How to Draw a Sierpinski Triangle

A Sierpinski triangle is several triangles in one.

A Sierpinksi Triangle is an example of fractal geometry (snowflakes are another example), a relatively recent language for describing complex forms found in nature. Sierpinki triangles are elegant to look at, yet extremely easy to draw. The Sierpinski Triangle was named after Polish mathematician Waclaw Sierpinski, who not only discovered its properties, but also provided us with a new perspective on viewing the world.

Things You'll Need

• Drawing paper
• Soft pencil

Instructions

Draw the base triangle

1. Draw an equilateral triangle with base parallel to the horizon.

2. Connect the midpoints of each side. You now have an inverted triangle within the first triangle.

3. Fill in the three exterior triangles. Leave the inverted triangle in the center white.

Create the first patterned triangle section

1. Draw two additional triangles following and identical to the instructions above.

2. Position one triangle with the top point touching the lower left side of the base of your original triangle.

3. Position the second triangle with the top point touching the lower right side of the original triangle's base. You now have one complete patterned section.

Draw two more patterned sections

1. Follow the procedure above, create two more patterned triangles identical to the one created by joining the triangles in Sections 1 and 2.

2. Position the first patterned triangle with the point touching the lower left side of the original triangle's base.

3. Position the second patterned triangle with the point touching the lower right side of the triangle above it. You now have three patterned triangles with a large white interior triangle.

References

• Sierpinski Triangle

Resources

• Math at Rice University