I'm not sure if this was done more out of demonstrating the code, but why not take:

    double ***ptr3;
    ptr3 = new double**[2];
    for( int i = 0 ; i < 2 ; i++)
    {
        ptr3[i] = new  double*[3];
    }
    for( int i = 0 ; i < 2 ; i++)
    {
        for( int j = 0 ; j < 3 ; j++)
        {
            ptr3[i][j] = new  double[4];
        }
    }

    for( int i = 0 ; i < 2 ; i++)
    {
        for( int j = 0 ; j < 3 ; j++)
        {
            for( int k = 0 ; k < 4 ; k++)
            {
                ptr3[i][j][k] = ( i * 3 + j ) * 4.1 + k * 0.1;
            }
        }
    }

And make it:

    double ***ptr3;
    ptr3 = new double**[2];
    for( int i = 0 ; i < 2 ; i++)
    {
        ptr3[i] = new  double*[3];
        for( int j = 0 ; j < 3 ; j++)
        {
            ptr3[i][j] = new  double[4];
            for( int k = 0 ; k < 4 ; k++)
            {
                ptr3[i][j][k] = ( i * 3 + j ) * 4.1 + k * 0.1;
            }
        }
    }