Peano's Curve and Koch's Snowflake

Use the slider from n = 1 to n = 5 to see how Peano's Curve relates to Koch's Snowflake.

1. What are defining characteristics you see with Peano's Curve?
2. What type of mathematical function would you define Koch's Snowflake to be?
3. What do you think the next iteration (next n value) would look like? Why?

Through this construction the user should be able to see how Peano's Curve relates to Koch's Snowflake. They should see that it is drawing Koch's snowflake, a fractal, the more iterations it produces, thus making it appear to have fractal-like characteristics (recursive). The user should also be able to identify that with each iteration the length of the line gets larger, due to these recursive fractal properties. Along with that,
the user should identify Koch's Snowflake to be a fractal and understand that the next iteration would provide a more complex fractal of Koch's Snowflake.

Alycia Jacobson, 24 November 2013, Created with GeoGebra