Out of curiosity I searched for a similar cellular automaton as Conway’s game of life on a hexagonal lattice. It should have gliders and use the Moore neighborhood as defined in the earlier post “hexagonal cellular automata“. I found gliders for the rule that a cell of state 1 remains in state 1 if it has 3 or 4 cells of state 1 in the neighborhood and that a cell of state 0 will be in state 1 for the next generation if it has exactly 4 neighboring cells of state 1. This numbers are larger than for the game of life on the square lattice because the neighborhood is now larger.
In this video, you will see a glider emerging from a random starting configuration. It resembles Conway’s glider: