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Fractals

Parent Category: Geometry
"Fractals are mathematical constructions of fractal geometry, a relatively new geometric form only discovered/defined in the 1970's by Benoit Mandelbrot who actually coined the term ""fractal"". Previously considered mathematical ""monsters"" fractals were largely ignored by mathematicians as they behaved in ways that were difficult to describe/define, in particular they were ""monster"" curves that were non-differentiable. Benoit Mandelbrot deliberately got a job at IBM in the 1970's so he could gain access to the computing power necessary to study these objects in more detail and since his initial studies Fractal Geometry has become part of every branch of science and given rise to the increasingly popular Fractal Art medium.
  object orient is a things that makes collaberating and has a communication between them, that are send via message
yes i think so because a fractal is an object that is self-similar all squares are similar; so are all cubes
yes! the best example would be the Koch snowflake.
    a curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or...
Either the koch snowflake or the Sierpinski triangle
  Complex mathmatic equations.
Press the "Run Script" button.. looks like a green "Play" button.. alternatively, F9.
Fractals are geometric shapes that you can break up into parts and each part has a property known as self similarity. This property simply means that each little part has the same general shape as the big part it came from. Fractals occur in nature so why cannot simply answer the question why were...
star wars and Jurassic Park
It really depends on the fractal, and there are many possible ways to define them. As an example, for the Mandelbrot set, a number of calculations involving complex numbers are done for each point in the complex plane, to determine whether a point is part of the set or not. However, other...
Yes. When broken down, the other tiny cubes resemble the large cube together, thus making it a fractal. Remember that a fractal is any a shape that can be split into parts, and the smaller parts resemble the whole.
The dragon curve was first described by Benoit Mandelbrot.
You can't have a complementary antonym for a noun. For example, could you tell me what the antonym for 'cat' is? And please don't say dog.
No.add And interestingly enough, apple seeds seldom breed true to the parent. If you find a desirable 'sport' on your apple tree, it may be propagated from the wood of that twig, not the seed.
  A fractal is a geometric shape that when zoomed in on, will look approximately the same as it did before. Fractal geometry is a more complex version of regular Euclidean geometry. Euclidean geometry included just circles, squares, triangles, hexagons, octagons and all other regular shapes....
There is an element of fractal property in the manner in which anartery divides into smaller vessels and these in turn to stillsmaller vessels and so on until you reach capillaries. And then,you have the reverse process of capillaries joining together toform veins which join up to form larger veins...
ungaluke theriyala enaku epudi theriyum.
Design computer textiles and graphics. Dot matrix was the first type of computer graphics
Fractals are situations where the geometry seems best approximated by an infinitely "branching" sequence - used, for example, in modeling trees. For work on fractals that I have done as a theoretician, I recommend the included links. I just happen to have an original answer, and I want to make it...
"Chaos theory" seems to be one of those misnomers that smell much more of Greek paganism than rational physics. It is safe to say that "chaos theory" was the last thing that Johannes Kepler needed in order to simplify astronomy for high-school students. Chaos theory (in my opinion) is more...
After a year of intensive music theory classes every weekday at 9 AM, hopefully I can explain it to you with the extent of my knowledge. This is how it works fractally. The piano is an accurate diatonic and chromatic representation of tones, so I will use it as an example in my next sentence....
They are used to model various situations where it is believed that some infinite "branching" effect best describes the geometry. For examples of how I have employed fractals as a theoretician, check out the "related links" included with this answer. I hope you like what you see.
Seperation of atomic structures including but not limited to non biological elements such as stone, rock, even water. It induces a weird sort of decay which literally rearranges atoms at times to form something completely different... different atoms, different structures and different material. In...
Personally i would buy the Arbor Axis Koa because its a much smoother ride but its for advanced riders so if its your first longboard its going to be so much easier to learn on the Sector 9 fractal but it all comes down to your personal preference!!
By their very nature fractals are infinite in extent.
Yes - as you "zoom in" on the sides of the snowflake, the same pattern occurs infinitely.
Fractals began to take shape (no pun intended) in the 17th century.
Their highest common factor is 18. Dividing both parts by that gives us 2 over 7.
Some examples: a coastline, the tributaries of a river, a branching tree, a snowflake. Some examples: a coastline, the tributaries of a river, a branching tree, a snowflake. Some examples: a coastline, the tributaries of a river, a branching tree, a snowflake. Some examples: a coastline, the...
Technically, you can't. The Koch snowflake is self-similar. So the perimeter is infinity.
Some common techniques for generating fractals would be to use iterated function systems, strange attractors, escape-time fractals, and random fractals.
It is sqrt(6^2 + 5^2) = sqrt(36+25) = sqrt(61) = 7.8102, approx.
There are a variety of online sites which contain pictures of fractal patterns and lists of places where fractal patterns can be seen in nature. The web domain FractalFoundation, for example, provides this service.
Benoit Mandlebrot was the first to discover fractal equations.
The Torus vector equilibrium is a vortex by which nature forms energy into matter. The Phi spiral also known as the Golden ratio is commonly found in nature. At this time there is no link between the torus vector equilibrium and the phi spiral, although a link between the two has not been...
  No, there is no relation between the two.
No, it is not.
1. It has a fine structure at arbitrarily small scales. 2.It is too irregular to be easily described in traditional Euclidean geometric language. 3.It is self-similar (at least approximately or stochastically).
A fractal in a 2-dimensional plane has a dimension between 1 and 2.
The Koch curve was first described in 1904.
Many things in the real world are approximately fractal orlogarithmic. For example, if you examine a shore line it will be awriggly line. Examine it at more detail and you will see a similarpattern but at a smaller scale. Even more detail and you still havethe same (or similar) pattern at yet more...
-- The shoreline of any coastal land is a fractal. -- The distant view of any mountain range is a fractal. -- Your eyes perceive changes in light brightness on a logarithmicscale. -- Your ears perceive changes in sound loudness on a logarithmicscale.
  == C++ ==   C++, a more advanced version of C, based on the C language, but also supporting object oriented programming features.
No. Although the area of every triangle is equal to half the area with the same base and height, only right angled triangles are half a rectangle.
The cast of Fractals - 2013 includes: Farrah Forke as Laurie Joe Lombardo as Frank Turi
The cast of Fractals - 1991 includes: Farrah Forke
An ovoid (egg-shape) is one possible answer. A smooth blob (to use a very technical term!) is another.
The Beauty of Fractals was created in 1986.
The ISBN of The Beauty of Fractals is 0-387-15851-0.
Fractal Analytics was created in 2000.
The population of Fractal Analytics is 250.
There is not enough information to provide an answer. You need to know the coordinates of three vertices before you can find the coordinates of the fourth. Otherwise, there are alternative solutions using translations, reflections and rotations.
Seymour the Fractal Cat was created in 1996-04.
Fractale was created in 2011.
Fractal Possession was created on 2007-05-02.
Ultra Fractal was created in 2006-05.
The Fractal Prince was created in 2012.
5/6 x 4/5 is 2/3.
When the middle third of a line segment is removed and repeated infinitely on the resulting line segments the result is the Cantor Set. When shifting to 2 dimensions, starting with a triangle, dividing it up into 4 similar smaller triangles and removing the middle triangle results in the Sierpinski...
Applications of fractal structures include:   computer generation of special effects animations  biological studies  ecological studies  improved transistor designs  urban growth studies  file compression algorithms  military camouflage  computer networks  etc.  
Light per se is not fractal, but I have done work as a theoretician that indicates that photons can interfere with one another to form fractal patterns. See the links for further information on my own investigations. I hope I have been a real help. (The first answer someone posted was "not spatial...
  What does > mean?
It is a shape that can be split into two parts and is one of those hipnotising patterns
  it would basicly be a sine wave that is declining simalarly to a fractal does, good life example is something bounceing up and down and slowing down till it stops or a sound that fades off.
    IN what?????????????? a cell? an organism? an eyelash? a leaf?   it all depends.   in each of these there are tens of hundreds of thousands of millions etc.   be more specific, then maybe we can answer your question.       your welcome,     the fractal twins  ...
A fractal by definition is actually a curve that has infinite length, like the Koch snowflake and Cantor set, to name a few.
a robot is only a machine and fractal is reconfigurable machine.
http://images.google.com/imgres?imgurl=http://www.astrolog.org/labyrnth/maze/fractal.gif&imgrefurl=http://www.astrolog.org/labyrnth/algrithm.htm&usg=__iHGZHvdLrs3xst49pNZyPrlwf7E=&h=513&w=513&sz=16&hl=en&start=4&um=1&tbnid=aWXIuk_zIRbOOM:&tbnh=131&tbnw=131...
If you look closely and carefully enough, nature is ALL fractals; snowflakes, leaves, tree branches, coastlines, everywhere.
  Benoît B. Mandelbrot[ is a French mathematician, best known as the father of fractal geometry
put your pencil to the paper and begin drawing a line, and never stop... (you are going need an infinitely large sheet of paper) * * * * *You do not need an infinitely large piece of paper. But you will need infinitely many pencils and an infinite amount of time!