• IME
• Tucson Teachers' Circle

Ginny Bohme presented An Introduction to Fractals

    March 3, 2011

Fractals are self-similar patterns created with a starter "seed" and a repeated iterative process. For the first exploration, participants started with an isoceles triangle (seed). Fold the triangle so that the vertex angle meets the midpoint of the base. Unfold the crease & draw the midsegment at the crease (iterative process). Repeat the process 4 times using the small new triangle at the top for each new iteration. We counted the number of triangles and the number of trapezoids (of all sizes) that appeared in the figure. Two different numerical patterns appeared. Algebraic formulas were determined and shared for each pattern.

One of the patterns found involved the triangular numbers. Four different "proofs" for the formula were demonstrated.

After dinner, participants each chose one of three different geometric fractals to explore- the Sierpinski Triangle, The Geome Tree, or the Koch Snowflake. After working in groups on the explorations, each group presented their "research".

We finished the evening by creating a "fractal cut".

For a copy of the introductory activity, click here.
For a copy of the Sierpinski triangle activity, click here.
For a copy of the geome tree activity, click here.
For a copy of the Koch snowflake activity, click here.
For a copy of the Sierpinski carpet activity, click here.
For a copy of the fractal cut activity, click here.
For a copy of the PowerPoint, click here.
You may click on any of the images below to see a larger image. The table data is easier to read in the larger images.