Fractal Folds

Background

Cantor Middle Thirds Set Construction

Start with a line segment of length 1.

The generating process is to remove the open middle third of each line segment.

Applying the process to the segment of length 1 gives two segments of length 1/3.

Applying the process to each of these segments gives four segments of length 1/9.

Continue.

The initial segment and the first three stages of the Cantor middle thirds set.

The Cantor middle thirds set is the limit of this process.

Equivalently, it is the intersection of all the stages.

The Cantor middle thirds set has several interesting properties.

It contains no intervals.

Every point is a limit point.

The endpoints of the removed intervals are in the Cantor set, yet most of the points of the Cantor set are not endpoints.

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