Dragon curve (memory inefficient)

dragon.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;


namespace dragon
{
	internal struct Vector2
	{
		public Vector2(double x, double y)
		{
			this.x = x;
			this.y = y;
		}

		public double x;
		public double y;

		public static Vector2 operator +(Vector2 l, Vector2 r)
		{
			return new Vector2(l.x + r.x, l.y + r.y);
		}

		public static Vector2 operator -(Vector2 l, Vector2 r)
		{
			return new Vector2(l.x - r.x, l.y - r.y);
		}

		public Vector2 turn()
		{
			return new Vector2(y, -x);
		}

		public override string ToString()
		{
			return "(" + x.ToString() + ", " + y.ToString() + ")";
		}
	}

	class Program
	{
		private static int u(int n)
		{
			if (n == 0)
			{
				return 2;
			}
			return u(n - 1) * 2 - 1;
		}

		private static Vector2[] v(int n)
		{
			if (n == 0)
			{
				return new Vector2[]
				{
					new Vector2(-1, 0),
					new Vector2(0, 0)
				};
			}

			Vector2[] prev = v(n - 1);

			return prev.Take(prev.Length - 1).Concat(
					prev.Reverse()
					.Select(x => (x - prev.Last()).turn() + prev.Last())
				).ToArray();
		}

		private static void plot(Vector2[] curve)
		{
			double[] borders = new double[4];
			foreach (Vector2 vec in curve)
			{
				borders[0] = Math.Min(borders[0], vec.x);
				borders[1] = Math.Min(borders[1], vec.y);
				borders[2] = Math.Max(borders[2], vec.x);
				borders[3] = Math.Max(borders[3], vec.y);
			}

			int w = (int)(borders[2] - borders[0] + 1) * 2;
			int h = (int)(borders[3] - borders[1] + 1) * 2;
			char[,] chars = new char[w, h];
			for (int x = 0; x < w; ++x)
			{
				for (int y = 0; y < h; ++y)
				{
					chars[x, y] = ' ';
				}
			}
			Vector2 prev = curve.First();
			prev.x -= borders[0];
			prev.y -= borders[1];
			for (int i = 1; i < curve.Length; ++i)
			{
				Vector2 curr = curve[i];
				curr.x -= borders[0];
				curr.y -= borders[1];
				for (int x = (int)Math.Min(curr.x, prev.x) * 2; x <= (int)Math.Max(curr.x, prev.x) * 2; ++x)
				{
					for (int y = (int)Math.Min(curr.y, prev.y) * 2; y <= (int)Math.Max(curr.y, prev.y) * 2; ++y)
					{
						chars[x, y] = '#';
					}
				}
				prev = curr;
			}
			StringBuilder builder = new StringBuilder();
			for (int y = 0; y < h; ++y)
			{
				for (int x = 0; x < w; ++x)
				{
					builder.Append(chars[x, y]);
				}
				builder.AppendLine();
			}
			System.IO.File.WriteAllText(curve.Length + ".txt", builder.ToString());
		}

		static void Main(string[] args)
		{
			const int numIt = 21;
			Vector2[][] iterations = new Vector2[numIt][];
			double[,] borders = new double[numIt, 4];
			for (int i = 0; i < iterations.Length; ++i)
			{
				iterations[i] = v(i);
				plot(iterations[i]);
			}
			Console.ReadKey();
		}
	}
}