Java Sierpinski Triangle Random

Java program to generate Sierpinski Triangle (Fractal) of specified resolution using Random algorithm, even in high resolutions ? tested for 40000x40000px with increased Java VM heap size ? -Xmx8g option.

Note that the more steps, the more acurate triangle is represented.

Main.java

import javax.imageio.ImageIO;
import java.io.File;

// 2018 TheFlyingKeyboard and released under MIT License
// theflyingkeyboard.net
public class Main {
    public static void main(String[] args) {
        SierpinskiTriangle sierpinskiTriangle = new SierpinskiTriangle();

        try {
            ImageIO.write(sierpinskiTriangle.generate(40000, 10000000), "png", new File("SierpinskiTriangle.png"));
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
}

Point2D.java

// 2018 TheFlyingKeyboard and released under MIT License
// theflyingkeyboard.net
public class Point2D {
    private final double x;
    private final double y;

    public Point2D(double x, double y) {
        this.x = x;
        this.y = y;
    }

    public Point2D(Point2D point) {
        this.x = point.getX();
        this.y = point.getY();
    }

    public double getX() {
        return x;
    }

    public double getY() {
        return y;
    }
}

SierpinskiTriangle.java

import java.awt.*;
import java.awt.image.BufferedImage;
import java.awt.image.DataBufferInt;
import java.util.concurrent.ThreadLocalRandom;

// 2018 TheFlyingKeyboard and released under MIT License
// theflyingkeyboard.net
public class SierpinskiTriangle {
    private final int foregroundColor;
    private final int backgroundColor;
    private int[] imagePixelData;

    public SierpinskiTriangle() {
        this.foregroundColor = Color.BLACK.getRGB();
        this.backgroundColor = Color.WHITE.getRGB();
    }

    public SierpinskiTriangle(final Color foregroundColor, final Color backgroundColor) {
        this.foregroundColor = foregroundColor.getRGB();
        this.backgroundColor = backgroundColor.getRGB();
    }

    public BufferedImage generate(final int triangleSize, final int steps) {
        BufferedImage bufferedImage = new BufferedImage(triangleSize, triangleSize, BufferedImage.TYPE_INT_RGB);
        imagePixelData = ((DataBufferInt) bufferedImage.getRaster().getDataBuffer()).getData();

        setBackground(triangleSize);

        int triangleHeight = (int) Math.round(triangleSize * Math.sqrt(3.0d) / 2.0d);
        Point2D pointA = new Point2D(0, triangleHeight);
        Point2D pointB = new Point2D(triangleSize / 2, 0);
        Point2D pointC = new Point2D(triangleSize, triangleHeight);

        Point2D newPoint = new Point2D(pointA);

        for (int i = 0; i < steps; ++i) {
            imagePixelData[(int) (newPoint.getY()) * triangleSize + (int) (newPoint.getX())] = foregroundColor;

            switch (ThreadLocalRandom.current().nextInt(3)) {
                case 0:
                    newPoint = middlePoint(newPoint, pointA);
                    break;
                case 1:
                    newPoint = middlePoint(newPoint, pointB);
                    break;
                case 2:
                    newPoint = middlePoint(newPoint, pointC);
                    break;
            }

            System.out.println(((double) i / steps) * 100.0d + "%");
        }

        return bufferedImage;
    }

    private void setBackground(final int triangleSize) {
        for (int x = 0; x < triangleSize; ++x) {
            for (int y = 0; y < triangleSize; ++y) {
                imagePixelData[y * triangleSize + x] = backgroundColor;
            }
        }
    }

    private Point2D middlePoint(Point2D pointA, Point2D pointB) {
        return new Point2D((pointA.getX() + pointB.getX()) / 2, (pointA.getY() + pointB.getY()) / 2);
    }
}