The answer to the question, "How do you make a Sierpinski
Gasket?" is a procedure which is recursively defined.
Procedure for Making a Sierpinski Gasket
Making Sierpinski Gaskets involves making Sierpinski Gaskets. Each time
you do the procedure, you do the procedure some more, but not in a repetitive way.
(Otherwise we would be talking about repetition and not recursion!)
- Connect the midpoints of two equilateral trianges.
- Cut out the triangle which results
- Make Sierpinski Gaskets out of the three remaining triangles.
You don't make the second, third and
fourth Sierpinski Gaskets after you make the first one. Making
the next three is part of making the first one. All the ones
you make after that will be part of those three which are part of the first