There is a tombstone in Dota 2 that summons zombies every second for each enemy monster nearby. So if you're standing next to it, a zombie would spawn on you every second.
But what if you had a tombstone on both teams? One tombstone would spawn a zombie on an single enemy first, which would then cause the other tombstone to spawn a zombie for that new zombie. This process would repeat over and over again, spawning more and more zombies each time.
Since the number of zombies spawned is based off of the number of zombies that exist, the total number of zombies turns out to be something known as the fibonnaci sequence. By writing out the number of zombies we can see that this is the case:
| Allies | 1 | 2 | 5 | 13 | 34 | 89 | 233 | 610 | 1597 | 4181 | 10946 | 28657 | 75025 | 196418 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Enemies | 1 | 3 | 8 | 21 | 55 | 144 | 377 | 987 | 2584 | 6765 | 17711 | 46368 | 121393 | 317811 |
We can calculate the growth by dividing out successive terms.
This gives us
or about
zombies after n ticks.
That exponent means our zombies grow geometrically. We've got zombies for days.
Unfortunately the server could only spawn so many before crashing.
Valve decided to patch it after I made a short post about it.
