0
Fractals
"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.
203 Questions
How do you draw freehand fractal?
ruler, protractor, pencil, paper, calculator or knowledge of calculus , think smooth think slow think even, practice or artistic ability both is better.
0 what are characteristics of efficient market hypothesis?
Multiply the previous number of segments by 2.
The study of fractals has been around since the Greeks first constructed them in the first century?
False.
Apex.
What are examples of fractals in everyday life?
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 because of the fractal dimension.
Is an apple seed a fractal of an apple tree?
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.
How would you find the vertices of an image of a figure were rotated 270 degrees clockwise?
The image of a vertex at (x, y) would be (-y, x).
How do fractals and logarithms relate to the real world?
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 more detail. Computer-aided graphics use this property to generate landscapes: storing a small amount of "data" and replicating it at different scales is far easier than storing masses of data.
The logarithmic function also has this scale-invariant property. If you are interested, read the attached link about Benford's Law. The article does not require much mathematical knowledge - only curiosity.
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 definitions are possible as well.
How do fractals explain nature?
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 known.
How many triangles can fit in an rectangle?
Infinitely many. Each triangle can be divided in two and then that triangle can be divided and so on.
How do you cut a rectangle of 12x16 into triangles?
Simply make a cut from any point on one side to any point on an adjacent side.
The answer is b.
What year was fractal first used?
Fractals began to take shape (no pun intended) in the 17th century.
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.
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.
