FOTD -- December 28, 2010 (Rating 8)
Fractal visionaries and enthusiasts:
I named today's image "Multiple-Moon Light", implying light from
multiple moons. The rating of an 8 might be a little liberal,
but what the heck, it's a rather pleasing and peaceful image to
meditate upon, so why not give it a rating of 8?
The formula behind the peacefulness combines 8 negative parts of
Z^(-1.5) with one negative part of Z^(-5.5), then adds (1/C).
The resulting parent fractal is a north-south string of large
irregular bays, with a cut-off ring just south of the main mass
of bays. Today's scene is located in the interior of this cut-
off ring.
Actually, the image is 'evaporated'. The escape radius of one-
googol makes sure that all outside parts have evaporated. The
scene consists entirely of 'bof61' inside fill.
The calculation time of 33 seconds will pass in a flash for
those who run this letter as a parameter file. Others will need
to surf electronically down to the currently active FOTD web
site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
where the finished image will soon be posted.
The original web site at:
<http://www.Nahee.com/FOTD/>
is presently inactive, but will be brought up to date when Paul
gets back on his feet.
The generous sunshine here at Fractal Central on Monday was
nullified by a temperature of 25F +1C and a strong blustery wind
from the north. The Sunday evening snow amounted to a whopping
trace. The fractal cats, who are indoor cats and never concern
themselves with outside conditions, were quite happy all after-
noon on their sunny shelf in the window.
The humans' day featured getting back into the everyday routine,
which took very little effort. The next FOTD will be posted in
24 hours. Until then, take care, and activate your chi energy.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Multiple-MoonLight { ; time=0:00:33.34-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip float=y
center-mag=+0.0784946918398598/-2.088888523004933\
/5.5e+009/1/-7.5/0 params=-1/-5.5/-8/-1.5/0/1e+100\
/0/0 maxiter=1500 inside=bof61 sound=off
colors=000boIaoJaoJ`oK`oK_pLZpLZpM000YpNXpNXpOWpOW\
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O03L05J06H07E08C09A0A70B50C30D60H80KA0NC0QE0TG0WI0\
Zf0Ef0Fe0Fe0Gd0Gc0Hc0Hb0I }
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 -- December 27, 2010 (Rating 6)
Fractal visionaries and enthusiasts:
Today's super-fast image rates only a 6. This is because it is
the third consecutive image of a minibrot lying in the field of
chaos near the shore line of a Mandelbrot bay or bud. Today's
scene is located on the western shore line of the period-5 bud
on the northwest shore line of the main bay of the Mandelbrot
set.
The name "Repeat Performance" indicates that today's image is
similar to the two most recent FOTD images. It might actually
be the best of the three, but 'might be's' carry little weight
when rating images.
The calculation time of 8 seconds will pass in a flash. Those
with non-cooperative machines may see the finished image on the
presently active FOTD web site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original FOTD site may be accessed at:
<http://www.Nahee.com/FOTD/>
Sunday brought lots of clouds, brisk north winds and a tempera-
ture of 27F -3C to Fractal Central. Snow showers moved in just
after nightfall, but at post time had amounted to only a dusting.
The fractal cats passed the unusually chilly day on their shelf
by the heat, exhausted after yesterday's battle with the gift
wrappings. The humans' day was spent recovering from yesterday.
The next FOTD will be posted in 24 hours. Until then, take
care, live to learn and learn to live.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Repeat_Performance { ; time=0:00:08.51-SF5 on P4-2000
reset=2004 type=mandel passes=2 center-mag=-0.5407\
452833814538/+0.577023247902471/3.5297e+011/1/87.5\
/0 params=0/0 float=y maxiter=15000 inside=0
logmap=-1242 periodicity=6
colors=000PTjQTkRUkSUlSVmTWnUXoVYoWZpX_qY`rZar_bs`\
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AzL9zL9zL9zL8zL8zL7zL7zL6 }
END PARAMETER FILE=========================================
FOTD -- December 26, 2010 (Rating 7)
Fractal visionaries and enthusiasts:
Today's image is not only late, it is very simple -- another
scene on the northwest shore line of the main bay, but this
time the main bay of the large minibrot on the main stem of the
Mandelbrot set. The scene lies on a filament, just beyond the
point where it separates from the main body of chaos.
I named the image "Surprise Mandelbrot" because of the elements
surrounding the central minibrot, which surprisingly point in
toward the center rather than outward.
The rating of a 7 is perhaps a bit above what might be expected
for a fractal found on a day with so many other things to do.
The calculation time of 10 minutes is due to the necessity of
using arbitrary precision math, and is slower than I would have
preferred.
But calculation may be avoided by checking the web site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
where the finished image will soon be posted.
and don't forget the original web site at:
<http://www.Nahee.com/FOTD/>
Clouds all day and a temperature of freezing kept things subdued
here at Fractal Central on Christmas day. The fractal cats were
too busy romping in the wrapping paper to notice the outside
conditions. The next FOTD will be posted in 10 hours or more.
Until then, take care, and relax.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
SurpriseMandelbrot { ; time=0:10:17.80-SF5 on P4-2000
reset=2004 type=mandel center-mag=-1.7652273461461\
26424/0.00851359743301010303/9.468406e+014/1/147.5\
/0 params=0/0 float=y maxiter=5600 bailout=36
inside=0 logmap=-565 periodicity=6
colors=000QAGRAGSAGTAGUAGVAGWAFXAEYADZAC`ABaAAcA9d\
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IVzGVzDVzAVz7Vz5NzCGzI8zO }
END PARAMETER FILE=========================================
FOTD -- December 25, 2010 (Rating 7)
Fractal visionaries and enthusiasts:
Today's image is an unpretentious scene deep on the northwest
shore line of the main bay of the Mandelbrot set. I have named
it "Merry Season" because it covers a multitude of festivals
connected with bringing light to the darkest time of the year,
the winter solstice.
The most celebrated solstice festival in our culture is
Christmas, which unfortunately has become more of a marketing
opportunity than a celebration of divine salvation.
The colors traditionally associated with Christmas are red and
green, probably associated with red holly berries. I have given
the image a red and green theme in keeping with the seasonal
colors.
Red and green also remind me of the holly grove back at Old
Fractal Central, where the now deceased original fractal cats
romped and lurked for almost twenty years. New Fractal Central
has but one scrawny holly tree, but that tree is presently
covered with a full crop of red berries, which add their share
to the feeling of the season. The new fractal cats get their
share of action indoors however.
The image rates a 7, fair enough for a mere Mandelbrot scene.
The calculation time of under 2 seconds is as fast as Santa
coming down the chimney. The finished image is or soon will be
posted on the current FOTD web site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
And don't forget the original FOTD web site at:
<http://www.Nahee.com/FOTD/>
which Paul has kept going for over 13 years.
While tending to last-minute Christmas details on Friday, I
heard a version of 'Oh Come Emanuel' on the radio, with drums
and traps beating out a syncopated rhythm in the background.
I wondered why the beat had been added to such a simple song.
The traditional melody is an old plainchant, which has no
rhythm. The only reason for the intrusive beat that I could
think of was that over the years the purpose of music has
changed from lifting the spirit through melody, to getting the
body moving with a catchy beat. (But then again, times keep
changing, and I just might be old-fashioned. FL heard nothing
intrusive in the arrangement.)
The mix of sun and clouds with a temperature just above freezing
that we had here at Fractal Central on Friday made the day just
about average. The fractal cats enjoyed the sun, and when the
sun failed, they went to the heat.
The day of the humans was filled with last minute preparations
for whatever may come. The next FOTD is due in 24 hours, but if
it does not appear until Sunday, do not be surprised. Until
whenever, take care, and I don't want to leave the impression
that I'm cynical at this time of year. I want to state it
outright.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Merry_Season { ; time=0:00:01.92-SF5 on P4-2000
reset=2004 type=mandel center-mag=-0.4228394615443\
275/+0.5720091755518583/4.164996e+011/1/11.5/0
params=0/0 float=y maxiter=15000 inside=0
logmap=266 periodicity=6 mathtolerance=0.05/1
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END PARAMETER FILE=========================================
FOTD -- December 24, 2010 (Rating 7.5)
Fractal visionaries and enthusiasts:
Things are rather busy here at Fractal Central as I write this
on the evening of the 23rd. The discussion will be short.
On the surface, today's image, with its preponderance of dark
blues, is a bleak one indeed. But in its depths it holds a
minibrot with a warm and shining heart. After a minute of deep
thought, I named the image "Light in Darkness".
The parent fractal came about when I mixed three negative parts
of Z^(-1.3) with one negative part of Z^(-3.3). This parent is
obviously a Mandeloid of some sort, though I was unable to make
any sense of it. If it actually has a Seahorse Valley and an
East Valley, they are quite hard to locate.
The rating of a 7-1/2 includes 1/2 point reward to myself for
the coloring, which is the major part of the effect of the
image. The calculation time of 4-2/3 minutes is within reason.
The easiest way to view the image is to truck down to the
current FOTD web site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
where the finished image is or soon will be posted.
All the past FOTD images are available on the original FOTD web
site at:
<http://www.Nahee.com/FOTD/>
though the site is not up to date.
Morning clouds and afternoon sun kept the fractal cats happy on
their window shelf here at Fractal Central on Thursday. The
temperature of 37F +3C was warmer than we have seen recently,
but still chilly. The humans were kept busy with holiday tasks.
The next FOTD will be posted in 24 hours. Until then, take
care, and be at peace with the powers that be as you try to
figure out what this time of year is really all about.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Light_in_Darkness { ; time=0:04:41.17-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip
center-mag=+2.340247772835/-0.41997288768/6.5e+007\
/1/-37.5/0 params=-3/-1.3/-1/-3.3/0/0/0/0 float=y
maxiter=5400 inside=0 logmap=-760 periodicity=6
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zzzzzzzzzzzzzzzzzzzzzzzzzzzIzzKzzMzzOzzQzzSzzUzzWz\
zYzz_zzazzczzezzfzzgzzhzz }
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 -- December 23, 2010 (Rating 7)
Fractal visionaries and enthusiasts:
Today (Dec 22) is the first full day of winter in this part of
the northern hemisphere, so what could be more appropriate than
a screen filled with pink apple blossoms, bringing a hint of
the warmth that is yet three months away.
I named the preview image "Spring Comes Early". It was created
with the iterated expression Z^(-11)+11(1/Z)+C. The parent
fractal created by this expression must be seen to be believed.
In my opinion, the image is worth an above-average 7, a rating
made all the more worthwhile by the fireball calculation time of
27 seconds.
Those who run parameter files with difficulty can soon find the
finished image on the new FOTD web site maintained by Hal Lane
at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original web site at:
<http://www.Nahee.com/FOTD/>
maintained by Paul Lee is still there, but Paul has not been
able to update it for a while.
Sun, clouds and a temperature of 34F +1C made Wednesday a rather
pleasant day here at Fractal Central. The fractal cats soaked
up the sun when it was shining on their window shelf and kept
warm on their shelf over the heat when it was not. My day was
typically busy for a day three days before Christmas.
The next FOTD will be posted in 24 hours. Until then, take
care, and if spring and summer are coming soon up here, autumn
and winter are coming soon down there.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Spring_Comes_Early { ; time=0:00:27.57-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=ident passes=1
center-mag=-1.5378244047/+1.1918257186/199729/1/15\
/0 params=1/-11/11/-1/0/0/0/0 float=y maxiter=767
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BHCBHCBHCBHCBHBBHBBGBBGBBGBBGBBFBBEBADAACAABAAAAA9\
AA8AA7AA6AA5AA4AA3AA2AA1A }
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=========================================
I just spoke with a friend of Paul Lee's who says that
Paul is still "under the weather."
We all wish you a speedy recovery, Paul!
- Hal Lane
#########################
# hallane(a)earthlink.net #
#########################
FOTD -- December 22, 2010 (Rating 5)
Fractal visionaries and enthusiasts:
Today's image is a very lucky one. My finger was one inch from
the delete button that would have sent it to neverland when I
decided to make it FOTD for the day. Nothing is really wrong
with the image, but nothing is really right either. It's an
*everyday event*, the kind of image I turn up all the time in my
never ending search for a better fractal. This is what I named
it.
The formula behind the image is Z^(1.95)+C, iterated at ground
level. The parent fractal is quite a bit more distorted than
what might be expected from a formula so close to Z^2+C, but all
the parts are there, even though they are not so easily
recognized.
There is nothing wrong with the rating of a 5. It's equal to a
grade of 'C', which means average performance. If its calcula-
tion time had been a bit faster than 6 minutes, the image might
have rated a point higher.
Those who do not calculate may view the finished image on the
new FOTD web site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original web site is still there, though it is not up to
date. The original site may be accessed at:
<http://www.Nahee.com/FOTD/>
Wall-to-wall sunshine and a temperature of 36F +2C made the
shortest day of the year somewhat pleasant here at Fractal
Central on Tuesday. The fractal cats must have agreed, for they
spent most of the day on the shelf by the sunny southwest
window. Most everything else went according to plan. The next
FOTD will be posted in 24 hours. Until then, take care, and
they say it's all a dream.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Everyday_Event { ; time=0:06:16.89-SF5 on P4-2000
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formulaname=MandelbrotBC3 function=ident passes=1
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frm:MandelbrotBC3 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)+PI-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 -- December 21, 2010 (Rating 6)
Fractal visionaries and enthusiasts:
Today's image shows a minibrot of order 1.1. For some reason I
continue to search for interesting minibrots down in this range,
even though I rarely find anything worthwhile. (Today's image
shows a rare exception.)
The parent fractal of today's image came about when I calculated
the formula Z^(1.1)+C at a level 11 turns up the logarithmic
hyper-spiral with no function applied. This parent is shaped
like a cut-off parabola with a few areas of chaos along its
edges. Not surprisingly, today's image is found in one of these
chaotic areas.
I named the image "Test Pattern" because of the flat, highly
colored, sharp-edged shapes filling it, which might be only a
test of what might lie deeper in the parent. The rating of a
humble 6 indicates that I do not consider it one of the better
FOTD images.
With a calculation time of a mere one-minute however, the image
is worth the effort despite its modest achievements.
Calculation may be totally avoided by viewing the finished image
on the currently active FOTD web site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The classic FOTD web site at:
<http://www.Nahee.com/FOTD/>
might not be up to date, but it is worth a quick check.
A mix of sun and clouds, with a high temperature of 34F +2C,
made Monday pretty close to normal here at Fractal Central. The
fractal cats spent their time alternating between the shelf over
the heat and the shelf by the window, which is also pretty close
to normal. The rest of the activity at FC was totally routine.
The next FOTD will be posted in 24 hours. Until then, take
care, and maybe we're all serfs, laboring on the lands of our
overlords, the big corporations.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Test_Pattern { ; time=0:01:04.05-SF5 on P4-2000
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formulaname=MandelbrotBC3 function=ident passes=1
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frm:MandelbrotBC3 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)+PI-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=========================================
In article <4D0FB01F.3050909(a)fractalus.com>,
Damien Jones <dmj(a)fractalus.com> writes:
> > The Nyquist-Shannon sampling theorem says that a sampling frequency
> > f cannot possibly represent signals with frequencies greater than 2f.
>
> I think you meant 1/2 f and not 2f.
Yes, you're correct, I had my factor of two in the wrong direction.
--
"The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download
<http://legalizeadulthood.wordpress.com/the-direct3d-graphics-pipeline/>
Legalize Adulthood! <http://legalizeadulthood.wordpress.com>
