Quilting Patterns

In a common style of quilting, each square patch is constructed from a simple "core square" design. In the Mathlet below, the large core square at the top can be designed by first choosing a color from the palette and then clicking one of the eight sections of the core square.

Below the core square appear three common ways to assemble the core squares into a quilt patch. In each of the quilt patch designs, the original core square appears in the upper right.

• Repeated: In the repeated pattern, the core square is simply copied three times without being transformed.
• Reflected: In the reflected pattern, the core square is first reflected over a vertical line, and the result is placed to the left of the original. Then that square is reflected over a horizontal line, and the result is placed below the previous result. Finally, that core square is flipped over a vertical line and the result is placed in the lower-right of the quilt patch.

• Rotated: In the rotated pattern, the core square is rotated 90 degrees counter-clockwise several times, each time the result being placed around the quilt patch, starting in the upper-right and going around to the lower-right.

Using the Mathlet below, create several different core square designs, and investigate the different kinds of quilt patches you can create. After you have explored a bit, try to answer the questions appearing below the Mathlet.

Questions:

1. Can you create a core square for which the repeated and reflected patterns look the same?
2. Can you create a core square for which the repeated and rotated patterns look the same?
3. Can you create a core square for which the reflected and rotated patterns look the same?
4. Can you create a core square for which all three patterns look the same?