WHY scientists play in the sand
(C) Dr.Dismal
- Do you know what a fractal??
-Yes you that, lamer what?? Shtu
ka so funny, there's still all
repeated ... "
Hmm ... But I recently pondered the question, what is at
Indeed - the fractal. Who came up with this very thing?? Say
Honestly, the first of fractals I learned a long time. Of course
foot under the table has not gone, but the school has not yet
matured, appears 5-6 years. So, gave me a toy, interesting -
Magic Caleidoscope. Well, a kaleidoscope, a kaleidoscope, only
Big is so beautiful - with foreign labels, snowflakes. But
it's almost to the point does not apply ...
So, as a child curious and precocious its
shocking adults began to ask what was inside
obtained. Someone limited explanation of what was beautiful
uzorchiki, someone (probably with a technical education):)
told me that there mirrors and shards of glass and different
stuff-dryuchek form a symmetry that pleases the eye of many
children. And someone blurted out a strange word - FRACTALS. Out
in a kaleidoscope fractal snowflakes are drawn. Naturally I
not only as a curious child, but also as a curious,
wanted to reach those most fractals, because no one did not
have them! An autopsy revealed that no fractals and does not
exist, only mirrors yes' stuff-dryuchki "...
The second time I've encountered with fractals, which
defended the diploma on the occasion of receiving the
profession. Even still remember the name thesis' Computer
Graphics. Computed images and data visualization. " Then I had
to casually mention fractals. It was then that I have more
details about them. But of any rigid definition of fractals I
have not found. Well abstract words do not count. What is
causing chaos, symmetry of the disorder, trinkets for
scientists-mathematicians may say even the announcer on TV. To
me, though, and just like the general words in explaining, at
least once to hear a good make, and simple determination and a
little explanation of the essence.
Subsequently, interested in becoming, in my opinion about
ALK'a Fractals in OBERON'e. Just recently, another article on
this topic.
Of course you can ask - you're a kid Th
brake? Could not for a long time to find the answer to
theme?? Yes, no and maybe yes, but not - then I knew I
nearly enough to explain in general terms, it is still
someone. Well, then I'm pretty lazy person, I do not even
hide. Well broke me delve into the literature, sitting in the
library not like I sit there, but go there to ... :)
So that's fallen into the hands me an article that tells the
a very instructive story, which I would like you
tell.
The most accurate in the world is in the sandbox
Technical Research Centre of the world famous company
"IBM". Here's the "play in the sand in a scientific way." Glass
bulb "sandbox" is enshrined in the terminals with a little
motor in such a a way that makes one revolution per second.
When you rotate the bulb grains of sand in it trickle trickles
down a long narrow neck, which has a small, just 2 degrees
slope. C every turn of a few grains of sand are moving on the
inclined neck, while one iznih not drop out. Usually this
occurs once in 10 seconds.
Thirty thousand fallen grains form a mound at 2, 5 cm
height, which is its base fills the entire area
plastic disc with a diameter of 4 cm And now comes
critical moment. Once the incident is one more grain of sand, it
knocks from the top of another, that - the third ...
Mikrolavina begins. Part of the sand wakes up from the disc on
the tray and ... In general, anything a special happens:) At
this point stops mikromotorchik, because it turns off the
signal to the computer received information from the electronic
scales, platform which rests a disc. When mikrolavina ceases
During the computer records the weight remaining on a platform
of sand and again includes a motor. Slide again begins to grow.
And so on following an avalanche ...
No, a physicist Glenn Heald, designed this intricate
device is not going to modernezirovat hourglass.
Moreover, the properties of sand themselves to have little
interest - even though had to be thoroughly washed and calcined
to grains of sand do not stick together in the nose bulb.
Researcher on the basis of its "Sand model tries to confirm the
validity of the theory, according to which the formation and
destruction of the sand hills obey the same laws of statistics,
and river floods, earthquake, and even fluctuations in prices
and demand for goods in stock Exchange.
A quarter century ago such an idea suggested has worked
here, in "IBM", mathematician Benoit Mandelbrot. He tried to
analyze the statistics of the annual flooding of the Nile, for
which Egyptians watch thousands of years. At first glance, the
schedule, constructed from observational data, no particular
trends were discovered: in some years the water in the Nile
rises above average, more often fluctuates somewhere near the
middle mark. Well, what of it?
Mandelbrot, when carefully analyzed the
statistics, we found that, regardless of the time
interval - 4OOO, 4OO or 4O years - the picture is
almost identical, consisting of a series of look-alike
deviations. Where any part of the diagram, however small it
does not was, was a kind of miniature display more
major parts.
And here Mandelbrot remembered that back in 1904
little-known German mathematician Eric von Koch, studying the
work his predecessors George Cantor and Karl Weierstrass
stumbled upon a description of the country made their curves
with unusual behavior. Strangeness as their was that anyone,
even negligibly small segment of this curve is exactly the same
in their properties of the whole curve.
Intrigued, Koch took a sheet of paper and tried to
draw something like that yourself. Everything was very
simple. Need to draw an equilateral triangle. Divide
each side into 3 parts. in middle part again to build
equilateral triangle, as if pulling the initial edge
out. On small edges, again divided sodium, again
construct a triangle ... And so, step by step until there is
room for paper. That will have a figure, known in mathematics as
"Koch snowflake."
Initially, researchers treated the "snowflake" as a sort of
mathematical trifle: fun, but do not know which of her
proc. However, after some time the British meteorologist L.
Richardson needed to measure the length of coastline
UK. At first he tried to make measurements
by curvimeter on the map. But I soon realized: with this method
measurement result depends on the scale. With more
scale on the map are visible all the smaller capes
and coves, coastline length is extended. In general, the Coast
line showed the same properties as the Koch snowflake, the
schedule flooding of the Nile ... So, these laws have a
practical sense and deserve to do them thoroughly.
Mandelbrot, then tried to put on the full schedule
the number of spills given height of the Nile - one foot above
average, two feet above average, etc. In this case revealed
that the graph formed by the smoothed curve, which is quite
simply described by mathematical equations.
Disordered form of graphics Mandelbrot called "fractal"
from the English word "fractanial" - float, thereby, as it were
alluding to the fact that within this whole lot of Fractional
parts. Themselves fractional parts that make up the mysterious
order of within the chaos, called "frikker-noise ratio.
Dalneshee developments Mandelbrot himself as described in
his book "The Fractal Geometry of Nature," published in 1983
year: "uchenye with great surprise and delight clarifies for
himself that many, many forms that they still had to
gidropodobnye described as similar to algae,
tangled, branched, etc., can now be studied and
described in strictly quantitative terms. "
And indeed, now that every day, there is increasing
information about the use of fractals in the most unexpected
areas Science that the most beautiful melodies obey fractal -
one and the same musical phrase can vary in their
countless times, gaining all the new paint. Biologists
found that the fern, cauliflower and broccoli, and many
other plants are a good examples of fractals,
because they have individual leaves resemble in shape all
plant as a whole, and besides all this can easily be described
mathematically. Doctors and Biophysics have discovered that when
simulation of the respiratory tract, cardiovascular and nervous
systems, they also faced with fractals. Even the thought
processes, turns out to have a certain amount of fractality.
That's good see, for example, encephalogram - recordings of
brain activity.
More examples of fractality in inanimate nature.
Brownian motion of molecules, turbulent fluid flow and
gas, all the diversity of mountain chains and the Cumulus clouds
zigzags of lightning and thunder acoustic - just some
examples of fractals in nature.
Even the star formation occurring in the giant
interstellar clouds, too, can be described by fractal
structures. Moreover, the formulas and methods that are used in
this description, are similar to those used in the analysis
processes occurring in the laboratory. So;
through fractals, scientists were able to clearly
observe the processes of birth of protostars, which in nature
occupy at least 20-30 million years.
... Here, in brief the content of articles, which dates back
92-th year. And what now?? Definitely we can say that
the study of fractals in progress. Relatively recently I
talked about the transfer of television, which explains
just the use of fractals in modern computer
technologies in the field of visualization and computer
graphics. Many of What was told, and retold to me naturally,
but here application of fractal filter I remember specifically.
The bottom line that a magnified image, which is naturally
divided into large square point - the essence of piklely,
applied fractal filter, after which the detail
zoom does not differ from the original,
down to the smallest detail and shades of colors.
In general, fractals are a very interesting topic, but here,
for some reason, little information about them ...
