A simple geometric substitution leads to a jagged fractal much like a coastline In this exercise, students learn to transform a simple shape into a complex fractal curve by repeating the same operation at smaller and smaller scales and track changes to the perimeter of the object at each step. The resulting shape is highly […]
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Fractal Trees
Measure the ratios and angles of a tree’s branches to uncover its fractal structure In this activity, we use the natural fractal branching of a tree to explore quotients and ratios in a simple, tangible way. We also use tools such as rulers and protractors to measure lengths and angles, seeing how mathematical a complicated […]
Watersheds and Rivers
Learn about the fractal nature of rivers, what a watershed is and use your creativity to produce a fractal design In this exercise, students learn about fractal rivers, create their own watershed using a spray bottle and a plastic trash bag, and discover what a watershed is. This activity wraps up with students creating their […]
Fractal Tetrahedrons
Teams of students learn to build a fractal tetrahedron made of toothpicks and mini-marshmallows Each student creates his/her own fractal tetrahedron of six toothpicks four mini-marshmallows and then combines four individual tetrahedrons to form a larger tetrahedron. Four of those can be combined to make a bigger tetrahedron and so on. You can use our […]
Educators’ Guide
We’ve created a 20-page educators’ guide intended to accompany our planetarium fractal shows. The guide explains what fractals are and illustrates examples of fractals in nature and mathematics. It includes two fractal activities (Fractivities) to share with students and also contains a list of national science and math educational standards addressed by fractals. Download the […]
Fractal Trianglethon
Help us Create the World’s Largest Fractal Sierpinski Triangle! Every year we build a giant fractal triangle made of thousands of individual fractals triangles made by students all over the world. A few years ago, we constructed the 8th order version of this fractal, comprised of 3^8 individual triangles (6,561). And we’re still growing! Our […]
Fractal Scavenger Hunt
Explore the outdoors and discover fractal shapes in the nature world 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 education and outreach page! Ages: 1st-12th grades Materials: None needed. Optional notebook and pencil, digital camera Time: Approx 30-45 minutes; could […]
Fractal Cutout Card
Cut out a 3-dimensional fractal and turn it into a pop-up card Students make a 3-dimensional fractal cutout card by repeating a simple process of cutting and folding. They can turn their cutout into a fractal popup greeting card, decorate it artistically and share the lessons of fractals with others. Although it is formed by […]
Fractal Triangle
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 […]
What are Fractals?
A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. […]