I think it'd work like this:
Imagine you decide to show a "1" instead of the black sphere. You then look behind you. Most likely you see a 1.
Whatever number you see, increment that number by one in the next simulation. If you see nothing, congrats, you're at the top and leave the number as-is.
So initially what each level sees is behind them is: x-1-1-1-1-1
Then after everyone increments by one: x-1-2-2-2-2
Now repeat the step. Everyone looks behind them and increments the number they see by one.
x-1-2-3-3-3
Eventually you'll look behind you and the number won't have changed. You're at one level higher than that.
If there are millions of levels that'd take ages of course. But I think you could use the same idea do it instantly on the computer instead. Just have your simulation computer modify a number on the simulation computer in the next level down.
Imagine you decide to show a "1" instead of the black sphere. You then look behind you. Most likely you see a 1.
Whatever number you see, increment that number by one in the next simulation. If you see nothing, congrats, you're at the top and leave the number as-is.
So initially what each level sees is behind them is: x-1-1-1-1-1
Then after everyone increments by one: x-1-2-2-2-2
Now repeat the step. Everyone looks behind them and increments the number they see by one.
x-1-2-3-3-3
Eventually you'll look behind you and the number won't have changed. You're at one level higher than that.
If there are millions of levels that'd take ages of course. But I think you could use the same idea do it instantly on the computer instead. Just have your simulation computer modify a number on the simulation computer in the next level down.