| First, here is an animation
that may help us interpret the geometry of fractal dimension. |
| Today we consider some algebraic relations between dimensions of
shapes and the dimensions of their pieces, at least in some special cases. Also, we consider
some examples of computing dimensions in physical settings. |
| As an aid to calculation, here are some of the
algebraic properties
of dimensions: how the dimensions of fractals are related to the dimensions
of their unions, products, and intersections. |
| Here
are some examples of calculating dimensions of natural objects. Can dimension express the
evolutionary complexity of sea shells, the roughness of coastlines and mountains, the distribution
of earthquakes? |
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