java - 放大 Java 中的 Mandelbrot 集分形

Question

我开始制作一个 mandelbrot 集分形查看器。在放大分形时，我遇到了很多问题。如果您尝试缩放，查看器只会靠近中心。我已尽我所能来理解这种困境。我如何才能以这样一种方式放大我的分形，即当我放大时，它会放大到屏幕的中心，而不是分形的中心？

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



public class Mandelbrot extends JFrame implements ActionListener {

    private JPanel ctrlPanel;
    private JPanel btnPanel;
    private int numIter = 50;
    private double zoom = 130;
    private double zoomIncrease = 100;
    private int colorIter = 20;
    private BufferedImage I;
    private double zx, zy, cx, cy, temp;
    private int xMove, yMove = 0;
    private JButton[] ctrlBtns = new JButton[9];
    private Color themeColor = new Color(150,180,200);

    public Mandelbrot() {
        super("Mandelbrot Set");
        setBounds(100, 100, 800, 600);
        setResizable(false);
        setDefaultCloseOperation(EXIT_ON_CLOSE);
        plotPoints();

        Container contentPane = getContentPane();

        contentPane.setLayout(null);




        ctrlPanel = new JPanel();
        ctrlPanel.setBounds(600,0,200,600);
        ctrlPanel.setBackground(themeColor);
        ctrlPanel.setLayout(null);

        btnPanel = new JPanel();
        btnPanel.setBounds(0,200,200,200);
        btnPanel.setLayout(new GridLayout(3,3));
        btnPanel.setBackground(themeColor);

        ctrlBtns[1] = new JButton("up");
        ctrlBtns[7] = new JButton("down");
        ctrlBtns[3] = new JButton ("left");
        ctrlBtns[5] = new JButton("right");
        ctrlBtns[2] = new JButton("+");
        ctrlBtns[0] = new JButton("-");
        ctrlBtns[8] = new JButton(">");
        ctrlBtns[6] = new JButton("<");
        ctrlBtns[4] = new JButton();

        contentPane.add(ctrlPanel);
        contentPane.add(new imgPanel());
        ctrlPanel.add(btnPanel);

        for (int x = 0; x<ctrlBtns.length;x++){
            btnPanel.add(ctrlBtns[x]);
            ctrlBtns[x].addActionListener(this);
        }

        validate();

    }

    public class imgPanel extends JPanel{
        public imgPanel(){
            setBounds(0,0,600,600);

        }

        @Override
        public void paint (Graphics g){
            super.paint(g);
            g.drawImage(I, 0, 0, this);
        }
    }

    public void plotPoints(){
        I = new BufferedImage(getWidth(), getHeight(), BufferedImage.TYPE_INT_RGB);
        for (int y = 0; y < getHeight(); y++) {
            for (int x = 0; x < getWidth(); x++) {
                zx = zy = 0;
                cx = (x - 320+xMove) / zoom;
                cy = (y - 290+yMove) / zoom;
                int iter = numIter;
                while (zx * zx + zy * zy < 4 && iter > 0) {
                    temp = zx * zx - zy * zy + cx;
                    zy = 2 * zx * zy + cy;
                    zx = temp;
                    iter--;
                }
                I.setRGB(x, y, iter | (iter << colorIter));
            }
        }
    }

    public void actionPerformed(ActionEvent ae){
        String event = ae.getActionCommand();

        switch (event){
        case "up":
            yMove-=100;
            break;
        case "down":
            yMove+=100;
            break;
        case "left":
            xMove-=100;
            break;
        case "right":
            xMove+=100;
            break;
        case "+":
            zoom+=zoomIncrease;
            zoomIncrease+=100;
            break;
        case "-":
            zoom-=zoomIncrease;
            zoomIncrease-=100;
            break;
        case ">":
            colorIter++;
            break;
        case "<":
            colorIter--;
            break;
        }



        plotPoints();
        validate();
        repaint();
    }




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

Answer 1

Mandelbrot 集存在于具有自然坐标的数学平面中。您使用“视口(viewport)”坐标用 BufferedImage 来“查看”它。这一切都在这些之间的映射中。您已将视口(viewport)坐标标记为 x 和 y，并将进入 Mandelbrot 空间的“真实”坐标标记为 cx 和 cy。这些是公式:

        cx = (x - 320+xMove) / zoom;
        cy = (y - 290+yMove) / zoom;

为了放大和缩小特定的“真实”点，您希望位移量在缩放时保持不变。问题是位移量按缩放量缩放。请记住 cx 和 cy 是 Mandelbrot 平面中的实际坐标，x 和 y 是视口(viewport)坐标。因此，当您查看视口(viewport)的中间时，随着您更改缩放比例，您希望 cx 和 cy 保持不变。

我猜你想要这样的东西:

    cx = ((x - 320) / zoom) + xMove;
    cy = ((y - 290) / zoom) + yMove;

这将使 Mandelbrot 平面中的“移动”与缩放量无关。我假设 320 和 290 与视口(viewport)大小有关，并在视口(viewport)中间给你一个零。

您希望 xMove 和 yMove 在击键时更改的量不是固定量 (100)，而是取决于缩放级别的量。当您放大很多时，您希望每次击键时真实 Mandelbrot 平面中的移动量更小。