As promised from the "Update" Febuary 6th post, we can now recur to produce the total number of triangles inside the \(n^{th}\) iteration of the Sierpinski triangle using the code below written in Scheme.

1
2
3
4
5

(define sierpinski
  (lambda (n)
    (cond 
     ((zero? n) 1)
      (else (+ 1 (* 3 (sierpinski(- n 1))))))))

To do the recursion on your computer, install mit-scheme, then copy and paste the code to your mit-scheme implementation. You then will be able to call the function for any desirable \(n\). Now go ahead and recur!