FOTD -- September 11, 2013 (Rating A-6,M-7)
Fractal visionaries and enthusiasts:
Today's image takes us to the second critical point of the
current parent Julibrot, which is -0.26... The resulting parent
Mandeloid again appears much like the non-critical one that
results when Z is initialized to zero. Today's scene lies in a
bit of debris inside the period 2 bud on the NNW shore line of
the main bay of the parent. (The 'bud' on the negative X-axis
of the parent Mandeloid is not a true bud.)
I named the image "Island Universe". The name refers to the
central fractal complex, which because of the coloring, appears
to be an island.
Today's ratings have dropped from those of the previous FOTD
fractal. The reason is partly the growing familiarity of the
theme and partly the image itself, which is adequate, but not
really good or great.
Perhaps the best feature of the image is the calculation time of
a fireball 40 seconds. This high-speed calculation will leave
no spare time for impatience to raise its ugly head. As is
always the case with FOTD images however, satisfaction with the
result is not guaranteed. The web sites will make satisfaction
more likely however.
Those who prefer doing it the easy way may view 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>
Exciting weather prevailed here at Fractal Central today. Until
5pm it was partly cloudy, very hot and humid, with a temperature
of 95F 35C. But things changed by 6pm when a whopper thunder-
storm moved in with high winds, torrential rain, crackling
lightning and even a few small hailstones. The fractal cat
weathered the storm well enough until lightning struck a
transformer a half block away, causing a brief power outage,
when he sought a more secure place. After the storm, the
temperature was a far more comfortable 72F 22C. As one who
enjoys wild weather, I had an enjoyable day. FL endured the
action until the storm died down.
The next FOTD will be posted in the proper time. Until whenever
that might be, take care, and to bomb or not to bomb . . . that
is the question.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Island_Universe { ; time=0:00:40.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotMix3a function=ident
center-mag=-0.0938330879721098/+0.8852092567717744\
/1168124/1/35/0 params=0.1/2/1/3/0.5/6/0.01/-1/\
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9G68E67D57C56A45944834623 }
frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }
END PARAMETER FILE=========================================
FOTD -- September 12, 2013 (Rating A-7,M-6)
Fractal visionaries and enthusiasts:
Today's image returns us once again to the Julibrot of the past
several days. Today we check the Mandeloid created when Z is
initialized to the third critical value, which is -0.975...
This Mandeloid shows the greatest degree of difference from the
non-critical one that results when initial Z equals zero.
Yesterday's image rather resembled a minibrot totally isolated
from its 'outside' surroundings. The image was a sham, since
the disconnection was achieved by the coloring. Today's image
is the real thing however. It was found inside a strange mini
Mandeloid just inland of the northwest shore line of the parent
fractal. This mini Mandeloid has a bit of disconnected debris
in its center, with today's scene lying in this debris.
The result is a minibrot totally cut off from the rest of the
fractal by a ring of 'inside' stuff. The minibrot is actually
doubly disconnected. And yes, the open hole that contains the
minibrot and its 'star' is symmetrical, as is true of almost all
features surrounding minibrots.
Since the minibrot's immediate 'outside' surroundings are shaped
like a star, I named the image "Floating Star". The heavily
blue cast I gave to the image emphasizes the stellar appearance.
The ratings could have been a point higher if the theme were not
becoming so shopworn.
The calculation time of 7-1/4 minutes might be a bit much to ask
to see the image. Visiting the web sites is a better deal.
The finished 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>
Today was partly cloudy and very humid until mid-afternoon, with
a temperature of 84F 29C. But then a heavy thunder shower
suddenly arose and dropped the temperature to 72F 22C. The
crackling lightning striking within 100 meters or so sent the
fractal cat scurrying for cover again. He came out as soon as
the all-clear was sounded. Other than the excitement of
watching the big storm, the fractal humans had an uneventful day.
The next FOTD will be posted when the same particle entity can
be in two different places at the same time. Since this is
already the case, the FOTD will be posted in the near future.
Until bilocation occurs, take care, and real magic might be
irrational, but according to quantum science, it does exist.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Floating_Star { ; time=0:07:15.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotMix3a function=ident passes=1
center-mag=-0.1354452771282252/+0.7340443868840427\
/414258.8/1/-35/0 params=0.1/2/1/3/0.5/6/0.01/-1/\
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frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }
END PARAMETER FILE=========================================
FOTD -- September 10, 2013 (Rating A-7,M-8)
Fractal visionaries and enthusiasts:
While yesterday's fractal was a non-critical loser, today's
fractal, which is critical, is a notable improvement. It is a
scene in the fractal that is generated when yesterday's fractal
is re-calculated with Z initialized to the first of the three
critical values of the iterated expression. This value appears
as the real(p5) parameter of today's image.
At first glance, today's parent fractal, which is critical,
appears little changed from yesterday's image. In its depths
however it is totally different, with intact minibrots lurking
where least expected. Today's image, which I named "Spiraling
Onward", lies on the west side of the north branch of what could
be called a kind of Seahorse Valley.
The math value remains a superb 8, while the artistic value has
risen from an abysmal 3 to a very respectable 7.
The three critical values of initial Z in yesterday's loser
image were found by entering the same parameters into the
CriticalPoints formula, which appears in today's parameter file.
This calculates the Parabolic plane of the iterated expression
and creates an image that is a rough graph of the expression.
All that is then necessary is to find the 'Y' coordinates of the
tips of the three obvious though distorted parabolic curves. I
always choose the place where the default red adjoins light
blue. The tedious part is continually stretching the curves
horizontally to determine the exact 'Y' coordinates. The second
image, named "Points Revealed", shows the resulting image-graph
that must be analyzed.
The method is tricky, especially with negative and fractional
exponents, and sometimes does not work, but it is still better
than trying to write a formula to do the job or finding the
points by hand calculation.
The calculation time of 2-2/3 minutes is somewhat slow, and I'm
not sure the result is worth the wait. Luckily, the web sites
can speed up the viewing.
Save time and effort by checking the finished images 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, and a temperature of 88F 31C made today
quite summer-like here at Fractal Central. The fractal cat was
undecided whether to stretch out or curl up, and finally settled
half stretched in my favorite chair. The fractal people passed
the day getting things done.
The next FOTD will soon be posted. To see how soon, check back
here frequently, and before you know what happened, the next
fractal will be here. Until whenever the fates decide, take
care, and let's admit it -- according to science, objective
reality is probably an illusion, which means that our mighty
scientific method is founded on nothing more than an illusion.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Spiraling_Onward { ; time=0:02:40.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotMix3a function=ident passes=t
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zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }
Points_Revealed { ; time=0:00:20.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=CriticalPoints function=ident
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frm:CriticalPoints {; Jim Muth
z=imag(pixel), c=fn1(real(pixel))
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=real(p3), h=imag(p3), j=real(p4), k=imag(p4):
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| < 10000 }
END PARAMETER FILE=========================================
FOTD -- September 09, 2013 (Rating A-3,M-8)
Fractal visionaries and enthusiasts:
I have received a couple inquiries over the past few days about
critical points and their relation to fractals, and also how I
use Fractint to graphically find critical points. This will be
the topic for the next several FOTD discussions. Hopefully, my
limited math knowledge will be equal to the task.
To begin, a critical point is a point on the graph of a function
where the rate of change is zero and the tangent is therefore
parallel to the X-axis. This point can appear as the tip of a
parabola or a point of inflection, where the direction of
curvature changes.
In fractals, when Z is initialized to a critical value, the
fractal will consist of undistorted Mandelbrot stuff, such as
appears all around the edges of the classic Mandelbrot set, and
the fractal's depths will be filled with intact minibrots. In
the classic M-set, the critical value is zero, but in today's
fractal, in which Z is initialized to zero, the result is
distinctly non-critical. No perfect minibrots lie in its
depths, and no undistorted buds lie along the edges of the large
bays. For those who cannot wait, if any, today's fractal has
three actual critical points. These are:
+0.2246790860663939 -0.2602855645470608 -0.9753887460956279
If one of these values is entered as the value of real(p5), the
resulting fractal will closely resemble today's non-critical
version, but it will have many critical areas, especially along
the negative X-axis, with intact buds, and minibrots in their
depths.
The name "Not Critical" is a simple truism.
Since the math, which rates a lofty 8, is the chief topic of
today's image, I put little effort into the coloring, which
rates a lowly 3. The fractal is a parent fractal, this is true
by definition, but it holds little of interest. The thin
vertical column in the center of the main bay is created by the
0.01 part of (1/Z) in the iterated expression.
I will resume this topic tomorrow, when I will describe my
rather convoluted technique of finding critical points
graphically with the Fractint program.
The calculation time of a fireball 20 seconds will cause no
grief. The web sites can bring extra assurance of satisfaction.
The finished 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>
An un-notable day passed with little fanfare here at Fractal
Central today. The sky was mostly cloudy, but the clouds were
thin enough to give the impression of a mostly sunny day. The
morning temperature of 45F +7C made sweaters comfortable, but
the afternoon high of 73F 23C was near perfect. The fractal cat
slept through most of the afternoon, while the fractal humans
accomplished what needed to be done.
The next FOTD will be posted in the appropriate time. Until we
see what is appropriate, take care, and, "I think that crocodile
is still alive!" Tom said off-handedly.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Not_Critical { ; time=0:00:20.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotMix3a function=ident passes=1
center-mag=-0.12/0/0.8 symmetry=xaxis
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frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }
END PARAMETER FILE=========================================
> Animation of FOTD August 26, 2013: Undersea Scene is posted:
> http://www.fractal-animation.net/vid/xenomorphs.zip
> It is 2 min 21 sec runtime, 40Meg download.
That's a great video!
I especially like the yellow sparkles on the dark purple
background at about a minute in.
There was a lot of suspense the first time I watched it as to
whether it could possibly keep zooming in and finally arrive
at an M-set or not!
I didn't see the "pumping" up and down of the color map in
this video:
Did you have another value in Logmap other than 2? <---<<
- Hal Lane
########################
# hallane(a)earthlink.net
########################
Author: JackOfTradeZ
Date:
To: fractint
Subject: [Fractint] AOTD 9_7_2013
.
Animation of FOTD August 26, 2013: Undersea Scene is posted:
http://www.fractal-animation.net/vid/xenomorphs.zip
It is 2 min 21 sec runtime, 40Meg download.
-----
FOTD -- September 06, 2013 (Rating A-6,M-7)
Fractal visionaries and enthusiasts:
Today's fractal was created with the same iterated expression as
yesterday's, but it is found in an entirely different parent
fractal. This is because today's parent fractal was initialized
to a different critical point, which appears as the value of the
real(p5) parameter.
I used the Fractint program to plot a second critical point
graphically. (Fractint can draw basic graphs in which critical
points can be tracked down and measured.) I do not do this very
often because the process is tedious, but in today's case the
result was satisfying. I found a new fractal, resembling
yesterday's parent in some aspects but differing in other ways.
I named today's image "The Other Half" because it is a scene in
a parent fractal that is the second critical slice of
yesterday's Julibrot.
Once again, the artistic value of 6 lags behind the math value
of 7, which makes the 13-minute calculation time not much of a
bargain. But the web sites are always there to save time and
frustration.
Be rational and unfrustrated. Check the finished images 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>
With its totally cloudless skies, today would have been
absolutely perfect if it had been just a few degrees warmer here
at Fractal Central. As it was, the morning low of 43F +6C and
afternoon high of 70F 21C were a little too chilly for relaxing
in the outdoor shade. The fractal cat relaxed under a chair
cover, where he spent the afternoon as little more than a lump.
The fractal humans, who are anything but normal, had a normal
day.
The next FOTD will be posted when I get in the mood to do it.
Long experience says that the time will be either 24 or 48
hours. To be sure when, check back at these times. Until
whenever, take care, and when bad guys use guns to kill innocent
people, the liberals say we should solve the problem by passing
laws that will affect only the good guys who have guns.
(Criminals don't obey laws.) This is crazy enough, but then the
conservatives say we should solve the problem by increasing the
number of guns in circulation, so we will be ready to protect
ourselves from the bad guys. Would the rational side please
stand up.
Jim (reason prevails but no one wants to hear it) Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
The_Other_Half { ; time=0:13:30.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix3a function=ident passes=t
center-mag=+0.04948459960925363/+0.000012428074251\
36/2.714126e+010/1/-50/0 params=4/2/3/4/2/3/-100/5\
/0.2765676348110211/0 float=y maxiter=4250
inside=0 periodicity=6
colors=000ZGGYDHYAJX7KX4L_EHaODgOFmJKlMIlOGlQElSCl\
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w8gtCfrHeoLdlQcjUbgZagZbebaceaaia_laYpaWsaUvaF5_J9\
WMCSQFOTJKXMG`TA_PC_MDZJF }
frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }
END PARAMETER FILE=========================================
FOTD -- September 05, 2013 (Rating A-7.5,M-7)
Fractal visionaries and enthusiasts:
The math behind today's image combines 4 parts of Z^2 with 3
parts of Z^4 and 2 parts of Z^3, then subtracts a whopping 100
parts of Z^5 before adding C on each iteration. This crazy
mixture creates a parent fractal shaped somewhat like a sickle
cell, with X-axis symmetry and a large main spike pointing west.
This large period-2 bud on the negative X-axis appears quite
normal, but the shapes of the other buds around the main bay
are wildly varied. Today's scene is located in a bud on the
northeast shore of the large sickle-shaped main bay of the
parent.
I did not try to find an additional critical point of the
generating expression. The value of zero so frequently works as
a critical point with this formula that I generally try it
first. In today's case, zero works quite well, though I might
check for other critical points and see what kind of parent
fractal results.
The unusual coloring effect in today's image was achieved by
rendering the scene with the outside set to 'fmod' with the
proximity unchanged from the default 0.01. This is what
inspired the name "Proximity 0.01".
With a rating of 7-1/2, the artistic value, at least in my
opinion, is worth a little more than the math value, which rates
a whole-number 7.
The MandelbrotMix3a formula is a slow one, which slows the
calculation to a turtle-like 3 minutes. So don't let the turtle
win the race. Check the finished image at one of the web sites.
Enjoy freedom from turtles by viewing the finished images 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 here at Fractal Central began with cloudy skies, but the
clouds cleared off by noon, leading to a pleasant, mostly sunny
afternoon with a temperature of 75F 24C, low humidity and a
refreshing north wind. The fractal cat, fully refreshed, spent
the afternoon watching the local pigeons, which are starting to
get out of control and might eventually have to be cleared from
the surrounding eaves. The fractal humans had a routine day, as
most days are here at FC.
The next FOTD will be posted in the right time. Until that time
arrives, take care, and check the first FOTD web site for the
politically charged comments of the day.
Jim (neither right nor left) Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Proximity_0.01 { ; time=0:03:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix3a function=ident passes=1
center-mag=+0.05921017762628365/+0.181266449610439\
/4.5583e+008/1/82.5/0 params=4/2/3/4/2/3/-100/5/0/0
float=y maxiter=600 inside=0
outside=fmod periodicity=6
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LQnMRoMRoMSoNSoNSoNTnOToOTnOUnPUnPUnPUnQUnQUnQUnRU\
nRUnRUnSVnSWnSWmSWmSWm6CU }
frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }
END PARAMETER FILE=========================================
FOTD -- September 04, 2013 (Rating A-7,M-8)
Fractal visionaries and enthusiasts:
Today's image was created with the MandelbrotMix3a formula,
which mixes together various portions of four different powers
of Z. In today's image, one negative part of (1/Z) is combined
with straight (Z), then mixed with one part of Z^(-1.6) and one
negative part of Z^(-1.4) before (1/C) is added on each
iteration. The 0.2858095886402 value of the real(p5) parameter
is the critical point of the iterated expression, which I
determined using the tedious graphic method.
The parent fractal is little more than a nest of zigzagging
filaments with small Mandelbrot sets scattered about. Today's
scene is located in a knot of filamentary debris near one of
the small M-sets.
In today's image the math value of 8 exceeds the artistic worth
of 7. This unusual situation is due mostly to the unusually
large number of different exponents of Z involved in the
calculation.
I use today's formula so rarely for two reasons. First, the
images tend to become boringly similar as the number of
exponents of Z grows. Second, it is too tiresome to work out
a critical point by calculation or graphically.
The name "Trouble in Sight" refers to the effort of finding a
critical point and the marginally satisfactory result when I did.
The calculation time of 2-1/4 minutes borders on slowness. The
slowness may be eliminated however by checking the web sites.
Finished images may be viewed 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 perfect day passed uneventfully here at Fractal Central. The
fractal cat said the temperature of 79F 26C was perfect. The
fractal humans said the low humidity was perfect, while the
photoshop blue skies and cottonball clouds kept everyone else
and every other animal in town happy.
The next FOTD will be posted right here when I work up the
energy to do it. Until the energy strikes, take care, and no
one can be a true liberal unless they hate guns and are worried
about climate change and equality. Too bad! Since guns are
here to stay and the climate will continue changing and all
people will never be equal, I guess liberals are doomed to a
life of endless frustration.
Jim (am I left or right) Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Trouble_in_Sight { ; time=0:02:15.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotMix3a function=recip passes=1
center-mag=+3.26650108165485/-0.05084635835292/\
1.326488e+008/1/-112.5/0 params=-1/-1/1/1/1/-1.6/\
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zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }
END PARAMETER FILE=========================================
