Task: Archimedean spiral
Go: package main

import (
	"image"
	"image/color"
	"image/draw"
	"image/png"
	"log"
	"math"
	"os"
)

func main() {
	const (
		width, height = 600, 600
		centre        = width / 2.0
		degreesIncr   = 0.1 * math.Pi / 180
		turns         = 2
		stop          = 360 * turns * 10 * degreesIncr
		fileName      = "spiral.png"
	)

	img := image.NewNRGBA(image.Rect(0, 0, width, height)) 
	bg := image.NewUniform(color.RGBA{255, 255, 255, 255}) 
	draw.Draw(img, img.Bounds(), bg, image.ZP, draw.Src)   
	fgCol := color.RGBA{255, 0, 0, 255}                    

	a := 1.0
	b := 20.0

	for theta := 0.0; theta < stop; theta += degreesIncr {
		r := a + b*theta
		x := r * math.Cos(theta)
		y := r * math.Sin(theta)
		img.Set(int(centre+x), int(centre-y), fgCol)
	}

	imgFile, err := os.Create(fileName)
	if err != nil {
		log.Fatal(err)
	}
	defer imgFile.Close()

	if err := png.Encode(imgFile, img); err != nil {
		imgFile.Close()
		log.Fatal(err)
	}
}

Java: import java.awt.*;
import static java.lang.Math.*;
import javax.swing.*;

public class ArchimedeanSpiral extends JPanel {

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

    void drawGrid(Graphics2D g) {
        g.setColor(new Color(0xEEEEEE));
        g.setStroke(new BasicStroke(2));

        double angle = toRadians(45);

        int w = getWidth();
        int center = w / 2;
        int margin = 10;
        int numRings = 8;

        int spacing = (w - 2 * margin) / (numRings * 2);

        for (int i = 0; i < numRings; i++) {
            int pos = margin + i * spacing;
            int size = w - (2 * margin + i * 2 * spacing);
            g.drawOval(pos, pos, size, size);

            double ia = i * angle;
            int x2 = center + (int) (cos(ia) * (w - 2 * margin) / 2);
            int y2 = center - (int) (sin(ia) * (w - 2 * margin) / 2);

            g.drawLine(center, center, x2, y2);
        }
    }

    void drawSpiral(Graphics2D g) {
        g.setStroke(new BasicStroke(2));
        g.setColor(Color.orange);

        double degrees = toRadians(0.1);
        double center = getWidth() / 2;
        double end = 360 * 2 * 10 * degrees;
        double a = 0;
        double b = 20;
        double c = 1;

        for (double theta = 0; theta < end; theta += degrees) {
            double r = a + b * pow(theta, 1 / c);
            double x = r * cos(theta);
            double y = r * sin(theta);
            plot(g, (int) (center + x), (int) (center - y));
        }
    }

    void plot(Graphics2D g, int x, int y) {
        g.drawOval(x, y, 1, 1);
    }

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

        drawGrid(g);
        drawSpiral(g);
    }

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