# Exercises for Chaos Under Control

## Chapter 3: A Dimension Primer

2. Can a fractal in the plane ever have a dimension greater than 2?
Explain your answer.

3. Imagine a version of the Cantor MTS in three dimensions:
start with a 1 x 1 x 1 cube and remove middle third slices so only eight
little cubes (1/3 x 1/3 x 1/3) remain, one at each corner of the original cube.
The first few stages are animated here.
Try sketching the first stage in the construction. Repeat this process for
each of these little cubes, and continue. What is the dimension of the
resulting Cantor MTS in space? Answer

Return to Chapter 3 Exercises

Return to Chapter3 exercises:
Simplicity and Complexity in Classical Geometry

Go to Chapter3 exercises:The Logarithm Function

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