The formula I have is
 //Pixel(x,y)
 for(int xi=0; xi<n;xi++){
    double rx = Math.random();
    double ry = Math.random();
    double xs = x + (xi+rx)/n;
    double ys = y + (yi+ry)/n;
    ...
 }

public class Main {

    static String   name    = "doc/a01.png";
    static int      width   = 480;
    static int      height  = 270;

    public static void main(String[] args) {
        BufferedImage image = new BufferedImage(width, height, BufferedImage.TYPE_INT_RGB);

        for (int x = 0; x != width; x++) {
            for (int y = 0; y != height; y++) {
                double rx = Math.random();
                image.setRGB(x, y, StratifiedSampling(x,y));
            }
        }

        try {
            File outputfile = new File(name);
            ImageIO.write(image, "png", outputfile);
            System.out.println("Wrote image: " + name);
        } catch (IOException e) {
            System.out.println("Something went wrong: " + e);
        }
    }
    static int StratifiedSampling(int x,int y){
        double sum = 0;
        final int samples = 100;
        for(int xi=0; xi<samples;xi++){
            for(int yi=0; yi<samples;yi++){
                double rx = Math.random();
                double ry = Math.random();
                double xs = x + (xi+rx)/samples;
                double ys = y + (yi+ry)/samples;
                //System.out.println((int)xs+" "+(int)ys);
                sum = sum + colorForCircle((int)xs,(int)ys);
            }
        }
        return (int)sum/samples;
    }

    static int colorForCircle(int x1, int y1){
        double x2 = x1;
        double y2 = y1;
        //System.out.println( 0 + (255 - 0) * y1/height);
        int centerX = 240;
        int centerY = 135;
        double radius = 40;
        if( Math.pow( (x2 - centerX),2) +  Math.pow((y2 - centerY),2) < Math.pow(radius,2)){
            return new Color(255, 0, 0).getRGB();
        }
        else {
            double t = y2/height;
            int value = (int) (t* 255);
            int value2 = (int) (Math.pow (t,1/2.2)* 255);
            return new Color(0, 0, value).getRGB();
        }
    }
}