A cellular automaton is a state machine which is controlled by external input. The input is given by geometrical space around a cell. In a square matrix, each automaton gets input from 4 surrounding cells, while a hexagon grid has 6 neighbor cells which can be used as automaton input. For example, a 4-cells input may be the string “1011”. This string specify a state of the cellular automaton. The automaton will switch to a different state according to the lookup table. I want to know if increasing the number of input cells in a hexagon automaton will make the resulting computer more powerful.
Is using a plane tiled with regular hexagons more efficient and reliable than using square cells? What is the difference and how do I know which one to use in which scenario?
In other words, the more efficiently flexible that it grows, the more difficult scenarios it can be used for (for me, hexagonal implicates more possibilities, because it can send/share the signal with/to more tiles). Or maybe one is more modern than the other, or they're both on the same level? In general, I'd like to learn the differences between them to know when I should use one over the other.