"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." This definition of fractals comes from the Fractal Foundation.
This project is open-ended enough to allow for colors and designs from many different cultures and the students enjoy coming up with their own designs. And I love the calm mindful work of children coloring their repeating patterns and experiencing mathematics.
Here are the steps for the project with illustrations below:
1) Cut out a 27x27 grid from graph paper and draw lines making 3 rows and 3 columns so that each square is a 9x9 grid
2) Draw a simple, colorful design for the four corner squares and the middle square.
3) With the four remaining 9x9 squares, draw lines making 3 rows and columns so that each square is a 3x3 grid.
4) Shrink the five original designs by 1/9 and draw them in the five 3x3 squares that correspond to their original locations in the 27x27 grid.
5) In the four remaining 3x3 squares, draw lines making 3 rows and columns where each square is a 1x1 grid.
6) Shrink the five original designs by 1/9 again and draw them in the five 1x1 squares that correspond to their locations in the original 27x27 grid (and also in the 9x9 grids).
Below are more designs that were completed by students.