Was one of those 4096 ancestors the Heliographer who made this picture?

There’s an incorrect assumption here that makes the whole math portion meaningless. That assumption is that ancestors must be unique.

In reality, you can have two parents each having two children, and then those two children having two children, etc.

Hell, you can do it with two initial parents, and then each generation only having 1 child, which then mates with its parents, and then the family tree looks kind of like a braid.

So, in reality, you only need 12 ancestors to be the 12th generation. Thanks for coming to my Ted Talk.