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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
Do all fractals have an infinite perimeter and finite area?
yes! the best example would be the Koch snowflake.
you can find fractals downtown in albuquerque, new mexico. you can go to google and type fractal pics they are awsome to watch.
What are facts about fractals?
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).
How do you use fractal in a sentence?
A fractal is a geometric curve or figure such that each part of it has the same statistical character as the whole. An alternative definition is a curve which appears the same at any level of magnification.
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koch curve
How do fractals relate to math?
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).
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 they made.
One example is frost crystals that appear on a glass window.
In math we create these patterns for many reasons. One is just because they are very pretty.
But the also interest mathematicians. People who study calculus like them because they have certain very interesting properties. ( some of them do0.
One example is that of being everywhere continuous but nowhere differentiable.
It is not too important to understand exactly what it means, just to know that it is a very surprising result in math.
It turns out that fractals are important in studying complex numbers too. Something that most people would never guess. There are fractals called Julia sets named after a mathematician with the last name Julia.
I will post a link of a gallery of fractals. Many people enjoy looking at them. Now you know their beauty goes much deeper than just their looks!
It's called a Sierpinski triangle.
Is the Koch Snowflake a fractal?
Yes - as you "zoom in" on the sides of the snowflake, the same pattern occurs infinitely.
What do fractals have to do with real life?
Fractals are patterns that repeat at different scales and can be found throughout nature, such as in the branching of trees, the structure of snowflakes, and the formation of coastlines. They help scientists and mathematicians model complex structures and phenomena, including the distribution of galaxies and the growth patterns of plants. In technology, fractals are used in computer graphics, telecommunications, and even in analyzing financial markets, demonstrating their relevance across various fields in real life.
