FOTD -- August 17, 2011 (Rating 8.5)
Fractal visionaries and enthusiasts:
Today's image is named "Low in Saturation". The name refers to
the color palette, which, except for a few registers, is of very
low saturation. Sometimes, less of something is actually more
effective than too much of it however. In today's image, for
example, the almost-gray outer parts cause the few brilliantly
colored inner spots to appear all the more intense. Less color
on the outside gives the impression of more color on the inside.
I rewarded myself a half-point for this minor example of color
theory. The other 8 points of the rating are due to the
underlying image itself, which is a scene not all that deep in
the star of the period-30 elephant on the southern shore line of
East Valley.
The calculation time of 19-3/4 minutes borders on annoying
slowness. The arbitrary precision math routine certainly does
give the ability to wander as deep as one wishes into the
Mandelbrot and Julia sets, but it takes its good old time
getting there. Still a slow fractal is better than no fractal
at all, and isn't something worth having worth waiting for.
But time is time, and to save time, view the finished image on
the official FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
Or view it is high definition at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original web site may be accessed at:
<http://www.Nahee.com/FOTD/>
The day began with a shroud of fog here at Fractal Central, but
by 9am the fog gave way to a crystal blue sky. The rest of the
day featured continued near cloudless skies and a temperature of
86F 30C.
The humans' day was another in a long string of days so similar
that it is hard to tell one day from another. The fractal cats
never worry themselves about boredom however, they are too busy
just being cats.
The next FOTD fractal will be posted in about 24 hours. It
might be late, it probably will not be early, but it is
virtually certain to be there. Until then, take much care, and
preserve the faith that technology can save the race from self-
destruction.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Low_in_Saturation { ; time=0:19:46.22-SF5 on P4-2000
reset=2004 type=mandel center-mag=0.26061764366814\
702894431163/-0.00176708064896804837819666/6.32257\
1e+020/1/140/0 params=0/0 float=y maxiter=6400
bailout=16 inside=0 logmap=1076 periodicity=6
colors=000JJ`KK`LL`MM`NNaOObPPcQQdRReSSfTTgUUfVVfW\
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zzzzxzyvzxszvizoczj`zeZzb }
END PARAMETER FILE=========================================
FOTD -- August 16, 2011 (Rating 8)
Fractal visionaries and enthusiasts:
Today's image again departs from the August theme of images very
deep in the Mandelbrot set. The departure was necessary to give
me a chance to find another worthy image. These deep images are
very slow and sometimes I simply have no chance to find one.
But today's image is nothing to sneeze at. It's a scene in the
parent fractal that results when the expression, (it's really
not a formula), Z^(2.2)+C is calculated 22 levels up the complex
logarithmic hyperladder. This parent fractal resembles a Mandel-
brot set rotated about 200 degrees CW, with two East Valleys on
the west side of its main bay. Today's image is located in one
of the last islands in an archipelago of debris extending from
the center of the southern valley.
The name "A Midget in a Spot" has little meaning beyond the
sound of the words. The rating of an 8 is what I thought the
image is worth at the time I rated it. The calculation time of
33 seconds is thankfully brief, about the same time required to
view the finished image on the web site.
The official FOTD web site, with the finished image is online at:
<http://www.crosscanpuzzles.com/Archives.html>
A high definition version of the image may be viewed at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The venerable classic FOTD web site may be accessed at:
<http://www.Nahee.com/FOTD/>
The day began with a light rain shower here at Fractal Central,
but by midday the clouds parted, leading to a mostly sunny
afternoon with a temperature of 82F 28C. The fractal cats spent
an unusually long time in the window, which means they approved
of the more pleasant conditions.
The humans spent the day doing little out of the ordinary,
though 'ordinary' implies enough work to keep us busy. The next
FOTD will be posted in 24 hours. If all goes according to plan,
it will be a great one. Until then, take care, and if you can't
believe what religion teaches, turn to science; if you don't
like what science has found, turn back to religion. If you wish
to find the real truth, welcome to the group.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
A_Midget_in_a_Spot { ; time=0:00:33.18-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=recip
center-mag=-0.3441515092977831/-0.0530208699951345\
/1.967296e+007/1/54/0 params=2.2/0/22/0 float=y
maxiter=1800 inside=0 logmap=74 periodicity=6
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9hzA_zCRzDbzZWzSPzLYzZnz` }
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=========================================
This fractal was made by repeatedly zooming in on ever smaller versions of a
self similar feature. Each time another zoom point was picked it added
another rotated square to the fractal.
Here is a link to an image:
http://dl.dropbox.com/u/33642054/image/do_it_again_800_5.jpg
The parameter file used to make the image:
Do_It_Again { ; Exported from Fracton.
; time = 45 sec at 640 x 480 with no aa
; on a Mac Pro 2 x 2.8 Ghz Quad-Core Xeon
; by Mike Frazier, public domain
reset=2004 type=mandel passes=1 float=y
center-mag=-0.637200981531797321929241216142613588\
79610418726/-0.49499504327751979843855327780682656\
575746254617/3.921568676470588e+24/1/43/0
params=0/0/0/0/0/0/0/0/0/0 maxiter=4000 inside=0
proximity=0
colors=000y_TxZSuYRsXQpVOlSNhQLcNJZKGUHEOEBIA8C756\
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UBNQ9KM8HI6ED5A937413000632C75IA8OEBUHEZKGcNJhQLlS\
NpVOsXQuYRxZSy_Tz`Tz`Uz`T }
--
Mike Frazier
www.fracton.org
FOTD -- August 15, 2011 (Rating 8.5)
Fractal visionaries and enthusiasts:
Today's image is named "Antibifurcation" because it shows the
scene of the horrendous crime of antibifurcation, where, in
total violation of the laws of fractal math, the number of
elements around the center shrinks to a tiny fraction of its
value instead of steadily doubling as the laws of fractal math
state it must do.
But actually, there is no crime at all. The image shows a
minibrot in the basin of attraction of a larger but still
infinitesimal minibrot lying near the limit of the main spike of
the Mandelbrot set, which is (-2). When a minibrot lies in the
basin of a larger minibrot, this antibifurcation always happens.
By contrast, minibrots in the basin of the M-set itself continue
bifurcating in the normal manner, with no setbacks, until
reaching the limit of infinity at the edge of the M-set.
The curving tentacles in the image are caused by the closeness
of the scene to the cutoff point of 2. Why the tentacles curve
and twist in such an unlikely manner is known only to the gods
of mathematics, and since I am not one of that exalted group, I
have no idea why the image appears as it does. All I can do is
apply colors to the forms that were already there.
The rating of an 8-1/2 is held down because such scenes are
quite common in the world of fractals. I added a half-point
bonus for the coloring work I put into the image, but even this
seems a bit liberal.
The calculation time of 23-1/3 minutes is slow, but still
reasonable for an image with a magnitude of almost 10^58.
The finished image is posted at:
<http://www.crosscanpuzzles.com/Archives.html>
The high-definition version is at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original classic site may be accessed at:
<http://www.Nahee.com/FOTD/>
Heavy clouds and light rain spoiled Monday here at Fractal
Central. The fractal cats approved of the temperature of 73F
23C even though to the humans it felt unusually chilly for mid-
August.
The next FOTD will be posted in 24 hours. Until then, take
care, and I once had faith in science, but now I'm not so sure.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Antibifurcation { ; time=0:23:20.93-SF5 on P4-2000
reset=2004 type=mandel passes=1 center-mag=-1.9999\
99999999996712761384990600054608875639729347944959\
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maxiter=7500 bailout=4 symmetry=xaxis periodicity=6
colors=000SqdTocUlaWj`XhZZeY_cW``VbZTcWSdUQfSPgPNi\
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NfdNecNebOdaOd`Od_PcZPQtf }
END PARAMETER FILE=========================================
FOTD -- August 14, 2011 (Rating 9)
Fractal visionaries and enthusiasts:
With today's FOTD image we return to the theme of the month --
the land deep within the Mandelbrot set. We check a minibrot
that lies in the East Valley of a larger minibrot that in turn
lies just beyond the main spike of the still larger minibrot at
-1.417 on the main spike of the Mandelbrot set.
The image rates a lofty 9, one point of which is due to the
coloring. At first I considered adding more colors to the
image, but the more I looked at it, the more pleased I became
with the subdued blue theme.
The name "Sparking Elephants" is a play on the word 'spiking',
which might not be a word at all. The spikes are evident
throughout the image, pointing straight away from the barely
visible minibrot at the center. And the image does have a kind
of electric atmosphere about it.
The calculation time of 52 minutes is slow enough to make
viewing the image on the FOTD web site the better choice.
The web site may be accessed at:
<http://www.crosscanpuzzles.com/Archives.html>
The high-definition is at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The classic web site with all images since April 1997 may be
accessed at:
<http://www.Nahee.com/FOTD/>
Sunday left a lot to be desired here at Fractal Central. Heavy
clouds kept a blanket over the area all day, while intermittent
rain killed all hopes of a pleasant day. The fractal cats
showed their fractal nature by being in two places at once. But
since there are two fractal cats, this is not much of a paradox.
The humans found enough indoor stuff that needed doing to
prevent boredom from setting in. I killed one hour counting the
scientific errors in one of those pop-science shows on one of
the supposedly 'educational' channels. The next FOTD will be
posted in 24 hours. Until then, take care, and Atheists should
be more specific in describing what they *DO* believe about the
origin of the universe. When they claim that 'it all just
happened by meaningless cosmic accident', they are not answering
the question, they are expressing their ignorance, which leaves
them open to attack from believers who feel they 'know' where
the universe came from.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Sparking_Elephants { ; time=0:52:41.67-SF5 on P4-2000
reset=2004 type=mandel passes=1 center-mag=-1.4189\
1243194492188838422868091/0/3.22027e+025 params=0/0
float=y maxiter=32767 inside=0 symmetry=xaxis
colors=000GOMIOMIOOIOOIPOIPPIPPIPPIPRIPRIRRIRRIRTI\
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GFLGGMIGMIGMIGMKGMKGOKGOM }
END PARAMETER FILE=========================================
FOTD -- August 13, 2011 (Rating 7)
Fractal visionaries and enthusiasts:
The theme of August is fractals from deep in the Mandelbrot set.
Today's image is not from the Mandelbrot set however. It is
from the fractal that results when Z^(2.25)+C is iterated 1/2
level up the complex logarithmic hyperladder, (actually more of
a hyperspiral). I had to depart from the theme of the month for
one day to get caught up. The very deep images are quite slow,
and I have been falling behind.
The parent fractal appears as a distorted M-set rotated so that
its distorted main period-2 bud lies on the north side of the
main bay. There is a small valley on the east side of this bud,
with today's image lying in that valley.
I named the image "Half a Spider". Spiders have eight legs, but
there are only four spidery legs radiating from the central
minibrot in the image. Since four is one-half of eight, the
name is quite appropriate. (The circular disk closer in around
the minibrot holds nine legs however.)
The rating of a 7 places the image just about at the center of
FOTD ratings. The calculation time of under 1-1/2 minutes
assures that no precious time will have been wasted if the eager
fractalist is disappointed with the image.
For even more assurance, the finished image is posted at:
<http://www.crosscanpuzzles.com/Archives.html>
The image is available in high definition at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The classic FOTD site may be accessed at:
<http://www.Nahee.com/FOTD/>
Threatening clouds moved in here at Fractal Central on Saturday
morning, and a heavy thunder-shower arrived at 3pm, putting a
finish to any outdoor activities. The fractal cats' outdoor
activities are limited to gazing out the windows anyway, so they
had no problem with their outdoor activities. If the day had
been dry, the temperature of 79F 26C would have been pleasant.
The humans, with no outdoor activities planned, had a typical
day indoors. The next FOTD should be posted in 24 hours, which
is the typical interval. Until then, take care, and be a
rational skeptic who doubts that physical aliens are visiting
earth in flying saucers. Such visits are impossible. Due to
the cosmic speed limit of light, (186,000mps), there is no way
for physical aliens to get here. If you must believe in some-
thing irrational, believe in ghosts. They are very disturbing
to skeptical rationalists, but at least they are not impossible.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Half_a_Spider { ; time=0:01:25.03-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=recip passes=1
center-mag=-0.1522280397550513/+0.9940388789985681\
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maxiter=1800 inside=0 logmap=141
periodicity=6 mathtolerance=0.05/1
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zzhzzhzzhzzhzzhzzbzzXzzRzzLzzFzz9zz8zz7zz7zz6zz5zz\
5zz4zz3zz3zz5zz2zz1zz1zz0 }
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 -- August 12, 2011 (Rating 7.5)
Fractal visionaries and enthusiasts:
The August FOTD theme is scenes deep in the Mandelbrot set. But
this does not necessarily mean the images must be deep enough to
require arbitrary precision math. At the scale of today's
image, the entire M-set is about the size of the solar system.
And at least IMO, this magnitude is quite large enough for the
scene to be considered 'deep'.
The image comes in two versions -- a slow version that finishes
in 24 minutes and a fast version that finishes in 4 seconds. I
have included a parameter file for each version. The difference
in quality is very small, but it is there. Those who value time
above quality should run the fast version. Others will run the
slow version and have an inner satisfaction that their image is
marginally the better.
The scene is located in the East Valley of a larger Minibrot
that lies in a chaotic knot on the long filament extending from
the north bud of the minibrot at -1.417 on the main spike of the
Mandelbrot set -- a rather well-explored area, but one that
still holds surprises.
The flat, (sky-blue), background was achieved by rendering the
image with the logmap set to an artificially large 1260. The
correct value is around 970.
The rating of a 7-1/2 includes 1/2 point for the coloring, even
though most of the coloring was done by the Fractint program,
with only a few tweaks applied by me. The name "Colors Without
End" is based on the richness of colors in the image.
The slow, top-quality version is posted on the FOTD web site.
The web site may be accessed at:
<http://www.crosscanpuzzles.com/Archives.html>
A higher-definition version is posted at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The venerable FOTD web site may be accessed at:
<http://www.Nahee.com/FOTD/>
Today here at Fractal Central was a repeat of yesterday, with
the same kodachrome skies, puffy clouds, low humidity, and a
slightly warmer temperature of 84F 29C. The fractal cats also
had a repeat day. They passed the time taking it easy, coming
to the alert only when a beat-up old yellow-orange tomact passed
through the yard and sprayed the fence.
The humans passed the day doing routine things such as finishing
the work. The next FOTD will be posted in 24 hours. Until
then, take care, and when all activity and all change in the
universe finally ceases, how will we tell the past from the
future?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Colors_Without_End { ; time=0:24:14.37-SF5 on P4-2000
reset=2004 type=mandel passes=1 center-mag=-1.4175\
686044006788/0.00225633082302048/1.706292e+012/1/\
105/0 params=0/0 float=y maxiter=6400 inside=0
logmap=1260 periodicity=6 mathtolerance=0.05/0
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zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
ColorsWithoutEnd { ; time=0:00:03.88-SF5 on P4-2000
reset=2004 type=mandel passes=1 center-mag=-1.4175\
686044006788/0.00225633082302048/1.706292e+012/1/\
105/0 params=0/0 float=y maxiter=6400 inside=0
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zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
END PARAMETER FILE=========================================
This one looks sort of like a shuriken or throwing star. It was synthesized
by repeatedly building a line fractal and doubling the number of arms.
Here is a link to a web page with an image:
http://www.fracton.org/fmlposts/shuriken.html
The parameter file used to make the image:
Shuriken { ; Exported from Fracton.
; time = 14 min 48 sec at 640 x 480 with no aa
; on a Mac Pro 2 x 2.8 Ghz Quad-Core Xeon
; by Mike Frazier, public domain
reset=2004 type=mandel passes=1 float=y
center-mag=-0.637200976755101990090375751704920316\
4129285920553172950221050123642148620218915862204/\
-0.49499504293951702730512003147598679071318907247\
67733511982230245678938692912016518461/1.302083349\
609375e+75/1/-21/0
params=0/0/0/0/0/0/0/0/0/0 maxiter=16000 inside=0
proximity=0
colors=000y_TxZSuYRsXQpVOlSNhQLcNJZKGUHEOEBIA8C756\
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mIFlIElIEjHEiHDgGDdFCaEBZDAVB9RA8N87J75E5493241100\
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KpJJlHHhFFcDDZBBU99O77I44C226000641C92IE3OJ4UN5ZR6\
cV7hZ8la9pdAsgBuiBxjBylCzlCzmCzlCylCxjBuiBsgBpdAla\
9hZ8cV7ZR6UN5OJ4IE3C92641000413937D5AI6EM8HQ9KUBNX\
CQ_DSbEVdFXfGYhGZiH_jH`jH`jH`iH_hGZfGYdFXbEV_DSXCQ\
UBNQ9KM8HI6ED5A937413000632C75IA8OEBUHEZKGcNJhQLlS\
NpVOsXQuYRxZSy_Tz`Tz`Uz`T }
--
Mike Frazier
www.fracton.org
FOTD -- August 11, 2011 (Rating 9.5)
Fractal visionaries and enthusiasts:
The FOTD theme for August is deep images in the Mandelbrot set,
but until today we have not ventured to any real depth. Today
however we get bold and dive to a depth of over 6*(10^112),
where we find a 'reset' (anti-bifurcation) point in the huge
basin around a minibrot that is still well beyond visibility.
The scene is located on a filament extending from a larger but
still very deep, (10^59), minibrot on the west branch of the
filament extending from the north bud of the large minibrot on
the main spike of the Mandelbrot set.
The rating of a 9-1/2 includes a 1/2-point bonus for the extra
effort I put into coloring this very difficult image. The
mathematical interest is responsible for another point.
The name "Deep in the Abyss" refers to the depth of the image.
At the scale of the image, the entire Mandelbrot set would be
something like a trillion times the size of the visible
universe. (This is a guess. If anyone wants to do the math, go
ahead. It would be interesting to see how many universes could
fit into the main bay of this huge abstract M-set.)
The great depth comes at a great time price however. On my
2000mhz unit, the image takes 2-3/4 hours to finish -- slow by
anyone's standards.
When I finish the day's tasks, I might check the minibrot at the
center of today's image. I suspect that it will be little more
than a mess of Moire patterns however.
Those who are put off by spending nearly 3 hours calculating a
fractal may make their lives far more pleasurable by viewing the
finished image at:
<http://www.crosscanpuzzles.com/Archives.html>
Or by viewing it in high definition at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original FOTD site may be accessed at:
<http://www.Nahee.com/FOTD/>
A near perfect day prevailed at Fractal Central today. The
mostly sunny, kodachrome-blue skies were decorated with just
enough puffy white clouds to make a picture postcard, while the
low humidity and temperature of 81F 27C completed the
perfection. The fractal cats enjoyed the outdoor conditions as
much as is possible from the inside. They spent several hours
in the window, watching the clouds and birds pass by.
If the current economic anxiety is discounted, the humans had
another quiet peaceful day, and there is no reason why tomorrow
will not be yet another. One thing almost, but not quite,
guaranteed, is that the next FOTD will be posted in 24 hours.
Until then, take care, and if the world is doomed to come to an
end, have no concern. The planet will survive.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Deep_in_the_Abyss { ; time=2:42:17.31-SF5 on P4-2000
reset=2004 type=mandel passes=1
center-mag=-1.760253238150842578924572047306459168\
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62/6.500128e+112/1/122.5/0 params=0/0 float=y
maxiter=5000 bailout=16 inside=0 periodicity=6
colors=000MbGJ_EHXBEU9CR69O42K17L2BL3FL4KL4OM5SM6X\
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fJdfLcfNbfP`fR_fTkNRhLOeI }
END PARAMETER FILE=========================================
FOTD -- August 10, 2011 (Rating 8)
Fractal visionaries and enthusiasts:
Today's image is named "Silver Elephants". Yes, I realize that
elephants are more of a leaden gray color than a silvery one.
But the phrase 'leaden elephants' has no oomph. It wouldn't
sell the latest wireless internet device. So I stretched
reality a bit and decided that elephants sometimes might have a
silvery sheen about them. The colors of the image would confirm
this fantasy.
The rating of an 8 is a bit liberal. I actually feel that the
high-magnitude images of this month are becoming rather routine.
Their magnitudes are just not large enough. A more accurate
rating might have been a 7-1/2, but what the heck, an 8 seems
far better than a 7.5.
The scene is located on the west shore line of the period-17 bud
on the south side of East Valley. Perhaps the most interesting
feature is the near-perfect square with its silvery inner
elements and its bits and pieces of elephant trunks twisting
outward.
The calculation time of 51-2/3 minutes is slow, but they say
something worth having is worth waiting for, so why not go ahead
run the parameter file and risk dissatisfaction.
The alternative is to remove the risk by viewing the finished
image on the FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
The image is available 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/>
Today's high temperature here at Fractal Central equalled
yesterday's high of 84F 29C, but lower humidity, lots of sun and
no rain made it a far more pleasant day. The fractal cats
approved of the outside conditions, but they approved even more
when their treat was served.
The humans had nothing to approve of, but they had nothing to
complain about either. The next in the apparently endless
series of FOTD images will be posted in 24 hours. If all goes
well, it could have a far greater magnitude. Until then, take
care, and should someone who wants to know whether God exists
ask the Pope or Richard Dawkins?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Silver_Elephants { ; time=0:51:38.83-SF5 on P4-2000
reset=2004 type=mandel passes=1 center-mag=0.28112\
03832938940597038/-0.01144622278067799682577/2.334\
839e+017/1/50/0 params=0/0 float=y maxiter=12000
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8B67B67B67B67B67A67A67A57 }
END PARAMETER FILE=========================================
