Conjecture 1. For the first and second values in a Fibonacci-like sequence (denoted here as $f, s$. respectively) in a 4 by $r$ fibonacci square (using Nelson’s modified rules as noted in the original post), where $f \equiv 1 \mod 2$, then the determinant of any 2 by 2 square is $(s*f)*(s+f)*r$, where $r$ is the starting “row” of the fibonacci square.
Conjecture 2. For the first and second values in a Fibonacci-like sequence (denoted here as $f, s$ respectively) in a 4 by $r$ fibonacci square (using Nelson’s modified rules), where $f \equiv 0 \mod 2$, then the determinant of any 2 by 2 square is $f*(s+f)*r$, where $r$ is the starting “row” of the fibonacci square.