FOTD -- November 25, 2013 (Rating A-7,M-8)
Fractal visionaries and enthusiasts:
Today's image is the parent fractal that results when the
expression Z^(1.09+C is iterated at ground level of the
hyperladder with no function applied. I rarely use parent
fractals as FOTD's, but today's parent struck me as having
enough bite to earn the honor of being declared FOTD for
25-11-13. The reason for the name "Toothache" is now obvious.
As the exponent of Z is decreased toward unity, the resulting
parent fractals tend ever closer to a circle. But this tendency
can be avoided for a while by calculating the fractal as it
appears on one of the remote levels of the hyperladder. In
today's image however, we need no remote level. The fractal is
interesting enough right at the ground level, where we find a
Mandeloid that resembles nothing as much as a newly extracted
tooth.
Despite surface appearances, the image is filled with well
hidden and quite hard to find smaller minibrots. I will present
a few of these in future FOTD's, though do not expect any
paradoxical images to magically appear.
The art rating of the image is a reasonably respectable 7. The
math rating is a very respectable 8, mostly due to the
unexpected richness of the outer filaments of the fractal.
The calculation will cause no problems. The image will finish
in less than one minute on most units, at least those that do
not panic at the sight of a DOS prompt. Panicky units can be
spared the panic by checking the finished image on the FOTD web
sites.
The finished image is online at:
<http://www.crosscanpuzzles.com/Archives.html>
with grand themes and symphonic variations at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
After a morning low of 16F -9C the temperature rose to a not
very warm afternoon peak of 34F +1C. Helped by hazy sun, it
felt almost comfortable after the biting winds of yesterday.
The fractal cats agreed, as did the fractal humans.
The next FOTD will be posted when both it and I are ready.
Until that marvelous moment arrives, take care, and how could
one communicate the directions of left and right to an alien
imprisoned in a ship in outer space, with no knowledge of the
outside universe?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Toothache { ; time=0:00:55.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident
center-mag=-3.94562/-2.28956/0.2032885/1/-45/0
params=1.09/0/0/525 float=y maxiter=13000
inside=0 logmap=7 periodicity=6
colors=00000E00I00M00Q10U20Y30`40g50i60m70q80q90sA\
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zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
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 -- November 24, 2013 (Rating A-6,M-5)
Fractal visionaries and enthusiasts:
Today's image lies in the parent fractal that results when the
expression Z^(1.85)+C is iterated 0.5094505 part of one level up
the hyperladder. I picked this odd height because it produces a
fractal that almost has X-axis symmetry, not that it makes much
difference in the resulting fractal. (Since the symmetry is
illusional, X-axis symmetry, which appears right, will not work
with today's particular parameters.)
This parent fractal resembles a Mandelbrot set with its west
half cut off and its East Valley split into two halves. Today's
scene lies on the north shoreline of the northern East Valley.
The name "Bad Translateration" might refer to some abstruse
point of advanced matrix math, with deep philosophical
ramifications involving reality. Actually, it means nothing.
The nearly shapeless minibrot at the center bears little
resemblance to any kind of M-set, while the overall pattern is
far too haphazard, with no central theme. As a result, the art
value is an unimpressive 6, while the math stuff, which has
often been seen before, rates no higher than a humdrum 5.
To make things worse, the calculation time of over 5 minutes
will lead to impatience in those so prone. My solution to the
problem is to rush to the web sites.
View the finished image on the web sites without the chore of
doing the calculation. The sites may be accessed 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 mostly sunny skies here at Fractal Central today were
spoiled by a temperature of 23F -5C and a biting northwest wind.
The fractal cats spent the day being glad they were inside. The
fractal humans spent the day doing the things humans do indoors
on a cold Sunday afternoon.
The next FOTD will be posted in probably 24 hours. Until
whenever, take care, and we should feel sorry for the liberal
environmentalists, who care about both the environment and the
underprivileged. I have rarely seen anyone in such a dilemma.
They say the world must cut its carbon emissions, and at the
same time help the emerging nations achieve a better standard of
living.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
BadTranslateration { ; time=0:05:30.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident passes=1
center-mag=+0.20097930259243/+0.12797587283477/3.8\
5526e+010/1/-50/0 params=1.85/0/0.5094505/0 float=y
maxiter=6400 inside=0 logmap=736 periodicity=6
colors=00000D00L00M60N51O42P00R34R35S26T26U16V16W0\
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zz8zzKzzKzzKzzKzzKzzKzzKzzKzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
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 -- November 22, 2013 (Rating A-6,M-5)
Fractal visionaries and enthusiasts:
Today's image lies in one of the two East Valleys of the parent
fractal that is generated when the expression Z^(1.85)+C is
iterated 0.5094505 levels up the complex hyperladder. The level
is set to such a critical value because at this particular level
the parent appears to have X-axis symmetry. The appearance of
symmetry is false however. It exists only on the surface.
The art value of the image, with its overbearing minibrot, rates
only a 6, and the math rates only an average 5. All is not lost
however, for the minibrot is surrounded by smaller detached
minibrots just waiting to be explored. I will check some of
these smaller minibrots in the next few FOTD's.
The name "A Passing Minibrot" refers to the way I found the
minibrot. At first I passed right by it, but then I returned to
have a second look. After a few minutes I saw enough there to
make it today's FOTD.
The calculation time of 2-1/4 minutes will pass fast enough,
though it may still be a bit too slow for such a mediocre image.
Mediocrity can be avoided however by checking the FOTD web sites.
The calculated 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>
Thick clouds and occasional light showers held spirits to a low
level here at Fractal Central. The temperature of 50F 10C was
mild enough, but was wasted by the clouds. The fractal cats
seemed cranky this afternoon, possibly due to the weather. The
humans had a very average Friday.
The next FOTD will be posted in two days, on November 24. Until
then, take care, and pay no attention to those who say we are
becoming too dependent on technology and are even becoming
addicted to it. Even higher technology will solve all our
problems and put the doomsday prophets in their proper places.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
A_Passing_Minibrot { ; time=0:02:15.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident
center-mag=+0.2005901796/+0.1279569602/21526.13/1/\
27.5/0 params=1.85/0/0.5094505/0 float=y
maxiter=6400 inside=0 logmap=84 periodicity=6
colors=000LIWKMVJRTIVSH_QGcPFgNElMDpKCtJBoIAkIAgI9\
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xzUyzczzczzczzczzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
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 -- November 21, 2013 (Rating A-7,M-5)
Fractal visionaries and enthusiasts:
To find today's image we checked the parent fractal that results
when the expression Z^(1.9)+C is iterated only one step up the
hyperladder with no function applied. This parent consists of a
reasonably recognizable Mandeloid rotated so that east faces
south and twisted so that the main bud faces northwest. A very
obvious but disconnected minibrot lies just southeast of the
main bay. Today's scene lies a short distance north of this
minibrot.
I named the image "Random Searching", which describes the
technique I used to dredge up today's scene. The minibrot at
the center resembles the parent fractal rather closely, though I
did not check to see if that disconnected minibrot exists nearby.
The art rating of a 7 indicates that I am less than fully
satisfied with today's image. The math rating of a 5 shows that
nothing new exists in the math aspect.
The calculation time of a little over 2 minutes will pass
quickly enough. Those who like their fractals at turbo speed
can check the web sites.
The finished image is available on the following web sites:
<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 clouds that ruled the roost today kept things suppressed.
The temperature, which began at 21F -6C and rose only to 43F +6C
merely added to the chill. The fractal cats spent the day
sleeping and playing. When ten-year-old Nico grew tired of play
and eight-week-old Jasmine wanted to continue, we had to put her
in the spare room to give Nico a break from the action.
The next FOTD will be posted in a reasonable time, until then,
take care and when one person's common sense contradicts another
person's common sense, they cannot both be right . . . or can
they? . . .
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Random_Searching { ; time=0:02:15.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident passes=1
center-mag=+0.718487803007509/-0.01658645125406608\
/1.659661e+007/1/150/0 params=1.9/0/1/0 float=y
maxiter=2500 inside=0 logmap=238 periodicity=6
colors=00000821942A63B84CA5DRBETCFVDGPE9RFCVFJZFEX\
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mz_zzbzzfzzjzznzzrzzvzzyzzszzmzzhzzbzzYzzPzzHzz9zz\
DzzHzzLzzPzzXzzczzDzzMzzK }
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 -- November 21, 2013 (Rating A-7,M-5)
Fractal visionaries and enthusiasts:
To find today's image we checked the parent fractal that results
when the expression Z^(1.9)+C is iterated only one step up the
hyperladder with no function applied. This parent consists of a
reasonably recognizable Mandeloid rotated so that east faces
south and twisted so that the main bud faces northwest. A very
obvious but disconnected minibrot lies just southeast of the
main bay. Today's scene lies a short distance north of this
minibrot.
I named the image "Random Searching", which describes the
technique I used to dredge up today's scene. The minibrot at
the center resembles the parent fractal rather closely, though I
did not check to see if that disconnected minibrot exists nearby.
The art rating of a 7 indicates that I am less than fully
satisfied with today's image. The math rating of a 5 shows that
nothing new exists in the math aspect.
The calculation time of a little over 2 minutes will pass
quickly enough. Those who like their fractals at turbo speed
can check the web sites.
The finished image is available on the following web sites:
<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 clouds that ruled the roost today kept things suppressed.
The temperature, which began at 21F -6C and rose only to 43F +6C
merely added to the chill. The fractal cats spent the day
sleeping and playing. When ten-year-old Nico grew tired of play
and eight-week-old Jasmine wanted to continue, we had to put her
in the spare room to give Nico a break from the action.
The next FOTD will be posted in a reasonable time, until then,
take care and when one person's common sense contradicts another
person's common sense, they cannot both be right . . . or can
they? . . .
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Random_Searching { ; time=0:02:15.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident passes=1
center-mag=+0.718487803007509/-0.01658645125406608\
/1.659661e+007/1/150/0 params=1.9/0/1/0 float=y
maxiter=2500 inside=0 logmap=238 periodicity=6
colors=00000821942A63B84CA5DRBETCFVDGPE9RFCVFJZFEX\
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DzzHzzLzzPzzXzzczzDzzMzzK }
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 -- November 20, 2013 (Rating A-8,M-7)
Fractal visionaries and enthusiasts:
"This is a Minibrot"
This phrase is not only the name of today's image, but it is
also a harsh fact of the image. The tiny hole at the center of
the scene is a minibrot in the parent fractal that came about
when I calculated the expression Z^sqrt(2)+C at a height of 14
levels up the hyperladder with no function applied.
This parent is a shapeless thing, impossible to describe in
words, with no resemblance at all to a recognizable Mandelbrot
set. Today's image lies on a filament extending from a mis-
shapen bud on the northeast side of the parent.
I chose sqrt(2) as the exponent of Z because the minibrots in
this family of fractals are sometimes surrounded by two- and
four-way symmetry, making them easier to find, though nowhere
near as easy as straight quadratic minibrots.
I sometimes wonder what separates a minibrot from the countless
other holes that parent fractals are often filled with. As I
see it, the difference is that true minibrots do not fill in
regardless of how high the maxiter is raised. Also, minibrots
almost always lie in a basin, with the number of surrounding
elements increasing without limit as the edge of the open area
is approached. The other holes that fill fractals are often
simply random open areas that never fill in, or open areas at
the center of bottomless spirals that will fill in with a higher
maxiter.
Most minibrots are of the quadratic variety, even in fractals
created by a combination of exponents other than 2. This
quadratic shape appears to be the generalized shape of
minibrots, much as parabolas are the generalized shape of curves
in the graphs of many functions. Today's minibrot is of order
1.414... a variety which has no generalized shape at all, and is
therefore quite interesting.
The art rating of an 8 shows that I am quite satisfied with the
colors. The math rating of a 7 was given a boost by the colors.
There is little new math stuff in the image however.
The calculation time of 2-3/4 minutes is slower than I would
have preferred, but the FOTD web sites can eliminate the
slowness.
These web sites may be accessed 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 biting cold temperature of 23F -5C but the
clear sky and resulting strong sun bumped it up to 43F +6C by
afternoon. The fractal cats, who are just learning to play
together, were too busy chasing each other up and down the
fractal hallway to take advantage of the afternoon sunlight
flooding their shelf in the southwest window. The humans, much
less playful, spent the day tending to more pressing but less
interesting things.
The next FOTD will be posted when the time is right. Until
whenever that might be, take care, and I admit that fractals are
awesome, but are they groovy?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
This_is_a_Minibrot { ; time=0:02:45.00 SF5 at 2000MHZ
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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 -- November 19, 2013 (Rating A-6,M-5)
Fractal visionaries and enthusiasts:
Today's image combines 3.4 negative parts of Z^(-1.4) with 0.85
negative part of Z^(-5.4) on each iteration. The parent fractal
is a typical double negative thing with the usual north-south
chain of large bays and a large 'fan' pointing east from the
origin. A cloud of cut-off fractal rings surrounds the whole
thing. Today's image lies on the eastern rim of the 'fan'.
The over-rich effect of the image was achieved by rendering the
scene with the outside set to 'tdis', which divides the elements
into extremely narrow bands.
The name "Over-Stimulation" refers to the super-abundance and
super-richness of the colors in the image. This overkill holds
the art rating to a mediocre 6. The math has been doing its
thing for over 10 years, so I could rate it no higher than an
unimpressive 5.
The calculation time of 3-3/4 minutes borders on slowness, but
the web sites will greatly reduce the wait for satisfaction.
The finished images are 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>
A mix of sun and clouds with a temperature of 43F +6C made today
a typical November day here at Fractal Central. The fractal
cats, who are getting along quite well, paid little attention to
the outside weather, looking instead for more food. The fractal
humans, who sometimes deny their fractal nature, had another
near normal day.
The next FOTD will be posted, most likely but not certainly, in
24 hours. Until the time it actually is posted, take care, and
scientific truth occasionally changes, while religious doctrine
almost never changes. Which is more likely to be true?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Over-Stimulation { ; time=0:03:45.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=1
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vhhhiv`dzJ_zCXzCPzC611611 }
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=========================================
There are many new images on my "variations on
Jim Muth's FOTD" site -- from Oct 29th - Nov 8th
so far:
http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html
I've been having trouble accessing my server to
upload images and web pages. My rented server
in Utah is serving OK, and is successfully seen
in a Canadian proxy server, but is intermittently
available to me -- to view and/or upload.
Repeated TRACERT commands (in the cmd window
of my WinXP) show repeated, consistent loss of
connections during several of the "hops" between
me and my server on a scale of hours to months.
In the past these kinds of problems "within" the
internet have cleared themselves up in 24 - 48
hours, but this one has stayed with me.
I just got a window of good connectivity and
uploaded several days worth of images. I've
been calculating the images every day, but I
just couldn't get them onto the server reliably.
I'd like to know if any of you had / are having
trouble viewing my site -- and, if so, what
state / country you are in.
Thanks!
- Hal Lane
########################
# hallane(a)earthlink.net
########################
---
This email is free from viruses and malware because avast! Antivirus protection is active.
http://www.avast.com
FOTD -- November 18, 2013 (Rating A-7,M-6)
Fractal visionaries and enthusiasts:
The chaos in today's image is awesome. (I think that's the
currently trendy word to describe something that is very
impressive.) The name "Awesome Chaos" is therefore fully
justified.
The image came about when I calculated the expression Z^(2.0075)
at a level 17.2 steps up the complex logarithmic hyperladder,
which would probably prove to be closer to a hyperspiral if we
could comprehend higher dimensions. All this hyper stuff exists
because the complex log function is multi-valued, which means
there are an infinity of fractals that can result from an
expression as simple as Z^(2.5).
The parent fractal appears as a Mandelbrot set rotated 180
degrees so that the main spike points out to the east along the
positive X-axis. Strange things are happening in this area, but
in today's image we check the East Valley, which lies on the
western negative X-axis and is broadened into a small wedge.
Today's scene lies near the southern edge of the wedge blade, in
an area where the chaos is near its maximum.
The chaos here is in the form of herringbone arcs and crescents,
several of which appear in today's image. The total chaos is so
extreme that it actually detracts from the overall artistic
effect, and holds the art rating to a 7. The math rating
remains at a 6. Nothing new appears in the fractal math.
The calculation time of 3-1/4 minutes borders on slowness, so
why take a chance. Check the finished image on the web sites.
Be thrifty, save time by viewing the finished image 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 sun, a brisk breeze and a temperature of 57F 14C made
for a rather pleasant autumn day here at Fractal Central. The
new fractal cat Jasmine leaped onto the rim of the tub then
lost her grip and slipped in, She spent a couple hours drying
off. The old fractal cat Nicholas wondered how any cat could be
so clumsy. The humans watched the action with amusement.
The next FOTD will be posted in a not-too-long period of time.
Until whenever, take care, and can something considered awesome
also be considered groovy?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Awesome_Chaos { ; time=0:03:15.00 SF5 at 2000MHZ
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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=========================================
