## Open Peano

### Info

Denote the elements of the field `$F_4$`

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

, where `$w$`

satisfies the following equation with coefficients in `$F_2: w2 + w + 1 = 0$`

.
Open Peano is a recurrent double sequence defined by `$a(i, 0) = a(0, j) = w + 1$`

and `$a(i, j) = f(a(i, j-1), a(i-1, j-1), a(i-1, j))$`

, where `$f(x, y, z) = w x^2 + w y + w z^2$`

.
This recurrent double sequence can be also obtained using a system of substitutions of type 2 -> 4 with 7 rules, as it follows.

### Substitution Rule

### Patch