There are lots of visual representations of geometric series. Take for instance a $1$ by $1$ square and apply some action iteratively. Say that the final area is a piece of this square so you can deduce the value of the geometric sum.
Is there anything similar to this for Zeta series? I am familiar with the idea of having two circles next to each other, then putting a circle in between them, and so on, and the sum of the areas gives a Zeta sum. However, there are way fewer examples like this for sums progessing this way. Moreover, for Apery's constant, since the argument of Zeta is in that case $3$, it stands to reason one could find a visual representation in $3$-dimensional space, but I have never seen any such example.