Utilizing Excel's turing capabilities to create Conway's 'Game of Life'

Riny_van_Eekelen 

I've updated the Conway Lambda in the first post and replaced the workbook.  The issue was IFERROR was resolving to "" when it should have been 0.

PeterBartholomew1 

In re:

Stepλ(board)
=LAMBDA(r, c,
    LET(
        n, 18,
        state, INDEX(board, r, c),
        onboard, SIGN(MOD(r + δr, n + 1)) * SIGN(MOD(c + δc, n + 1)),
        count, SUM(IF(onboard, INDEX(board, r + δr, c + δc), 0)) - state,
        IF(state, SUM(SIGN(count = {2, 3})), SIGN(count = 3))
    )
)

This a really clever use of the functions available!  I like how you've really simplified the logic by approaching it this way.  My use of IF-AND-OR is slowing calculations a bit.

Below is my MAKEARRAY version.  I've compared the results up to 20 iterations against my original and Peter's solution and they're identical.

'Conway with MAKEARRAY
=LAMBDA(matrix,iterations,IF(
    iterations = 0,
    matrix,
    Conway(
        LET(
            height, ROWS(matrix),
            width, COLUMNS(matrix),
            CheckNeighbors, LAMBDA(r, c,
                LET(
                    grid_val, INDEX(matrix, r, c),
                    ext_rows, SEQUENCE(3, , r - 1),
                    ext_cols, SEQUENCE(, 3, c - 1),
                    Square3x3, INDEX(matrix, ext_rows, ext_cols),
                    neighbors, IF(
                        OR(r = 1, c = 1, r = height, c = width),
                        0,
                        SUM(Square3x3) - grid_val
                    ),
                    IF(
                        AND(grid_val = 0, neighbors = 3),
                        1,
                        IF(AND(grid_val = 1, OR(neighbors = 2, neighbors = 3)), 1, 0)
                    )
                )
            ),
            MAKEARRAY(height, width, CheckNeighbors)
        ),
        iterations - 1
    )
))

My goal was to simplify things - mainly the directional checks.  For this version I'm supplying the Lambda with a 'padded' matrix:

With MAKEARRAY I then 'offset' from the 'grid-val' with INDEX and the rest becomes simpler.