## Infinity

### Info

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

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

, where `$w$`

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

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

.
This recurrent double sequence can be also obtained using a system of substitutions of type 2 -> 4 with 5 rules.

What we present here are only the rules, renormed as system of substitutions of type 1 -> 2.
The 2 × 2 minors appearing in the double sequences in even positions are replaced by simple squares,
introducing for every of the 5 occurring 2 `$\times$`

2 minor a new color.
The system of substitutions of type 1 -> 2 got this way is called skeleton of the original system of substitutions.
What you see here is “the skeleton of Infinity”.

### Substitution Rule

### Patch

download vectorformat Infinity