This tag is used both for questions about iterated function systems in fractal geometry (finite families of contractions $f: X \to X$ on a complete metric space $(X,d)$ that are used to construct fractals) and questions about iterated function systems in probability theory (a random process associated to a finite family of maps $f_i:E \to E$ on a topological space $E$ and corresponding probabilities $p_i(x)$ for each $x \in E$).
Questions tagged [iterated-function-system]
70 questions
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1 answer
How can multivariate iterated functions be generalized?
Alright, so we all know how single variable functions work with iteration:
If
f(x) = x^2
Then
f^2 (x) = (x^2)^2
This works really well because in with only one independent variable there is one input and one output. So it’s not so hard to understand…
0
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2 answers
For which $k$ we have: $|x_k-\alpha|\le10^{-16}|\alpha|$ where $\alpha$ is a solution of the equation $10x-\sin x=3$?
Let iterative method which is determined by the formula $x_{n+1}=\frac{\sin (x_n)+3}{10}$ for $x_0=0.33$. For which $k$ we have: $|x_k-\alpha|\le10^{-16}|\alpha|$ where $\alpha$ is a solution of the equation $10x-\sin x=3$?
The iterative function…
dsk62
- 307
0
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2 answers
iteractively solve power equation
I have an equation like that:
$$
x = (x-A)^{2/3}+B $$
And I want to find the value of x.
The problem is that during the iteration, x can became negative and then appears complex number. But that x is a distance, then I don't want complex…
