IFS and Addresses

Exercise 2 Answer

123		312		124

That address 123 gives the same region in problems 1 and 2 may be a bit of a surprise, because T3 is different in problems 1 and 2.

However, notice that in both problems T3(S) is the upper left corner of the unit square, so

T2(T3(S)) is T2(upper left corner)

and

T1(T2(T3(S))) is T1(T2(upper left corner))

so T1(T2(T3(S))) is the same in both problems 1 and 2.

To compare the regions with address 312, view the tranformations T3 as made of their respective components.

In problem 1, T3 is made of scale and translate.

In problem 2, T3 is made of scale, reflect, and translate.

That address 124 gives the same region in problems 1 and 2 is no surprise.

Transformations 1, 2, and 4 are the same in both problems, so the function T1(T2(T4)) is the same in problems 1 and 2.

Return to Exercise 2.