{"id":3715,"date":"2011-07-16T10:49:18","date_gmt":"2011-07-16T09:49:18","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=3715"},"modified":"2011-07-16T10:49:52","modified_gmt":"2011-07-16T09:49:52","slug":"interactive-slinky-thing","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=3715","title":{"rendered":"Interactive ‘Slinky Thing’"},"content":{"rendered":"

Over at Playing with Mathematica, Sol Lederman has been looking at pretty parametric and polar plots<\/a>.\u00a0 One of them really stood out for me, the one that Sol called ‘Slinky Thing’ which could be generated with the following Mathematica<\/a> command.<\/p>\n

ParametricPlot[{Cos[t] - Cos[80 t] Sin[t], 2 Sin[t] - Sin[80 t]}, {t, 0, 8}]<\/pre>\n
Out of curiosity I parametrised some of the terms and wrapped the whole thing in a Manipulate to see what I could see.  I added 5 controllable parameters by turning Sol’s equations into<\/p>\n
{Cos[e t] - Cos[f t] Sin[g t], 2 Sin[h t] - Sin[i t]}, {t, 0, 8}<\/pre>\n
Each parameter has its own slider (below).  If you have Mathematica 8, or the free cdf player<\/a>, installed then the image below will turn into an interactive applet which you can use to explore the parameter space of these equations.
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