{"id":5393,"date":"2014-03-12T16:50:33","date_gmt":"2014-03-12T15:50:33","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=5393"},"modified":"2014-03-12T16:50:33","modified_gmt":"2014-03-12T15:50:33","slug":"waves-from-circles-with-mathematica","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=5393","title":{"rendered":"Waves from Circles with Mathematica"},"content":{"rendered":"

A recent Google+ post from Mathemania4u<\/a> caught my attention on the train to work this morning. I just had to code up something that looked like this and so fired up Mathematica and hacked away. The resulting notebook can be downloaded here<\/a>. It’s not particularly well thought through so could almost certainly be improved on in many ways.<\/p>\n

The end result was a Manipulate which you’ll be able to play with below, provided you have a compatible Operating System and Web browser. The code for the Manipulate is<\/p>\n

Manipulate[\r\n Graphics[Map[dotCirc, \r\n   circArray[circrad, theta, pointsize, extent, step, phase, \r\n    showcirc]]]\r\n , {{showcirc, True, \"Show Circles\"}, {True, False}}\r\n , {{theta, 0, \"Dot Angle\"}, 0, 2 Pi, Pi\/10, Appearance -> \"Labeled\"}\r\n , {{pointsize, 0.018, \"Dot Size\"}, 0, 1, Appearance -> \"Labeled\"}\r\n , {{phase, 2, \"Phase Diff\"}, 0, 2 Pi, Appearance -> \"Labeled\"}\r\n , {{step, 0.25, \"Circle Separation\"}, 0, 1, Appearance -> \"Labeled\"}\r\n , {{extent, 2, \"Plot Extent\"}, 1, 5, Appearance -> \"Labeled\"}\r\n , {{circrad, 0.15, \"Circle Radius\"}, 0.01, 1, Appearance -> \"Labeled\"}\r\n , Initialization :>\r\n  {\r\n   dotCirc[{x_, y_, r_, theta_, pointsize_, showcirc_}] := If[showcirc,\r\n     {Circle[{x, y}, r], PointSize[pointsize], \r\n      Point[{x + r Cos[theta], y + r Sin[theta]}]}\r\n     ,\r\n     {PointSize[pointsize], \r\n      Point[{x + r Cos[theta], y + r Sin[theta]}]}]\r\n   ,\r\n   circArray[r_, theta_, pointsize_, extent_, step_, phase_, \r\n     showcirc_] := Module[{},\r\n     Partition[\r\n      Flatten[Table[{x, y, r, theta + x*phase + y*phase, pointsize, \r\n         showcirc}, {x, -extent, extent, step}, {y, -extent, extent, \r\n         step}]], 6]\r\n     ]}]<\/pre>\n
If you can use the Manipulate below, I suggest clicking on the + icon to the right of the ‘Dot Angle’ field to expose the player controls and then press the play button to kick off the animation.<\/p>\n