Iterated Function Sequences Accumulation: Help

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SUMMARY

The discussion focuses on the convergence of iterated function sequences that generate the Sierpinski right triangle using three specific contractions: A0, A1, and A2. The sequence in question is A22(A1n(), where A1 and A2 are defined as linear combinations of the coordinates. The goal is to determine the limit point of this sequence, which is essential for understanding the properties of fractals and their generation through iterative processes.

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  • Understanding of iterated function systems (IFS)
  • Familiarity with the Sierpinski triangle and its properties
  • Basic knowledge of linear algebra and coordinate transformations
  • Experience with convergence concepts in mathematical sequences
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aridneptune
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Not quite sure how to approach this problem at all. We are given three contractions which generate the Sierpinski right triangle:

A0 = \frac{1}{2} <x , y>

A1 = \frac{1}{2} <x-1 , y> + <1 , 0>

A2 = \frac{1}{2} <x , y-1> + <0 , 1>

We are asked to find the point to which the sequence

A22(A1n (<x0 , y0>)

converges. Any ideas/help would be greatly appreciated!
 
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