Period trippling bifurcation is similar to the period doubling one.
You see here how Douady's rabbit appears out of a "single embryo cell" :)
At c = -0.125 + 0.65i on the border of the main cardioid the attracting fixed point loses its stability with multiplier l = exp(2p /3) . You see below this 120 o angle of rotation symmetry of the critical orbit near the bifurcation point. Unstable period-3 orbit approch to the fixed point.