Spirolaterals

Imagine you have a little robot that holds a pencil. Set it down on a sheet of paper and give it these instructions:

  1. Move forward 3 units and turn right.
  2. Move forward 1 unit and turn right.
  3. Move forward 2 units and turn left.
  4. Move forward 1 unit and turn left.
  5. Move forward 2 units and turn right.
  6. Repeat.

If the robot makes its turns at 90° angles, it will produce this figure:

swastika

But, remarkably, if it turns at 120° it will draw this:

star of david

April 26, 2010  |  Science & Math