Game of Life Algorithm

The Rules

Conway's Game of Life is a cellular automaton with simple rules:

1. Birth: A dead cell with exactly 3 live neighbors becomes alive
2. Survival: A live cell with 2-3 live neighbors stays alive
3. Death: All other cells die (overcrowding or loneliness)

Implementation Approach

Grid Representation

Two common approaches:

1. 2D Array:

struct Universe {
    width: u32,
    height: u32,
    cells: Vec<Cell>,
}

2. Flat Array with Index Calculation:

fn get_index(&self, row: u32, col: u32) -> usize {
    (row * self.width + col) as usize
}

Double Buffering

To avoid conflicts when updating cells:

• Read from current state
• Write to next state
• Swap buffers

Counting Neighbors

For each cell at (row, col), check the 8 surrounding cells:

const NEIGHBORS: [(i32, i32); 8] = [
    (-1, -1),
    (-1, 0),
    (-1, 1),
    (0, -1),
    (0, 1),
    (1, -1),
    (1, 0),
    (1, 1),
];

Each number corresponds to NEIGHBORS array index. The tuples show (row_offset,col_offset)

[0][1][2]     (-1,-1) (-1, 0) (-1,+1)   
[3][X][4]  ←  ( 0,-1)    X    ( 0,+1)  Current cell
[5][6][7]     (+1,-1) (+1, 0) (+1,+1)

fn live_neighbor_count(&self, row: u32, column: u32) -> u8 {
    NEIGHBORS
        .iter()  // Iterate over all 8 neighbor offsets
        .map(|&(dr, dc)| {
            // Apply offset and wrap around edges
            // rem_euclid handles negative numbers correctly for wrapping
            let neighbor_row = (row as i32 + dr).rem_euclid(self.height as i32) as u32;
            let neighbor_col = (column as i32 + dc).rem_euclid(self.width as i32) as u32;
            
            // Get the cell state (0 = dead, 1 = alive)
            let idx = self.get_index(neighbor_row, neighbor_col);
            self.cells[idx] as u8
        })
        .sum()  // Count total live neighbors
}

Optimization Ideas

• Bit packing: Store cells as bits instead of bytes
• SIMD: Use vectorized operations for neighbor counting
• Sparse representation: Only track live cells in sparse grids
• WebWorkers: Divide grid into chunks for parallel processing

Next Steps

• Implement basic algorithm
• Add performance profiling
• Explore WebGPU compute shaders for massive grids