## Mothman

### Info

Denote the elements of the field `$F_{4}$`

by `$\{0, 1, w, w + 1\}$`

, where `$w$`

satisfies the following equation with coefficients in `$F_{2}: w^{2} + w + 1 = 0$`

.
Mothman 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 `$f(x, y, z) = x^{2} + (w + 1) y^{2} + z^{2}$`

.
This recurrent double sequence can be also obtained using a system of substitutions of type 2 -> 4 with 15 rules, as it follows.

### Substitution Rule

### Patch