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# The Fun Filled Fractal Phenomenon

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 Sierpinskis triangle Kochs snowflake and the length of a coastline Fractals were brought to the publics attention by the work of French mathematician Benoit B Mandelbrot in the 1970s Mandelbrot discovered how to calculate fractal dimensions The formula for fractal dimension is N2D 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 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

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