7.7. Extension: Self-Similarity http://www.ck12.org
TABLE7.7:(continued)
Number of Segments Length of each Segment Total Length of the Seg-
ments
Stage 5- How many segments are in Stagen?
- What is the length of each segment in Stagen?
- Draw Stage 3 of the Koch snowflake.
- Fill in the table from Example 2 for Stage 3 of the Koch snowflake.
- A variation on the Sierpinski triangle is the Sierpinski carpet, which splits a square into 9 equal squares,
coloring the middle one only. Then, split the uncolored squares to get the next stage. Draw the first 3 stages
of this fractal. - How many shaded vs. unshaded squares are in each stage?
- Fractals are very common in nature. For example, a fern leaf is a fractal. As the leaves get closer to the end,
they get smaller and smaller. Find three other examples of fractals in nature. - Use the internet to explore fractals further. Write a paragraph about another example of a fractal in music, art
or another field that interests you.