
Check the finished image online at:
<http://www.crosscanpuzzles.com/Archives.html>
High-definition variations are at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
and the back images are at:
<http://www.Nahee.com/FOTD/>
We had a preview of spring here at Fractal Central today when
the temperature reached 55F 13C and the sky was horizon-to-
horizon blue. The fractal cat stretched to his fullest cat
length in the warm sun and was as happy as a cat could be. The
humans were a satisfied neutral, which is the usual condition of
earth-bound humans.
The next FOTD will be posted in about one day. Until then, take
care, and how did we ever get into a situation where we must
have ever-higher technology if we hope to survive? Can no one
see that it's a dead end?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Forever_Seven { ; time=0:02:20.00 SF5 at 2000MHZ
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formulaname=MultiExp function=recip passes=1
center-mag=-26.21766685865878/-0.00673733985958567\
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frm:MultiExp { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
b=imag(p1)+0.00000000000000000001:
z=z*z*fn1(z^(a)+b)+c
|z| < 100000000 }
END PARAMETER FILE=========================================
FOTD -- March 08, 2013 (Rating 8)
Fractal visionaries and enthusiasts:
Today's image is an exploration into the detail of the cap over
the minibrot that appeared as the 'Translateration' image of
March 4. This spurious cap is rather sensitive to parameter
changes, most of which I have yet to check.
Today's image shows the result of one such change. In it, I
increased the exponent of the real(p4) parameter 15 orders of
magnitude and checked the chaos the change creates in the
minibrot cap.
The underlying minibrot lies in the trunk of the period-34
elephant on the south shore line of East Valley of the
Mandelbrot set, but this number appears to be totally lost in
the image, where the topmost pattern has 8 elements and the next
pattern inward has 10.
I have named the image "Vacuum Energy". The name indicates that
the image overlies the emptiness of the interior of a minibrot,
and sometimes, just as in the 'real' physical world, the nothing
of a fractal vacuum can be filled with quite a bit of something.
The rating of an 8 indicates both mathematical and artistic
value. The color palette is a tweaking of the palette I used in
the March 4 image.
The calculation time of 1 minute, 25 seconds is fast enough. Of
course, the web sites are even faster.
The big-time business pros will view the finished image at:
<http://www.crosscanpuzzles.com/Archives.html>
But wait! High-definition variations are at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
And the back images are stacked at:
<http://www.Nahee.com/FOTD/>
A mix of sun and clouds with a temperature of 43F +6C made today
a typical end-of-winter day here at Fractal Central. With all
the talk on the big news outlets of snow in the Northeast, one
would think FC was buried. Actually, not a flake has fallen in
the past week and the ground is bare, with bulbs already popping
up in FL's garden. The fractal cat is unconcerned with snow or
flower bulbs. All he wants to do is get into the places where
he is not permitted, such as storage closets and the outdoors.
The humans, with enough to keep them busy, want little.
The next FOTD will be posted in a number of hours. Until
whenever, take care, and we will never solve our problems until
we fully understand them and have the courage to accept them for
what they are.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Vacuum_Energy { ; time=0:01:25.00 SF5 at 2000MHZ
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formulaname=HyperMandelbrot2 center-mag=+0.2587410\
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QiXBlT0pQ4sNDwJLzGTC1lD1l }
frm:HyperMandelbrot2 {; periodicity must be turned off
a=(p1),b=(p2):
q=sqr(a)-sqr(b)+pixel,
b=(p3+2)*a*b+p4,
a=q,
|a|+|b| <= 100 }
END PARAMETER FILE=========================================
FOTD -- March 07, 2013 (Rating 7.5)
Fractal visionaries and enthusiasts:
The ship that in yesterday's image was sailing space has
foundered. Someone has let the wind out of its solar sails. It
is stuck in the intergalactic doldrums, where it will remain
forever, a derelict to remind us that our fondest dreams must
remain unfulfilled. And despite the technophiles' optimistic
pronouncements, technology will never be able to match our
ability to dream unfulfillable dreams.
Before we will be able to venture peaceably into space, we will
need to solve the economic and environmental problems facing us
on the surface of our planet. The rest of the world is tired of
seeing people in the U.S. and other advanced countries living
lives of luxury at their expense. They rightfully demand part
of the material action. They claim that it is time for all
people in all countries to enjoy lives like we in the West have
been living for a century or more. The problem is that it would
take at least four planet earths to supply the resources for
this to be possible, and it would be politically impossible to
squander resources to venture into space until the economic
inequalities are solved one way or the other and we are able to
live in peace.
Since this is not about to happen, we're stuck on earth, where
we will continue to dream awesome dreams and watch them pop like
bubbles. The time could never be better to turn to fractals for
distraction from this harsh reality.
Today's image lies in the center of the 'fan' of one of those
'double negative' parent fractals. I rated it a 7-1/2 out of
generosity. Most of the color was created by the Fractint
program, the DOS program that will not die, and might even
outlive the PC it was written to run on.
The calculation time of 4-3/4 minutes is slow, but the web sites
are still there.
The finished image is available online at:
<http://www.crosscanpuzzles.com/Archives.html>
With hi-def variations at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
and thousands of back images at:
<http://www.Nahee.com/FOTD/>
Today produced a mix of clouds and sun, with more clouds than
sun here at Fractal Central. The fractal cat, realizing early
that he would have little sun to stretch out in, spent most of
the day eating and sleeping, wishing he could have lived back at
the Old Fractal Central when it was the one and only official
Fractal Central and the old fractal cats (now gone) spent their
days outside, watching, chasing and occasionally catching birds
and bugs. The humans spent the day feeling down because of what
we see on the declining news channels as the declining condition
of our culture.
As for the next FOTD, it will be posted when the time comes.
Until whenever, take care, and what is the evolutionary
advantage of the human ability to so vividly imagine so many
things that, because of the body's limitations, we will be
forever incapable of doing?
Jim (what a waste of imagination) Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Back_to_Earth { ; time=0:04:45.00 SF5 at 2000MHZ
reset=2000 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=1
center-mag=+2.744488223675127/-0.04951958592821827\
/1.377578e+010/1/-140/0 params=-1/-11/-11/-1.1/0/\
800/0/0 float=y maxiter=2400 inside=0
logmap=364 periodicity=6
colors=000hCNbJWXQdEKMHC2KSMKUcbUFUfb9RNCUWFXdI_mO\
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czsmztmzumzEmzTmzgzzWzzIzzVzzczzlzzDzz2zzUzzCzzZzz\
KzzXzzizzYzzezzmzzuzzuzzu }
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 -- March 06, 2013 (Rating 8)
Fractal visionaries and enthusiasts:
A ship that sails on the stellar winds of space -- how romantic.
A fractal ship that sails abstract mathematical hyperspace on
the winds of numbers -- well, maybe not quite as romantic, but a
lot more real than space ships will ever be.
Today's image shows a fractal ship plowing through four-
dimensional space on its way to who knows where. I named it
"Ship of Space" when I luckily turned the original image, which
looked nothing like a ship, upside down before discarding it.
The formula, MandelbrotBC2, is an early version of the
MandelbrotBC3 formula. I like to bring up the old formulas now
and then to see what I can do with them.
The calculation time of 1-1/2 minutes is a fair price for the
scene. And luckily, the FOTD web site problem has been solved
for good (I hope) and the image is posted there.
The finished images are once again being posted to the official
FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
High-definition variations are at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The FOTD back images are at:
<http://www.Nahee.com/FOTD/>
Lots of clouds darkened the skies here at Fractal Central today,
while the temperature held around a quite reasonable 43F +6C.
The fractal cat, now into the 'senior cat' group, spent the day
sleeping on his high bookcase. The humans passed the day doing
lots of human and a few inhuman things.
The next FOTD will most likely be posted in 24 hours. Until
whenever, take care, and we will never get any significant part
of our energy from things like solar panels and wind turbines
for the same reason that we stopped using wind to propel our
large sea-going ships.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Ship_of_Space { ; time=0:01:30.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC2 passes=1
center-mag=-0.6537202144440802/+0.4582235896757069\
/14661.82/1/-149.4/0 params=1.5/0/-1.5/0 float=y
maxiter=1000 inside=0 outside=fmod periodicity=6
colors=000OdDSfEXiG`lIdoKiqLmtNqwPvzRuwRstRqqSomSm\
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o7Bo78o50K50K50K50K50K50K }
frm:MandelbrotBC2 { ; by several Fractint users
e=p1, a=imag(p2)+100, p=real(p2)+PI
q=2*PI*floor(p/(2*PI)), r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z)>r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z|<a }
END PARAMETER FILE=========================================
FOTD -- March 05, 2013 (Rating 7)
Fractal visionaries and enthusiasts:
Today's image is named "Fuzzy-Wuzzies". The name refers to the
overall fuzziness of the image, which is due to the limited math
precision. If I had backed out a little, I could probably have
found a very similar scene with perfect resolution, but laziness
prevailed.
The rating of a 7 might have been higher if the math routine
could have dredged up a little more resolution. But even as it
is, the image is striking enough to be declared FOTD.
The parent fractal is actually a hugely oversized field of
scattered fractals, with today's scene lying in the main stem
area of the centermost fractal.
The calculation time of 1-1/3 minutes will pass in a flash,
especially on newer machines. (And who other than myself still
uses those older dinosaurs?)
The finished image is at:
<http://www.crosscanpuzzles.com/Archives.html>
The hi-def versions are at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
Back images are at:
<http://www.Nahee.com/FOTD/>
A cloudy morning gave way to a sunny afternoon here at Fractal
Central today, while the temperature of 41F +5C brought a
feeling of spring to the area. The fractal cat had just about
lost all hope when the sun burst forth, giving him an enjoyable
afternoon on his shelf. The fractal humans made it through the
day without incident.
The next FOTD will be posted when it is ready. Until whenever,
take care, and why worry about oversized sugary sodas. Let's
pass legislation to solve our real problems. Let's make it
illegal for asteroids to threaten the earth, and for hurricanes
to strike the U.S., and for tornadoes to strike in Oklahoma, and
of course for the climate to grow warmer, and for volcanos to
erupt. And it certainly should be illegal to carry illegal
guns. (BTW, I actually heard on a certain un-named news channel
that we can't crack down on illegal guns in the cities because
we would end up putting too many city criminals in jail.)
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
The_Fuzzy-Wuzzies { ; time=0:01:20.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=t
center-mag=+3.429528921055554/+0.2562473412832453/\
2.329006e+012/1/-28.75/0 params=1/-1.5/0.01/-150/0\
/0/0/0 float=y maxiter=1200 inside=0 logmap=135
periodicity=6 mathtolerance=0.05/1
colors=00000G00H00H00I00I12K22K34N44N58Y68Y7EkFEfM\
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m4zp7zk9zgszzhzeZzLPz1Oz7 }
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=========================================
