One way to draw a Sierpinski gasket is to start with 3 corners. To generate a point, randomly pick a corner and move halfway between the current position and the selected corner. See Draw a Sierpinski gasket in C# for more information.

This example lets you pick corners at run time. Left-click on the form to pick at least 2 points. Then right-click to start the program running. The program uses the following code to draw the modified gasket.

// Draw 1,000 points.
private void tmrDraw_Tick(object sender, EventArgs e)
{
    // Draw points.
    Random rand = new Random();
    using (Graphics gr = this.CreateGraphics())
    {
        // Draw the corners.
        foreach (PointF pt in Corners)
        {
            gr.FillEllipse(Brushes.White, pt.X - RADIUS, pt.Y - RADIUS, 2 * RADIUS, 2 * RADIUS);
            gr.DrawEllipse(Pens.Blue, pt.X - RADIUS, pt.Y - RADIUS, 2 * RADIUS, 2 * RADIUS);
        }

        // Draw 1000 points.
        for (int i = 1; i <= 1000; i++)
        {
            int j = rand.Next(0, Corners.Count);
            LastPoint = new Point(
                (LastPoint.X + Corners[j].X) / 2,
                (LastPoint.Y + Corners[j].Y) / 2);
            gr.DrawLine(Pens.Blue, LastPoint.X, LastPoint.Y,
                LastPoint.X + 1, LastPoint.Y + 1);
        }
    }
}

For some interesting results, try:

• Use four corners that make a rectangle.
• Use a scalene triangle.
• Use a triangle and add 4 or 5 "corners" in the same spot near the middle.
• Try other arrangements with duplicate corners.