Similarity Dimension

Example Calculations

The shape can be decomposed into

N = 7 pieces, each scaled by a factor of r = 1/3.

Consequently,

d_s = Log(7)/Log(3).

Note this fractal is gotten from the previous example by moving the bottom middle (green) piece.

Comparing this and the previous example emphasizes that the dimension is determined by the number and size of the pieces, not by their locations. (Except some care must be taken if the pieces overlap significantly.)

Return to Similarity Dimension Exercises.