Koch Snowflake?

Posted on 2016-04-14 18:20:00 in Math by WILLIAMS

Construct a sequence of figures, T_0,T_1,T_2,…,T_n,… in the following way. T_0 is an equilateral triangle of side length one; T_1 is obtained from T_0 by replacing the middle third of each edge of T_0 by an outward equilateral triangle whose side length is 1/3 of the side length of the triangle T_0. Now, T_2 is obtained from T_1 by replacing the middle third of each edge of T_1 by an outward facing triangle who side length is 1/3 of the side length of the triangles in T_1 and so on. (The limit of this sequence is called the “Koch Snowflake”) 

A) Let {L_n } denote the sequence of side lengths of {T_n }. Write the first five terms of {L_n }. 
B) Find the general term of {L_n } both as a function of n and also as a recursive definition. 
C) Let {S_n } denote the sequence of the numbers of sides of {T_n }. Write the first five terms of {S_n }. 
I am not sure how to do this. I will give full points to whom ever can explain this to me.

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