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Fractals

Chapter 10 sec 7. Fractals. What is fractal geometry? That describes real-life objects and patterns more accurately than we can by using Euclidean geometry and hat has many important real-life applications. Fractal geometry. Def. of an object is a number D that satisfies the equation

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Fractals

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  1. Chapter 10 sec 7 Fractals

  2. What is fractal geometry? • That describes real-life objects and patterns more accurately than we can by using Euclidean geometry and hat has many important real-life applications. Fractal geometry

  3. Def. • of an object is a number D that satisfies the equation • Where s is a scaling factor and n is the amount by which the quantity we are measuring (length, area, vol.) of the object changes when we apply the scaling factor to the object. Fractal dimension

  4. Is a line segment, then it is divided into three equal parts. It forms into a equilateral triangle. This process keeps going on. Koch curve

  5. Step 1 Step 0 Step 2 Step 3

  6. Assume that the length of the line segment is 1 in step 0. Each of the line segment in step 1 is Therefore, the Koch curve is 4/3 as long as the original line segment. In step 2, each line segment is now

  7. In each successive step, the curve is 4/3 as long as the curve in the previous step. This means that the curve’s length keeps growing larger and larger as we construct further steps of the curve.

  8. At step 40, we would find that the length of the Koch curve is , which is slightly more than 99,437 units long.

  9. http://www.youtube.com/watch?v=JdMgvSWSKZI

  10. Use the mathematica files

  11. Some fractal art

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