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Simple fractal

  • To: mathgroup at
  • Subject: [mg121790] Simple fractal
  • From: Tom De Vries <tidetabletom at>
  • Date: Sun, 2 Oct 2011 02:36:57 -0400 (EDT)
  • Delivered-to:

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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