Answer Happy

The Sierpinski carpet is a fractal point-set in the plane that has inspired the design of WiFi antennas. It is constructed by removing the centre one-ninth square of a square, then removing the centres of the eight smaller remaining squares, and so on ad infinitum. The first four stages of the construction are shown here: At the each step, of the previous step's area is removed. Thus the sequence of areas is a geometric progression an = ran–1 with common ratio and the area of the Sierpinski carpet is lim ay = The Sierpinski triangle is constructed as follows: AAA in this case, the sequence of areas is a geometric progression with common ratio

and the area of the Serpinski carpet is The Sierpinski triangle is constructed as follows. AA In this case the sequence of areas is a geometric progression with common ratio and the area of the Sierpinski triangle is