Results:  After 4 iterations, the tree fractal remained bounded within the original rectangle within which it was drawn.  Although it became impossible to measure individual segment lengths accurately for iterations beyond stage 4 with the tools available in the classroom, when the pattern is generalized it indicates the following:

For any stage n,

• the number of segments will be 5 to the nth power
  
• the segment length will be the length of the stage 0 segment divided by 3 to the nth power
• the perimeter will be the product of the number of segments and the segment length
• the area appears to remain constant (The area of the entire figure remained visible on the screen of the graphing calculator and within the preselected boundaries through 25 iterations.)
  

Discussion:  From both the hand drawn iterations and the graphing calculator generated iterations it appears that while the perimeter increases at a factor of 5/3 with each iteration, the area remains within the constant boundaries set up in the initial lab conditions.  Because the iterations are changing at a constant rate, our group was able to generalize the pattern.  The number of segments increases with each iteration by a factor of 5, and the segment length decreases with each iteration by a factor of one-third.  The data indicate that the perimeter grew towards infinity by a factor of five with each iteration while the area remained constant, therefore, our group concluded that the hypothesis is true.  It is possible for a geometric shape with a finite area to have an infinite perimeter.

Conclusion:  The number of segments grew at a constant factor of five with each iteration.  The length of each segment decreased at a constant factor of one-third for each iteration.  The perimeter increased at a constant factor of five-thirds with each iteration, while the area remained constant.  It is possible for a geometric shape with a finite area to have an infinite perimeter.