Fractals
Fractals have been one of the tools used in Euclidean geometry to explain the abnormal shapes in nature. Fractals are able to explain the irregular shapes that are a far cry from the normal circle or square. It is an object of symmetry that uses components to create the picture of a self-similar entity.
Fractals first appeared on the scene in 1918 due to the mathematician, Felix Hausdroff. A Poland mathematician by the name of Beniot B. Mandelbrot began the term fractals. Fractals originated from the Latin term fractus meaning broken or fractured. It is a series of self-similar images repeated; The Koch snowflake, the Mandelbrot set, the Julia set and the Box fractal are many examples. The idea of a fractal is a pattern of repetitive images of the entire picture. When magnified upon, the image continues to look the same and builds upon the whole picture. “A key characteristic of fractals is fractal dimension.” [http://www.reference.com/browse/wiki/Fractal] This is the parameter of the fractal that uses fractions or nonintergers. “The table below shows the complexity of a figure as it increases its dimension.” [http://library.thinkquest.org/26242/full/index.html.]
F A finite number greater than 0
I An infinite number
Dimension Num of Points Length Area Volume
D = 0 F 0 0 0
0 < D < 1 I 0 0 0
D = 1 I F 0 0
1 < D < 2 I I 0 0
D = 2 I I F 0
2 < D < 3 I I I 0
D = 3 I I I F
[http://library.thinkquest.org/26242/full/index.html.]
Fractals are most often found in nature where the patterns aren’t exactly self-similar. These fractals are known as stochastic. This can be seen in tree bark, leaves, and snowflakes. All fractals aren’t exactly self-similar, such as the Julia set, or stochastic but are random or statistical. These fractals involve a numerical measure that is “preserved across the scale.” [http://www.reference.com/browse/wiki/Fractal] Fractals are used in an assortment of fields such as computer programming, art, nature, astronomy, molecules, and the
Fractals first appeared on the scene in 1918 due to the mathematician, Felix Hausdroff. A Poland mathematician by the name of Beniot B. Mandelbrot began the term fractals. Fractals originated from the Latin term fractus meaning broken or fractured. It is a series of self-similar images repeated; The Koch snowflake, the Mandelbrot set, the Julia set and the Box fractal are many examples. The idea of a fractal is a pattern of repetitive images of the entire picture. When magnified upon, the image continues to look the same and builds upon the whole picture. “A key characteristic of fractals is fractal dimension.” [http://www.reference.com/browse/wiki/Fractal] This is the parameter of the fractal that uses fractions or nonintergers. “The table below shows the complexity of a figure as it increases its dimension.” [http://library.thinkquest.org/26242/full/index.html.]
F A finite number greater than 0
I An infinite number
Dimension Num of Points Length Area Volume
D = 0 F 0 0 0
0 < D < 1 I 0 0 0
D = 1 I F 0 0
1 < D < 2 I I 0 0
D = 2 I I F 0
2 < D < 3 I I I 0
D = 3 I I I F
[http://library.thinkquest.org/26242/full/index.html.]
Fractals are most often found in nature where the patterns aren’t exactly self-similar. These fractals are known as stochastic. This can be seen in tree bark, leaves, and snowflakes. All fractals aren’t exactly self-similar, such as the Julia set, or stochastic but are random or statistical. These fractals involve a numerical measure that is “preserved across the scale.” [http://www.reference.com/browse/wiki/Fractal] Fractals are used in an assortment of fields such as computer programming, art, nature, astronomy, molecules, and the
Bibliography: “Fractal.” Wikipedia. The free encyclopedia. 31 Mar. 2008. <Reference.com http://www.reference.com/browse/wiki/Fractal>. “Fractal.” Encyclopedia Britannica. 2008. Encyclopedia Britannica Online School Edition. 1 April 2008. http://school.eb.com/eb/article-9035083. Fractals Unleashed. 1 April 2008. http://library.thinkquest.org/26242/full/index.html.