C# Linqpad script with classes, to model a problem I was trying to solve.

Squares.linqpad

void Main()
{
	new Square(-3,-1).Dump();
}

public class Square
{
	public Square(int x, int y)
	{
		this.x = x;
		this.y = y;
	}
	
	private int x;
	private int y;
	
	public Ring Ring => new Ring(Math.Max(Math.Abs(x), Math.Abs(y)));
	
	public void MoveUp() {
		y++;
	}
	
	public void MoveLeft() {
		var currentRing = Ring;
		x--;
	}
	
	public void MoveRight() {
		x++;
	}
	
	public void MoveDown() {
		y--;
	}
	
	public int Number 
	{
		get 
		{
			if (Ring.Number == 0)
				return 1;

			if (Math.Abs(y) == Ring.Number) {
				return (y >= 0 ? Ring.PositiveYValue + x : Ring.NegativeYValue -x);
			}
			 
			// If y doesn't equal ring number, X must, or it'd be a different ring.
			return (x >= 0 ? Ring.PositiveXValue - y : Ring.NegativeXValue + y);
		}
	}
}

public class Ring
{
	public Ring(int number)
	{
		Number = number;
	}
	
	public int Number;
	
	public int Size => GetSize(Number);
	
	public static int GetSize(int ring) 
	{
		if (ring == 0)
			return 1;
			
		if (ring == 1)
			return 8;
			
		return GetSize(ring - 1) + 8; 
	}
	
	public int PositiveXValue => GetPositiveX(Number);
	public int PositiveYValue => GetPositiveY(Number);
	public int NegativeXValue => GetNegativeX(Number);
	public int NegativeYValue => GetNegativeY(Number);
	
	private int GetNegativeX(int ringNumber)
	{
		if (ringNumber == 0)
			return 1;
				
		return GetNegativeXJump(ringNumber) + GetNegativeX(ringNumber - 1);
	}
	
	private int GetNegativeY(int ringNumber)
	{
		if (ringNumber == 0)
			return 1;
		
		return GetNegativeYJump(ringNumber) + GetNegativeY(ringNumber - 1);
	}
	
	private int GetPositiveY(int ringNumber)
	{
		if (ringNumber == 0)
			return 1;

		return GetPositiveYJump(ringNumber) + GetPositiveY(ringNumber - 1);
	}
	
	private int GetPositiveX(int ringNumber)
	{
		if (ringNumber == 0)
			return 1;
		
		return  GetPositiveXJump(ringNumber) +  GetPositiveX(ringNumber - 1);
	}
	
	private int GetPositiveXJump(int ringNumber)
	{		
		if (ringNumber == 1)
			return 3;
		
		return 8 + GetPositiveXJump(ringNumber - 1);
	}
	
	private int GetPositiveYJump(int ringNumber)
	{	
		if (ringNumber == 1)
			return 1;
		
		return 8 + GetPositiveYJump(ringNumber - 1);
	}
	
	private int GetNegativeXJump(int ringNumber)
	{	
		if (ringNumber == 1)
			return 7;
			
		return 8 + GetNegativeXJump(ringNumber - 1);
	}
	
	private int GetNegativeYJump(int ringNumber)
	{	
		if (ringNumber == 1)
			return 5;
			
		return 8 + GetNegativeYJump(ringNumber - 1);
	}
}