I have a 6x6 grid, and in its first cell (row 1, column 1), its value is (-3, 2) and on its last cell (row 6, cell 6), its value is (2, -3).
Another values inside this grid are:
$(x_0, y_0) => (x_1, y_1)$
(1, 2) => (-2, 2)
(1, 3) => (-1, 2)
(1, 4) => (0, 2)
(1, 5) => (1, 2)
(1, 6) => (2, 2)
(2, 1) => (-3, 1)
(3, 1) => (-3, 0)
(4, 1) => (-3, -1)
(5, 1) => (-3, -2)
(6, 1) => (-3, -3)
$(x_0, y_0)$ are the row, column of the grid, and $(x_1, y_1)$ are the values on each cell.
Is there any formula to translate $(x_0, y_0)$ into $(x_1, y_1)$?
Maybe the grid will be bigger than 6x6 (or smaller...). All the grids will be nxn., and the first cell will be always (-n/2, n/2 - 1).
Based on the data you provided, for the $6\times 6$ grid the formulas would be \begin{align} x_1 &= y_0 - 4, \\ y_1 &= 3 - x_0. \end{align}
Based on the information that the grid is always square and that for an $n\times n$ grid, the cell at $x_0=y_0=1$ has $x_1 = -\frac n2$ and $y_1 = \frac n2 - 1,$ the general formulas are \begin{align} x_1 &= y_0 - \left(\frac n2 + 1\right), \\ y_1 &= \frac n2 - x_0. \end{align}
Note that $\frac n2$ is not an integer if $n$ is odd. If $n$ is always even, however, then $x_1$ and $y_1$ will be integers.
The clues that lead to these formulas are that $x_1$ is constant when $y_0$ is constant, $y_1$ is constant when $x_0$ is constant, $x_1$ increases when $y_0$ increases, and $y_1$ decreases when $x_0$ increases. This tells us we need formulas $x_1 = y_0 + a$ and $y_1 = b - x_0$ for some constants $a$ and $b.$ Then use the values of $x_1$ and $y_1$ when $x_0=y_0=1$ to figure out what $a$ and $b$ must be.