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Check out this video of the Featherino Fractal. 

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Check out this video of the Featherino Fractal. 

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So what exactly IS a fractal? Check out the link below.

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Use the internet to find an example of a fractal in nature.  Post a picture here on the class Fractal Padlet so your peers can see what you found.

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You'll need scissors, a ruler, markers or colored pencils, and a copy the handout below.  If you can't print, ask your teacher for to print a copy for you.

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Draw your own Sierpenski's Triangle using these instructions:

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Draw your own Sierpenski's Triangle using these instructions:

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Learn to draw a fractal Sierpinski triangle and combine yours with others to make a bigger fractal triangle

The Sierpinski triangle activity illustrates the fundamental principles of fractals - how a pattern can repeat again and again at different scales and how this complex shape can be formed by simple repetition. Each students makes his/her own fractal triangle composed of smaller and smaller triangles. Next, students cut out their own triangle and assemble them into a larger fractal pattern that replicates the same shape.

You can use our curriculum for free or can hire us to come to your school to lead fun, hands-on activities. Check out our educa tion and outreach page!

Ages: 1st - 8th grades

Materials:
Markers, crayons or colored pencils
Scissors
Ruler and protractor for older grades
Triangle worksheet

Time:
Approx 30-45 minutes

The template is both on page 6 of the teacher instructions and on page 2 of the student worksheet.
DOWNLOAD THE INSTRUCTIONS DOWNLOAD THE WORKSHEET ANSWER KEY FOR TEACHERS
DOWNLOAD THE TEMPLATE TO DRAW AND COLOR IN - just the blank triangle

DOWNLOAD THE TEMPLATE TO COLOR IN - the Sierpinski triangle drawn out

Teachers - if you have comments or suggestions about this or any of our other fractivities, please email us at

See what people are saying about this activity on our feedback page!

Orient the template so the triangle points up. Dots show the midpoints of the edges, half way between the corners. Connect the dots as shown below to form a new triangle, pointing down. Color it in.

You are left now with three white triangles. Find the midpoints of each of these three triangles, connect them, and color in the resulting downward-pointing triangles.

Each of the three triangles now turns into three smaller triangles, leaving nine small white triangles.

Connect the midpoints of each of the nine white triangles to form 27 smaller downward-pointing triangles. Color those in.

Continue this process for as long as you like, creating triangles in factors of three: 81, 243 or even 729! Use the student worksheet to explore the math behind this and work on mathematical notation.

Be as creative as you wish in coloring the triangles.

When you're done, cut the big triangle out and write your name on the back.

Next, join your fractal triangle with two other fractal triangles to form a bigger triangle. Then add two more groups of three triangles to form a bigger triangle made of nine triangles. If you're doing this with your whole class, you can join three groups of nine to make a giant triangle made of 27 individual triangles. If you want to continue, three classes could join all their 81 triangles into an even bigger one. And why stop there???

If you do this project with your class, please consider contributing your fractal triangles to our Giant Fractal Trianglethon Project to help make the world's largest Sierpinski Triangle! On April 10, 2011, we built an 8th order fractal triangle, made of 6,561 triangles. Help us reach the next level, and build one out of 19,683 triangles!

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Learn to draw a fractal Sierpinski triangle and combine yours with others to make a bigger fractal triangle The Sierpinski triangle activity illustrates the fundamental principles of fractals - how a pattern can repeat again and again at different scales and how this complex shape can be formed by simple repetition.

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This time, you need a long, thin strip of paper. Using one of the long sheets of construction paper, cut a strip along the long side about 1 inch wide.  Or you can use regular paper and tape strips together. Watch the video below and follow along.

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More iterations of Jurassic Park Fractal

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More iterations of Jurassic Park Fractal

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What would happen if you folded your paper 5 times instead of 4?  6 times?  Try it. Click the next link to see what repeated iterations would look like. If you want to, you can even try to draw it.

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These high school students won an award for creating this model.

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You're going to need more paper,(triangular graph paper is great if you have it), a ruler, and a pencil with a good eraser.  Precision is important with this one! Watch this video to show you have to draw this fractal.

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Equilateral triangles, fractals and Koch's snowflake

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Shodor > Interactivate > Activities > Koch's Snowflake

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A really interesting characteristic of the Koch Snowflake is its perimeter.

Ordinarily, when you increase the perimeter of a geometric figure, you also increase its area. If you have a square with a huge perimeter, it also has a huge area. But wait till you see what happens when you investigate the perimeter of a Koch Snowflake fractal!

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In this video, we explore the topic of the Koch Snowflake; a two-dimensional shape with fixed area but infinite perimeter. ~~~ Support me on Patreon! https://www.patreon.com/randydobson ~~~ I'd like to show you a shape that has some really interesting properties.

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How are fractals used in science, technology, and engineering?  Create a presentation in Google and post a link in our class Fractal Padlet.

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Sierpinski's Triangle + Pascal's Triangle

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Sierpinski's Triangle + Pascal's Triangle

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Investigate Pascal's Sierpinski's Triangle.

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Investigate Fractals in the form of trees.

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Investigate Fractals in the form of trees.

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You may not have time to complete everything. Print pages 1-3 and then do more if you have time.

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Think about the word "recursive."  How might we apply that to poetry or music?
Listen for an example.

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Compose your own recursive poem or song using Google Docs. Post a link below to share with the group!

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Compare the triangle you stated with in step 1 to later iterations. Think about the following questions:

1. What fraction of the triangle did you NOT color out in the first iteration?

2. What fraction of the triangle in the 2nd iteration is NOT colored?

3. What fraction did you NOT color in the the 3rd iteration ?

4. Do you see a pattern here?

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Use the "+" button to answer the following question below:

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Use the "+" button to answer the following question below:

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What fractional pattern did you see?  What are your predictions?

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What  do you think it means to say "An infinite perimeter encloses a fixed area?"

Use the "+" button below to answer this question.