Paper Ball and Bean Bag Dimensions

Answers

10. The paper ball experiments produce fractals. Recall often a fratal is as well characterized by what is removed as it is by what remains. For example, the Sierpinski gasket can be constructed by specifying the triangles removed: 1 of side length 1/2, 3 of side length 1/4, 9 of side length 1/8, 27 of side length 1/16, and so on. Crumpling paper to form a paper ball produces a range of sizes of holes. The slice of exercise 6 reveals a few large holes, more medium holes, many more small holes, very many very small holes, and so on. The scaling of hole number and size is responsible for the fractal structure of the paper ball.

The close packing of nearly uniform size beans in bean bags leaves spaces of about the same size. This is no more fractal than are the red squares on a chess board.

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