// numNeighbours
    // ------------------------------------------------------------------
    // Return the number of neighbours of the cell at (row,col) in my grid.

    public int numNeighbours (int row, int col) {
    
        // Set num to -1 if theGrid[row][col] has a LiveCell, 0 otherwise.
        // This allows us to write much nicer while loops below; we don't need
        // an extra if-statement to skip the current cell at (row,col).
        int num = theGrid[row][col] instanceof LiveCell ? -1 : 0;

        // The current row we are looking at.  We must modulo with numRows()
        // because we want to wrap around the board.
        int r = (row-1+numRows()) % numRows();
        
        // While we are within 1 row of the current location...
        while (r != (row+2) % numRows()) {

            int c = (col-1+numCols()) % numCols();

            // While we are within 1 column of the current location...
            while (c != (col+2) % numCols()) {

                // If theGrid is a LiveCell, increment num.
                if (theGrid[r][c] instanceof LiveCell)  {
                    num ++;
                }

                c = (c+1) % numCols();
            }

            r = (r+1) % numRows();
        }

        return num;
    }

    // nextGeneration
    // ------------------------------------------------------------------
    // Compute the next generation of cells and store it in theGrid.

    public void nextGeneration () {
    
        // The next generation of Cells.
        Cell [][] nextGrid = new Cell [numRows()][numCols()];

        // For each row and column, tell the Cell at that location in theGrid
        // to evolve, and store the result in nextGrid.
        int row;
        for (row = 0; row < numRows(); row++) {
            int col;
            for (col = 0; col < numCols(); col++) {
                nextGrid[row][col] = theGrid[row][col].evolve 
                                           (numNeighbours (row, col));
            }
        }

        // The new generation is now computed, and stored in nextGrid.  Save
        // it in theGrid.
        theGrid = nextGrid;
    }
}