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MathGroup Archive 2006

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Re: circular infinity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72204] Re: circular infinity
  • From: mcmcclure at unca.edu
  • Date: Thu, 14 Dec 2006 05:49:29 -0500 (EST)
  • References: <elotg7$pe2$1@smc.vnet.net>

On Dec 13, 7:59 am, Eep² <e... at tnlc.com> wrote:
>  Hi, I'm trying to create the image athttp://tnlc.com/eep/circles.html
> in Mathematica but I don't have much programming (or math)
> experience and am wondering if anyone here could help me out.

How about this:

CircleToCircles[Circle[{a_, b_}, r_]] :=
    {Circle[{a - r/2, b}, r/2],
     Circle[{a + r/2, b}, r/2]
};
CircleToCircles[l_List] := CircleToCircles /@ l;
Show[Graphics[NestList[CircleToCircles, Circle[{0, 0}, 1], 8]],
    AspectRatio -> Automatic, PlotRange -> All];

A few comments:
  * This is an example of functional programming,
    which you definitely want to learn to use Mathematica.
  * The function CircleToCircles has two definitions
    depending upon the type of pattern it encounters.
    Pattern matching is another major topic you need
    know.
  * NestList and related commands tend to be much
    more efficient than loops.

Have fun,
Mark


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