Open Peano

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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

Rule Open Peano

Patch

Patch Open Peano