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The Fun Filled Fractal Phenome - Online Term Paper

The Fun Filled Fractal Phenome

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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 ...

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to their initial conditions. Chaotic systems follow precise laws but their irregular behavior can appear to be random to the casual observer. For example, weather is a chaotic system. If the rays of the sun bounce off the hood of a car in a certain way, causing a breeze, the breeze could blow a leave off a tree, which starts a series of additional events that could alter the weather in some other part of the world. Chaos can be related to fractals. In a fractal if one tiny change occurs in a repeated pattern, the entire fractal will change. The above picture is an example of a strange attractor that charts the trajectory of a system in chaotic motion. It is a fractal. The fractal exhibiting chaos is predictably unpredictable. This is because, in a chaotic system, it is predictable that there will be minute changes that will alter the entire shape.
Koch's snowflake, (above ) exhibits the concept of an infinite perimeter with a finite area. Koch's snowflake is created by ...

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The Fun Filled Fractal Phenome. (2008, July 24). Retrieved December 23, 2024, from http://www.essayworld.com/essays/The-Fun-Filled-Fractal-Phenome/87234

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PAPER DETAILS

Added: 7/24/2008 01:40:45 AM
Category: Miscellaneous
Type: Free Paper
Words: 1199
Pages: 5

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