Making Moiré Patterns

8393 /www/nrich/html/content/id/8393/ 1 0000-00-00T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <ul id="stemLinks"> <li><a href="http://nrich.maths.org/8045">Warm-up</a></li> <li><a href="http://nrich.maths.org/8866">Try this next</a></li> <li><a href="http://nrich.maths.org/7406">Think higher</a></li> <li><a href="http://nrich.maths.org/8194">Read: mathematics</a></li> <li><a href="http://www.exploratorium.edu/snacks/moire_patterns/index.html">Read: science</a></li> <li><a href="http://www.physics.org/explorelink.asp?id=1721&q=text&currentpage=2&age=0&knowledge=0&item=19">Explore further</a></li> </ul> <div> </div> Moiré patterns are a type of interference pattern made when lines overlap. Here are some examples of Moiré patterns: <mdo:image src="moire1.png"></mdo:image> <mdo:image src="moire2.png"></mdo:image> <mdo:image src="moire3.png"></mdo:image><mdo:image src="moire4.png"></mdo:image> These patterns were created using LOGO. Can you work out which LOGO commands give rise to each pattern? <ul> <li>cs setpc 16 repeat 360 [fd 100 bk 100 rt 7 fd 25 bk 25 rt 5 fd 15 bk 15 rt 2] ht</li> <li>cs setpc 2 repeat 90 [fd 100 bk 100 rt 3 fd 100 bk 100 rt 1] ht</li> <li>cs setpc 13 repeat 360 [fd 100 bk 100 rt 7 fd 25 bk 25 rt 7 fd 10 bk 10 rt 7] ht</li> <li>cs setpc 1 repeat 360[fd 200 rt 1 bk 200 rt 1] ht</li> </ul> If you are unfamiliar with LOGO, click below to see a glossary of the terms used above. <div class="toggle">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</div> 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. <div class="framework">Notes and Background You can download free software for LOGO: <a href="http://fmslogo.sourceforge.net/">FMSLogo for Windows</a> (<a href="http://www.jonhoff.net/docs/logo.pdf">tutorials</a>), <a href="http://www.alancsmith.co.uk/logo/">ACSLogo for Mac</a> (<a href="http://www.alancsmith.co.uk/logo/LogoUserGuide151.pdf">user guide and tutorials</a>).</div></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">We only had one person submit a Moiré pattern for us! Thank you to Daniel from Wilson’s School who sent in: <div style="text-align: center;"><mdo:image src="moiresubmission1.png"></mdo:image></div> cs setpc 13 repeat 360 [fd 79 bk 56 rt 8 fd 123 bk 125 rt 34 fd 10 bk 10 rt 34] ht Do try out some more Moiré patterns on the <a href="http://twilgo.com/nrich/">nrich TWILGO site</a> and then send them to us. </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><h3>Why do this problem?</h3> Read <a href="/8194">this article</a> for a discussion on the importance and the benefits of programming in the classroom. <a href="https://nrich.maths.org/8393">This problem</a> 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. <h3>Possible approach</h3> Students will need to work on computers, with free software for LOGO: <a href="http://fmslogo.sourceforge.net/">FMSLogo for Windows</a> or <a href="http://www.alancsmith.co.uk/logo/">ACSLogo for Mac</a>. If students have never used LOGO before, you may wish to use some of the <a href="/8045">First Forward Into LOGO</a> resources before exploring Moiré patterns. Hand out <a class="pdflink" href="/content/id/8393/Moire.pdf">this worksheet</a>. "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. <h3>Key questions</h3> 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? <h3>Possible extension</h3> Once students know how to program these simple Moiré patterns, use the links at the top of the problem page to explore further. <h3>Possible support</h3> Encourage students to experiment by changing one variable at a time in the example programs and noting what happens.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Try typing in each of the LOGO programs to see what you get. Then try changing each of the variables in turn. What do you notice?</mdoxml> 2 3 0 0 1 1 1 Making Moiré Patterns Moiré patterns are intriguing interference patterns. Create your own beautiful examples using LOGO! 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