Imagine a civilization, long dead, leaving a gravestone. A laser in orbit of there homeworld, beaming short "candles" aka datapulses to the projected locations

Imagine a civilization, long dead, leaving a gravestone. A laser in orbit of there homeworld, beaming short "candles" aka datapulses to the projected locations of worlds in other habittable star systems. We can see these worlds, we could beam a message there, even a short story how we failed with warnings. So what could be seen at the endpoint? A flickering light disk traversing a cloud cover, with the speed of planetary rotation. (400 m/s) I do want to believe, that this is whats out there. Lots of failed societies trying to warn us, the message encoded in math. Exponential Series.. for 100 years. Zero forever.