A looser weave. Let’s modify the carpet-designing process yet again. Instead of dividing the original square into a 3 × 3 or 5 × 5 grid and making the inner one gold, suppose we divide the square into a 4 × 4 square and make the central 4 squares gold. Then take each of the 12 remaining squares, divide each of them into a 4 × 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.
A looser weave. Let’s modify the carpet-designing process yet again. Instead of dividing the original square into a 3 × 3 or 5 × 5 grid and making the inner one gold, suppose we divide the square into a 4 × 4 square and make the central 4 squares gold. Then take each of the 12 remaining squares, divide each of them into a 4 × 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.
A looser weave. Let’s modify the carpet-designing process yet again. Instead of dividing the original square into a
3
×
3
or
5
×
5
grid and making the inner one gold, suppose we divide the square into a
4
×
4
square and make the central 4 squares gold. Then take each of the 12 remaining squares, divide each of them into a
4
×
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.
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