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Re: Simple fractal

  • To: mathgroup at smc.vnet.net
  • Subject: [mg121829] Re: Simple fractal
  • From: Heike Gramberg <heike.gramberg at gmail.com>
  • Date: Tue, 4 Oct 2011 01:31:58 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201110020636.CAA28033@smc.vnet.net>

You could do something like this:

Manipulate[
 Module[{pts = N@Table[{Cos[i*360./sides*Degree], 
Sin[i*360./sides*Degree]}, {i, sides}]},
  Graphics[{FaceForm[Opacity[0]], EdgeForm[Black],
    NestList[ Translate[Scale[#, scale, {0, 0}], dist pts] &, 
{Polygon[pts]}, depth]}]],
 {{sides, 3}, Range[3, 6]},
 {{scale, 0.5}, 0, 1},
 {{dist, 1}, 0, 2},
 {{depth, 2}, Range[7]}]


Heike


On 2 Oct 2011, at 08:36, Tom De Vries wrote:

> I am trying to create a very simple fractal, but I am not having any success.
>
> I'd like to learn how to do this recursively, and hoping someone can
> give me a bit of a push in the right direction.
>
> It's a simple triangle with triangles at each corner, with triangles
> at each corner, etc.
>
> Below,  a simple "level 1" graphic.
>
> scale = 0.5;
>
> list1 = Table[{0, 0} + {Cos[i*120*Degree], Sin[i*120*Degree]}, {i, 
1,
> sides + 1}];
>
> list2 = (Table[#1 + scale*{Cos[i*120*Degree], Sin[i*120*Degree]}, 
{i,
> 1, sides + 1}] & ) /@  list1;
>
> Graphics[{Line[list1], Line[list2]}]
>
>
> Ideally I'd like to have a Manipulate with a slider for the level of
> the fractal,  the scale applied to each level, and the distance each
> corner triangle is from the centre triangle.
>
> Sorry,  I know this is simple programming,  but I don't have any ideas
> how to start.
>
> Tom De Vries
>




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