How to resolve the algorithm Julia set step by step in the Java programming language

Problem Statement
Step by Step Solution
Sourcecode

Problem Statement

Generate and draw a Julia set.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Julia set step by step in the Java programming language

Julia Set

The Julia set is a beautiful and complex fractal that can be generated using a simple mathematical formula. This Java program draws the Julia set using the Graphics class and the BufferedImage class.

How the Program Works

The program begins by creating a JuliaSet object and adding it to a JFrame. The JuliaSet object extends the JPanel class and overrides the paintComponent() method. The paintComponent() method is where the actual drawing of the Julia set takes place.

The drawJuliaSet() method is called from within the paintComponent() method. This method takes a Graphics2D object as an argument and uses it to draw the Julia set.

The first step is to create a BufferedImage object. The BufferedImage object will be used to store the pixels of the Julia set.

Next, the program loops through each pixel in the BufferedImage object. For each pixel, the program calculates the complex number c that corresponds to that pixel. The complex number c is then used to calculate the Julia set value for that pixel.

The Julia set value is a complex number that represents the number of iterations it takes for the complex number c to escape from the Mandelbrot set. If the complex number c does not escape from the Mandelbrot set, then the Julia set value is set to 0.

The program uses the Color.HSBtoRGB() method to convert the Julia set value to a color. The color is then used to set the pixel in the BufferedImage object.

Once all of the pixels in the BufferedImage object have been set, the program draws the BufferedImage object onto the Graphics2D object.

Parallelization

The program parallelizes the drawing of the Julia set by using the IntStream.range() and parallel() methods. This means that the program can draw the Julia set much faster than it could if it were to draw the set one pixel at a time.

Conclusion

This Java program is a simple but effective way to draw the Julia set. The program uses the Graphics class and the BufferedImage class to create a beautiful and complex fractal image.

Source code in the java programming language

import javax.swing.*;
import java.awt.*;
import java.awt.image.BufferedImage;

public class JuliaSet extends JPanel {
    private static final int MAX_ITERATIONS = 300;
    private static final double ZOOM = 1;
    private static final double CX = -0.7;
    private static final double CY = 0.27015;
    private static final double MOVE_X = 0;
    private static final double MOVE_Y = 0;

    public JuliaSet() {
        setPreferredSize(new Dimension(800, 600));
        setBackground(Color.white);
    }

    void drawJuliaSet(Graphics2D g) {
        int w = getWidth();
        int h = getHeight();
        BufferedImage image = new BufferedImage(w, h, BufferedImage.TYPE_INT_RGB);

        for (int x = 0; x < w; x++) {
            for (int y = 0; y < h; y++) {
                double zx = 1.5 * (x - w / 2) / (0.5 * ZOOM * w) + MOVE_X;
                double zy = (y - h / 2) / (0.5 * ZOOM * h) + MOVE_Y;
                float i = MAX_ITERATIONS;
                while (zx * zx + zy * zy < 4 && i > 0) {
                    double tmp = zx * zx - zy * zy + CX;
                    zy = 2.0 * zx * zy + CY;
                    zx = tmp;
                    i--;
                }
                int c = Color.HSBtoRGB((MAX_ITERATIONS / i) % 1, 1, i > 0 ? 1 : 0);
                image.setRGB(x, y, c);
            }
        }
        g.drawImage(image, 0, 0, null);
    }

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

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


import javax.swing.*;
import java.awt.*;
import java.awt.image.BufferedImage;
import java.util.stream.IntStream;

public class JuliaSet extends JPanel {
    private static final int MAX_ITERATIONS = 300;
    private static final double ZOOM = 1;
    private static final double CX = -0.7;
    private static final double CY = 0.27015;
    private static final double MOVE_X = 0;
    private static final double MOVE_Y = 0;

    public JuliaSet() {
        setPreferredSize(new Dimension(800, 600));
        setBackground(Color.white);
    }

    void drawJuliaSet(Graphics2D g) {
        int w = getWidth();
        int h = getHeight();
        BufferedImage image = new BufferedImage(w, h, BufferedImage.TYPE_INT_RGB);

        IntStream.range(0, w).parallel().forEach(x -> {
            IntStream.range(0, h).parallel().forEach(y -> {
                double zx = 1.5 * (x - w / 2) / (0.5 * ZOOM * w) + MOVE_X;
                double zy = (y - h / 2) / (0.5 * ZOOM * h) + MOVE_Y;
                float i = MAX_ITERATIONS;
                while (zx * zx + zy * zy < 4 && i > 0) {
                    double tmp = zx * zx - zy * zy + CX;
                    zy = 2.0 * zx * zy + CY;
                    zx = tmp;
                    i--;
                }
                int c = Color.HSBtoRGB((MAX_ITERATIONS / i) % 1, 1, i > 0 ? 1 : 0);
                image.setRGB(x, y, c);
            });
        });
        g.drawImage(image, 0, 0, null);
    }

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

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

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