I tried to design a menger sponge capacitor.
I read something like "infinite surface area" and I immediately think I will make a capacitor with infinite capacitance.
I worked out the formula for surface area/iteration, and thought of some ways to build it. I figured how big it would have to be to store charge at a really high voltage without dielectric breakdown, so that it could be an ~infinite energy battery.
Then I realized I never considered the geometry and how it might affect the electric field, and so my infinite surface area didn't sound so promising. I didn't even want to start on the nightmare of trying to figure out the capacitance from that kind of geometry. Luckily, that stopped me before I tried to build one.
I'm still interested in making capacitors out of fractal geometries, but I don't know if its feasible. The closest thing that tries to maximize surface on a small scale is a tantalum capacitor that uses powder grains to increase surface area.
