Iterated Function Sequences Accumulation: Help

In summary, iterated function sequences are sequences of functions where the output of one function is used as the input for the next function in the sequence. They accumulate by repeatedly applying the same sequence of functions to a starting value, and have various real-world applications in mathematics and science. The convergence of an iterated function sequence can be determined by analyzing its behavior as the number of iterations increases, and they can be used to solve a variety of mathematical problems.
  • #1
aridneptune
5
0
Not quite sure how to approach this problem at all. We are given three contractions which generate the Sierpinski right triangle:

A0 = [tex]\frac{1}{2}[/tex] <x , y>

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

A2 = [tex]\frac{1}{2}[/tex] <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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  • #2
Please excuse me...didn't realize this forum wasn't for HW problems. Delete/lock please.
 

1. What are iterated function sequences?

Iterated function sequences are sequences of functions where the output of one function is used as the input for the next function in the sequence. This process is repeated multiple times, leading to a chain of functions that are applied one after another.

2. How do iterated function sequences accumulate?

Iterated function sequences accumulate by repeatedly applying the same sequence of functions to a starting value. Each iteration produces a new value, which is then used as the input for the next iteration. As the number of iterations increases, the values produced by the sequence tend to accumulate and converge towards a specific value.

3. What are some real-world applications of iterated function sequences?

Iterated function sequences have various applications in mathematics and science, such as in fractal geometry, chaotic systems, and population dynamics. They can also be used in computer science for generating random numbers and in image processing for creating patterns and textures.

4. How do I determine the convergence of an iterated function sequence?

The convergence of an iterated function sequence can be determined by analyzing its behavior as the number of iterations increases. If the values produced by the sequence approach a specific value or a cycle of values, the sequence is said to converge. However, if the values become increasingly chaotic or do not approach a specific value, the sequence is said to diverge.

5. How can I use iterated function sequences to solve mathematical problems?

Iterated function sequences can be used to solve a variety of mathematical problems, such as finding the roots of equations, approximating solutions to differential equations, and solving optimization problems. By applying a sequence of functions to a starting value, the values produced by the sequence can be used to approach the solution to the problem.

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