Mind, Body, World- Foundations of Cognitive Science, 2013a

In the code given above, recursion was evident because MoveStack () called itself. There
are other ways in which recursion can make itself evident. For instance, recursion
can produce hierarchical, self-similar structures such as fractals (Mandelbrot, 1983),
whose recursive nature is immediately evident through visual inspection. Consider
the Sierpinski triangle (Mandelbrot, 1983), which begins as an equilateral triangle
(Figure 3-3).
Figure 3-3. The root of the Sierpinski triangle is an equilateral triangle.
The next step in creating the Sierpinski triangle is to take Figure 3-3 and reduce it
to exactly half of its original size. Three of these smaller triangles can be inscribed
inside of the original triangle, as is illustrated in Figure 3-4.
Figure 3-4. The second step of constructing a Sierpinski triangle.
The rule used to create Figure 3-4 can be applied recursively and (in principle) infinitely.
One takes the smaller triangle that was used to create Figure 3-4, makes it
exactly half of its original size, and inscribes three copies of this still smaller triangle
into each of the three triangles that were used to create Figure 3-4. This rule can be
64 Chapter 3