FOTD -- June 14, 2011 (Rating 8)
Fractal visionaries and enthusiasts:
Today's image takes us ever deeper into the world of near-
linearity. The exponent of Z in today's image is 1.009. Both
common sense and instinct tell us that a fractal with an
exponent so close to unity can only be a lopsided circle or a
featureless ellipse at best. But as is the case with so many
things that are known to be true in the world of science, common
sense and instinct are wrong.
The parent fractal of today's scene is an ellipse, that's for
sure, but when calculated at the particular height of 4.45
levels up the logarithmic ladder, the ellipse becomes irregular
along its edges. Today's image shows a close-up of some of this
irregularity.
I named the image "Tsunami-Plus". The reason for the 'tsunami'
part of the name is obvious. The 'plus' refers to the shaft of
total chaos shooting down and disappearing behind the wave.
The rating of an 8 expresses my opinion of the mathematical
worth of the image. If I had put more effort into the coloring,
I might have given the image more artistic value and worked the
rating up to an 8-1/2.
The calculation time of 4-1/2 minutes will pass in a flash once
the peak of the mighty wave appears, decorated almost like the
wave in the famous Japanese drawing.
The image is posted, fully calculated, on the official FOTD web
site at:
<http://www.crosscanpuzzles.com/Archives.html>
and in high definition with possible variations at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original FOTD web site may be accessed at:
<http://www.Nahee.com/FOTD/>
Sun, clouds and a temperature of 75F 24C made Monday a
refreshingly pleasant day here at Fractal Central. At least the
fractal cats thought so. They reverted to their winter curl-up
modes. The humans spent the day doing routine things such as
gardening and serious work. The next FOTD, likely another in
the how-low-can-you-go series, will be posted in 24 hours.
Until then, take care, and all good things must come to an end,
but so must all bad things. In fact, everything with a
beginning in time must come to an end in time.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Tsunami-Plus { ; time=0:04:31.27-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=recip passes=t
center-mag=0.787447/-1.99784/1.8675/1/-77.5/0
params=1.009/0/4.45/2400 float=y maxiter=5000
inside=255 logmap=205 periodicity=6
colors=000U7AV8BW9CW9DXAEXBFYCGZDHZEI_FJ_FK`GLaHMa\
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Hp9Io9Cr4Jo9QlDWjIbgMheRobVu`ZucSufLuiEul7IjaJk_Jk\
YL_QNPJPDCR25S36T47T58F0F }
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=========================================
Folks,
Fractint version 20.04 patch 11 was released today. The executables can
be found at:
www.fractint.net or www.fractint.org
Here is what's new:
Fixed creation of sound PARs so that the sound= parameter appears after
any other sound related parameters. Fixed sound related PARs in
fract200.par.
Fixed turning off sound when an image with sound is completed.
Marcus Pallinger provided changes to allow compiling Xfractint on an
Intel Mac.
Fixed Xfractint version DivideBrot5 fractal type broken with patch 10.
Fixed Xfractint ncurses interface broken with patch 10.
Added a pause to the sound options via the use of the scalemap feature.
Allowed scalemap value of 0 in PAR entries.
Jonathan
FOTD -- June 13, 2011 (No Rating)
Fractal visionaries and enthusiasts:
My fractal energies were at an absolute minimum on Sunday.
Nothing I tried worked out. I finally settled on the Julia set
of the Seahorse Valley area of the Quaternion Mandelbrot set,
where the two arms have just begun to merge.
I put almost no effort into the coloring. (They say a fractal
artist is judged by the effort he puts into the coloring. If
this is so, today's image must be considered a total flop.)
But the angular aspects of the scene are just notable enough to
make the image worth the minute required to calculate it.
I gave the image no rating because I did not want to embarrass
myself with a rating of something like a 3. The name "Quarter
Something" means nothing. It might have meant a little more if
I had named it "Quat Something."
The finished image is available at:
<http://www.crosscanpuzzles.com/Archives.html>
The high-definition version is posted at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The classic FOTD web site may be accessed at:
<http://www.Nahee.com/FOTD/>
A mix of sun and clouds, with a few light showers and a
temperature of 81F 27C, made Sunday an acceptable day here at
Fractal Central. The fractal cats spent the day lounging, while
the humans found more productive things to keep them occupied.
The next FOTD will be posted in 24 hours. Until then, take
care, and the world seems real, but how do we know that it is
really real?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Quarter-Something { ; time=0:00:59.27-SF5 on P4-2000
reset=2004 type=quatjul passes=1 periodicity=0
center-mag=0/0/8/1/-90/0 params=-1.74925/0/0.01/0/\
0/0 float=y maxiter=2400 inside=0 logmap=8
colors=000BCC7EC4GC8IACK9GM8KQ7OU6SX5W`4_d3cg2gk1j\
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oQLpNLpKLqHLqFLpJLoMLnPLmTLlWLkZLjbLieLihLgWNeJPc7\
RaAQ_CPYFOWHNUJMSMLROLPQK }
END PARAMETER FILE=========================================
FOTD -- June 12, 2011 (Rating 6)
Fractal visionaries and enthusiasts:
Today's image is in two parts, the lower left half and the upper
right half. The viewer may choose which half he prefers. The
lower left half is intact, while the upper right half is
partially evaporated, with the evaporation front running
diagonally through the central minibrot. The strange bailout
value assigned the imag(p3) parameter controls the position of
the evaporation front.
The coloring is quite different in the opposing halves. I have
worked on the coloring to emphasize the difference, but the
result still rates no higher than a 6. The coloring effect in
the upper right half was achieved by rendering the image with
the inside set to 'zmag'. The other inside fills have varying
effects.
Actually, the image holds an error. I had intended to enter 8.8
as the value of the imag(p2) parameter, but somehow the decimal
point never showed up, and I didn't notice the value of 88 until
the image was completed. It was another of those serendipitous
accidents that happen so often in fractals.
The name "Take Your Choice" implies that the viewer can have it
both ways. Those who prefer the lower left half of the image
may reduce the bailout a bit and get an entire image like the
lower left half. Those who prefer the upper right half may
simply increase the bailout. (Setting the inside fill to
'bof61' has the same effect as lowering the bailout.)
The calculation time of 4-3/4 minutes is slightly tiresome, but
calculation may be eliminated by viewing the completed image on
the FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
A hi-def version of the image is available at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original FOTD web site, which was started in 1997, may be
accessed at:
<http://www.Nahee.com/FOTD/>
A mix of sun and clouds, with a few sprinkles of rain and a
temperature of 86F 30C, made Saturday a routine weather day here
at Fractal Central. The fractal cats forgot the day even before
it began.
I took things as easy as possible, aided by FL, who came to the
rescue when I showed signs of doing some useful work. In reply,
I gave her some morale support when she went to work in her
garden. The next FOTD will be posted in 24 hours. My next
fractal 'hot' spell is due soon, so check then to see it it has
arrived yet. Until next time, take care, and if a physicist
should prove that the world is not real. Would he really have
proved it . . .
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Take_Your_Choice { ; time=0:04:45.38-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=1
center-mag=+1.433407804720116/+0.02731266503619226\
/1.578536e+008/1/-132.5/0 params=3/-1.8/0.6/-88/0\
/1.233827121e+027/0/0 float=y maxiter=1600
inside=zmag logmap=170 periodicity=6
colors=000rU2cY2a`1_c0Zf0Yc2Xa4W_6VX7UV9TTBSRDSOER\
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U`homO_`c7hqJ2EKEZK1wK7uKDtKJsOUdMSiLQnlpsbfrTYrWP\
9QPWY7URGfcVdMnCLeR000B00 }
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 -- June 10, 2011 (Rating 7.5)
Fractal visionaries and enthusiasts:
In today's image we return to the DivideBrot4 formula, one of
the formulas I wrote while developing the FinDivBrot-2 formula,
the one I now use most often for images with mixed characteris-
tics. The FinDivBrot-2 is satisfactory enough, but the
DivideBrot4 does a few things better than the FinDivBrot-2.
Today's image shows one of these 'better' things. The scene is
located rather deep in the East Valley of the oversized parent
fractal, which on the surface resembles an everyday Mandelbrot
set. Down at the depth of today's image however, things get out
of control. The quadratic minibrots have transformed into
order-7 minibrots, but these minibrots have lost all pretense of
7-part symmetry, and are surrounded by patterns that appear to
be a combination of Z^2 and Z^7 features.
The image shows an order-7 minibrot with every lobe doing
something entirely different. Some lobes connect out to the
surface, while other lobes quickly come to a dead end.
Countless smaller minibrots fill the image, easily located by
their brilliant orangish coloring. Though these smaller
minibrots share a similarity, no two of them are exactly the
same.
The result of all this chaos is a rating of a 7-1/2, 1/2 point
of which is due to the extra effort on the coloring. (If I had
totally eliminated the color bands, the image could have rated
an 8.) The calculation time of 3-1/4 minutes is not quite a
bargain, but a fair price to pay.
The name "Two Times Seven" refers to the mixture of quadratic
and order-7 elements in the image.
The fully calculated finished image is posted at:
<http://www.crosscanpuzzles.com/Archives.html>
The image is posted in high-definition at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The 14-year-old original classic FOTD web site with all the
early images may be accessed at:
<http://www.Nahee.com/FOTD/>
Another hot, hazy, muggy day prevailed here at Fractal Central
on Thursday, with a temperature of 95F 35C. Heavy storms
threatened all afternoon, but at 6pm they had not moved in. The
fractal cats took things slowly, even asking for their treats in
subdued slow motion.
The humans also had a slow day. FL was concerned with a rain
gutter that overflows on her garden, but the repair is not yet
in sight. The next FOTD will be posted in 24 hours. Until
then, take care, and when we finally do work out a theory of
(almost) everything, will we be able to understand it?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Two_Times_Seven { ; time=0:03:16.15-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideBrot4 center-mag=+1.864192528962\
/-0.0236455806899/1.28447e+009 params=7/7/2400/0
float=y maxiter=6400 inside=0 logmap=696
colors=00059L5AM5BN5CO5DP5EQ5FR5GT5HU5HW5GX5GZ5G_5\
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uzlwzhyzeszcnzahz_czYZzWTzUOzSJzRIzQHzPHzOGzNGzMFz\
LFzKEzJEzIDzHDzGFzFGzEHzD }
frm:DivideBrot4 { ; Jim Muth
z=0, c=pixel, a=real(p1)-2,
b=imag(p1), d=real(p2)+100:
z=sqr(z)/(z^(-a)+b)+c
|z| < d }
END PARAMETER FILE=========================================
FOTD -- June 11, 2011 (No Rating)
Fractal visionaries and enthusiasts:
Today's image is a scene in the Z^101+C Julibrot. It is a
simple diversion from the heavier things that the FOTD somteimes
gets involved in. It's the type of thing I might have done 10
years ago, so I could give it no rating. But it's still a very
fast 44-second image, well worth a glance.
The image is not part of a Julia set, nor of a Mandelbrot set.
It is sliced in a direction rotated 4-1/2 degrees from the Julia
toward the Oblate orientation. This makes the image almost a
Julia set, though one would never guess it from the appearance
alone.
The name "Way to the Unknown" sounds full of deep meaning.
Actually, it has little if any connection to the image, and even
less meaning. The most obvious features in the image are the 3
similar openings, though they failed to be mentioned in the name.
The finished image is posted at:
<http://www.crosscanpuzzles.com/Archives.html>
Check the high-definition version 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/>
Friday brought a refreshing break to Fractal Central as a bit of
cooler air slipped in from the north, dropping the temperature
to 86F 30C and clearing away the haze and humidity. The fractal
cats must have missed the change. They spent most of the day
stretched in the coolest places they could find.
The humans had a rather dull day, which appears to be typical of
how things go in the summer here at FC. The next FOTD will see
its moment of glory in 24 hours. Until then, take care, and if
the answer is not what you had hoped for and expected, believe
it anyway.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Way_to_the_Unknown { ; time=0:00:44.21-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot4 passes=1
center-mag=-0.995001/0.963568/19.79345/0.7593/180
params=85.4/0/90/0/-0.9737/0/1.0066/0/101/0 float=y
maxiter=1500 inside=255 periodicity=0
colors=000D07D08E0AF0CFAIEFOIJVMNWRQRVT7ZW7cVzmUzz\
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KOXKOXKOXKOWKOWKOWKOVKNVKNVKNVKNUKNUKNUJNTJNTJNTJM\
SJMSJMSJMSJMRJMRJMRJMQJMQJMQILPILPILPILOILOILOILOI\
LNILNIKNIKMIKMHK7Gm6EfUsz }
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 -- June 09, 2011 (Rating 7)
Fractal visionaries and enthusiasts:
I named today's image "A Great Sea-Change". It's kind of a
redundant name, since a 'sea-change' implies a total transforma-
tion, and a change cannot be any greater than total.
What has changed in today's image is the surroundings of the
tiny order-6 minibrot at the center, as well as the surroundings
of the other minibrots scattered about the scene. Normally, the
high-order minibrots are notably uninteresting, but when created
by the FinDivBrot-2 formula, they leap to life, their surround-
ings bursting forth with the most surprising kinds of widespread
features.
Enough said about today's image. The rating of an everyday 7
means that the calculation time of a measly 40 seconds will not
have been spent in vain if the image proves to be a let-down.
It also means that if I had worked harder, I might have improved
the coloring.
Avoid the calculation altogether by checking the FOTD web site
at:
<http://www.crosscanpuzzles.com/Archives.html>
The high-definition version is at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
And check the original FOTD web site at:
<http://www.Nahee.com/FOTD/>
Heat, haze and humidity prevailed here at Fractal Central on
Wednesday. The fractal cats escaped the heat by lying on the
cool tile of the bathroom floor; the humans chose the artificial
coolness of the air conditionier. With all this taken into
account, the next FOTD will be posted in 24 hours. Until then,
take care, and if someone tells you they know all the answers,
ask them why there are still questions.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
A_Great_Sea-Change { ; time=0:00:40.26-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=FinDivBrot-2 function=recip passes=1
center-mag=-1.251911971871246/+0.342786793999404/\
5.2845e+011/1/-20/0 params=6/6000000/0/0 float=y
maxiter=1500 inside=0 logmap=69 periodicity=6
colors=000kmzjkyiixhgwgevfcueatd_sdYrbWqaUp`So_QnZ\
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cR`fRbiRdkQgnQiqQktQmvQommYlgUlbRlYOlTLlOHlJElEBl9\
8l45g8FcCO_GYVKfRalQclQdl }
frm:FinDivBrot-2 { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
esc=(real(p2)+16), b=imag(p1):
z=(b)*(z*z*fn1(z^(a)+b))+c
|z| < esc }
END PARAMETER FILE=========================================
FOTD -- June 08, 2011 (Rating 7)
Fractal visionaries and enthusiasts:
Today's image, with its brain-like shape and complex networks,
reminded me of a human brain. But it is not made of meat, it is
made of numbers, so I named it "The Inhuman Brain".
The image is part of a near-Julia view of the eastern extremity
of the main bay of the (-Z)^(2.5)+C Mandeloid. It is not a
Julia set, since it is rotated 45 minutes of arc away from the
Julia orientation toward the Oblate orientation. Julia sets are
2-dimensional slices cut in a particular orientation through the
4-dimensional Julibrot figure. Today's image just misses the
proper Julia direction.
I rated the image at a 7, which is FOTD average. We have seen
similar images several times in the past, so I could rate it no
higher. The calculation time of 2-1/4 minutes is close to FOTD
average also.
As always, the completely calculated image is posted at:
<http://www.crosscanpuzzles.com/Archives.html>
along with the day's philosophizing.
The hi-def version of the image is posted at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
Paul's FOTD web site may be accessed at:
<http://www.Nahee.com/FOTD/>
Things were reasonably pleasant here at Fractal Central on
Tuesday. The hazy sky and temperature of 86F 30C made things
seem quite summer-like. But summer is expected to come in much
stronger on Wednesday, so we'll see what happens then. The
fractal cats had no complaints about the weather, though they
did appear annoyed with each other at times. The humans had a
typical day.
The next FOTD will be posted in 24 hours. Until then, take
care, and watch out for that conscious universe. It knows what
you're doing even when you're asleep.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
The_Inhuman_Brain { ; time=0:02:17.14-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot5 passes=1
center-mag=0.621705/0/8.385427/1/90/0
params=89.25/0/90/0/0.3831/0/0/0/2.5/0 float=y
maxiter=64000 inside=255 logmap=6 periodicity=6
colors=000cSobUmaWj_YgZ_dXaaWcZUeWTgTRiQQkNOkGPlKQ\
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UUzUQzTNzSKzRHzQEzPBzP8zRCzSFzUIzVMzXPzYSzfZzodzwj\
zmXzdKzW7zZDz`IzbNzgOzeQz }
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 -- June 07, 2011 (Rating 8)
Fractal visionaries and enthusiasts:
Today's image is another one found in haste, but thanks to the
extra coloring effort, emphasizing grays and blues, it rates a
respectful 8.
The scene lies in the west "Elephant Valley" of the Z^(3.003)+C
Mandeloid, which, due to the fractional exponent, has broadened
into a kind of wedge. It is located in the chaos along the
southern edge of this wedge.
We have been to this area several times before, but I think
today's visit, with its carry-over 'fishbone' theme from
yesterday and somber blue coloring, is the most productive yet.
The tiny minibrot at the center is rather poorly defined, a
flaw that could be eliminated by raising the maxiter. But doing
this messes up the colors, so I let the image go as it is.
After all, everyone knows what a cubic minibrot looks like.
The calculation time of 3 minutes is a fair price to pay for the
finished product.
The finished image may be seen on the FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
without the need to calculate it.
The image may be seen in high definition at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original FOTD web site may be accessed at:
<http://www.Nahee.com/FOTD/>
The string of perfect days continued here at Fractal Central on
Monday, with blue skies, low humidity, puffy white decorator
clouds and a temperature of 81F 27C. The fractal cats enjoyed
the outdoor conditions from indoors, where they stretched on the
carpet in solid comfort.
The humans' day was not quite as comfortable, but still a notch
above average. The next FOTD will be posted in 24 hours. Until
then, take care, and if a worrier lacks something to worry
about, something will be provided.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Deep_Blue_Fantasy { ; time=0:03:26.85-SF5 on P4-2000
reset=2004 type=formula formulafile=slices.frm
formulaname=MandelbrotN passes=1 center-mag=-0.386\
8917576744657/-0.00190443108910178/1.911204e+010
params=3.003/0/0/0/0/0 float=y maxiter=3600
inside=255 logmap=471 periodicity=6
colors=000CHRDIREJTFKXGLXHMZIN_JOaKPbIQdHReFSgEShC\
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XN0XO0XO0XO0WO0VO0UO0Uzzz }
frm:MandelbrotN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=z^(b)+c,
|z| <= 16 }
END PARAMETER FILE=========================================
