What causes the strange behavior of $s=1$ in the graph $c=\sin^2(s+2^x)$?

Question

I came across a very weird graph on Desmos and I can't figure out how this thing works. It is $$c=\sin^2(s+2^x)\qquad s=1$$

Note: it makes a difference if $s=2$.

Answer 1

The function with $s=1$ is $$\text{sin}^2(1+2^x),$$ which is the square of the sine function, so it's value is always within the interval$[0, 1]$ since the value of the sine function is always within the interval$[-1, 1]$.

Also, the graph oscillates faster in the right because $2^x$ gets larger more quickly when $x$ is large than it does when $x$ is small.

Lastly, the graph of the function becomes different when $s$ changes from $1$ to $2$ because for the same value of $x$, the input into $\text{sin}^2$ changed (larger by $1$ than before).