### Spirostars

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

### LOGO Challenge - the Humble Square

Look at how the pattern is built up - in that way you will know how to break the final pattern down into more manageable pieces.

### LOGO Challenge - the Logic of LOGO

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

# Making Moiré Patterns

### Why do this problem?

Read this article for a discussion on the importance and the benefits of programming in the classroom.

This problem uses the free-to-download LOGO software to introduce students to some programming through the engaging context of Moiré patterns. The patterns produced are pleasing to the eye, and students can be encouraged to be playful with their LOGO constructions in order to produce attractive patterns, while considering the geometry of different constructions.

### Possible approach

Students will need to work on computers, with free software for LOGO: FMSLogo for Windows or ACSLogo for Mac.

If students have never used LOGO before, you may wish to use some of the First Forward Into LOGO resources before exploring Moiré patterns.

Hand out this worksheet.
"For each pattern, try to work out which set of commands created it, and then try it out on the computer to see if you were right."

Bring the class together to discuss how they matched the patterns with the commands. Then challenge them to create some patterns of their own.

Finally, invite students to share the patterns they are most pleased with, and to describe how they created them.

### Key questions

What effects can you get by changing the length of the lines?
What effects can you get by changing the angle between the lines?
What effects can you get by changing the number of radial lines?

### Possible extension

Once students know how to program these simple Moiré patterns, use the links at the top of the problem page to explore further.

### Possible support

Encourage students to experiment by changing one variable at a time in the example programs and noting what happens.