Sierpinski

Please take out a sheet of paper and pen and follow these instructions:

1. Draw an up-pointing, equilateral triangle that fills most of the page.

2. Lightly mark the midpoint of each line of that triangle.

3. Draw straight lines connecting each of those marks. This forms four new triangles: three that point up, one that points down.

4. Choose any empty, up-pointing triangle on the page.

5. Go to instruction 2.

 

Yes, these instructions will go on forever. I'll interrupt you in a minute.