Thursday, Sept 27, 2012

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?

Homework 4

Practice homework

Homework 3 Solutions