MAED 5352 : Patterns and Algebra assignment
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University of Texas Arlington
Patterns and Algebra (MAED 5352)
Added on 2020-05-01
MAED 5352 : Patterns and Algebra assignment
University of Texas Arlington
Patterns and Algebra (MAED 5352)
Added on 2020-05-01
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Running head: FractalsFractals.Fractals are patterns that to not have an end, which are very complex and they are the same acrossdifferent scales at a specific part. Fractals explain the objects that occur naturally. The fractals that are artificially made show same shapes at increasingly smaller patterns. Unlike normal shapes like rectangle and circle that are termed as smooth, Fractals are normally rough and complex. According to Benoit Mandelbrot [ CITATION Jun08 \l 1033 ], he said that Fractals are shapes that are repeated if divided into small parts.Modifications made to present the activity.In this case the “students” are teenagers that were presented to. The teenage group are friends in my neighborhood and they have learnt in school about geometry. During the activities with the triangle grid, we drew the triangle with different colors making them smaller and smaller, and coloring each step triangles with different colors to differentiate the triangles made after every step done. We made sure that all new triangles are divided into equal shapes.Discoveries made during the activityMy students discovered;1.The smaller triangle shapes being made from the bigger triangle are the same in shape and all are equals when divided at the center. Following this discovery, the idea of Fractals shows that large structures are made by small equal shapes to make one big complex structure. The nature also have many fractal shapes, example the fern plant.2.They further discovered that the scale of each new iteration is increasing at the ratio of one is to two in every new iteration. This shows that in each iteration, there is a completerecurrence of the first shape.3.During the activity, the students discovered that the idea of Fractals was discovered by Benoit Mandelbrot in the 1970’s, although they were in existence for a long time.The General pattern.The general fractal pattern is set to a certain n sequence whereby, a particular pattern is followed as shown below (zn), where zn+1=zn2+c. Where c is a constant that is not changing and n is the n column showing the new pattern that has been created after several iterations.[ CITATION Sar14 \l 1033 ]Additional information.The study of Fractal has helped a lot especially in scientific research for example the study in biology of how bacteria’s multiplies. Engineers also are not left behind because they are using the idea of fractals to do practical engineering problems in their field. Therefore the study of fractals generally has helped a lotSnowflakes use the idea of Fractals as they form in water.Generally, the idea of Fractals are all over around us.
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