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Patrick2788's avatar
Patrick2788
Silver Contributor
Jan 26, 2024
Thank you for taking a look. I've determined the 'SW' check is missing. The formula sees the cell as 0 with the neighbors for the cell at 2 so it's not making it live. If I'm able to have some uninterrupted time at work I may be able to fix it.
Patrick2788's avatar
Patrick2788
Silver Contributor
Jan 27, 2024

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.

  • Patrick2788's avatar
    Patrick2788
    Silver Contributor
    Jan 29, 2024

    Here are the timings for each solution:

     

    timer used: vba - fullrecalc

    100 iterations - average of 5 times

    Original - 3.33 seconds
    PB - .6189 seconds
    MAKEARRAY- .8585 seconds
    - on a 36x150 board - 10 iterations - about 8 seconds

    • m_tarler's avatar
      m_tarler
      Bronze Contributor
      Feb 01, 2024

      Patrick2788  Again a fun and interesting challenge but I went a very different route (I know imagine that).  Here is my solution without any LAMBDA inside:

       

      LIFE=LAMBDA(matrix, iterations,
  LET(
    matrix2, IF(iterations > 1, Life(matrix, iterations - 1), matrix),
    m, IFERROR(VSTACK(0, HSTACK(0, matrix2, 0), 0), 0),
    neighbors, VSTACK(0, HSTACK(0, m)) + VSTACK(0, m) + VSTACK(0, DROP(m, , 1)) + DROP(m, , 1) +
        HSTACK(0, m) + HSTACK(0, DROP(m, 1)) + DROP(m, 1) + DROP(m, 1, 1),
    alive_neighbors, neighbors * m,
    --DROP(
        DROP(((neighbors = 3) + ((alive_neighbors > 1) * (alive_neighbors < 4)) > 0), 1, 1),
        -2,
        -2
    )
)

       

      • Patrick2788's avatar
        Patrick2788
        Silver Contributor
        Feb 02, 2024

        m_tarler 

        I like the way you terminate the loop immediately within the first parameter ('matrix2') of LET. My usual go-to is terminating the function with an IF before the function is called in predicable fashion. It's good to see it done smoothly with your formula.

        Pad the matrix to make sure each cell has 8 adjacent cells and some clever stacking and addition to find the neighbors. The use of DROP here is a throwback to ctrl+shift+enter arrays and it's elegant here and no logical IF/AND/OR needed! I like the economy of this formula. Thanks for sharing!

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