Fractals

Begin with a square (try a 9 x 9 square on square dot paper). 
Trisect each side, then construct a new square on the center section,
making a figure consisting of 20 sides. 

Repeat the process, trisecting each of the 20 sides, and 
constructing squares on the middle sections, thus forming a polygon 
of 100 sides. Repeat the process on to infinity.

What is the perimeter and the area of the polygon?

Fill in the chart below for each stage of the polygon (up to stage five).


          No. of
Stage     sides     length        perimeter         area
------   -------   --------      -----------       -------

1          4         a              4a                a^2

2        ------    -------        --------         -------

3        ------    -------        --------         -------

4        ------    -------        --------         -------

5        ------    -------        --------         -------

n        ------    -------        --------         -------


Now examine the chart on the next page to check your work.