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

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.