Looking for ideas how to refactor my algorithm

It should not be difficult to write your algorithm to search all of the cells within the reach distance of a particular cell C. Each cell that has an inhabitant would have a particular force of repulsion on cell C. This force of repulsion is based on the distance from the cell to cell C. In the example that you have given, that force of repulsion is based upon the L-1 distance and is 2^(reach-distance). Each repulsion force is then added together to create a cumulative force that dictates the direction in which to move the inhabitant in cell C.

You do not need to write an algorithm for each different reach. The magnitude of the force can be determined via a simple formula. If you change that formula to something else such as a Fibonacci number, you should still be able to calculate the magnitude as needed based upon the distance and the reach.

---

Here is some rough code written in pseudo-Java showing the basic ideas: http://codepad.org/K6zxnOAx

enum Direction {Left, Right, Up, Down, None};

Direction push(boolean board[][], int testX, int testY, int reach)
{
    int xWeight = 0;
    int yWeight = 0;
    for (int xDist=-reach; xDist<=+reach; ++xDist)
    {
        for (int yDist=-reach; yDist<=+reach; ++yDist)
        {
            int normDist = abs(xDist) + abs(yDist);
            if (0<normDist && normDist<reach)
            {
                int x = testX + xDist;
                int y = testY + yDist;
                if (0<=x && x<board.length && 0<=y && y<board[0].length)
                {
                   if (board[x][y])
                   {
                       int force = getForceMagnitude(reach, normDist);
                       xWeight += sign(xDist) * force;
                       yWeight += sign(yDist) * force;
                   }
                }
            }
        }
    }
    if (xWeight==0 && yWeight==0) return Direction.None;
    if (abs(xWeight) > abs(yWeight))
    {
        return xWeight<0 ? Direction.Left : Direction.Right;
    }
    else
    {
        return yWeight<0 ? Direction.Up : Direction.Down;
    }
}

int getForceMagnitude(int reach, int distance)
{
    return 1<<(reach-distance);
}