Similarity Dimension/Examples

Examples of Similarity Dimensions

Cantor Set

The similarity dimension $D$ of the Cantor set is given by:

$D = \dfrac {\ln 2} {\ln 3}$

Closed Unit Interval

The similarity dimension of the closed unit interval:

$I = \closedint 0 1$

is $1$.

Koch Snowflake

The similarity dimension $D$ of the Koch snowflake is given by:

$D = \dfrac {\ln 4} {\ln 3}$

Unit Square

The similarity dimension of the unit square is $2$.