By far the most daunting task facing nano-electronics are the wires, being at the heart of power/energy consumption, as: (i) their numbers are increasing exponentially (as each device needs a few wires); and (ii) they do not scale well for quite some time (their parasitic capacitances and RC-delays are not scaling in synch with devices). Innovations on both classical (i.e., based-on-wires, hence evolutionary) as well as on advanced (i.e., without-wire/beyond-wire, hence revolutionary) communication schemes are urgently needed. Trying to find inspiration from the neurons, we investigate here how axons are able to communicate at quite large distances on a very limited power budget. In particular, the paper analyzes axon-inspired communications as dense locally-connected arrays/lattices of voltage-gated (i.e., non-linear) ion channels. The theoretical results presented here suggest that hexagonal (or hex-connected) arrays would be the least power hungry ones.