Fractals and dimension

What is the dimension of a figure? It is natural to say that a segment is 1-dimensional, a rectangle 2-dimensional, and a box 3-dimensional. But what about figures that are not this simple?

In this discussion we talked about figures that are self-similar, which means that it is the same or almost the same as a smaller part of itself. For examples we looked at simple shapes such as rectangles and at more interesting ones such as the Koch snowflake and the Sierpinksi triangle:

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We found that in each case it was possible to assign a dimension to these figures, and that the dimension was fractional, in fact between 1 and 2!

Check out the handout from the session!

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