I'm using a trigonometric function to generate binary strings by sampling the function at regular intervals and mapping each sample value to a binary bit.
As a simple example: if the function is $g(x)=sin(fx)$, and I need a 4-bit binary string, I sample $g(x)$ at $x=0, 1, 2,$ and $3$. Then, if $g(x) > 0$, record a $1$. Else, record a $0$. So, let's assume that $f=1$, then in this case the binary string is 0111, because
$g(0) = 0$, $g(1)\approx 0.8$, $g(2)\approx 0.9$, $g(3)\approx 0.1$.
My question is this: is it possible to prove (or disprove) that one can generate all possible binary strings of length $n$ by varying $f$?
And then, I should add that I'm actually working with the following function:
$g(x)=sin[2\pi(x-a)b~cos(2\pi(x-a)c)]+d$
so, the question becomes: can one generate all possible binary strings of length $n$ by varying $a, b, c,$ and $d$?
Thanks!
