The Koch Snowflake

   Introduction

  Why study fractals?
    What's so hot about
    fractals, anyway?

  Making fractals
    Sierpinski Triangle
         Using Java
         Math questions
         Sierpinski Meets Pascal
    Jurassic Park Fractal
         Using JAVA
         It grows complex
         Real first iteration
         Encoding the fractal
         World's Largest
    Koch Snowflake
         Using Java
         Infinite perimeter
         Finite area
         Anti-Snowflake
            Using Java

  Fractal Properties
    Self-similarity
    Fractional dimension
    Formation by iteration

  For Teachers
    Teachers' Notes
    Teacher-to-Teacher

  Comments
    My fractals mail
    Send fractals mail

  Fractals on the Web
    The Math Forum

  Other Math Lessons
    by Cynthia Lanius

You may print and use this triangle grid paper to help you with this drawing.

Step One.

Start with a large equilateral triangle.

Step Two.

Make a Star.
1. Divide one side of the triangle into three equal parts and remove the middle section.

2. Replace it with two lines the same length as the section you removed.

3. Do this to all three sides of the triangle.

Do it again and again.

Do it infinitely many times and you have a fractal.

Want to take a long, careful look at what it looks like?

See a few of the steps below.