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'Making Moiré Patterns' printed from

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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 (tutorials), ACSLogo for Mac (user guide and tutorials).