FOTD -- January 10, 2014 (Rating A-7,M-7)
Fractal visionaries and enthusiasts:
Today's image lies in the northern branch of the Seahorse Valley
of an oversized Mandelbrot set corrupted in its depths by Z^9
energies. It lies at a depth where ninth-order elements predomi-
nate close to the minibrots, while quadratic elements prevail
farther out, and the in-between areas are a confused but interes-
ting mix of Z^2 and Z^9 elements, but with no discontinuities.
The image abounds with smaller order-9 minibrots, the most
obvious of which lie at the upper left and lower right edges of
the scene. I checked these minibrots and found them much the
same as the large one in today's image, though somewhat more
chaotic.
The name of the image is paradoxical. I named it "Image With No
Name" because I could think of nothing better. But this still
identifies the image, so I guess it's up to the wise philoso-
phers and logicians to decide if the image actually has a name.
The art and math both rate a 7, which is good enough but leaves
plenty room for improvement. The calculation time of 4 minutes
is slow however, and could give impatience a chance to arise.
The web sites can eliminate this threat.
The completely calculated image is available online at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
Two inches (5cm) of snow fell overnight here at Fractal Central,
but ended before daybreak. The rest of the day was cloudy with
a temperature of 36F +2C. The fractal cats noticed the fresh
cat footprints in the new snow, then settled down for a day of
tussling, eating and sleeping. The fractal humans were happy to
have made it through another day and week.
The next FOTD will be posted in either one or two days, depen-
ding on how much of an antiquing expedition happens tomorrow.
Until whenever, take care, and I wonder why the existence of
global warming has become such a big political debate. The
earth certainly is getting warmer. It has been for thousands
of years, and there is nothing we can do to stop it by passing
meaningless laws.
For some strange reason, I suspect that a potential transfer of
money is involved.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Image_With_No_Name { ; time=0:04:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MultiExp function=recip inside=0
center-mag=-74.83193719158429/+7.494763709824741/\
7.2e+009/1/-22/0 params=9/100 float=y maxiter=3000
logmap=524 periodicity=6 mathtolerance=0.05/1
colors=333BjUBjUBkVBmWAoYAqYBrXCrWDrUFtUHtUItTKvSN\
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zzizzfzzczzazzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
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 -- January 08, 2014 (Rating A-8,M-6)
Fractal visionaries and enthusiasts:
Today's image is a scene in the East Valley area of a tiny
half-morphed minibrot just beyond the large minibrot on the main
spike of its parent fractal, which is a hugely oversized
Mandelbrot set corrupted in its depths by Z^15 energies. At the
depth of today's scene, the Z^15 energies have completely taken
over, though the outer elements still retain much quadratic
detail.
I named the image "Magical Fifteen" because I have always seen
something magical in the way the higher-order energies take over
in the depths of apparently perfectly ordinary Mandelbrot sets.
In my opinion, the art rates an 8. I did put about an extra
half hour into the coloring to justify the rating. And the
calculation finishes in only 2-1/3 minutes, making the image
quite a bargain. For those shy about calculating fractals, the
finished image is posted on the web sites.
Check it at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
Lots of clouds were the rule today here at Fractal Central.
The temperature of 19F -7C was still quite cold, but after the
past week, it felt not too bad. The fractal cats spent the
afternoon waiting for the sun to appear. When it never did,
they decided to have a meal. The humans, who are always
occupied with one thing or another, had a busy but un-notable
day.
The next FOTD will be posted right here in only a few hours.
Until then, take care, and why do angels, who are apparently
mammals, have feathered wings? One would think they would fly
with bat-like wings such as the devil has.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Magical_Fifteen { ; time=0:02:20.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MultiExp function=recip passes=1
center-mag=-1796.053377352276/-0.00002501424642828\
/1.77998e+009/1/42.5/0 params=15/1000 float=y
maxiter=1600 inside=0 logmap=282
periodicity=6 mathtolerance=0.05/1
colors=00000A00A00A00A00A30A60AA2AE5AK9AQDAWLAaRAg\
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iGzkGzmGznGzoFzpFzqFzrFzzFzjEizEizEhzEgzEgzEfzDezD\
ezDrzDrzDrzCrzCrzCrzCrzCrzBrzBrzBrzBrzBrzBrzArzArz\
JrzJrzJrzHrzGrzFrzDrrCrrB }
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 -- January 09, 2014 (Rating A-7,M-7)
Fractal visionaries and enthusiasts:
Today's image is a scene I found in a distorted Mandelbrot set
corrupted all the way through by Z^(1.001) energies. The East
Valley area of this parent fractal is shrunken out of sight,
while the main spike area is blown up like a balloon. A large
bay lies between the extremes, with today's scene located near a
kind of knot at the tip of a filament extending from a small bud
on the northern shore line of this large main bay.
I named the image "Feminine Features" because of the shades of
pink. It is a strange name because I usually avoid the lacy,
flowery, pink stuff found in shops that specialize in feminine
things. (FL has no such aversion, but that's her problem, not
mine.)
The art rating of a 7 might have been a point or so higher if I
had given more attention to the colors and brightened them up a
little. The math rating of a 7 shows that I was rather sur-
prised at the things Z^(1.001) corruption can do to a Mandelbrot
set.
The calculation time of 2 minutes is right on the mark for such
an image. It's just enough time to leave the room, pour a
drink, and get back to the computer. Checking the image on the
web sites will save the hike.
Relief from fractal thirst may be found at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
Today brought a big improvement to Fractal Central, with cloud-
less skies, brilliant sunshine, and a temperature of 27F -3C,
which was still well under the freezing point, but with light
winds felt almost like a day in early spring. The fractal cats
welcomed the sun on their window shelf, but couldn't decide who
would get the top-cat spot. The fractal people simply made it
through another day. Hey, life is no soap opera, so don't
expect constant, ever more interesting, storm and stress.
The next FOTD will be posted before too long. Until whenever,
take care, and I hear that God is infinitely forgiving and
merciful -- as long as we are still alive, that is. But when we
die, watch out. They say He turns into the most unforgiving,
vengeful being we could possibly imagine.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Feminine_Features { ; time=0:02:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MultiExp function=recip
center-mag=+2.110941340568/+6.205610652844/1568031
params=1.001/11 float=y maxiter=1400 inside=0
logmap=360 periodicity=6 mathtolerance=0.05/1
colors=000zzz0ZS0YV0YX2XZ6XaAWcEWeCPfAIg8Bh75i50j3\
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mpmmpmzxmzxzzxzzxzzxzzxzzxzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
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=========================================
This fractal has a lot of symmetry yet it also has a lot of different
shapes. It has circles, a square, and an octagon. The formula is a
variation of the parallel resistor formula and has a z ^ 4 term as its
lowest z component. I have noticed previously that the lowest z term seems
to set the types of minibrots you see in the fractal and this one follows
the same pattern. This fractal has the four way symmetry you expect to see
with a z ^ 4 term but it also has a structure with 12 arms which isn't as
common.
The color palette is one I have used numerous times before because it seems
to work with any fractal with no adjustments. Fracton's color palette
editor is very tedious to use so I tend to reuse the same palette. I have
plans for upgrading the color palette editor but those will likely take a
few months to complete (at best). I recently updated Fracton with some
improvments to other areas of Fracton's user interface. If anyone is
interested, Fracton can be downloaded from the www.fracton.org website.
Fracton is FractInt PAR file compatible and free but Mac only.
I have quite a few other fractals I am hoping to post in the coming weeks.
Most of them are in the same color palette as todays fractal. So now you
know why.
Here is a link to an image:
http://dl.dropboxusercontent.com/u/33642054/image/medalion_of_four.jpg
The Fractint compatible PAR file for the image is:
medalion_of_four { ; Exported from Fracton.
reset=2004 type=formula formulafile=fracton.frm
formulaname=F_20140108_1141 passes=1 float=y
center-mag=-3.618931505229473/-7.152557203304979e-\
14/60606061363.63636/1/0/0
params=-1/1/0/4/-1.13/0/1/0/0/0 maxiter=2000
inside=0 logmap=14 periodicity=6
colors=000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O\
40C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40\
C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C1\
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0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0u\
a0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0\
ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0ym\
0zy0ym0ua0oS0hI0ZA0O40C10 }
frm:F_20140108_1141 {
; Similar to the parallel resistance formula
a=real(p1),b=real(p2),d=imag(p1),f=imag(p2),
z=0,c1=pixel-p3,c2=pixel-p4:
z=1/(1/(a*z*(cos(z)-1)*sin(z)+c1)+1/(d*(z^f)+c2)),
|z|<100
}
--
Mike Frazier
www.fracton.org
FOTD -- January 07, 2014 (Rating A-?,M-5)
Fractal visionaries and enthusiasts:
Today's scene lies deep inside one of the strange rectangles
that haunt the area of the Z^(2.003)+C Mandeloid that lies on
the negative X-axis just east of the large minibrot complex.
I could not give the art aspect a rating. I'm not sure the
image, with its apparently random splash of colors, even has an
art aspect. The math rating however is an everyday 5. We have
been this way quite a few times before.
The image is double rotated 0.4,0.4 degrees from the true Julia
orientation, so the parent rectangle is quite distorted. This
distortion inspired the name "Rectangle Vestige"
The calculation time of 2-1/4 minutes will pass quickly enough.
And if the image fails to bring gratification, not much time
will have been wasted. To eliminate all chance of wasted time,
try the web sites.
The easy path to fractal gratification may be found on the FOTD
web sites at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
The day began with a temperature of -8F -22C and rose to a balmy
afternoon high of +5F -15C, accompanied by media warnings of the
danger of frostbite. The sky was mostly sunny, but with the air
so cold, the sun had no effect on the icy roads and sidewalks.
The fractal cats were unusually playful, which for a cat is
worth being mentioned. The humans were successful at keeping
warm.
The next FOTD will be posted in the near future human time,
almost instantly cosmic time. Until then, take care, and I
heard that global warming is the cause of the unusual cold.
Either that or a nuclear winter has begun. In either case, I
guess a hefty tax on carbon emission would solve the problem.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Rectangle_Vestige { ; time=0:02:15.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot4 passes=1
center-mag=-0.00048501099573621/+0.002209588115359\
59/1.6116e+008/1/-73.75/0 params=89.6/0/89.6/0/\
-1.7435/0.0001/0.000175/0.073883/2.003/0 float=y
maxiter=1800 inside=0 logmap=265 periodicity=0
colors=00001c02c23c45c66c97cB9cDAcGBcIDcLEcNFcPHcS\
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103314516728829A3BC3CE4EG4GH5HJ5JL6KN6MO7OQ7PS8RU8\
TW90211431652972B93DB4FD4IF5KG5MI6OK7RM7TO8VQ8XS9_\
U9aVAcXBeZBh`CjbCldDnfEqh }
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 06, 2014 (Rating A-7,M-7)
Fractal visionaries and enthusiasts:
While yesterday's image took us to East Valley of the parent
almost-Mandelbrot set, today's image takes us to the main spike,
where we examine the northeast shore line of the large minibrot,
which at today's orientation lies on the southwest side. The
minibrot itself is beginning to break up, a sure sign that
interesting things are likely to be found there.
I named the image "Trouble in the East", not as a comment on
world affairs, but as a reminder that the scene lies in a
troubled area of the parent fractal. The fact that I skewed the
image to twist the chain of 'yellow teeth' from a rhombus to a
near-perfct square also entered into the name.
The art and math both rate a 7, making the image well worth the
1-1/3 minutes required to calculate it. But time is time, so
remember the web sites.
Save both time and energy by checking the finished images on the
web sites at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
A mix of clouds and sun added interest to the sky here at
Fractal Central today. But the temperature of 50F 10C at
daybreak fell to freezing by afternoon, which with a blustery
wind, made the interesting sky not too enjoyable. And the low
of 0F -18C forecast for tonight will make things only worse.
The fractal cats passed the day wondering what kind of trouble
to get into, while the fractal humans tried to keep out of
trouble.
The next FOTD will be posted within a reasonable time. Until
next time, whenever that might be, take care, and I already see
politicians trying to buy votes with promises of increased
benefits for the voters if they are elected. I wonder what the
difference might be between this kind of bribery and classic
political corruption.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Trouble_in_theEast { ; time=0:01:20.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident passes=1
center-mag=+1.744506240835/+0.014698570775/2673270\
/1/-61.25/6.0885268721 params=2.001/0/4.7/0 float=y
maxiter=2000 inside=0 logmap=120 periodicity=6
colors=000C0LC0MB0OA0QA0R90T91U82W73Y74Z65`66a57c4\
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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 -- January 05, 2014 (Rating A-6,M-6)
Fractal visionaries and enthusiasts:
Today's image is found in the everyday parent fractal that
results when the formula Z^(2.001)+C is iterated 4.7 levels up
the hyperladder with no function applied. This parent is a
near-Mandelbrot set rotated 180 degrees so that East Valley
falls on the negative X-axis, and the main spike, where even
more action is happening, lies on the positive X-axis.
Today we focus our attention on East Valley, which instead of
coming to a sharp point, has been broadened into a wedge
infested with sickle-shaped debris. Today's scene lies in this
debris.
The coloring is rather chaotic, and both the art and math tricks
have been seen before, which holds the ratings of both of them
to a routine 6.
The name "Herringbone Filters" has nothing to do with the field
of TV repair. It came to mind when something in the scene
reminded me of herringbones.
Most of the coloring effect was produced by rendering the scene
with the outside set to 'tdis'. Other options produce different
effects, some of which have potential.
The calculation time of a dragging 11-1/2 minutes will pass
slowly even for the most devout fractal fans. But relief is
always at hand on the web sites.
To view the image without calculating it, check the FOTD web
sites at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
The morning was sunny here at Fractal Central today. But clouds
moved in by noon and by mid-afternoon freezing rain was falling,
with a temperature of 28F -2C. The fractal cats were too busy
chasing each other up and down the hallway and tussling to worry
themselves with the weather. The fractal humans were simply
glad there was no reason to go out.
The next FOTD will be posted in a matter of minutes, which will
also be a matter of seconds, hours, weeks, months or years,
depending on how time is measured. To find the exact numbers,
check back at regular intervals. Until whenever, take care, and
a local eight-year-old boy was recently asked what was the best
thing that happened to him in 2013. He replied it was when he
got his mini I-pad for Christmas.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
HerringboneFilters { ; time=0:11:30.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident passes=t
center-mag=-0.2521599928326848/-0.0019727729038808\
/2.614896e+009/1/-40/0 params=2.001/0/4.7/0 float=y
maxiter=8600 inside=0 outside=tdis periodicity=6
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MddMddMecNecNfcNfcNfcOgbO }
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=========================================
1
0
CheckItOut
by JackOfTradeZï¼ comcast.net
04 Jan '14
FOTD -- January 03, 2014 (Rating A-6,M-4)
Fractal visionaries and enthusiasts:
Today's image is a quick trip to the main spike of a Mandelbrot
set corrupted in its depths by Z^(11)+C energies. The scene is
located on the west side of a half morphed minibrot lying just
beyond the limit of the main series of Mandelbrot buds.
Due to the unusually large iteration count of the elements, this
is a rather difficult area to investigate, which inspired the
name "Difficult Territory".
The art rates a 6. Such images are easily found in the classic
M-set, and only the coloring raises today's image a little above
average. The math fully rates its lowly 4.
The image takes 3-1/2 minutes to calculate. The individual
viewer must decide if such an average image is worth the time.
Those who decide the image is not worth the effort may view it
sooner on the web sites. But how will they know if it is worth
the effort unless they have already seen it.
The completed image is posted at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
Bright cloudless weather prevailed here at Fractal Central
today. But with 7.5 inches 19cm of snow on the ground and a
temperature that began at +3F -16C and rose to a high of only
14F -10C, along with a biting north wind, it was hardly a day to
be out enjoying the sunshine. The fractal cats felt the chill
early and avoided the draftiest windows. One fractal human (me)
spent an hour clearing the sidewalk, while the other human (FL)
supplied the hot coffee.
The next FOTD will be posted before long. Until whenever, take
care, and be fortunate.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
DifficultTerritory { ; time=0:03:30.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=FinDivBrot-2 function=recip passes=1
center-mag=-1.401945986326833/+0.00000000226729686\
/6.572439e+009/1/-90/0 params=11/1e+024/0/0 float=y
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GzeHzeHzeIzeJzfJzfKzfKzfL }
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=========================================
