[Nition]

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.

[_Donny]

That makes perfect sense. Thanks for the excellent explanation, Nition!