Tupper's so-called "self-referential" formula is a way to generate any 106x17 image for any $k$ provided that $\frac{k}{17} \in \Bbb Z^*$ (set of nonnegative integers). By taking any binary number, converting it into decimal and plugging it into $k$, we can find any 106 x 17 image possible.
The total amount of images possible is therefore $2^{106\cdot17}$ and the height at which the last image possible appears is $k=17\cdot2^{106\cdot17}$.
What happens when $k$ is made to go higher than that?