Task: Polyspiral
C#: using System;
using System.Drawing;
using System.Drawing.Drawing2D;
using System.Windows.Forms;
using System.Windows.Threading;

namespace Polyspiral
{
    public partial class Form1 : Form
    {
        private double inc;

        public Form1()
        {
            Width = Height = 640;
            StartPosition = FormStartPosition.CenterScreen;
            SetStyle(
                ControlStyles.AllPaintingInWmPaint |
                ControlStyles.UserPaint |
                ControlStyles.DoubleBuffer,
                true);

            var timer = new DispatcherTimer();
            timer.Tick += (s, e) => { inc = (inc + 0.05) % 360; Refresh(); };
            timer.Interval = new TimeSpan(0, 0, 0, 0, 40);
            timer.Start();
        }

        private void DrawSpiral(Graphics g, int len, double angleIncrement)
        {
            double x1 = Width / 2;
            double y1 = Height / 2;
            double angle = angleIncrement;

            for (int i = 0; i < 150; i++)
            {
                double x2 = x1 + Math.Cos(angle) * len;
                double y2 = y1 - Math.Sin(angle) * len;
                g.DrawLine(Pens.Blue, (int)x1, (int)y1, (int)x2, (int)y2);
                x1 = x2;
                y1 = y2;

                len += 3;

                angle = (angle + angleIncrement) % (Math.PI * 2);
            }
        }

        protected override void OnPaint(PaintEventArgs args)
        {
            var g = args.Graphics;
            g.SmoothingMode = SmoothingMode.AntiAlias;
            g.Clear(Color.White);

            DrawSpiral(g, 5, ToRadians(inc));
        }

        private double ToRadians(double angle)
        {
            return Math.PI * angle / 180.0;
        }
    }
}

Java: import java.awt.*;
import java.awt.event.ActionEvent;
import javax.swing.*;

public class PolySpiral extends JPanel {
    double inc = 0;

    public PolySpiral() {
        setPreferredSize(new Dimension(640, 640));
        setBackground(Color.white);

        new Timer(40, (ActionEvent e) -> {
            inc = (inc + 0.05) % 360;
            repaint();
        }).start();
    }

    void drawSpiral(Graphics2D g, int len, double angleIncrement) {

        double x1 = getWidth() / 2;
        double y1 = getHeight() / 2;
        double angle = angleIncrement;

        for (int i = 0; i < 150; i++) {

            g.setColor(Color.getHSBColor(i / 150f, 1.0f, 1.0f));

            double x2 = x1 + Math.cos(angle) * len;
            double y2 = y1 - Math.sin(angle) * len;
            g.drawLine((int) x1, (int) y1, (int) x2, (int) y2);
            x1 = x2;
            y1 = y2;

            len += 3;

            angle = (angle + angleIncrement) % (Math.PI * 2);
        }
    }

    @Override
    public void paintComponent(Graphics gg) {
        super.paintComponent(gg);
        Graphics2D g = (Graphics2D) gg;
        g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
                RenderingHints.VALUE_ANTIALIAS_ON);

        drawSpiral(g, 5, Math.toRadians(inc));
    }

    public static void main(String[] args) {
        SwingUtilities.invokeLater(() -> {
            JFrame f = new JFrame();
            f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
            f.setTitle("PolySpiral");
            f.setResizable(true);
            f.add(new PolySpiral(), BorderLayout.CENTER);
            f.pack();
            f.setLocationRelativeTo(null);
            f.setVisible(true);
        });
    }
}