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Math Letters Presentation

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Harry Stoltz

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Letter 7: Fractals

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Letter 7: Fractals (cont.)

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Letter 7: Fractals (cont.)

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Letter 7: Fractals Activity

  • What kinds of fractals can you make?

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  1. On a piece of paper, start with some shape.
  2. Come up with a rule! Be creative.
  3. Repeat a couple times.
  4. Have you made a fractal?

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Letter 7: Fractals Activity II

  • Let’s play a "chaos game”
  • On a piece of paper, start with three points which form the vertices of an equilateral triangle.
  • Graph a random point in the triangle
  • The game is progressed by applying the following rules:
    1. Randomly select one of the 3 base points.
    2. Move half the distance from the current point to the selected base point, and draw a point.
    3. The new point becomes the current point. Repeat from step 1.

Our triangle, with the first point

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Letter 7: Another Fractals Activity

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Why does the Sierpinski triangle arise from the chaos game? (Boston University)

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Letter 7: Fractals Activity

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Letter 7: Fractals Activity

  • Can you modify the chaos game to make a cool fractal?
  • Some ideas:
    • Start with a square
    • Place the new points somewhere other than the midpoint

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