http://www.ck12.org Chapter 7. Similarity
Fractals
A fractal is another self-similar object that is repeated at successively smaller scales. Below are the first three stages
of the Koch snowflake.
Example 2:Determine the number of edges and the perimeter of each snowflake.
TABLE7.6:
Stage 0 Stage 1 Stage 2
Number of Edges 3 12 48Edge Length (^11319)
Perimeter 3 4 489 = 5. 3
The Cantor Set
The Cantor set is another fractal that consists of dividing a segment into thirds and then erasing the middle third.
Review Questions
- Draw Stage 4 of the Cantor set.
- Use the Cantor Set to fill in the table below.
TABLE7.7:
Number of Segments Length of each Segment Total Length of the Seg-
ments
Stage 0 1 1 1Stage 1 (^21323)
Stage 2 (^41949)
Stage 3
Stage 4