(a) Animation 6a corresponds to Fig. 2a of Friedman+2013 for the case α = 180 degrees where the redshift of event A is fixed to z_A=0.5 and the redshift of event B is allowed to vary in the range 0.5 < z_B < 71.91. For z_B < z_B ~ 50, events A and B have intersecting past lightcones and a shared causal past. For z_B > z_B ~ 50, the events do not have a shared causal past. This corresponds to fixing z_A and α = 180 degrees and increasing z_B until the point (z_A, z_B) lies in the light gray region in Fig 3b of Friedman+2013. For z_A <= z_B <= 3.65, events A and B both have shared causal pasts with Earth's worldline, whereas event B does not when z_B > 3.65. The critical redshift z_B is computed from Eq. 30 of Friedman+2013 (substituting labels A <--> B), and using Eq. 12 of Friedman+2013 to determine redshift for a given comoving distance.

(b) Animation 6b corresponds to Fig. 2a of Friedman+2013 for the case α = 180 degrees with symmetric redshifts z_A=z_B, where both redshifts are increased in the range 1 <= z_A=z_B <= 24.47. The symmetric case illustrates the role of the causal independence redshift z_ind=3.65. For z_A=z_B <= z_ind=3.65, events A and B have intersecting past lightcones and shared causal pasts with each other and Earth's worldline. For z_A=z_B > z_ind=3.65, events A and B have no shared causal past with each other or our worldline. The finite redshift resolution of the movie shows a frame with z_A=z_B=3.62 where the past lightcones of A and B clearly intersect (green circles), while the next frame with z_A=z_B=3.67 clearly shows that the past lightcones of the events no longer intersect.