The Fun Filled Fractal Phenomenon
A fractal is a type of geometric figure. It is generated by starting with a very simple pattern such as a triangle and, through the application of many repeated rules, adding to the figure to make it more complicated. Often, an input will be entered into a recursive function and it will yield an output. This output is then inserted back into the function as an input and the process is repeated infinitely. Fractals often exhibit self-similarity. This means that each small section of the fractal can be viewed as a reduced-scale replica of the whole. Some famous fractals include Sierpinski's triangle, Koch's snowflake and the length of a coastline. Fractals were brought to the public's attention by the work of French mathematician Benoit B. Mandelbrot in the 1970's. Mandelbrot discovered how to calculate fractal dimensions. The formula for fractal dimension is N=2D where N equals the number of copies of the original figure, which is calculated by doubling its size and D is the dimension. Mandelbrot named his creations fractals because each part is a fraction of the whole figure. The Chaos Theory describes the complex and unpredictable motion of systems that are sensitive to their in
Lampton, Christopher, Science of Chaos (New York: Franklin Watts, 1992) 9-16. "Choas Theory," Encarta Encyclopedia, 2000. Fractal research can be used to predict how complicated organ systems in the body will respond to changes. This is important for understanding how to treat diseases. A body as a whole is a fractal. It is a group of dissimilar systems working together, which are composed of groups of dissimilar organs working together, which, in turn, are composed of groups of dissimilar tissues working together, which is a group of dissimilar cells working together, which is a group of dissimilar organelles working together. The body begins with the creation of cell organelles that are formed together to make a cell. These cells, as stated above, duplicate to form tissues, which duplicate to form organs and so on until a human body is conceived. "Fractals," Encarta Encyclopedia, 2000. A real life example of self-similarity is a tree. The tree has a trunk on which limbs grow. Branches grow from the limbs, and twigs grow from the branches, which is followed by sticks on the twigs and so on. The sticks growing on the twigs are just a smaller version of the twigs growing on the branches, which are a smaller version of the branches growing on the limbs, which are a smaller version of the limbs growing on the trees. Another example is a universe, which is composed of a collection of spinning galaxies, which are composed of a collection of spinning solar systems which is a collection of spinning plants and so on. Each step is self-similar to the universe. Finally, a cloud exhibits self-similarity. A cumulus cloud is a collection of smaller puffs, which, in turn, are a compilation of smaller puffs and so on. Each puff is a smaller replica of the large puff. itial conditions. Chaotic systems follow precise laws but the
Some common words found in the essay are:
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