C# - Need help creating program that simulates Prime Number behavior by drawing lines

Question

I challenged myself to create a program to experiment with Prime Numbers, I already have an idea how to do it, but not the coding skills..

My plan is this: First ill create a program in C# that makes straight lines that follow some rules:

rule 1: all lines have the same length.

rule 2: all lines are either horizontal or vertical (no diagonals).

rule 3: Every new line begins where the previous line has ended (that way all the lines are joined).

Now for the tricky part:

I would like to make a counter that goes up by 1 each time a new line is created (starting value is 1 I presume), and whenever it reaches a prime number, the lines change 'direction' and start 'going' to the left of the original direction.

The first 10 lines will look something like this:

      |
 __   |
|  |  |
|__ __|

Notice how it changed direction at the 2nd, 3rd, 5th and 7th line.

(starting from the inside ending at the outside)

This will create a long twisting line and it will be pretty cool to see what pattern it makes.

Thanks for helping!

Answer 1

This was a fun project to play with. Thanks for my morning entertainment!

I used SLaks code in this SO thread to get a list of Primes less than a specified number.

Here is some sample output:

After generating the Primes, I walk the list and store the lines in a GraphicsPath . Using the Graphics.GetBounds() method then allows us to appropriately scale and transform the Graphics in the Paint() event of our Panel so that the entire drawing can be seen:

public partial class Form1 : Form
{

    private const int segmentLength = 10;
    private GraphicsPath gpPrimes = null;

    public Form1()
    {
        InitializeComponent();
        nudLessThanMax.Minimum = 15;
        nudLessThanMax.Maximum = 500000;
        nudLessThanMax.Value = nudLessThanMax.Minimum;
        pnlPrimes.Paint += PnlPrimes_Paint;
        pnlPrimes.SizeChanged += PnlPrimes_SizeChanged;
    }

    private void PnlPrimes_SizeChanged(object sender, EventArgs e)
    {
        pnlPrimes.Invalidate();
    }

    private void PnlPrimes_Paint(object sender, PaintEventArgs e)
    {
        if (gpPrimes != null)
        {
            RectangleF rectF = gpPrimes.GetBounds();
            float max = Math.Max(rectF.Width + (2 * segmentLength), rectF.Height + (2 * segmentLength));
            e.Graphics.TranslateTransform(pnlPrimes.Width / 2, pnlPrimes.Height / 2);
            e.Graphics.ScaleTransform((float)pnlPrimes.Width / max, (float)pnlPrimes.Height / max);
            e.Graphics.TranslateTransform(-(rectF.Left + rectF.Width / 2), -(rectF.Top + rectF.Height / 2));
            e.Graphics.DrawPath(Pens.Black, gpPrimes);
        }
    }

    private void btnGraphPrimes_Click(object sender, EventArgs e)
    {
        btnGraphPrimes.Enabled = false;
        backgroundWorker1.RunWorkerAsync((int)this.nudLessThanMax.Value);
    }

    private List<int> PrimesLessThan(int num) // SLaks: https://stackoverflow.com/a/1510186/2330053
    {
        return Enumerable.Range(0, (int)Math.Floor(2.52 * Math.Sqrt(num) / Math.Log(num))).Aggregate(
            Enumerable.Range(2, num - 1).ToList(),
            (result, index) =>
            {
                var bp = result[index]; var sqr = bp * bp;
                result.RemoveAll(i => i >= sqr && i % bp == 0);
                return result;
            }
        );
    }

    private void backgroundWorker1_DoWork(object sender, DoWorkEventArgs e)
    {
        int diff;
        int num = (int)e.Argument;
        Point pt = new Point(0, 0);
        Point pt2 = pt;
        GraphicsPath gp = new GraphicsPath();
        List<int> primes = PrimesLessThan(num);

        for(int i = 1; i < primes.Count; i++)
        {
            diff = primes[i] - primes[i - 1];
            switch(i % 4)
            {
                case 1: // up
                    pt2 = new Point(pt.X, pt.Y - (segmentLength * diff));
                    break;

                case 2: // left
                    pt2 = new Point(pt.X - (segmentLength * diff), pt.Y);
                    break;

                case 3: // down
                    pt2 = new Point(pt.X, pt.Y + (segmentLength * diff));
                    break;

                case 0: // right
                    pt2 = new Point(pt.X + (segmentLength * diff), pt.Y);
                    break;
            }
            gp.AddLine(pt, pt2);
            pt = pt2;
        }
        gpPrimes = gp;
        e.Result = primes;
    }

    private void backgroundWorker1_RunWorkerCompleted(object sender, RunWorkerCompletedEventArgs e)
    {
        lbPrimes.DataSource = (List<int>)e.Result;
        pnlPrimes.Invalidate();
        btnGraphPrimes.Enabled = true;
    }

}

Answer 2

Once again I wish I had enough points to make this just a comment, but I wanted to make sure you knew ahead of time this will not result in a sprial all the way out. There are pairs of primes only 2 apart (n, n+2 both prime) which will make your snake do a 180 and cross over itself.

If you are OK with that, then look into the System.Drawing namespace, especially at the Graphics.Drawline method. Or have a look at a little code that will help give you the right idea. Just put a pictureBox in a Windows Form and this code will put a line on it. From there you can work on your pen colors, scale, finding your primes, etc.

        Bitmap bmp = new Bitmap(pictureBox1.Width, pictureBox1.Height);
        using (Graphics g = Graphics.FromImage(bmp))
        {
            g.DrawLine(new Pen(Color.Red), 300, 100, 100, 100);
        }
        pictureBox1.Image = bmp;