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## Homework Statement

We are given three contractions which generate the Sierpinski right triangle:

A

_{0}= [tex]\frac{1}{2}[/tex] <x , y>

A

_{1}= [tex]\frac{1}{2}[/tex] <x-1 , y> + <1 , 0>

A

_{2}= [tex]\frac{1}{2}[/tex] <x , y-1> + <0 , 1>

We are asked to find the points on which the sequence

(A

_{2}[tex]\circ[/tex]A

_{1})

^{n}(<x

_{0}, y

_{0}>) ) -- that's (A

_{1}COMPOSITE A

_{2})

^{n}

accumulates.

## The Attempt at a Solution

Not quite sure how to approach this problem at all. I've figured that A

_{1}

^{n}takes any <x , y> to <1 , 0>, and that A

_{2}

^{n}takes any <x, y> to <0, 1>. So my first instinct was to say that iterating A

_{2}n times on an n-iteration of A

_{1}would just converge to <0 , 1>. However, I'm fairly sure this is incorrect. But how can this system accumulate on >1 point?

Any ideas/help would be greatly appreciated!

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