Fractal Activity #1

Creating the Koch snowflake

STEP 1
Start with an equilateral triangle:

STEP 2

Replace all line segments in the following way:

is replaced with
so that the new section points outwards.

After one replacement, the new curve should look like this:

STEP 3

Repeat Step 2 ad infinitum to create the Koch snowflake.
 

THINGS TO THINK ABOUT

1. How long is the perimeter of the Koch snowflake?
2. What is the area contained inside the Koch snowflake?
3. Discuss the following statement: ``The Koch snowflake has a boundary that is spiky everywhere."
 

This page is maintained by James Ong.

Last edited: 1 October 2002