## Bumerang

### Info

Denote the elements of the field $F_{4}$ by ${0, 1, w, w + 1}$, where w satisfies the following equation with coefficients in $F2: w^{2} + w + 1 = 0$. Bumerang is a recurrent double sequence defined by $a(i, 0) = a(0, j) = 1$ and $a(i, j) = f(a(i, j-1), a(i-1, j-1), a(i-1, j) )$, where $f(x, y, z ) = w x^{2} + x + w y^{2} + w z^{2} + (w + 1) z$. This recurrent double sequence can be also obtained using a system of substitutions of type 4 -> 8 with 16 rules, as it follows.