Sierpinski triangle

A Sierpinski triangle or Sierpinski gasket, named after Wacław Sierpiński, is one of the most famous fractals. A fractal is an object with smaller details that contain repeating copies of itself.

Constructions

To make one, start with a triangle. Remove the center part, or copy 3 times and arrange those copies in the shape of a triangle, either way works. If you keep repeating this, you get a shape that looks like this:

The Chaos Game

  • Make a triangle.
  • Choose any point in the triangle.
  • Draw a line between that point and any corner of the triangle.
  • Find the midpoint of the line.
  • Draw a line from that point and repeat the process.

The process should look like this:

Pascal's Triangle

Pascal's Triangle is a special arrangement of numbers where every number is the sum of the ones above it.

The first 11 rows of Pascal's Triangle.

If you color in every even number (2, 4, 6, 8, 10, 12, 14, etc) in pink and every odd number (1, 3, 5, 7, 9, 11, 13, etc) in red, the result should look like the Sierpinski triangle.

References

  1. ↑ Feldman, David P. (2012-08-09). Chaos and Fractals: An Elementary Introduction. OUP Oxford. ISBN 978-0-19-956644-0.
  2. ↑ Stewart, Ian (2006-10-12). How to Cut a Cake: And other mathematical conundrums. OUP Oxford. ISBN 978-0-19-150071-8.