Fractals/Introductory Examples

There are several old geometric constructions for fractals in one- and two-dimensions that it is useful for the reader to become acquainted with. These are simple in that they can be constructed with no prior knowledge of analysis, algebra or fractal geometry.

Cantor set

Visual description of Cantor Set (seven iterations)

Construction

1. Take a segment of the real line and divide it into three equal parts. Remove the middle part.
2. Take the remaining two lines, divide them into three parts and remove the middle parts.
3. Repeat this till there is only a set of discrete and unconnected numbers.

This set is called the cantor set.