FOTD -- June 06, 2011 (Rating 7)
Fractal visionaries and enthusiasts:
Sometimes when I'm writing these FOTD discussions I feel like a
merchant trying not to sell his goods. (It's not so unusual.
After all, we hear electric power companies all the time telling
us to use less of their product.) But I believe in honesty in
fractal talk as well as in advertising, so I admit my fractal
shortcomings.
In today's image I'm playing catch-up fractaling, and the
quality appears to have suffered. I managed to get the quality
of today's image up from a rating of a lowly 5 to a rating of an
average 7. It's an improvement over yesterday for sure, but
still leaves us well below FOTD top quality.
But an image is an image, and even though it's late, today we
have an image. The parent fractal came about when I combined
0.001 part of Z^1001 with straight Z before adding straight C on
every iteration.
This uninspiring combination produces a parent fractal that is
little more than a vague circle with a bit of action at its
eastern extremity. Zooming in on this action reveals a tiny
distorted Mandeloid and a section of the large circular arc,
which in its entirety consists of 1000 lobes. Today's scene
lies toward the rounded tip of the lobe closest to the Mandeloid.
I named the image "Fishbone" because that's what came to mind as
I studied it in search of a name. (The search was a short one.)
The calculation time of 3-3/4 minutes will pass un-noticed.
The finished image is available 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 classic FOTD web site with fractal images from as far back
as April 1997 may be accessed at:
<http://www.Nahee.com/FOTD/>
The weather has been pretty pleasant for the past few days here
at Fractal Central, with lots of sun and near normal tempera-
tures around 79F 26C. I have been passing time trying to get
the FOTD caught up. Maybe I should have simply skipped the FOTD
for June 5. At least the fractal cats are sharing the work
load, giving morale support when the fractaling gets rough.
The next FOTD, the one for June 7, will likely be posted in a
few hours. Until then, take care, and be ready for what may
come.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Fishbone { ; time=0:03:44.13-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=ident float=y
center-mag=+0.00857153940435359/-0.000026928341367\
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frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
FOTD -- June 05, 2011 (Rating 5)
Fractal visionaries and enthusiasts:
Due to an antiquing expedition on Saturday, today's image is a
super-quickie, both in calculation time and the time I spent
creating it. It came about when I casually subtracted 0.67 part
of (1/Z) from 0.67 part of Z^2, which resulted in a parent
fractal consisting of a single large distorted Mandeloid with
disconnected debris scattered around it.
The north period-3 bud is the largest bud on the main bay of
this parent Mandeloid. This bud has a prominent zig-zagging
filament extending from it and terminating in a jagged string
of connected holes. The string of holes is mirrored many times
in today's image, which is located near the point where the
filament joins the string.
The image rates a 5, about as low as an image can go and still
qualify for FOTD status. The name "Iterative Old One" does not
refer to the fractalist. It refers to the image, which had
potentially existed for all eternity before I stumbled upon it.
The calculation time of 20 seconds is about as fast as an image
can be, (unless the image is type=mandel or type=julia).
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 web site is at:
<http://www.Nahee.com/FOTD/>
Saturday here at Fractal central began sunny, but clouds moved
in during the afternoon and built until a lively thunder-shower
erupted at nightfall. The fractal cats had no complaints about
the temperature of 77F 25C, but did not enjoy the noisy thunder.
Meanwhile the humans had an acceptably pleasant day. The next
FOTD will be posted within 24 hours. Until next time, take
care, and if you hate those big greedy corporations that pollute
the environment and take money from the people, punish them by
no longer using their products. But if you need these products
to maintain your life style, don't make yourself a hypocrite by
speaking out and protesting.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Iterative_Old_One { ; time=0:00:20.60-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=ident float=y
center-mag=+0.5565691575516971/+0.5157652874537672\
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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=========================================
.
Animation of FOTD 5/3/11 "Most Unexpected" is posted:
http://www.fractal-animation.net/vid/ttlg.zip
It is 34 Meg, running time 2 minutes.
Strange. There are "windows" of complexity immersed in "seas" of relative simplicity.
Almost look like 3D objects jumping out at you in the hi-rez 1024 AVI.
<i>Through the Looking Glass</i>
Enjoy.
Comments welcome.
JoTz
.
FOTD -- June 04, 2011 (Rating 8)
Fractal visionaries and enthusiasts:
Today's image is named "A Minibrot in Heaven". My concept of
heaven is a place that everyone says is wonderful, but no one
wants to go to. In my opinion, the reason for this contradic-
tion is that we're not sure that heaven really exists. In a
world built on science, faith does not carry the power it once
did, and the world's religions appear helpless to do anything
about it. What do I think of all this? Well, I spend time
wondering whether there are fractals in heaven.
Today's image offers a little hope of the beyond. It shows a
minibrot floating through the etherial realm of heaven. This is
the same minibrot that I mentioned in yesterday's discussion,
and indeed, yesterday's scene lies within the brilliant white
arc just southwest of the minibrot in today's scene.
Just as in yesterday's image, the better part of today's image
is inside stuff made visible by the 'bof60' inside fill. A good
part of the outside stuff has evaporated away.
The image rates an 8. It might have rated as high as a 9 if the
muddy left-over 'outside' debris in the upper part had not been
so intrusive. There could be a way to eliminate this stuff, but
once again laziness overtook me and I decided to let the image
go as is.
The calculation time of under 1-1/2 minutes will test the
patience of no one.
The completed image is posted on the FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
The high-definition version of the image may be accessed at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The 14-year-old classic FOTD web site may be accessed at:
<http://www.Nahee.com/FOTD/>
Friday here at Fractal Central was another perfect early June
day. The temperature of 77F 25C is right in the middle of the
comfort range, and the humidity of 45 percent simply added to
the comfort. The fractal cats spent most of the day being
comfortable, doing what cats do when they are comfortable. They
stretched out on the carpet.
The day of the humans, (not to be confused with the day of the
triffids), was slow. FL got caught up on some gardening, while
I got caught up on some fractals. The next FOTD is due in 24
hours, but if one of those antiquing expeditions comes up, it
might be late. Until whenever, take care, and what if we dis-
cover that heaven is really not there? . . . Gulp!!
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Minibrot_in_Heaven { ; time=0:01:25.23-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=1
center-mag=1.19207/-0.0303/5.911591/1/-110/0
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frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
FOTD -- June 03, 2011 (Rating 6)
Fractal visionaries and enthusiasts:
Today's image came to life when I combined 7 negative parts of
Z^(-1.7) with 0.7 negative part of Z^(-7.7) before adding (1/C)
on every iteration. The resulting parent fractal is one of
those shapeless, pretty much indescribable things with lots of
interesting detail.
Today's scene is located in the southeast part of the parent,
just beyond a ghostly pink Mandeloid that has pretty much
evaporated into the fractal astral plane. The blue background
was created by rendering the scene with the inside set to
'bof60'. The shredded, highly colored foreground stuff came
about when I raised the bailout radius to 500.
The overall effect is of a surrealist painting by one of the
early 20th-Century artists, when surrealism was all the rage.
It seems strange that artists were drawing fractal patterns well
before we knew fractals existed. And unless I'm mistaken, women
were quilting fractal patterns hundreds of years before the men
discovered the patterns.
When I stood back and carefully pondered the image on the
screen, I decided it was worth a rating of a 6, which is above
average, but nothing to get excited about.
I have no idea where the name "Random Mischief" came from. It
was simply on the screen when the time came to dream up a name.
But with a little imagination, the image actually might be seen
as getting into mischief.
Mischief aside, the finished image is posted at:
<http://www.crosscanpuzzles.com/Archives.html>
The high-definition version is posted at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original classic web site can be found at:
<http://www.Nahee.com/FOTD/>
A stellar day prevailed here at Fractal Central on Thursday.
The crystal clear sky and temperature of 75F 24C made outdoor
activity a pleasure, while the breeze from the northwest cooled
even the busiest outdoor worker. The fractal cats are never
busy, but even they seemed pleased with the conditions.
The humans had their own tasks to accomplish. FL is not quite
satisfied with the progress of this year's garden, so she spent
time gardening. I am never quite satisfied with anything, so I
spent time pondering the unknown. The next thing to be pondered
is the next FOTD, which will be posted in 24 hours. Until then,
take care, and start every day with a fractal. If you're out of
them, pick up a supply at the nearest fractal outlet store.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Random_Mischief { ; time=0:00:30.39-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=1
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frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
FOTD -- June 02, 2011 (Rating 5)
Fractal visionaries and enthusiasts:
Today's image is more a demonstration of the 'fmod' feature of
Fractint than an actual fractal discovery. The scene of the
action lies in a bit of satellite chaos circulating around the
rather impressive fractal that results when 0.2 part of Z^3 is
combined with Z^2 before C is added.
When rendered in the normal equal-iteration manner, the image
falls totally flat. Re-rendering it with the outside set to
'fmod' and the proximity set to 3 adds enough life to raise the
rating to a humble 5, just enough to qualify it for FOTD status,
at least on a fractalist's lazy day.
The name "FMOD to the Limit" indicates that the FMOD outside is
just about all there is to the image. The calculation time of
23 seconds means that little time will have wasted if the image
falls flat even with the FMOD outside.
The finished image is posted at:
<http://www.crosscanpuzzles.com/Archives.html>
The high-definition version of the image may be accessed at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original web site is available at:
<http://www.Nahee.com/FOTD/>
I read in the morning paper of another cell-phone cancer scare,
but I see no need for concern. All you wireless internet gadget
addicts out there can take comfort knowing that the phone compa-
nies would certainly warn us voluntarily if using their wireless
gadgets is dangerous, just as the tobacco companies voluntarily
warned us that using their tobacco products is dangerous.
Another heat-wave type day prevailed here at Fractal central on
Wednesday. The sun was scorching hot, while the temperature of
95F 35C made things uncomfortable even in the shade. The
fractal cats, seeking comfort, found it on the cool bare floor,
where they were happy all afternoon.
The humans had an uneventful day. A similar day is expected
tomorrow. The next FOTD will be posted in 24 hours. Until
then, take care, and what do those scare-monger scientists have
against wireless internet gadgets, which are so much fun?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
FMOD_to_the_Limit { ; time=0:00:22.94-SF5 on P4-2000
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formulaname=MandAutoCritInZ function=ident passes=1
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frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
FOTD -- June 01, 2011 (No Rating)
Fractal visionaries and enthusiasts:
Today's image is named "Rainy-Day Minibrot". I gave it this
name because the image was resurrected from my 'reserve' files
-- older images that I hold in reserve to recall when laziness
attacks as it did on Tuesday.
The image shows a minibrot of order 2.05 located near the
negative X-axis of the parent fractal that results when the
formula Z^2.05+C is iterated at a level of a measly 0.12 turn up
the log spiral with the 'recip' function applied. This parent
is shaped almost exactly like the minibrot.
Since the image is an older one and I put almost no new coloring
effort into it, I could give it no rating. But if I had rated
it, I would have given it a rating around a 5.5.
The calculation time is a very zippy 36 seconds. Calculation
may be avoided however by viewing the finished image at:
<http://www.crosscanpuzzles.com/Archives.html>
The high-definition is at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The classic FOTD web site is at:
<http://www.Nahee.com/FOTD/>
Total heat and humidity prevailed here at Fractal central on
Tuesday. When the temperature reached a high of 95F 35C the
fractal cats retired to the cool tile of the bathroom floor,
where they spent the next several hours.
Meanwhile the humans took things easy in their own way. FL
checked to see that the garden was well watered, while I
relaxed with a fractal. The next FOTD will be posted in 24
hours. Until then, take care, and the current issue of 'Time'
magazine has an article about the tendency of people to look at
the bright side of bad events instead of the realistic side. I
have not yet had a chance to read the article, but it is proba-
bly irrelevant. I am certainly not guilty of looking at the
bright side of bad things. (I'll have more to say about this in
an upcoming FOTD.)
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Rainy-Day_Minibrot { ; time=0:00:36.64-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=recip
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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 -- May 31, 2011 (Rating 7)
Fractal visionaries and enthusiasts:
I was surprised when yesterday's exponent of 1.009 actually
produced a fractal; I was astounded when today's exponent of
1.0009 produced one also.
In this range, all parent fractals are roughly egg-shaped, so I
searched for parents with slight irregularities on their edges.
In today's case, the parent fractal created by calculating the
formula 8.98 levels doen the complex log ladder with the 'recip'
function applied showed such an irregular area. When I zoomed
into this area, I found today's scene.
To me at least, the image resembles a view from deep in a cave,
looking out toward a brilliant sky. When I switched on my
thought processes, the name "Cave of the Ancients" soon came to
mind. This name sounds as though some deep mystical truth lies
in the depths of the image. Actually, nothing is implied but
the near-mystical behavior of complex numbers.
The basic color palette is a repeat of the black-and-white one
from yesterday's image, though in today's scene I did tweak the
colors a bit. The rating of an everyday 7 remains unchanged
however.
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 web site is at:
<http://www.Nahee.com/FOTD/>
Lots of sun and a temperature of 90F 32C brought a feeling of
midsummer once again to Fractal Central on Monday. The fractal
cats shared the midsummer effect as they found cool places to
stretch out and sleep.
FL spent most of the afternoon working in the garden, while I
got involved in a book about relativity (of all things). The
next FOTD is due to be posted in 24 hours, but we suspect the
day will be busy, so do not be surprised if it is late. Until
whenever, take care, search for a full-metal poet, and realize
that he or she might hold the key to the salvation of the earth.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
CaveOfTheAncients { ; time=0:26:24.87-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=recip
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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 -- May 30, 2011 (Rating 7)
Fractal visionaries and enthusiasts:
Today we enter "Uncharted Territory", which is what I named the
image. Never before have I checked a fractal with an exponent
as close to unity as 1.009, making today's image uncharted for
sure.
The graph of Z^1.009 is virtually a straight line, so how is it
possible that a fractal as rich and varied as today's could come
about? The answer is the multi-valued nature of the complex
logarithm.
The complex log is multi-valued. This means that it has many,
in fact an infinity of values, and all of them are 'correct'.
When applied to fractals with fractional exponents, these
different values create different fractals, all of which are
correct. But curiously, when applied to exponents very close to
unity, as is today's, these different values create some
unexpectedly rich images, in effect turning a 'sow's ear' into a
'silk purse'.
Today's image lies in one of these 'silk-purse' fractals. The
parent fractal is an apparently featureless ellipse, but a close
examination reveals a tiny bit of chaos on the southeast shore
line. Today's image lies in this chaos.
I used the built-in black-and-white color palette to create the
3-D effect. Other palettes might have worked better, but an
attack of terminal laziness prevented me from trying to find
one. This laziness held the rating to an everyday 7.
The finished image may be seen on the FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
and 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/>
Typical midsummer weather made Sunday a typical midsummer day
here at Fractal Central. The fractal cats spent the day doing
what cats do when the temperature reaches 88F 31C -- they
stretched out and went to sleep.
The humans took it just as easy, though we did stay awake at
least most of the time. The next FOTD is due to be posted in
24 hours. Until then, take care, and don't ask me what I think
is wrong with the new world being brought about by the recent
advances in technology. I just might start to answer.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
UnchartedTerritory { ; time=0:12:09.74-SF5 on P4-2000
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formulaname=MandelbrotBC3 function=recip 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=========================================
