# The Sierpinski Triangle

 Table of Contents

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.
Step One

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

How many equilateral triangles do you now have?

Cut out the triangle in the center.

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.

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

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 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!

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/
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