Chapter 7.2, Problem 35MS

A looser weave. Let’s modify the carpet-designing process yet again. Instead of dividing the original square into a $3\times 3$ or $5\times 5$ grid and making the inner one gold, suppose we divide the square into a $4\times 4$ square and make the central 4 squares gold. Then take each of the 12 remaining squares, divide each of them into a $4\times 4$ grid and make the central four gold, and continue this process forever. Starting with the square as stage 1, draw the first three stages of this replacement process.