Chapter 7.2, Problem 13MS

Sierpinski hexed (S). Take an equilateral triangle and remove a hexagon from the center as shown at right, leaving three equilateral triangles with sides 1/3 the length of the sides of the original triangle. Repeat the process of removing a hexagon from each sub-triangle. Repeat, repeat, repeat, forever. Make a sketch of what remains after one step, two steps, and three steps. Describe the locations of infinitely many points that are left after infinitely many steps. Let’s call the remaining points Sierpinski Dust.