Step by Step solution about How to resolve the algorithm Fractal tree step by step in the Java programming language

1. Import Statements:

• The code imports necessary libraries for graphics and window management.

2. FractalTree Class:

• This is the main class that extends the JFrame class to create a window to display the fractal tree.
• It defines a constructor that sets up the window's properties (title, size, etc.).

3. drawTree Method:

• This is the recursive function that draws the fractal tree. It takes the following parameters:
  • g: The Graphics object used to draw on the screen.
  • x1, y1: The coordinates of the starting point of the trunk.
  • angle: The angle at which the trunk is drawn.
  • depth: The current depth of the fractal tree.

4. Drawing the Trunk:

• The method first checks if the depth is 0, which is the base case where no more branches are drawn.
• It then calculates the end coordinates (x2, y2) of the trunk using trigonometry based on the given angle and depth.
• The trunk is drawn as a line from (x1, y1) to (x2, y2).

5. Recursive Branching:

• The method recursively calls itself twice to draw two branches from the end point of the trunk, one with an angle 20 degrees smaller and one with an angle 20 degrees larger.
• This creates the branching structure of the fractal tree.

6. Overriding the paint Method:

• The paint method is overridden to draw the fractal tree on the window.
• It sets the color to black and calls the drawTree method with the appropriate parameters to draw the tree.

7. main Method:

• This is the entry point of the program. It creates an instance of the FractalTree class and makes it visible.

import java.awt.Color;
import java.awt.Graphics;
import javax.swing.JFrame;

public class FractalTree extends JFrame {

    public FractalTree() {
        super("Fractal Tree");
        setBounds(100, 100, 800, 600);
        setResizable(false);
        setDefaultCloseOperation(EXIT_ON_CLOSE);
    }

    private void drawTree(Graphics g, int x1, int y1, double angle, int depth) {
        if (depth == 0) return;
        int x2 = x1 + (int) (Math.cos(Math.toRadians(angle)) * depth * 10.0);
        int y2 = y1 + (int) (Math.sin(Math.toRadians(angle)) * depth * 10.0);
        g.drawLine(x1, y1, x2, y2);
        drawTree(g, x2, y2, angle - 20, depth - 1);
        drawTree(g, x2, y2, angle + 20, depth - 1);
    }

    @Override
    public void paint(Graphics g) {
        g.setColor(Color.BLACK);
        drawTree(g, 400, 500, -90, 9);
    }

    public static void main(String[] args) {
        new FractalTree().setVisible(true);
    }
}