So this is the tent map:
$$ T(x) = \begin{cases} 2x & \text{if $x<0.5$} \\ 2-2x & \text{if $x \geq 0.5$} \end{cases} $$
if we take any ponit $x_0 \in [0,1]$ then $T(x_0) \in [0,1]$ so we can construct it's orbit $O(x_0) = (x_0,T(x_0),T^2(x_0),T^3(x_0),...)$ then we can take it into a binary using the rule if $x_{0}^{n} \rightarrow 0$ if $x_{0}^{n} < 0.5$ and $x_{0}^{n} \rightarrow 1$ if $x_{0}^{n} \geq 0.5$ where $x_{0}^{n} = T^n(x_0)$ for example:
$$(0.1,0.2,0.4,0.8,0.4,0.8,0.4,...)\longrightarrow (0,0,0,1,0,1,0,...)$$ $$(0.64,0.72,0.56,0.88,0.24,0.48,0.96,...)\longrightarrow (1,1,1,1,0,0,1,...) $$
What I'm wondering is something like the inverse, if a have a set of binary sequences is there a way in which I can get a function like the tent map that generates these sequences? I don't think it's posible to do it this generally or that they might be many, but are there a set of conditions which could help me?
Thanks.