Cynthia Lanius

Sierpinski TriangleThe Sierpinski Triangle

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Table of Contents

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

  Awards
    This Site has received

   
Let's make a famous fractal called the Sierpinski Triangle.

*You may print and use this triangular gridpaper.

Step One

Draw an equilateral triangle with sides of 2 triangle lengths each.
Connect the midpoints of each side.

Triangle

How many equilateral triangles do you now have?

Cut out the triangle in the center.

Step One

Step Two

Draw another equilateral triangle with sides of 4 triangle lengths each. Connect the midpoints of the sides and cut out the triangle in the center as before.

Step Two

Notice the three small triangles that also need to be cut out in each of the three triangles on each corner - three more holes.

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Step Three

Draw an equilateral triangle with sides of 8 triangle lengths each. Follow the same procedure as before, making sure to follow the cutting pattern.

Step Three
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Step Four

For this one, you'll need a larger paper, or cut smaller triangles. Follow the above pattern and complete the fourth stage of the Sierpinski Triangle. Use your artistic creativity and shade the triangles in interesting color patterns. Does your figure look like this one? Then you are correct!

Step Four
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You may obtain a print version of this page.

lanius@math.rice.edu
Copyright 1996-2009 Cynthia Lanius

URL http://math.rice.edu/~lanius/fractals/