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MathGroup Archive 2006

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Re: circular infinity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72230] Re: circular infinity
  • From: "Eepē" <eepNOSPAM at tnlc.com>
  • Date: Fri, 15 Dec 2006 07:06:24 -0500 (EST)
  • Organization: SBC http://yahoo.sbc.com
  • References: <elotg7$pe2$1@smc.vnet.net> <elrbdj$12u$1@smc.vnet.net>

Thank you! I've been trying to get all the circles to show since the beginning but didn't find "PlotRange -> All" yet. The 
documentation needs serious work and the program itself isn't very intuitive...

Is there a way to smooth/anti-alias the lines so they don't look so jagged?

Also, how would I do something like on http://local.wasp.uwa.edu.au/~pbourke/fractals/circles/ (specifically, 
http://local.wasp.uwa.edu.au/~pbourke/fractals/circles/circ4.gif)? I'd like to have the circles start out flat and then spiral up 
like that but not each level (iteration) be the same, but each circle in the iteration plane be on a different level--like steps or 
something. Animated would be cool too! :)

<mcmcclure at unca.edu> wrote in message news:elrbdj$12u$1 at smc.vnet.net...
> On Dec 13, 7:59 am, Eep² wrote:
>>  Hi, I'm trying to create the image at http://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. 


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