### 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

##### Age 11 to 18 Challenge Level:

Moiré patterns are a type of interference pattern made when lines overlap.
Here are some examples of Moiré patterns:

These patterns were created using LOGO.

Can you work out which LOGO commands give rise to each pattern?

• cs setpc 16 repeat 360 [fd 100 bk 100 rt 7 fd 25 bk 25 rt 5 fd 15 bk 15 rt 2] ht
• cs setpc 2 repeat 90 [fd 100 bk 100 rt 3 fd 100 bk 100 rt 1] ht
• cs setpc 13 repeat 360 [fd 100 bk 100 rt 7 fd 25 bk 25 rt 7 fd 10 bk 10 rt 7] ht
• cs setpc 1 repeat 360[fd 200 rt 1 bk 200 rt 1] ht

If you are unfamiliar with LOGO, click below to see a glossary of the terms used above.

cs: clear screen
setpc: set pen colour
fd: move turtle forward a specified distance
bk: move turtle back a specified distance
rt: right turn through an angle in degrees
lt: left turn through an angle in degrees
st: show turtle
ht: hide turtle

Try making some Moiré patterns of your own. Make changes to your LOGO code and see the effects you can create.
What do you notice?

Send us your examples of Moiré patterns, together with the LOGO code you used to generate them.

Notes and Background

You can download free software for LOGO: FMSLogo for Windows, ACSLogo for Mac (user guide and tutorials).