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Fractals

~200 answered questions
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.
A fractal by definition is actually a curve that has infinite length, like the Koch snowflake and Cantor set, to name a few.
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Fractals are commonly used for digitally modeling irregular patterns and structures in nature. They are also very useful for image compression, producing an enlarged picture with no pixilation.
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Press the "Run Script" button.. looks like a green "Play" button.. alternatively, F9.
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"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 appropri…
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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. Musi…
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Technically, you can't. The Koch snowflake is self-similar. So the perimeter is infinity.
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Benoit Mandlebrot was the first to discover fractal equations.
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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 b…
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It is a shape that can be split into two parts and is one of those hipnotising patterns
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The study of fractals is a part of mathematics. So fractals are a component of mathematics.
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a robot is only a machine and fractal is reconfigurable machine.
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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…
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If you look closely and carefully enough, nature is ALL fractals; snowflakes, leaves, tree branches, coastlines, everywhere.
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Self-similarity.
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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!
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Fractals are generated from recursive mathematical equations, this is why you can zoom-in on them infinitely and they will continue to repeat themselves (this is also why they are so computationally intensive)
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Benoit Mandelbrot is the man who is usually credited to have discovered fractals in the year 1975. He was the first person to use this word and was also the first man to represent them in visual form. But history also shows that some facts about fractals were known to mathematicians as early as the …
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They were first studied in the 17th century by Leibniz.
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No, they are not.
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ruler, protractor, pencil, paper, calculator or knowledge of calculus , think smooth think slow think even, practice or artistic ability both is better.
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I am a kid, so I might not nail it, but some examples are the dragon curve and julia set.
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You can never draw a fractal because it is an infinitely replicating pattern. Unlike the decimal representation of a number, for example 1/3 where you can put a dot over the 3 to indicate the fact that the digit recurs infinitely many times, there is no short-cut available for fractals. To draw an…
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you can find fractals downtown in albuquerque, new mexico. you can go to google and type fractal pics they are awsome to watch.
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because in fractal coding you save Coefficients of image blocks instead of values of block pixels. decoding starts from initial image and Coefficients applied on it. so the initial image can have any resolution
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Fractals can be generated with computer programs like Sterling or Apophysis. Both of these are freeware you can easily download. There are other programs, like Ultra Fractal and Tierazon, as well. With Sterling, you are given a default fractal that you can transform using various modes, and then zoo…
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Fractals are a special kind of curve. They are space filling curves and have dimensions that are between those of a line (D = 1) and an area (D = 2).
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Sierpinski's Triangle Sierpinski's Carpet The Wheel of Theodorus Mandelbrot Julia Set Koch Snowflake ...Just to name a few(:
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Discovered
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Examples of fractals in everyday life would be for example a fern. A fern is a type of leaf with a certain pattern. This pattern is the fractal because as you zoom in on the fern the pattern remains the same. It is the same thing over and over again no matter how far you look into it. This happens b…
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Fractals were discovered in 1975 by a scientist names Benoit Mandelbrot.
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Fractals that which includes the fourth dimension and with which we can identify that our body's veins and nature are self similar.
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A fractal is a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole (self similar).The term "fractal" was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured…
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yes i think so because a fractal is an object that is self-similar all squares are similar; so are all cubes
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yes! the best example would be the Koch snowflake.
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Either the koch snowflake or the Sierpinski triangle
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Multiply the previous number of segments by 2multiply the previous number of segments by 2
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Sierpinski gasket
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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 …
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star wars and Jurassic Park
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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 definition…
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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.
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The dragon curve was first described by Benoit Mandelbrot.
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There is no minimum number - it is simply not possible. Given any n points in 2-dimensional space, it is possible to find a polynomial of order (n-1) that will generate a curve going through each of those points. There are other functions which will also do the trick. So, given any number of points,…
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The Julia can be generated by a quadratic equation in the complex plane. Select a complex number c. Then for a point z in the plane, carry out the iteration, zn+1 = zn2 + c. Colour-code the point according to how many iterations are required before its magnitude exceeds any given threshold. Repeat f…
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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.
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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.
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There is an element of fractal property in the manner in which an artery divides into smaller vessels and these in turn to still smaller vessels and so on until you reach capillaries. And then, you have the reverse process of capillaries joining together to form veins which join up to form larger ve…
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No, it is not.
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ungaluke theriyala enaku epudi theriyum.
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Design computer textiles and graphics. Dot matrix was the first type of computer graphics
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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 k…
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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.
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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 …
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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!!
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By their very nature fractals are infinite in extent.
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Yes - as you "zoom in" on the sides of the snowflake, the same pattern occurs infinitely.
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Fractals began to take shape (no pun intended) in the 17th century.
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Their highest common factor is 18. Dividing both parts by that gives us 2 over 7.
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No.
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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 tributarie…
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Some common techniques for generating fractals would be to use iterated function systems, strange attractors, escape-time fractals, and random fractals.
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It is sqrt(6^2 + 5^2) = sqrt(36+25) = sqrt(61) = 7.8102, approx.
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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.
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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 disprove…
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No, it is not.
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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).
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A fractal in a 2-dimensional plane has a dimension between 1 and 2.
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The Koch curve was first described in 1904.
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Many things in the real world are approximately fractal or logarithmic. For example, if you examine a shore line it will be a wriggly line. Examine it at more detail and you will see a similar pattern but at a smaller scale. Even more detail and you still have the same (or similar) pattern at yet mo…
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-- 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 logarithmic scale. -- Your ears perceive changes in sound loudness on a logarithmic scale.
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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.
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The cast of Fractals - 2013 includes: Farrah Forke as Laurie Joe Lombardo as Frank Turi
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The cast of Fractals - 1991 includes: Farrah Forke
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An ovoid (egg-shape) is one possible answer. A smooth blob (to use a very technical term!) is another.
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Not necessarily. It can have 6 rectangular faces.
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